102/ENGR AEP 102 Introduction to Nanoscience and Nanoengineering
Instructors: Professor Robert Buhrman, Dr. Monica Plisch Fall 2006 Laboratory Manual
TABLE OF CONTENTS
Laboratory Section Information Safety Rules Lab 1 Lab 2 Lab 3 Lab 4 Lab 5 Lab 6 Lab 7 Lab 8 Lab 9 Lab 10 Appendix A Appendix B Appendix C Appendix D Appendix E Appendix F Appendix G Appendix H Appendix I Appendix J Appendix K Appendix L Appendix M Why Build Things Small?: Shrinking the Electronic Circuit Photolithography I: Thin Film Deposition and Mask Design Photolithography II : Pattern Transfer Synthesis of Carbon Nanotubes and Atomic Force Microscope Demonstration Imaging Carbon Nanotubes Atomic Resolution with Scanning Tunneling Microscopy Quantized Conductance I: Electronics for Detecting Atomic Wires Quantized Conductance II: Detecting Atomic Wires Quantum Dots Giant Magnetoresistance Brief History of Solid State Electronics How Does a Crystal Radio Work? Reading Resistor and Capacitor Values Physical Vapor Deposition Evaporation Procedure Vacuum Pumps Introduction to the Atomic Force Microscope Catalyst Synthesis Abbreviated Version of Software Help for WSxM Brief Introduction to Quantum Mechanical Tunneling Brief Introduction to Fourier Transforms LT1007 Operational Amplifier Specification Sheet The Particle in a Box Model v vi 1 7 13 21 27 33 39 47 53 59 I III V VII IX XII XIV XVI XVIII XXIII XXIV XXV XXVI
A&EP/ENGR 102 Introduction to Nanoscience & Nanoengineering Laboratory Section Information
Fall 2006 Laboratory: The laboratory section provides a hands-on introduction to techniques commonly used in nanoscale science and engineering (NSE). Topics include top-down and bottom-up approaches to nanofabrication; scanned probe microscopy; and electronic, magnetic and optical techniques for probing nanoscale structures. Labs will begin on the first full week of class (the week of August 28). Lab sections will meet every week except the weeks of Fall Break and Thanksgiving. In addition to the labs described in the manual, supplementary activities, demonstrations, and tours will be arranged. Lab Sections: Location: M, Tu, W, or Th 2:30-4:25 p.m. 111 Ward Lab, unless otherwise announced (Ward Lab is locked at all times. Please arrive five minutes prior to your lab section to be let in. If you are locked out, press the doorbell or call 255-0661 to ring the telephone in the lab room.) Monica Plisch 632 Clark Hall [e-mail] 607-255-2102 Tu, Th 11 a.m. - 12 p.m., or by appointment To be announced
Lab Instructor: Office: Email: Phone: Office Hours: Lab TAs:
Lab reports: Students are to prepare short written reports on each laboratory experiment. Reports should include answers to all questions listed in the Analysis section and a brief summary of the lab procedure and major results. Lab reports are to be typed or neatly handwritten. Reports are due the following week at the start of your lab section unless otherwise announced; late reports lose 10% for each day late. Grading: The laboratory grade will be based primarily on the lab reports and will constitute 50% of the course grade. In addition, the mid-term and final exam will include some material from labs. The Cornell Code of Academic Integrity will be enforced. Students are encouraged to discuss lab report questions with classmates prior to completing work. However, written work must be one's own and copying another's homework answers or lab reports is not permitted. Course documents: Supplementary documents for the laboratory will occasionally be available on the web at http://blackboard.cornell.edu. You must create a blackboard account if you do not already have one. Once you are logged into the system, use the online course catalog to find AEP102 and enroll in the course web site.
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** SAFETY RULES **
The safety of everyone, students and teaching staff alike, is a serious consideration in this course. In lab, you will encounter potential dangers when working with high voltage equipment, corrosive chemicals, high pressure gases, and even standard laboratory tools. While all these are harmless when properly handled and certain basic rules are followed, anyone not observing the rules may inflict serious harm and even death to himself or herself or to others. Correspondingly, it is of paramount importance that everyone in the laboratory read, understand and observe the following rules and considerations. Any significant breach of these rules--for whatever reason and even if no damage results--may be cause for immediate dismissal from the course. Always remember that when in doubt, ASK! There is no harm in asking, and a lot of potential harm guessing when hazards are involved.
HIGH-VOLTAGE EQUIPMENT
Voltages well above the usual line voltage of 117 volts will be present during various parts of our laboratory work, in particular in the electric power sources for the evaporator system and the chemical vapor deposition (CVD) system. Death may result if currents between 10 mA (10-2A) and 1A flow through the heart--even for a few hundred microseconds. Under normal conditions, such currents may be generated by voltage as low as 100 volts. Since current in the body tends to follow the blood vessels (which are relatively good conductors), any current flowing near the heart will go through it (hand to hand, hand to foot, etc.). Currents below 10 mA generally do not cause fibrillation, while those above 1A tend to clamp the heart, and it will usually start again when the current stops. However, large currents can cause other damage, most notably severe burns inside the blood vessels. The electronics of the evaporator system and CVD system are shielded, so there should be no exposure to the high voltages during normal lab procedures.
Still, be aware of the following rules:
1. NEVER put your hand (or other parts) into equipment where such voltages may exist or may have existed without properly checking if or where such voltages actually are present and - if possible - discharging such sources. (In particular, please be aware that capacitors may retain dangerous charge voltages for very long times if not properly shorted or discharged.)
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Also, never touch simultaneously two different points in the equipment (or one point with the external "ground"). Watch your feet or other hand! Voltages over a few kilovolts (1 kV = 1000 V) may "jump" across several centimeters of air and hit you; i.e., keep your body sufficiently away from such sources; do not point closely at such sources with your finger (it can act like a lightning rod)! 2. NEVER switch on such electric equipment without making sure that neither you nor anybody else has any parts of the body in dangerous proximity to the equipment. In this connection, watch in particular any cables (e.g., output cables) that may carry such voltages to other parts of the experiment and outside! 3. Wherever feasible, such electric equipment should not be switched on or operated without fully and safely closing a well-grounded and complete metallic cover or envelope around the equipment. Similarly, do not open the metallic cover of operating highvoltage equipment.
CHEMICALS
Small amounts of chemicals are handled during the photolithography lab, including photoresist, primer, etchant, and developer; they are all potentially hazardous to your health. Proper lab protective equipment should be worn when using these chemicals, including lab coats, chemical aprons, splash goggles, and proper gloves. Make sure all chemical handling occurs in the hood. If any amount of chemical is spilled on your clothing, or anywhere else, stop work immediately and notify your lab instructor. The instructions in the lab manual serve as the Standard Operating Procedure (SOP) for all labs that use chemicals. The small amounts of chemicals used are not dangerous as long as the SOP is carefully followed. The lab safety manual, located in the drawer next to the hood, contains the Material Safety Data Sheets (MSDS) for each chemical used in the lab. These can be consulted for additional safety information. Liquid nitrogen, used during the evaporator system operation, can be dangerous if held in prolonged contact with the skin. The extreme cold temperature of the liquid nitrogen can cause a painful burn. Avoid any contact with liquid nitrogen; if it soaks into an article of clothing, remove it immediately.
GASES
High-pressure gasses stored in gas cylinders are used in the CVD system. Such highpressure gasses need to be handled with caution. A gas cylinder can become a self-
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propelled torpedo capable of crashing through a cinder block wall if it topples over and the valve breaks open. Gas cylinders should always be chained securely to an immovable object such as a wall, and attachments such as pressure regulators should not be operated with excessive force. Methane is flammable; therefore the exhaust system should be properly connected and the hood powered on to avoid contamination of the air in the room. The methane gas detector should be powered on and indicating a safe concentration of methane.
TOOLS
In general, if you do not know the proper use of a tool, ask. A tool that requires special care is the soldering iron. The working end reaches 700 F and will cause second degree burns (blistering) on contact, usually before you feel it. When passing it to someone else, first return it to the holder, then let the other person remove it. Do not use it as a pointer, and be aware of the location of the tip at all times. Avoid inhaling the fumes produced during soldering.
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Why Build Things Small?: Shrinking the Electronic Circuit
Monica Plisch I. Introduction Why build things small? As you will learn throughout this course there are several reasons for doing so both for the sake of technology and of science. Nanoscale science and engineering, the fabrication and analysis of objects, devices, and systems on the length scale of 1 to 100 nm, is at the intersection of chemistry, physics, biology, and engineering. It is a field rich with opportunities where many new and exciting discoveries are being made. Consumer electronics is currently a major economic driving force for building things smaller. Basically, smaller circuits are more compact, run faster, and are cheaper to manufacture. In this lab, you will take a look at two particular electronic circuits: the crystal radio (one of the earliest circuits to use a semiconductor device, popular in the 1920's and 1930's) and the Pentium processor (an integrated circuit that appeared on the market in 1993). By comparing these two circuits from different eras, some of the advantages of building smaller circuit elements will be illustrated. Appendix A contains more information about the historical development of the electronics industry and Appendix B contains an explanation of how a crystal radio works. Photolithography is the technique that enables the manufacture of small circuits. It is a parallel fabrication process that uses light and photosensitive chemicals to transfer a pattern from a mask to a substrate. As engineers push the limits of this technique to smaller length scales, circuits become more powerful. You will learn more about photolithographic techniques in the following two labs. You will also gain experience in working with electronics that will be useful in subsequent experiments.
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II. Procedure Crystal Radio
Figure 1 A. Make the coil: 1. Thread an end of the magnet wire through hole "A" of the PVC tube (see Fig. 1) and then back through hole "B." Leave 4" of wire coming out of hole "B." 2. Neatly wind the magnet wire as shown in Fig. 1 so that there are no overlapping wires and each turn is touching the previous one. This is critical! 3. When you reach hole "C," insert the magnet wire, feed back through hole "D" and then through hole "C" again as shown in Fig. 1. 4. Brush a thin coat of Q-dope on the outside of the coil. Clip the excess wire from the end of coil with holes "C" and "D." Set the coil aside to dry.
Figure 2 2
B. Solder the circuit: 1. The circuit layout in Fig. 2 shows where to attach wires and circuit components. Note the orientation of the diode (indicated by the dark band). See Appendix C for an explanation of the encoding for resistor and capacitor values. 2. For each circuit element, thread the end of each wire through the small hole of a solder lug and wrap the wire around to form mechanically stable connection. For wires, use a wire stripper to first remove insulation from each end before attaching to lugs. 3. Solder each joint by first heating both surfaces with a hot iron. Then touch solder on the heated area and continue to heat with the iron until the solder flows into the joint. Use only as much solder as needed. 4. Clip any excess wire with a diagonal cutter after the solder hardens. 5. Attach all circuit elements as shown except for the coil, ground and antenna. Attach the earphone where labeled.
Figure 3 C. Attach the coil and slider rod: 1. When the coating on the coil is completely dry, bolt it securely to the board as shown in Figs. 2 and 3. 2. Using the emory cloth, remove the insulation from the end of the magnet wire from the coil. Solder a lug to the unattached the wire where indicated in Fig. 2. 3. Turn the nut attached to the copper slider rod onto the pivot screw, as shown in Fig. 2. Stop when the rod moves snugly across the top of the coil. Check that the pivot screw remains rigidly mounted to the board. 4. Note where the rod scrapes the top of the coil. Using the emory cloth, completely remove the coil coating and the magnet wire insulation in this area so the slider rod can make good electrical contact over the entire coil.
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D. Testing the crystal radio circuit (SKIP this part if there is a thunderstorm): 1. Take your circuit to the antenna drop and attach the antenna and ground wires where indicated in Fig. 2. 2. Place the earphone in your ear and slowly move the slider rod across the entire width of the coil. Stop when you have tuned in a radio station. 3. If you fail to hear anything across the entire coil, hit the earphone on a hard surface and try again. If you still fail to hear anything, check your circuit. 4. Once you have located a station, attach leads from an oscilloscope to the "antenna" and "ground" terminals of the radio. Can you observe the amplitude modulation (AM) of the carrier frequency? 5. Measure the diameter of one of the wires in your circuit. Use a scale loupe to get an accurate measurement.
Pentium Integrated Circuit A. Calibrate Etched Reticule on Microscope Eyepiece: 1. If necessary, turn on the power for the light source on the optical microscope, located at its base near the power cord. Adjust the light setting using the sliding switch. 2. Place the calibration slide under the microscope and focus on the metric crossbar at lowest magnification, 50X (the eyepiece is 10X and the objective is 5X). Align one arm of the crossbar the etched reticule on the microscope eyepiece. 3. Increase magnification by switching to higher power objective lenses. Refocus at each step until you reach highest magnification, 500X. 4. Record the number of marks of the etched reticule that correspond to a particular distance on the calibration slide. Use this information to calibrate the etched reticule. B. Image the circuit: 1. Return to the lowest power (5X) objective lens of the microscope. Place the Pentium chip under the lens and focus the image. Increase magnification and refocus at each step until you reach highest magnification, 500X. 2. Locate the narrowest interconnects you can find (interconnects are long metal strips that connect components in an integrated circuit, analogous to wires). 3. Measure the width of the narrowest interconnects using the eyepiece reticule and record this measurement.
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C. Print your image: 1. If necessary, start the software for the digital camera by double clicking on the "PixeLink" icon on the desktop. A realtime image should appear as well as a control panel. 2. Click on the "Save As..." button at the bottom left of the control panel and enter the file name for your image. 3. Click the "Capture" button on bottom right of the control panel to save your image. 4. To print your image, open the saved image by double clicking on the file, choose "Print..." and select the Tektronix Phaser 740. 5. Label your image with object, magnification, date, and your name. Print one image for each person in your group.
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III. Analysis 1. Draw a circuit diagram for your crystal radio, using appropriate symbols for components and labeling values where possible. Show connections with straight lines that meet at right angles and make the diagram as simple as possible.
2. Indicate the wire ("interconnect") you measured on the image of the chip and attach it to your report. What is the ratio of the width of a wire in the crystal radio to the width of an interconnect on the Pentium chip? 3. Using the ratio from question 2 as an estimate for linear scaling between the two circuits, calculate the area scaling ratio (hint: if the length of a side of a square triples, how does the area increase). 4. The Pentium chip contains 3.1 million transistors, which comprise most of the elements in the circuit. What is the ratio in the number of components in the Pentium chip to that of the crystal radio (not including wires)? How does this compare with the area scaling factor computed in question 3 (order of magnitude)? 5. If the Pentium chip were built of components the size of those in the crystal radio, how large an area would it cover? What advantage does a circuit with small components offer over one with components large enough to be assembled by hand? 6. Estimate how much time you spent per component for the circuit you assembled. If it took the same amount of time to solder each transistor in the Pentium circuit, how long would it take one person to assemble? What advantage does an integrated circuit offer over one with discrete components that must be assembled by hand? 7. Given that the crystal radio kit costs $14.95 and the processor chip is ~$500, calculate the cost per component for each circuit. What additional advantage does an integrated circuit offer over one with discrete components?
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Photolithography I: Thin Film Deposition and Mask Design
Kevin Huang, Alison Shull, Monica Plisch, Robert Buhrman
I. Introduction In this lab and the next, you will design, fabricate and test four Al resistors using some of the techniques that are employed to make integrated circuits. First, we will evaporate a thin film of aluminum on a Si wafer. Then you will use photolithographic techniques to pattern the film and etch away unwanted parts, leaving only your resistors. In this week's lab, you will complete the Al thin film deposition and mask design parts of the process. Next week, you will pattern the resistors and test them. Evaporation Evaporation is one of several methods that can be used to deposit a thin film on a substrate (see Appendix D for information on methods of physical vapor deposition). We will deposit a 50 nm thick film of Al onto a substrate using thermal evaporation. The substrate will be a silicon wafer with a 1 m thick layer of silicon oxide to electrically insulate the resistors from the semiconducting silicon. We will place the substrate in a vacuum chamber and reduce the pressure to ~10-6 Torr (atmospheric pressure is 760 Torr). In the low-pressure environment, we will heat a tungsten boat containing Al until the Al melts and begins to evaporate. The aluminum vapor will condense on the relatively cold surfaces in the chamber, including the substrate. A nearby sensor, the quartz crystal thickness monitor, will measure the thickness of the Al layer in real time and thus allow us to control the thickness (see Appendix D). Once the deposition is completed, we will remove the substrate with the Al thin film and "cleave" or break it so that each team has a piece approximately 2.5 cm 2.5 cm. A detailed procedure for operating the evaporation system, including a diagram of the system, and can be found in Appendix E. Appendix F describes the how the vacuum pumps work. Photolithography Photolithography is the primary method used to pattern devices in the manufacture of integrated circuits. In today's fab lines, it is used to make features smaller than 0.1 m (100 nm). A major advantage of photolithography is the ability to fabricate many devices at once (i.e. in parallel), making possible the production of very complex circuits in a relatively short time. A fundamental limitation of photolithography is diffraction, which limits the size of the features that can be made to approximately the wavelength of the light used. In photolithography, a uniform layer of photoresist is applied to a surface to be patterned. Ultraviolet (UV) light is shown on a mask positioned above the surface. Some regions of the mask are transparent to the UV light and allow exposure of the photoresist below while other regions are opaque and block the UV (see figure below).
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Exposure to UV light alters the chemistry of the photoresist and changes its solubility relative to unexposed resist. There are two types of resist, "positive" and "negative." When a positive resist is exposed to UV light, the energetic photons of the light break certain bonds in the long-chain polymers of the resist, causing them to become shorter and thus more soluble. A developer easily washes away the exposed areas, leaving behind a copy of the pattern on the mask. When a negative resist is exposed to UV light it causes cross-linking between the resist polymers making the exposed areas less soluble. The developer removes the exposed resist, leaving behind a negative image of the mask. After development, some parts of the Al film will be exposed while other regions will be protected under a layer of photoresist. Next, an acid or "etchant" will be used to remove the metal where it is exposed. The resulting pattern of metal lines will correspond closely to the original pattern on the mask. To remove the remaining photoresist, a variety of solvents can be used. Cleaving Each silicon wafer is a single crystal of silicon. For such a single crystal, there are certain directions along which the silicon breaks, or cleaves, easily. On a microscopic level, the density of chemical bonds per square centimeter is lowest along the crystal planes that separate most easily. For silicon, there are four orthogonal sets of planes that cleave easily to make dicing the wafer into square or rectangular pieces relatively easy (for <100> wafers). A diamond-tipped scribe can be used to etch a line in the silicon and weaken the wafer in that location. Gentle applied pressure will cause the wafer break, usually along the desired cleave line.
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II. Procedure A. Al deposition 1. Watch the demonstration of evaporation of an Al film on your Si wafer. (Appendix E contains the steps of the evaporation.) 2. Record the thickness of the Al film deposited. 3. Take notes as necessary for answering questions 1-3 in the Analysis section. B. Mask Design Your task is to design a mask for patterning four resistors in a 50 nm thick Al film. Note that bulk Al has a resistivity of 2.6510-8 m. 1. Mask design parameters: a. Two resistors will be 100 m wide with resistances of 20 and 40 . b. Two resistors will have a width of 200 m and resistances of 20 and 40 . c. All resistors must fit within a 2 cm 2 cm area. d. The end of each resistor will be terminated by a 2 mm 2 mm contact pad. e. Any thin lines should be oriented horizontally to avoid problems due to the poor vertical resolution of inkjet printers. 2. Mask planning a. To establish the lengths of your resistors, work through question 4 in the Analysis section. Round your answers to the nearest 100 m for ease of design. b. To establish the "tone" of your mask, work through question 5 in the Analysis section. 3. Start mask design program a. From the list of programs, open Intellisuite>>Intellimask. b. In the View menu open View Editor and choose a window with lower left corner (0, 0) and upper right corner (10000, 10000). Choose a grid spacing of 100 m. 4. Some commands you will probably find useful are listed below: and click, drag and a. To draw a rectangle, choose the Create Rectangle tool release the mouse to indicate location and size of rectangle. b. To delete an object, first select it using the Select Figures tool Delete key. c. To copy an object, use the 1-Copy Translate button . then hit the
d. To view region that is off your screen, choose the Pan tool and drag the background to a new location. e. To move the axis, which is helpful when creating new objects of the right size, choose the Reset Origin tool f. To undo your previous step, choose Undo from the Control menu
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5. Prepare design for printing a. In View menu select Coordinate Axes so that they are not visible. b. In View menu select Polygon Boundary so boundaries are no longer visible. c. In Layer menu choose Layer Editor>>Modify>>Select Color and highlight black. 6. Print enlarged version of mask on paper a. In View menu select Fit All Objects b. Go to File>>Print... and select inkjet printer HP Officejet Pro K550 c. Print one copy for each person on your team. 7. Scale mask a. Measure length of one side of a bonding pad on enlarged printout. b. Compute scaling factor by dividing desired length by length on enlarged printout. c. In Layer menu choose Select to highlight all objects in layer. d. Choose Layer>>Rescale and click on background. e. Enter rescale factor and hit OK. f. Deselect all objects by choosing Layer>>Deselect. 8. Print 1:1 scaled version of mask on paper a. In Print dialog box, be sure that the inkjet printer is selected. b. Print one copy for your team. c. Use a scale loupe to check the dimensions of your scaled design. 9. Print 1:1 scaled version of mask on transparency a. In Print dialog box, be sure that the inkjet printer is selected. b. From Print dialog box, click on Properties... c. Click on the Paper/Quality tab. Check that Type is Plain paper. (Do not select inkjet paper, or ink will not be dense enough.) Choose Best for Print Quality. d. Ask other groups to suspend printing until you are finished. e. Load an inkjet transparency in the top tray of the inkjet printer with the white strip with words facing up and towards the printer. Print one copy per team. 10. Check your mask a. Examine all parts of your mask with a 10X scale loupe. b. Check that all dimensions match your design. Look for and note any defects. c. If you see a discontinuous line or some other major defect, check with your TA about making another mask. d. When finished, hand your mask to your TA to keep for next week. C. Cleave wafer Each team will need a 1" or 2.5 cm square chip of silicon coated with Al. To prevent the chip from being contaminated by you or the environment, always wear nitrile gloves when handling your chip and handle your chip with wafer tweezers, not your hands. Take care to avoid damage to the Al film. It is best to always pick up your chip in the same place. 1. Place wafer Al side down on a clean-wipe.
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2. Using a diamond-tipped scribe, scratch a line where you want the wafer to break. A glass slide can be used as a straight edge. It is best to align the cleave line along a crystalline axis of the silicon wafer. 3. Place two glass slides on top of each other, then slide the Si wafer between them so that the scribed line is at the edges of the glass slides. 4. Press down on glass slide sandwich to hold the Si wafer in place, then press down on other side of the wafer until it breaks, hopefully along the line you scribed. 5. Use compressed air to remove unwanted particles on the Si wafer from cleaving process. 6. Place your chip, Al side down, in a chip carrier and label the carrier with your names, the date, and the sample inside.
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III. Analysis 1. Explain why a vacuum is necessary for evaporation and deposition of Al on the wafer. Give a brief description of how the diffusion pump and the mechanical pump create the necessary vacuum. 2. Explain how the Al is heated for evaporation. 3. Write the thickness of the Al film on your wafer with the appropriate number of significant digits. Explain how the crystal monitor measures the thickness of the Al film is monitored during deposition. 4. Given an Al film thickness of 50 nm and Al resistivity of 2.6510-8 m, calculate the lengths necessary to make resistors of 20 and 40 assuming a width of 100 m. Repeat for a 200 m width. Note that a resistor will have a resistance R given by R = l A where is resistivity, l is length, and A is cross-sectional area. Show your work. 5. Referencing the diagram in the Introduction, sketch subsequent diagrams showing the wafer: (i) after development, (ii) after Al etching, and (iii) after resist removal. Do this for the case of a positive resist and for the case of a negative resist. Should your resistor pattern be opaque or transparent to the UV light given that you will use a positive resist for patterning (this is the "tone" of the mask)? 6. Attach a printout of the enlarged version of your mask. Label the dimensions of your resistors on the enlarged version as if it were the 1:1 version. 7. Sketch a design for a 200 Al resistor (including 2 mm 2 mm contact pads) that is 50 nm thick, 100 m wide and fits in a 2 cm 2 cm area. Label dimensions.
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Photolithography II: Pattern Transfer
Kevin Huang, Alison Shull, Monica Plisch
I. Introduction In this lab you will fabricate and test four Al resistors using the mask you made in the previous lab. You will learn about and use basic photolithographic techniques for patterning thin metallic films. The rest of the Introduction section gives background information on these techniques. The section below on "Patterning metallic films" discusses two overall strategies for patterning films and the following sections discuss individual steps in the process in more detail. Overview of Patterning Thin Films In general, there are a few different ways to pattern thin films on surfaces, including "etch-back" and "lift-off" techniques. In the etch-back method, a thin film is deposited on the wafer. Then the thin flim is coated with a layer of photoresist, which is subsequently patterned. Various acids or etchants are used to remove areas of the thin film that are not protected by photoresist. Finally, the remaining photoresist is stripped leaving behind the patterned thin film.
In the lift-off method of patterning thin films, the first step is to apply a layer of photoresist on the substrate. Then the photoresist is exposed and developed in the desired pattern. Next, a thin film is deposited uniformly over the entire sample, on top of photoresist where present and on top of the wafer where photoresist has been removed. Finally, a photoresist stripper is used to lift off the remaining photoresist along with the thin film on top of it leaving behind only the thin film attached directly to the wafer.
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A challenge with the lift-off process is ensuring a clean break between the thin film on the wafer and the thin film on the photoresist. In some cases, a solvent is applied to swell the photoresist and break any connections In other cases, the photoresist patterning process is designed to create an undercut at the edges, preventing connections from forming during thin film deposition.
Prime Surface The sample is prepared for the photoresist with a primer, which promotes adhesion of the photoresist to the surface. The primer forms bonds with the substrate and produces a polar (electrostatic) surface to which the photoresist can adhere more easily. You will use P20 primer in the lab. Spin Photoresist The photoresist is applied to a surface through a process known as spin coating. This is done in a high-speed centrifuge and produces a very thin (1--2 m), uniform layer of the photoresist on the wafer. Artifacts such as a thick ring of resist at the edge of the wafer or streaks across the resist result from large, solid particles and contaminants remaining on the wafer's surface. Below is a spin curve for the Shipley 1813 photoresist you will use in the lab. Thickness of the photoresist in nanometers is plotted as a function of the spin speed in rotations per minute. In general, the thickness of the photoresist is not dependent on the length of time the wafer is spun beyond some initial time period.
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Bake The pre-exposure bake or "soft bake" is a critical step in which nearly all solvents are removed from the layer of resist and it is made photosensitive in anticipation of the light exposure. Photoresist is composed of three parts, a polymer matrix or resin, a solvent that controls viscosity, and a photoactive compound. Baking drives off the solvent and establishes the exposure characteristics of the photoresist. Over-baking degrades the photosensitivity of the resist by reducing the developer solubility or destroying the parts of the sensitizer. Under-baked positive resists will be attacked by the developer in both the exposed and non-exposed areas of the resist, decreasing the precision of the photolithographic process. Typically, the resist thickness is decreased by 25% during the soft bake. After exposure and development, and before processing the exposed thin film, the photoresist is sometimes baked a second time in what is called a "hard bake." The purpose of the hard bake is to further harden the photoresist and improve its adhesion to the surface. This step will not be needed in our process. Expose During exposure, a controlled dose of parallel light is shone on the wafer, typically by a mask aligner. The aligner also holds the mask and allows the user to position it relative to the wafer (important for processes involving more than one layer). Typically, photoresist is only sensitive to the total energy it receives, not the time over which the exposure occurs. For the Shipley 1813 photoresist you will use, the optimum dose for exposure is 150mJ/cm2. During exposure, in the case of a positive photoresist, the UV light breaks chemical bonds causing the long-chain polymers to become shorter and thus more soluble. In the case of a negative resist, UV light cross-links polymer chains causing the exposed resist
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to become less soluble. The change in solubility allows the resist to be selectively removed, as described in the following development step. Three different methods exist for exposing a wafer through a mask: contact, proximity, and projection (see diagram below). In contact printing, the mask is brought in direct contact with the resist-covered wafer. The wafer is positioned on a vacuum chuck that is slowly raised until it contacts the mask. Then UV light is applied on the assembly. While high resolution is possible with contact exposure, there exists the possibility of debris being caught between the mask and the wafer, causing serious defects in the pattern and damage to the mask.
Proximity printing is very similar to contact; in proximity, however, there is a small 1025 micron gap between the mask and the resist. This minimizes, but does not completely eliminate, the occurrences of defects. A resolution of about 2--4 m is possible, limited by diffraction. To entirely avoid damage caused by the mask and foreign contaminants, projection printing can be used. In projection printing, the mask image is projected onto the wafer which can be many centimeters away. Projection printing also has the advantage that the size of the image projected onto the wafer can be reduced using lenses; an image 5 or 10 times smaller than the mask can be achieved. Systems that can scan or step the mask image over the surface of a wafer can achieve resolutions well below 1 m. Develop In the development stage, the soluble photoresist is chemically washed away. The schematic below shows the amount of photoresist remaining after development as a function of exposure energy. At low exposure energies, the negative resist will still be relatively soluble in the developer. As energy increases, more and more will remain as the negative resist becomes more insoluble in the developer. Alternatively, for positive
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resists, solubility in developer is finite even without exposure. As exposure energy increases, a point is reached in which all of the resist becomes very soluble and none of the resist remains after using the developer. For properly exposed photoresist, the "soluble" areas will be ~100 times more soluble than the "insoluble" areas. You will use AZ developer to develop your pattern.
Etch You will use a wet chemical etch to remove the metal film in all areas that are not protected by photoresist. This type of etching involves submerging the wafer in an acidic solution (in the case of this lab "Al Etchant Type A"). Wet chemical etches are generally isotropic, meaning that they remove material at the same rate in all directions. Strip Photoresist To remove the remaining unexposed photoresist, a variety of solvents may be applied to the photoresist. For positive resists, such solvents include trichloroethylene and acetone. If the photoresist has received a hard bake after development, the remaining resist will be more difficult to remove and the solvents listed above will not be effective. After photoresist is stripped from the wafer, the photolithography step is completed.
References Some of the figures and text in the Introduction were accessed at the following sites: http://www.ece.gatech.edu/research/labs/vc/theory/photolith.html http://www.ee.washington.edu/research/microtech/cam/PROCESSES/PDF%20FILES/Ph otolithography.pdf http://fy.chalmers.se/assp/snl/public/resists/s1813.html
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II. Procedure General Notes To protect yourself from chemical exposure, take the following precautions: Wear long pants and shoes that entirely cover your feet. Always work at a hood when using chemicals. Wear chemical splash goggles, an apron, and gloves whenever handling chemicals. Notify TA of spills immediately. To protect your chip from getting contaminated by the environment (mainly from you): Always handle your chip with wafer tweezers, not your hands. Always wear nitrile gloves when handling your chip. Whenever possible, place your chip inside a wafer carrier with patterned side down. A. Steps for Pattern Transfer 1. Clean wafer (chemical hood) a. If needed, switch on power to spinner and mechanical pump. b. Center silicon chip on spinner chuck and press "Vacuum" button. c. Set "Timer I" to 0 s and "Timer II" to 30 s. Place acetone and isopropyl alcohol bottles near the spinner. Press "Start." d. While chip is spinning, spray it first with acetone for a few seconds, then isopropyl alcohol (IPA) for a few seconds, beginning IPA before ending acetone. e. Adjust spin speed to 3000 r.p.m. using "Speed II" dial if necessary. 2. Spin primer (chemical hood) a. Set "Timer II" to 10 s. b. Using the pipette, draw primer from the bottle marked "P20 primer." c. Dispense a few drops of primer in the center of the chip. Let rest for 10 seconds. d. Press "Start" and wait until spinner is done. Put remaining primer back in bottle. 3. Spin photoresist (chemical hood) a. Set "Timer II" to 30 s. b. Using the plastic pipette for photoresist, draw it from the "Shipley 1813" bottle. c. Drop photoresist in the center of the chip forming a nickel-sized spot. d. Press "Start" and wait until spinner is done. e. Press "Vacuum" to turn vacuum off, remove chip and place in carrier. 4. Bake in oven a. Check that temperature of oven is 110--115C. b. Place chip on Al block in oven. Start timer. c. After 120 seconds, remove chip from oven. 5. UV exposure through mask a. With scissors cut out mask and discard rest of transparency. b. Place chip onto stack of three clear plastic plates. c. Place mask in desired orientation on the chip with ink side down. 18
d. Place quartz plate on top of chip and mask. e. Place UV lamp onto the stack making sure light source is centered above the chip. f. Turn on UV lamp (power button) and expose for 60 seconds. 6. Develop (chemical hood) a. Remove cover plate from developer dish. b. Put chip in small Pyrex dish marked "AZ developer." c. Let develop for approximately 1 minute. Developer should be clear at the end, with no more red photoresist coming off of the chip. d. Remove chip and place in Pyrex dish of deionized (DI) water. e. When removing chip from DI water, spray with DI water and compressed air dry. f. Replace cover plate on developer dish 7. Al etch-back (chemical hood) a. Put chip in small Pyrex dish and cover with "Al etchant Type A." b. When darker Si wafer is visible and etched surfaces appear uniform, etching is complete. c. Remove chip, rinse in Pyrex dish of DI water for at least 10 s. d. When removing chip from DI water, spray with DI water and compressed air dry. 8. Strip remaining photoresist (chemical hood) a. Center silicon chip on spinner chuck and press "Vacuum" button. b. Set "Timer I" to 0 s and "Timer II" to 30 s. Place acetone and isopropyl alcohol bottles near the spinner. Press "Start." c. While chip is spinning, spray it first with acetone for several seconds, then isopropyl alcohol (IPA) for a few seconds, beginning IPA before ending acetone. d. Press "Vacuum" to turn vacuum off, remove chip and place in carrier. B. Resistor Characterization 1. Electrical characterization a. Place one probe of a handheld multimeter on each contact pad of a resistor. Be careful not to scratch your resistor! b. Measure and record the resistance for each of your resistors. 2. Optical inspection a. Use 10X scaled loupes and optical microscope as needed to inspect your resistors. b. Measure and record the lengths and widths of all your resistors as accurately as possible. Be sure to use an appropriate number of significant digits. c. Record any defects (holes, ragged edges, breaks, etc.).
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III. Analysis 1. Did you use an etch-back or a lift-off process in fabricating your resistors? Justify your answer. 2. Given a spin speed of 3000 r.p.m., what should be the thickness of the Shipley 1813 photoresist? How thick would the photoresist be if you spun it twice as fast (6000 r.p.m.)? What is the percentage change in thickness between the two speeds? 3. What type of exposure did you use (contact, proximity, projection)? Is it possible to reduce your mask pattern with this type of exposure? Which type(s) of exposure allow you to reduce a pattern? 4. Draw a cross-section diagram of your chip showing what would happen if you left it in the Al etchant for too long (i.e. "overetch" the Al film)? Do you expect overetching to significantly affect your results in this case? Why or why not? 5. Make a chart with the following columns for all four resistors: target resistance, measured resistance, target width, measured width, target length, measured length, target thickness and measured thickness (from crystal monitor reading in previous lab). Be sure to use an appropriate number of significant figures. 6. For each resistor, calculate the expected resistance based on its measured width, length and thickness. Can the observed deviations in length, width and thickness from their target values account for the deviation of resistance you observed? Explain. 7. Given R = l A , is there an additional quantity besides thickness, width and length that may be responsible for the deviation of resistance values from their targets? Explain. 8. Calculate the resistivity of each resistor, given its measured dimensions and resistance. Average your results to come up with a value for the resistivity of the evaporated Al film. Use the standard deviation to derive an uncertainty value. 9. How does your calculated resistivity from question 8 compare to the bulk resistivity of Al, 2.6510-8 m? If it is significantly different (i.e. the bulk resistivity does not lie within the uncertainty range of your measured value), can you explain what might have happened to change the resistivity of the Al? 10. What factor (width, thickness, length or resistivity) caused the largest deviation of resistance from target values? If you were to fabricate another set of resistors, describe what you would do differently to make the resistance values more accurate.
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Synthesis of Carbon Nanotubes and Atomic Force Microscopy Demonstration
Magdalena Preciado Lopez, David Zahora, Monica Plisch, Markus Brink, Paul McEuen
I. Introduction Carbon nanotubes are a new form of carbon discovered in 1991 by Sumio Iijima, a Japanese scientist who was examining soot in an electron microscope. He noticed nanoscale thread-like structures lying in the amorphous carbon. Since their discovery, carbon nanotubes have become the subject of intense scientific study and engineering due to their extraordinary properties. They have enormous tensile strength (45 GPa compared to 2 GPa for high strength steel alloys), are better thermal conductors than any known material, and possess unique electronic properties. Carbon nanotubes share some structural similarities with graphite. Graphite consists of sheets of carbon atoms; each sheet has its atoms arranged in a hexagonal structure with an atom at every vertex (see Figure 1). Imagine rolling a single sheet of graphite into a tube with a nanoscale diameter. If it were possible to do this, you would have a carbon nanotube. Depending on which way the sheet is rolled, different nanotube structures result. They have been nicknamed "armchair", "zigzag" and "chiral" (see Figure 1). The chirality of the nanotube can play an important role in determining its properties. For example, armchair tubes are metallic while others are semiconducting.
http://www.seas.upenn.edu/mse/research/nanotubes.html
Fig. 1 Structures of Carbon Nanotubes
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Carbon nanotubes can be single-walled or multi-walled. Single-walled tubes have diameters ranging from 0.4 nm up to a few nanometers. Multi-walled tubes consist of a group of concentrically nested single-walled tubes and have diameters ranging from 1.4 nm up to ~100 nm. There are three major methods for carbon nanotube production including carbon arc discharge, laser ablation, and chemical vapor deposition (CVD). The fundamental idea behind each method is the same: (1) heat a carbon-containing material to high temperature to release individual carbon atoms, and (2) encourage the reassembly of the free atoms into carbon nanotubes with carbon-absorbing catalyst particles (such as nickel, cobalt or iron nanoparticles). The first published method for making carbon nanotubes was the arc discharge method. Two graphite rods are placed a few mm apart, and a high voltage across the rods creates an electrical discharge. Carbon atoms vaporize and some (up to 30%) recombine to form nanotubes. In the laser ablation method, intense laser pulses hitting a graphite surface create a hot carbon gas. In the presence of the right catalyst, up to 70% of the carbon forms nanotubes. The method of choice for growing carbon nanotubes is Chemical Vapor Deposition (CVD). During this process a hydrocarbon gas flows through a hot furnace. As the gas decomposes, carbon atoms are absorbed by metallic catalyst nanoparticles and recombine to form nanotubes. It is possible to form nearly 100% nanotubes. The CVD method offers many control parameters, including temperature, ambient gas composition, growth time, and catalyst composition. Also, it has potential to be scaled up to industrial production. Although much progress has been made, better control of carbon nanotube growth is highly desirable. It remains a challenge to precisely control the length, diameter, and chirality of nanotubes, all of which determine the properties of individual carbon nanotubes. Another set of challenges comes with the ability to place nanotubes in desired locations, important in applications such as nanoscale circuits. This lab session will be split into two parts, first nanotube growth and second an introduction to Atomic Force Microscopy (AFM). In lab the following week, we will use an AFM to image our carbon nanotube samples. An introduction to AFM is included in Appendix G.
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II. Procedure A. Sample Preparation 1. Disperse catalyst nanoparticles in solution (see Appendix H for catalyst preparation) a. Stir the catalyst solution on hot plate/stirrer for 5 minutes at high speed. b. Sonicate the catalyst solution for 5 minutes. 2. Cleave a piece of Si wafer to make a chip approximately 1.5 cm 1.5 cm. 3. Place a clean glass capillary tube into the catalyst solution and allow it to soak up a small amount of the solution. 4. Orient the capillary tube vertically and very briefly touch the tip to the Si chip. The solution will expand outward from the tip and wet the surface. a. Make sure the solution does not wet the entire surface (the edge of the drop is best for imaging nanotubes). b. Allow several seconds for the methanol to evaporate. B. Nanotube Growth 1. Load substrate into furnace a. Using tweezers place your chip with the catalyst side up in the furnace tube b. Use the metal rod to carefully push the chip in to the center of the furnace. If there is more than one sample, record the position of your sample. 2. Close and seal furnace a. When all samples are in place inside the tube, close and latch the furnace hood. b. Wipe the o-ring of the furnace inlet connector with your fingers to remove any particles. Carefully place the connector on the open end of the quartz tube. Gently screw the connector tight to compress the o-ring. 3. Visually inspect the entire gas flow route from the gas tanks to the end of the tube in the vented hood. Make sure the hood is turned on. 4. Flow Ar through the furnace a. Open the main Ar tank valve a few turns (metal knob on top of tank) b. Open the valve at the outlet of the pressure regulator (small plastic knob). Do not adjust the outlet pressure of the regulator (large knob). c. Check that gas is bubbling through paraffin in the flask at the furnace outlet. d. Adjust the flow meter to a flow rate of 5 (5,000 cm3 per minute, or sccm). 5. Leak check the o-ring seal at the furnace inlet a. Gently spray Snoop (soapy liquid) around the tube connections and look for the formation and/or growth of bubbles. b. If bubbles appear, gas is leaking out. Close the Ar tank and remake the seal. 6. Raise the furnace temperature to 900 C a. Turn on the power to the furnace controller located below the furnace. b. Adjust the set point to 900 C and press the "set" button. c. Let the temperature rise until it reaches 900 C (about 15 minutes). Then let it stabilize for 2 minutes.
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7. Flow methane through furnace a. Begin flow of methane gas following the same procedure as the Ar gas. b. Close the outlet valve of the Ar regulator. (Do not reverse the order of 7a and 7b; this allows the flow to stagnate and hinders tube growth.) c. Adjust the flow rate of the methane gas to 5,000 sccm on the flow meter. d. Time methane flow for 10 minutes. 8. Resume Ar flow through furnace a. Open outlet valve on Ar regulator (check tank valve is also open). b. Close outlet valve on methane regulator and methane tank valve. (Do not reverse order of 8a and 8b or flow will stagnate.) c. Adjust flow rate of the methane gas to 5,000 sccm on the flow meter. 9. Cool down furnace a. Change the temperature controller set point to 0 C and press the "set" button. b. When the temperature falls to 700 C, you can slightly open (2-3 cm) the top of the furnace and insert a wedge to accelerate cooling. c. When the temperature falls to 500 C, you can fully open the top of the furnace to further accelerate cooling to below 200 C (~5 minutes). 10. Open furnace and remove sample a. When the temperature is below 200C, close all valves on gas cylinders. b. Immediately after stopping gas flow, disconnect furnace inlet connector (to avoid backflow of paraffin into furnace). Wrap the end of the connector in Al foil. c. Using the metal rod, drag your sample out being careful not to touch the surface. d. Using tweezers place your sample in a plastic wafer carrier and close it. e. Label the wafer carrier with date and sample type. C. Optical Inspection 1. Inspect your sample visually. Place it under the optical microscope and examine it at various magnifications. 2. Answer questions 5 and 6 in the Analysis section. D. Atomic Force Microscopy (AFM) Demonstration and Image Analysis 1. Observe the AFM demonstration of imaging the edge of an Al thin film resistor. Record the files name of the image and the maximum values of the x, y and z axes. 2. Launch WSxM (v3.0 or later) located on the desktop of any of the PCs in the lab (freeware available at www.nanotec.es). 3. Open the file containing the image of the patterned Al film acquired during the demonstration. To open the file with WSxM, you may have to change the File Type: to All Files (*.*). 4. Click on the Recalibrate tool (see Appendix I) and if necessary change the X, Y and Z Amplitude to match that of the original image.
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5. Use the Plane Local tool appears tilted.
(see Appendix I) to level the silicon surface if it
6. Measure the height of the Al film in several locations. to generate a profile of the Al step. Be careful to avoid a. Use the Profile tool any areas with a lot of dirt on the surface. b. Make the profile window active and click on the Measure Distance tool to generate two cursors that you can use to measure the difference in height between the Si and Al surfaces. c. Often there is dirt at the edge of the Al film. Avoid placing cursors on this or any other obvious dirt. d. Repeat steps a-c to generate several measurements of the Al film thickness.
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III. Analysis 1. Name the method used to synthesis the carbon nanotubes in lab and summarize the basic steps. 2. What is the source of carbon that forms the carbon nanotubes? 3. Why is Ar gas flowed through the furnace while heating up to 900 C and cooling down? 4. Explain the role of the catalyst in the synthesis of the carbon nanotubes. 5. Can you observe individual carbon nanotubes in the optical microscope? Why or why not? 6. Describe the distribution of the catalyst on your chip. Is it uniformly distributed? Where does the catalyst appear most dense? What areas are likely to be best for imaging C nanotubes with an atomic force microscope, given that nanotubes are easiest to image on flat surface (i.e. the Si wafer)? 7. Draw a diagram of an AFM and label its parts. Briefly describe how an AFM generates a topographic image of a surface. 8. Name at least three pieces of information you can expect to learn about carbon nanotubes from an atomic force microscope image. 9. List all of your trials for measuring the aluminum film thickness and report an average thickness. Be sure to include an uncertainty figure as well (calculate the standard deviation of your trails).
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Imaging Carbon Nanotubes
Magdalena Preciado Lpez, David Zahora, Monica Plisch
I. Introduction In this lab you will image your carbon nanotube sample from last week with an atomic force microscope. You will also analyze Atomic Force Microscope (AFM) and Scanning Electron Microscope (SEM) images of carbon nanotubes using image analysis software. The goals are to learn more about carbon nanotube growth, develop quantitative image analysis skills, and in general to understand the advantages and limitations of AFM and SEM imaging. Atomic Force Microscopy You were introduced to the AFM last week during the demonstration. An AFM generates a topographic image of a surface with nanoscale resolution. It is a versatile tool that can image almost any surface in a variety of ambient environments, including air and liquids. See Appendix G for a reminder of the basic operating principles of an AFM. The AFM has better vertical resolution than horizontal resolution. A vertical resolution of 0.01 nm (~1/20 height of atom) can be achieved with the laser sensor. Small deflections of the cantilever are translated to relatively large displacements of the reflected laser beam on the photodiode detector. The horizontal resolution of the AFM is limited by the radius of curvature of the tip. Commercial tips made of Si or SiN typically have a radius of 5-10 nm. They can be made using a wet chemical etch that preferentially etches along certain directions of the crystal lattice. In research labs, carbon nanotube tips can achieve a radius < 1 nm.
Figure 1. Tip-Sample Convolution Figure 1 shows a tip with a radius of 5 nm scanning a nanotube of radius 1 nm. Notice that the side of the tip contacts the tube well before the bottom of the tip. This causes the profile of the tube to appear much broader than it really is. However, the height of the profile remains accurate. The sharper the tip, the better the horizontal resolution.
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The AFM has a variety of modes of operation. In "contact mode," the tip is in constant contact with the surface. The z-piezo moves the cantilever up and down to maintain constant contact force. Dragging the tip across the surface can be damaging to soft samples and to the AFM tip. For this and other reasons, "tapping mode" is more commonly used. In tapping mode, the cantilever is driven at near its resonant frequency (~100 kHz) so that the cantilever vibrates the tip with a certain amplitude. As the tip approaches the surface, damping occurs and the amplitude of the vibration decreases. When the tip scans the surface, the z-piezo adjusts the height of the cantilever to maintain a constant amplitude of vibration. We will use tapping mode in the lab. Scanning Electron Microscopy A complementary nanoscale imaging technique is Scanning Electron Microscopy (SEM). The SEM operates analogous to an optical microscope, but it uses electrons instead of light for imaging surfaces. Energetic electrons (1-30 keV) are focused using magnetic lenses into a beam 2-10 nm in diameter. Figure 2 shows the electron optics of a SEM.
Figure 2. Scanning Electron Microscope When high energy electrons hit the sample, they ionize nearby atoms and create "secondary electrons." Some of the secondary electrons escape the surface and are collected and counted by a positively charged detector. To generate an image, the scan coils deflect the beam and raster it over the sample. The brightness of each pixel in the image is determined by the number of secondary electrons generated by the beam at each position on the surface. SEM imaging requires that the electron source, lenses, and sample are all in a vacuum. Otherwise, the electrons would collide with air molecules and quickly lose their energy. Since electrons are electrically charged, the sample needs to be conductive enough to dissipate this charge. This requires non-conducting samples to be coated with a thin layer of metal before imaging.
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The resolution of a SEM is determined primarily by the diameter of the beam (1-10 nm). Spreading of secondary electrons away from the beam slightly broadens the effective spot size. Information contained in a SEM image is similar to an optical microscope image; however, there are a few differences. One advantage of SEM is a large depth of focus due to the relatively small aperture angles. This allows a wide range of heights to be simultaneously in focus. SEM images of secondary electrons show excellent topographic contrast. The "inclination effect" causes the edges of a spherical particle to appear brighter than the center. This is due to the greater number of secondary electrons generated by an electron beam striking a surface at a shallow angle. In addition, increased electric field strength at sharp edges and spikes cause these features to appear bright. There are many other modes of imaging in SEM. Backscattered electrons approach close to a nucleus and are ejected at large energies. These electrons are sensitive to atomic number and are collected by a special detector. Characteristic X-rays are also emitted as ionized atoms return to their ground state, yielding information on elements present at the surface of the sample.
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II. Procedure A. AFM imaging You will image your carbon nanotube sample with an AFM and search for evidence of carbon nanotubes. The lab instructor will guide you through the process. Your goal is to take at least one low resolution image (~10 m 10 m) that shows several nanotubes and one high resolution image (~2.5 m 2.5 m) that shows at least one nanotube clearly. Record the files names and the maximum values along the x, y and z axes. If you are unable to obtain good images, you can use the files located in the desktop folder "AFM images." B. AFM and SEM Image Analysis 1. Launch WSxM (v3.0 or later) located on the desktop of any of the PCs in the lab (freeware available at www.nanotec.es). An abbreviated manual is in Appendix I. 2. View all images of carbon nanotubes in the folder "SEM images" on your desktop. These images are of samples prepared using the same method you used in lab. a. To open files, you may have to change the File Type: to All Files (*.*). b. Answer questions 1-3 in the Analysis section. 3. Open your high resolution AFM image or a similar resolution (~2.5 m 2.5 m) image in desktop folder "AFM images." a. To open files, you may have to change the File Type: to All Files (*.*). b. If it is your own image, click on the Recalibrate tool the Z Amplitude to match that of the original image. and if necessary change
4. Measure the height and width of one nanotube in several locations. a. Use the Profile tool to generate a profile of the tube. and/or Measure
b. Click on the profile window and use the Measure Point c. d. e. f.
Distance features to generate quantitative data. For the width, measure the Full Width of the nanotube profile at Half the Maximum height of the profile (f.w.h.m.). For the height, subtract the average background level from the maximum value of the profile. Repeat steps a-d for several profiles of the same nanotube. Answer questions 4-5 in the Analysis section.
5. Open your low resolution AFM image or a similar resolution images (~10 m 10 m) in desktop folder "AFM images." a. If it is your own image, click on the Recalibrate tool the Z Amplitude to match that of the original image. and if necessary change to level the
b. To see small nanotubes more clearly, use the Plane Local tool silicon surface.
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c. To see small nanotubes more clearly, also use the Z Scale Control feature adjust the vertical scaling. 6. Measure the diameter of at least 20 different carbon nanotubes. Be sure to include small diameter tubes in addition to large diameter tubes so that you get a representative sample. a. Use the Zoom feature as needed to magnify regions containing nanotubes.
to
b. Use the Profile tool to generate a profile of a nanotube. Avoid dirt on the Si surface to keep the profile clean. c. Click on the profile window and use the Measure Point and/or Measure
features to measure the height of the tube. Remember to subtract Distance the average background level from the maximum value of the profile. d. Repeat steps a-c for at least 20 nanotubes. Be sure to get a representative sample of tubes, including small diameter tubes. e. Answer questions 6-7 in the Analysis section. 7. Open a high resolution SEM image (at least 100 kX magnification). a. Use the Profile tool find. to generate a profile of the smallest nanotube you can
b. Click on the profile window and use the Measure Distance feature to measure the width (f.w.h.m.) of the profile. c. Repeat steps a-c to measure the five smallest diameter carbon nanotubes you can find in the image. d. Answer questions 8-9 in the Analysis section.
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III. Analysis 1. What is the maximum length of carbon nanotubes grown with the method used in lab (order of magnitude)? 2. Does there appear to be a preferential growth direction for nanotubes with the method you used in lab? Explain your answer. 3. Is there any evidence that carbon nanotubes interact with each other as they grow? Hint: look for "bundles" where separate carbon nanotubes come together. 4. Using a high resolution AFM image, make several measurements of the height and width (f.w.h.m.) of a single nanotube and organize your data neatly in a table. Report the average height and width and include an uncertainty figure for each (i.e. standard deviation). 5. Of the two numbers recorded in question 4, which number (height or width) most closely corresponds to the actual diameter of the carbon nanotube? Explain your choice. Why are the height and width are different? 6. Measure the diameter of at least 20 carbon nanotubes in AFM images. Create a histogram of the tube diameters. 7. Based on your data from question 6, does the CVD method used in this lab produce primarily single-wall (0.4 to 3 nm diameter) or multiwall (1.4 to 100 nm diameter) nanotubes? Explain your answer. 8. Report the width (f.w.h.m.) of five of the smallest diameter carbon nanotubes you can find in a high resolution SEM image. How do the minimum diameters measured with SEM compare to the minimum diameters measured with AFM? Can you explain any difference? What is the resolution of the SEM used to image the nanotubes? 9. Name any advantages you can identify for SEM imaging over AFM imaging. Do the same for AFM imaging over SEM imaging.
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Atomic Resolution with Scanning Tunneling Microscopy
Andrew Parella, Monica Plisch
I. Introduction The scanning tunneling microscope (STM) has the capability to directly image atoms on a surface. It was developed in the early 1980's by two scientists at IBM. Since its invention, the STM has become a widely-used tool to study surfaces at the atomic scale. For example, it has been used to investigate deposition and etching of materials, to map surface electronic structure, and to investigate electron transport in thin films. The STM can even be used in some cases to manipulate individual atoms and molecules and build designer atomic structures. In this lab, our goal will be to obtain an atomic-resolution image of a graphite surface and then use this image to determine the distance between nearest-neighbor carbon atoms. In order to achieve atomic resolution, the STM utilizes a quantum mechanical effect known as tunneling. The atomically sharp tip of a STM is brought to within 1 nm of a surface. If a small positive voltage ~100 mV applied to the tip, electrons will tunnel from the surface to the tip, even though the region between the tip and the surface is insulating. The tunneling current of electrons, typically ~1 nm, is extremely sensitive to the distance between the tip and the sample. See Appendix J for further information on tunneling. In normal operation, the STM maintains a constant tunnel current, and thus a constant distance between the tip and the sample, as the tip scans back and forth. If the tip scans across the surface and encounters a high point, the computer will send a signal to the scan head to retract the tip in order to keep the tunnel current constant; a low point will cause the scan head to extend.
x,y,z piezo scanner
tip
V
I ~1nA
Sample
tunnel
The STM scan head is based on piezoelectric ceramics, which can be precisely compressed or stretched on the nanoscale by applying modest voltages to the material. Separate voltage signals control the X, Y, and Z motion of the tip. The topographic image displayed by the STM software is a recording of the Z motion of the scan head as it changes to keep the tunnel current constant. Figure 1. Simple STM schematic. Electrons tunneling between the tip and the sample flow through the feedback circuit. The computer adjusts the Z piezo to keep the tunnel current constant.
pre-amplifier 108 gain
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The achievement of atomic resolution with the STM also depends on the stability of the tip and the sample. Vibration isolation systems designed to reduce relative motion between tip and sample is common to all STMs. For example, for the STM you will use in lab, the scan head rests on a heavy granite slab. The slab is mounted on four rubberlike legs that somewhat decouple the motion of the slab from the table it rests on. The inertia of the granite block helps the scan head remain stationary even if the table beneath is moving. Temperature also affects the stability. Many research grade STMs are cooled to low temperature to reduce thermal motion of the atoms on the tip and the sample. In addition, most STMs operate in ultrahigh vacuum to reduce contamination of surfaces and unwanted chemical reactions with the atmosphere.
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II. Procedure A. Acquire STM Images Obtaining atomic resolution images is not necessarily easy, but it is possible with some persistence and luck. If you do not obtain a good image in the time allotted, go on to parts B and C. Use the images located in the desktop folder labeled STM Images. 1. Follow the instructions on pp. 17-30 in the Nanosurf STM system manual for obtaining atomic resolution images of your graphite sample. a. If you crash your tip (LED turns red), call the instructor to replace your tip. b. If your images look like those on pp. 32-33, call the instructor to replace your tip. 2. Check for drift. a. Read p. 31 in the Nanosurf STM system manual for information about drift. Can you see evidence of drift in your images? b. How can you minimize the effect of drift on the accuracy of your atomic measurements? Think of all possible strategies and implement those that you can. 3. Be sure to save images as you go along. Your tip can go bad at any time. a. Click the Photo button before the image is complete. b. When the scan is complete, a window with the image will appear behind the scan window. c. To save an image to the hard disk, click on the save icon. 4. Maximize image quality. a. Often drift will diminish over time and the image quality will improve. Continue to scan as long as you can to take advantage of increasing stability over time. b. Optimize the I-Gain and P-Gain values. These values control the feedback loop that adjusts the tip to maintain a constant tunneling current. Increasing these values will give a sharper image up to a point; increasing them too much leads to instability and a noisy image. c. As time allows, try adjusting other parameters to optimize your image. d. Any time you get a better image than previous images, be sure to click Photo. B. Remove Noise from Images The typical STM image has artifacts such as random noise and scan lines. These artifacts can be removed by a Fourier transform filter so the real data is more easily seen and analyzed. See Appendix K for an introduction to Fourier Transforms (FT). 1. Open one of your graphite images in WsXM. a. Start the program WsXM. b. Change the File Type: to All Files (*.*) in order to see the *.ezd file which contains your data. c. Two images will open. Close the one with a grainy appearance and less contrast. 2. Open the 2d FFT Filter dialog box (see Fig. 2 below). a. Click on your image to make its window active. Press the Fast Fourier Transform (FFT) button to activate the 2d FFT Filter dialog box.
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b. Adjust the slider bar on the Zoom control so that all the bright peaks are clearly visible in the FT of your image (to the right of your original image).
Fig. 2 2d FFT Filter dialog box. 3. Filter your image. a. Press the Filter button. The lower right window will become active. b. Select the brightest peaks in the FT image. Place the mouse on the center of the bright peak, click and hold the left mouse button, and drag outward to make a small box around it. Release the left mouse button. Repeat for other bright peaks. c. Activate the filter by right clicking on the FT image. A new image will appear in the lower left window with only the frequencies you selected in the FT image. d. Click on Create Window to open a larger filtered image. Close the 2d FFT Filter dialog box. 4. Print out your best filtered image a. Experiment with filtering images. When you agree on your best image, print one for each person in your group. b. Be sure to label your image with sample type, magnification (or a scale bar), date, and your name. C. Analyze Images 1. Identify the hexagonal rings of carbon atoms on your filtered image. a. Find the center of a hexagonal ring of carbon atoms (it should be lower than anything else around it). Count the number of atoms around the center--can you find six? See p. 33 in the nanoSurf STM manual for help with interpretation of your graphite image.
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b. Draw a hexagon on your image that shows the location of a hexagonal ring of carbon atoms. There should not be any atoms in the center of the hexagon! 2. Determine the distance between a carbon atom and its nearest neighbor. a. Use the Profile tool and the Measure Distance tool to measure the distance between atoms in your image. You may not be able to directly measure the distance between nearest neighbor atoms. b. In general, it is more accurate to measure the distance across several atoms and divide by the number of atoms. c. Your determination of the nearest neighbor distance should include an uncertainty value. This means that you will need to make more than one measurement!
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III. Analysis 1. Typically, samples must be imaged in vacuum with the STM. Why? What properties of graphite allow us to image it in air? 2. What are the requirements to establish a quantum mechanical tunneling current between a tip and a surface? What are the advantages of using a tunneling current to image a surface? 3. Explain the concept of constant current imaging. What does it mean if two regions of your image are the same brightness? 4. The nanosurf STM is designed to reduce the impact of external mechanical vibrations and prevent unwanted motion of the tip relative to the sample. Describe the features of the STM that reduce mechanical noise. 5. Define "drift." How does drift affect an image? How can you orient your measurements of the distance between atoms to minimize the effect of drift? 6. Attach your best filtered image to your report (make sure it is properly labeled). Describe how the fourier transform (FFT) filter allow you to remove random fluctuations from the image. 7. Draw a hexagon on your image that shows the location of an individual ring of six carbon atoms. Why do some of the atoms appear lower, even though all the ion cores lie in the same plane? 8. Determine the distance between a carbon atom and its nearest neighbor (show all work). Your number should include an uncertainty value. How does it compare with the accepted value of 0.14 nm?
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Quantized Conductance I: Electronics for Detecting Atomic Wires
Ethan Minot, Sean Garner, Monica Plisch
I. Introduction Measurements of conductance ( G = I / V ), capacitance ( C = Q / V ) and other electrical quantities can reveal much about the structure and behavior of nanoscale materials. Once electrical contact is established, not a trivial task, electrical measurements become a sensitive probe of nanosized objects. The goal of this lab is to build and understand the electronic circuit that will be used in the following lab to measure the conductance of gold nanowires, some as narrow as one atom wide. A simplified circuit diagram is shown below. Approximately 20 mV will be applied across two macroscopic pieces of gold wire. The wires can be brought into and out of contact with each other; during this process a narrow bridge joining the two macroscopic wires often forms that is only a few atoms wide. This creates a varying resistance, which can be detected by monitoring the current as a function of time.
~20 mV
gold wires (intermittent contact)
I
monitor current
The full circuit diagram is shown below. It is somewhat more complex because there are a few techniques we must use in order to get a clear signal. This circuit can be broken down into three functional units: a voltage divider, a current-to-voltage amplifier, and a low-pass filter.
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Voltage Divider The voltage divider consists of the -9V power supply and the 27 k and 56 resistors in series. The purpose of the voltage divider is to decrease the 9V available from a standard battery to approximately 20 mV. This is necessary to avoid putting too much current through the gold nanowire, which could vaporize it. Note that -9V is achieved by attaching the positive terminal to ground and the negative terminal to the 27 k resistor. The current through the voltage divider can be calculated by using Ohm's Law:
i=
Vin R+r
To calculate the output voltage Vout Ohm's Law can be used again:
Vout = ir = Vout Vin r R+r r = Vin = -18.6 mV R+r
The output voltage for a battery of exactly 9V will be -18.6 mV. Note that a battery is used because it produces a stable voltage that changes only very slowly over time. Current-to-Voltage Amplifier The purpose of the current-to-voltage amplifier is to amplify the tiny current that passes through the gold nanowire (which forms as a bridge between the gold wires) and to convert this current to a voltage. The heart of the current-to-voltage amplifier is an operational amplifier, symbolized by a triangle as shown in the figure to the right. Op amps are composed of several transistors, resistors, etc., and are common in modern electronic devices. Op amps take the difference between the voltage at the two inputs (labeled "+" and "-"), multiply this difference by a large number (~106), and output the voltage at the tip of the triangle. The output voltage is Vo = A(V+ - V- ) , where A ~ 106. Op amps are active devices, meaning they require a source of power connected at the terminals labeled "+ power" and "- power." Op amps are most often used with the output connected to one of the inputs, forming a feedback loop. This is the case for the op amp used in our circuit; the 100 k resistor connects the output to the negative or "inverting" input (see the circuit diagram to the left).
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When an op amp is in feedback, this forces the two input voltages to be very close in value. If the inputs were significantly different, the output voltage would have to be very large, due to the high value of A. However, this is not possible because the op amp can only output values between +9V and -9V, the power that it receives. Therefore, when the op amp is in stable operation, the voltage at the positive or "non-inverting" input must be essentially the same as the voltage at the inverting input. In our circuit, since the noninverting input is grounded, the inverting input must be at essentially 0V. This forms what is called a "virtual ground." It is important to note that the virtual ground is different from a real ground because it cannot serve as a source or sink of current. The op amp does not allow any current to flow into its inputs (it has nearly infinite input resistance). Therefore, the current that flows through the gold nanowire igold must also flow through the 100 k resistor, since there is no other path for it to take. Now that we know the voltage on either side of the gold nanowire, we can calculate the current igold in terms of the nanowire resistance Rgold: i gold = 0 - Vin 18.6 mV = R gold R gold
We can also calculate the output voltage of the amplifier Vout in terms of igold:
Vout = i gold Ramp =i gold 10 5
Notice the net effect is an amplifier that multiplies the tiny current through the gold nanowire by 105 and outputs this value as a voltage. As the current through the gold nanowire changes in time, the amplifier will follow these changes. It is useful that the amplifier outputs a voltage, since the oscilloscope that we will use in the next lab can only monitor voltage and not current. Low-Pass Filter The final stage of the circuit is the low pass filter, which is composed of a 10 nF capacitor and a 1 k resistor. The low-pass filter allows relatively low frequency signals to pass through to the oscilloscope unaltered, but diminishes the amplitude of high frequency signals, which are likely due to electrical noise. To understand how this works, we will first look at how a capacitor responds to a time-varying voltage, VC = VC 0 sin t with frequency = 2f . This time varying voltage creates a time varying charge on the capacitor. The charge on a capacitor QC is related to the voltage by QC = CVC where C is the capacitance. Since current IC is defined as the time derivative of charge,
IC =
dQC d = (CVC 0 sin t ) = CVC 0 cos t dt dt
In an analogy to Ohm's Law, we can take the ratio of voltage to current for the capacitor:
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VC VC 0 sin t 1 sin t = = I C CVC 0 cos t C cos t
The ratio of the sine to the cosine function appears because the current and voltage are out of phase with each other. The most important result is that the magnitude of the voltage relative to the current is:
XC = 1 C
where XC is called the "reactance" of the capacitor. Reactance is analogous to resistance, but with some differences. Notice that the reactance of the capacitor depends on the frequency of the time-varying signal. This means that for very high frequency signals, XC approaches zero and the capacitor acts like a short, i.e. as if it has been replaced by a wire. For very low frequency signals, XC approaches infinity and the capacitor acts like an open circuit, i.e. as if it has been removed from the circuit and replaced by nothing. What implications does this have for our low pass filter? Notice the oscilloscope measures the voltage across the capacitor (the other lead on the oscilloscope is attached to ground). For very high frequency signals the capacitor acts as a short and the input voltage Vin mostly drops across the resistor Rlp; therefore, the oscilloscope measures very little signal and Vout 0 . (Recall that a similar situation occurs in the voltage divider.) For very low frequency signals, the large reactance of the capacitor means that most of the input voltage Vin drops across the capacitor Clp and Vout Vin . Hence the name "low pass filter." At what frequency does the filter begin to "reject" or attenuate the magnitude of timevarying voltage signals? Roughly speaking, when the reactance of the capacitor XC becomes smaller than the resistance of the resistor Rlp, the output voltage Vout starts to become attenuated. Therefore, the "cut-off" frequency approximately occurs when:
X C = Rlp 1 = Rlp Clp
=
1 Rlp C lp
The quantity = Rlp C lp gives the period of the signal at which the output voltage starts to become attenuated. The time constant is 10 s for this particular filter. Therefore, lowfrequency signals with a period greater than 10 s will pass through but higher-frequency signals will be attenuated.
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II. Procedure
A. Circuit Board 1. IMPORTANT: Leave your LT1007 op-amp chip safely embedded in the antistatic foam until you have built your entire circuit and checked your wiring. 2. Orient your circuit board so that the side with copper strips is on the back. 3. First solder in the 8-pin socket, then assemble the rest of the circuit board as shown in the diagram below. 4. Note that the 100 k resistor (dashed lines) is on the back of the board. 5. Use Appendix C to interpret and resistor capacitor values or measure with multimeter.
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B. Box Connections 1. Use a green wire to connect the negative terminal of one battery to the positive terminal of the other. This is defined as 0V or ground. Attach the other two battery terminals to the center terminals of the switch as shown below. Be sure to follow the color convention that green is ground, red is +9V, black is -9V. 2. For the seven wires that connect the circuit board to the BNC connectors and batteries, cut 6" lengths of appropriate color wire. Solder the end that attaches to a circuit element on the box. 3. Attach wires leading from the box to appropriate locations on the board as shown in the diagram below. Note that when the switch is up ("On"), the two center terminals are each connected to the terminal below it. Use a multimeter to investigate the switch if you are unsure how it works.
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C. Final Assembly 1. Visually trace all wiring paths and compare with circuit diagram. Retouch solder joints that look dull or have an irregular surface. It is best to have someone else check your work. 2. Install batteries in holders. Check that the voltage of both batteries is above 8V. 3. Make sure power is "off." If you have laid out the circuit as described above, plug in the LT1007 chip with the semicircle-shaped notch closest to the 56 and 27 k resistors. Consult Appendix L for the pinout of LT1007 chip. D. Test Circuit 1. Voltage divider a. Flip the switch "On" and measure the voltage across the BNC connector labeled "V." It should be approximately 20 mV. Record the value. b. If the voltage is very different from 20 mV, you will need to debug your circuit (consult your TA for help). 2. Current-to-voltage amplifier a. Connect the following resistances between the central pins of the BNC connectors labeled "Au Wire:" 20 k, 2 k, 0 (wire) and infinite (no connection). b. Measure the voltage across the BNC connector labeled "Out" for each resistor. Record the output values. c. You should get approximately the following values: 0.1 V, 1 V, 9 V, 0 V. If the voltages are very different, you will need to debug your circuit (consult your TA for help). 3. Low-pass filter a. Connect an oscilloscope to the BNC connector labeled "Out." b. Connect a function generator to the bottom BNC connector labeled "Au wire" through a 20 k resistor (be sure to attach the grounds). c. Set the function generator to output a sine wave with amplitude ~100 mV and frequency to the lowest setting. d. Increase the frequency of the sine wave over the full range of possible values and note what happens to the amplitude of the output from your box. e. Find the frequency at which the amplitude drops to one-half of its original value and record the time for one oscillation (i.e. the period).
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III. Analysis
1. Describe the purpose of the voltage divider. How does it help measure the conductance of gold nanowires? 2. Calculate the theoretical value of the output value from the voltage divider (i.e. the voltage at the point between the two resistors). How does this compare to the value you measured for the output of the voltage divider (the BNC marked "V")? 3. Describe the purpose of the current-to-voltage amplifier. How does it help measure the conductance of gold nanowires? 4. Calculate the current that flows through each of the four different resistors used to test the current-to-voltage amplifier. The voltage across each resistor is that of the voltage divider. (Note that this current is also the input current to your amplifier.) 5. For the 2 k and 20 k test resistors, calculate the amplification of your current-tovoltage amplifier by dividing the output voltage (measured at BNC marked "Out") by the input current (from question 4). Be sure to include units. How do your amplification values compare with the value of the 100 k resistor used in the feedback loop? For the case of the 0 resistor (i.e. the wire), can you explain the voltage output? 6. Describe the purpose of the low-pass filter. How does it help measure the conductance of gold nanowires? 7. Show that a resistance multiplied by a capacitance gives units of time. Hint: to convert units, use dimensional analysis of equations that involve these quantities. 8. Calculate the product R*C for the resistor and capacitor used in the low-pass filter. How does this compare with the measured period of the sine wave at which the amplitude has been reduced by one-half? 9. Look up "coaxial cable" on wikipedia.com or some other source. What advantage does a coaxial cable have over a conventional wire? In what situation would you want to use coaxial cables?
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Quantized Conductance II: Detecting Atomic Wires
Ethan Minot, Sean Garner, Monica Plisch I. Introduction When two wires of pure gold are brought in and out of contact with each other, a narrow bridge only a few atoms wide sometimes forms, joining the two macroscopic wires. Due to the affinity of gold atoms for each other, when two pieces of gold touch, they bond where they are in intimate contact, assuming the surfaces are clean. When the macroscopic pieces of gold are separated, the malleability of pure gold allows the contact to stretch into a thin wire before it finally breaks. Atomic wires that form in such a "mechanical break junction" cannot be seen with the human eye or an optical microscope. They can only be imaged with a microscope that has atomic or near-atomic resolution, such as a transmission electron microscope (see references below for images). Such images show that just before an atomic bridge breaks, it often narrows to only one atom in width, forming the ultimate nanowire. You do not have to use a multimillion dollar electron microscope to see whether a single bridge of atoms has formed. It turns out that a conductance measurement can be just as illuminating. (Recall that conductance G is the ratio of current I to voltage V, and is the inverse of resistance: G = I V .) The conductance of a single-atom wire is determined by quantum mechanical effects. Theoretically, the conductance is:
G0 = 2e 2 h = 7.75 10 -5 -1
This implies a resistance of h 2e 2 = 12900 for an atomic wire. Widening the nanowire to two atoms wide provides another conductance channel for electrons, so in theory the conductance would increase to 2G0. For an N atom wide wire, the conductance is predicted to be NG0. Thus, conductance can be used to probe the atomic structure of the gold nanowire. In the last lab, you built a circuit that will enable you to measure the conductance of the gold nanowire that forms at the contact between two macroscopic gold wires. A simplified version of your circuit is shown below:
~20 mV
gold wires (intermittent contact)
I
monitor current
A constant voltage of ~20 mV is applied across the contact between two pieces of gold wire while the current is monitored. Recall that the current is not measured directly; rather, it is amplified and converted to a voltage so that it can be read by an oscilloscope.
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The amplification factor is 100 mV for every 1 A of current or 105 V/A. The digital oscilloscope reads and displays the changing signal as a function of time. Gold bridges tend to last for ~1 ms, and changes in width tend to be relatively sudden. For example, if a bridge suddenly narrows from 3 atoms wide down to 2, from 2 to 1, and then breaks completely, the current vs. time graph will look like a staircase (see, for example, E.L. Foley). The sudden decreases in current correspond to the conformational changes of the gold atoms. Each plateau indicates the presence of a nanowire that is stable for the duration of the plateau. The current through the nanowire can be divided by the ~20 mV applied across it to give the conductance of the nanowire, which gives information about the atomic structure of the gold nanowire. Microscopic Origins of Resistance To better understand quantum resistance, it is important to review conduction of electrical current in macroscopic wires. Recall that resistance of an object depends on its cross-sectional area, A, its length, L, and the resistivity of the material :
R=
L
A
For gold at room temperature the resistivity is = 2.210-8 m; for copper at room temperature = 1.710-8 m. Gold has a greater resistivity than copper because electrons scatter somewhat more when they pass through gold. Scattering slows the progress of an electron through a conductor. The electric field established by the applied voltage causes an electron to accelerate in the direction opposite the field; the acceleration continues until the electron scatters. According to the Drude model, scattering randomizes the direction of the electron so that on average it has zero velocity along the direction of the field. The field then acts to once again accelerate the electron. The more an electron scatters, the lower its average velocity in the direction opposite the field, and the slower the current for a given voltage. Scattering occurs when there are imperfections in the crystalline arrangement of atoms. These imperfections can take the form of a missing atom (vacancy), an atom of a different type (substitution or impurity), a boundary between two adjacent crystalline regions with different orientations (grain boundary), or one of several other classes of defects. The thermal motion of atoms also causes deviation from perfect crystalline order and leads to scattering (collections of thermally excited atoms are called phonons). At room temperature scattering by phonons is the dominant cause of scattering and hence electrical resistance. Thermal motion is much reduced at low temperature, so cold metals have much less resistance. For example, gold at 1K has a resistivity = 0.0210-8 m. When electrons cross a one-atom-wide wire, they essentially are forced to go single file. The current is limited by this single-file process, and this leads to "quantum resistance." Notice that quantum resistance is independent of nanowire length and material. The only thing that matters is the number of "conductance channels" available to electrons. The full derivation of the conductance quantum requires quantum mechanics, and is beyond
48
the scope of this course. See E.L. Foley for a discussion of the quantum mechanics involved (listed in References section below). Scattering is negligible in atomic wires unless the wire has a defect. Phonons no longer play a significant role (except for very long nanowires) since they tend to scatter electrons at shallow angles, not an option in a one-dimensional conductor. If a wire does have a defect, some of the electrons will be scattered back in the direction they came from. This will lower the current through the nanowire for a given voltage, and such a wire will have a lower conductance than a perfect one. References J.L. Costa-Kramer, et. al. "Nanowire formation in macroscopic metallic contacts: quantum mechanical conductance tapping a table top," Surface Science 342 L1144 (1995). H. Yasuda, A. Sakai, "Conductance of atomic-scale gold contacts under high-bias voltages," Physical Review B, 56, 1069 (1997). E.L. Foley, et. al. "An undergraduate laboratory experiment on quantized conductance in nanocontacts," American Journal of Physics, 67 (5) 389 (1999). S.B. Legoas, et. al. "...Suspended Gold Chains." Physical Review Letters, 88 076105 (2002).
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II. Procedure A. Prelab 1. Turn on the power to the box containing the measurement circuit. Test that the voltage at the BNC labelled "V" is ~20 mV. If not, check the batteries and replace if necessary. Record this voltage. 2. Work through questions 1 and 2 of the Analysis section. B. Set up the equipment 1. On the metal box containing your measurement circuit, Use a coaxial cable to connect the BNC connector labeled "out" to the channel 1 input on the digital oscilloscope. 2. Attach the two coaxial cables that terminate in banana plugs to the BNC connectors labeled "gold wires." Put the banana plug connected to the central wire of the coaxial cable (not the banana plug labeled "GND") into the socket on the brass wire holder. 3. KEEP THE GOLD CLEAN, DO NOT TOUCH IT! Only touch the copper wires soldered to the gold, not the gold itself. 4. Unscrew the posts on the brass wire holders and insert the copper ends of the wires into the holes. Tighten the post tops on the ends of the copper wires. 5. Turn on the power switch on the back of the metal box with the measurement circuit. C. Set up the digital oscilloscope 1. Plug in the digital oscilloscope power cord. Make sure the USB connector is plugged into the back of the computer. 2. Turn on your computer. Double-click on the desktop icon labeled DSO2102 to start the digital oscilloscope software. 3. Click on the Go button for the oscilloscope and touch the gold wires together briefly. Your should see a trace recorded on the screen. If not, ask your TA for help. 4. Some useful initial settings are: for channel A1, set V/div to 200 mV; set Trig ch to A1, Trig mode to Normal, Rate to 2 MSa, Zoom to 10:1. Discuss with your lab partner what these settings mean. Try playing with them if you are not sure. 5. The green and blue dashed horizontal and vertical lines are cursors that are useful for measurement (the red dashed lines set trigger levels). Drag them around with the mouse while watching the digital readouts at the top change to get a feel for it. 6. Set the horizontal cursors at the voltages you would expect for one-atom and twoatom wide bridges. This will help you spot the formation of such bridges. 7. Make sure the vertical trigger (dashed red line) is approximately in the middle of the window. This is where the trace will transition from low to high (or high to low). 8. Check the horizontal trigger (dashed red line) is substantially above 100 mV to avoid triggering on noise.
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D. Get the gold wires in contact This part requires some practice and patience. If you persist you will get beautiful data! Here are a few tips on how to set up the gold wires so they form nanowires: 1. Start with the copper wires horizontal. Slight bend one copper wire so that it angles downward a few degrees. 2. Begin with the wires out of contact. Rotate one brass wire holder slowly until the gold wires overlap and just barely touch. 3. The wires should be touching softly enough that when you tap the table lightly with your fist they bounce in and out of contact for a few seconds. 4. On the oscilloscope trace, a plateau (i.e. constant current) indicates the presence of a stable nanowire for the duration of the plateau. 5. If you don't see any evidence of nanowires after five or ten table taps, reposition the wires to a new, hopefully cleaner, location and try again. The gold tends to be cleanest near the solder joint, so try to form your nanowires there. E. Data logging and Browsing Files Record all of your data using the data log feature. If you see a nice trace you would like to go back to later, remember the filename (it will appear in the top line of the window) so that you know which file to open. 1. Under the File menu choose Data log settings. In the window where it says File name enter "XXX" where "XXX" stands for a few letters such as your initials. Every data file will start with these letters. 2. Choose All where it says Save every N captures. 3. Select .DSO format for saving files. 4. To start saving data, go under the File menu and click on Data log. If you look at the File menu again, there should be a check mark in front of this option. 5. To browse files, first press the Stop button. Then choose Data log load... in the File menu. Choose Browse to select the first file you want to look at and Previous file or Next file to step to the next file. G. Recording and Analyzing Data You can stop recording data when you have at least five files that show nanowires. 1. Measure the height of all plateaus in the five files you saved, using the cursors in the digital oscilloscope software, and record this information. 2. With a gradually varying trace, it can be difficult to tell one plateau from another or to determine the end-points of a plateau. In this case, place a horizontal cursor on a plateau. As long as the trace touches the cursor, it is part of the same plateau. Where the cursor and trace diverge, this marks the end of the plateau. 3. Print a copy of the file that shows your longest-lasting nanowire for your lab report. Mark the height and duration of the plateaus on your printout. 51
III. Analysis 1. For a single-atom bridge, calculate the theoretical current that will pass though at the voltage measured from the voltage divider in your circuit. 2. The measurement circuit has a current-to-voltage amplifier with a gain of 105 V/A. Calculate the theoretical voltage output for a single-atom wide bridge. Also, calculate the output for a two-atom wide bridge. 3. Using the formula for resistance of macroscopic objects, compute the resistance of a gold bridge 4 atoms long and one atom wide, assuming the diameter of a gold atom is 0.2 nm and given that the room temperature resistivity of gold is = 2.2 10 -8 m. Repeat your calculation for a gold bridge that is one atom wide and 100 atoms long. How do these values compare to the quantum mechanical resistance value? 4. A metallic carbon nanotube behaves as a "two-channel" conductor, i.e. its conductance is twice the fundamental conductance quantum. What is the minimum resistance of a carbon nanotube? 5. Do nanowire bridges form when the gold wires are brought together, separated, or both? Explain your answer based on your observations. 6. Make a table with columns for your nanowire data "Vout (mV)," "I (A)," "G (-1)" and "G/G0." In the first column, record the plateau heights as measured on the oscilloscope. Use this to find the current through each nanowire I, its conductance G, and finally its conductance as a fraction of the theoretical conductance quantum G/G0. 7. Make a histogram using your data G/G0 from question 6. From your data, what size nanowire occurred most frequently? 8. Is there evidence of defects in the nanowires you made? Explain your answer. 9. Do your data provide evidence for the existence of a conductance quantum of value G0 as predicted by theory? Explain your answer. 10. Attach the labeled printout showing your longest-lasting nanowire. How long did your most stable nanowire last? Is the break junction method you used to form nanowires practical for building circuits?
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Quantum Dots
Jeff Harbold, Monica Plisch
I. Introduction Quantum dots are semiconductor nanoparticles that emit light at a characteristic wavelength when excited. The wavelength of the light emitted depends on the size of the nanoparticle; this behavior is quite useful since it is relatively easy to control size. Quantum dots are a subject of intense research at Cornell and other institutions. The figure below shows STEM images of quantum dots taken in the Silcox lab at Cornell.
Left: low resolution STEM image of quantum dots; small spheres of semiconducting material that appear as white dots. Right: high resolution STEM image of a single quantum dot; the brighter spots showing the location of individual columns of atoms.
Quantum dots have a variety of potential applications. A collaboration between the Wise and Webb labs at Cornell demonstrated the use of quantum dots for imaging blood flow in mice. Quantum dots may also prove useful as fluorescent tags for biological molecules so that the motion of individual biomolecules can be tracked in a microscope. Another possible application involves fiber amplifiers that boost signals after they have traveled long distances in optical fibers. Current fiber amplifiers work over a narrow range of wavelengths, limiting the bandwidth. Quantum dots of varying sizes could be embedded in a fiber and used to make a broad-band amplifier that would expand the capacity of a fiber several fold. Quantum dots can be synthesized with a variety of nanofabrication techniques. The CdSe quantum dots we will study in lab were fabricated by injecting Cd and Se precursors into a solution in a reaction vessel. They reacted and precipitated tiny CdSe crystals that grew atomic layer by atomic layer. The final size of the quantum dots was determined by the time of the reaction and the temperature. After fabrication, the quantum dots were embedded in a PLMA polymer matrix to make them stable and easy to handle.
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Some bulk semiconductors emit light when excited. In general, the composition of semiconductor material determines the wavelength of light emitted. For example, a light emitting diode (LED) that emits red light is made from Gallium Arsenic Phosphide (GaAsP) while an LED that emits green light is made from Gallium Phosphide (GaP). Certain colors are notoriously difficult to generate, due to material growth issues. However, when a semiconductor is made very small (~1 to 10 nm), something new happens--the frequency of emitted light changes with the size of the quantum dot! In a bulk semiconductor, the frequency (color) of the emitted light is the determined by the energy of the band gap. The energy diagram to the right shows two energy bands separated by a gap in which no states exist. In a semiconductor, the lower energy valence band is nearly filled with electrons and the higher energy conduction band is nearly empty. When an electron in the conduction band transitions to the valence band, it emits a photon of light with energy approximately equal to the energy of the band gap, Eg. As the dimensions of a semiconductor material are reduced to the nanoscale and begin to approach the wavelength of the conduction electrons, a phenomenon called "quantum confinement" occurs. Energy levels shift and the band gap becomes larger. Appendix M introduces the "particle-in-a-box" model, which can be used to describe the change in the energy diagram for quantum dots. The larger band gaps of the quantum dots result in the emission of higher energy or bluer photons. To investigate the optical properties of quantum dots, you will use a spectrometer and various light sources to make emission and absorption measurements. An emission spectrum can be used to determine the energy of the band gap. It characterizes the intensity of light emitted by quantum dots as a function of wavelength when they are excited by an ultraviolet source. The ultraviolet light excites electrons from the valence band to empty states in the conduction band. An excited electron loses energy by first giving off heat to the lattice until it reaches the bottom of the conduction band; then the electron emits a photon to fall to the valence band. The wavelength of the emitted photon is measured by the spectrometer. An absorption spectrum can be used to determine the density of empty states as a function of energy in the conduction band. First the spectrometer is used to collect a spectrum I 0 ( ) from a white light source that produces a broad range of wavelengths. Then a quantum dot sample is placed between the source and the spectrometer and another spectrum I ( ) is collected. The absorbance - log(I ( ) I 0 ( )) is plotted as a function of wavelength. Peaks show energies at which photons are most strongly absorbed, indicating energies that contain a high density of unoccupied states. 54
II. Procedure 1. Observe the CdSe quantum dot samples with your unaided eye: a. Observe the quantum dot samples in the room light. b. Please note--do not stare directly at the UV source! c. Turn on the UV source and illuminate the quantum dot samples. What differences do you notice compared to room light illumination? 2. Measure the spectrum of the UV source: a. Click on the desktop icon OOIBase32 to open the program. b. Make sure Correct for Elect. Dark is selected. With a cap over the end of the fiber optic cable, the intensity should be 0 (within noise) at all wavelengths. c. Turn on the UV source and orient the fiber so that it collects some UV light. d. When you get a reasonably smooth spectrum, click on the Save icon to save it. 3. Measure the emission spectrum of each quantum dot sample: a. Place a quantum dot sample under a UV light source. Orient the end of the fiber so that it collects light emitted by the quantum dot. b. Adjust Integ. time, the acquisition time for a single spectrum, and Average, the number of spectra to average, to minimize noise in your spectrum. c. When you see a well-defined peak, click on the Save icon. d. Repeat steps e-g for the other quantum dot samples. 4. Display all five spectra on screen and print: a. Open the UV spectrum by clicking on the Open icon. b. In the Overlay menu, click on one of the --Select to add overlay... menu items and open one of the quantum dot spectra. Repeat for remaining saved spectra. c. In the View menu select Display Properties... to adjust line color and other properties if needed. d. Print one copy of the data for each person. 5. Measure the peak of each spectrum: a. Point and click with the mouse on the maximum of the UV peak. The green vertical cursor should pass through the maximum. b. In the legend at the top right corner, the three numbers following "Master" are wavelength, pixel number, and intensity for the "Master" (UV) spectrum at the location of the green cursor. c. Record the wavelength and intensity at the UV peak. Label the UV peak on your hard copy with this information. d. Also measure the wavelength and intensity at the emission peak of the four quantum dot samples and label on your hard copy. Note that in the legend, the two numbers following each overlay file are the pixel number and the intensity. The wavelength appears only after the "Master" label. 6. Measure the extent of each spectrum: a. Divide the maximum intensity of each spectrum by two. Measure the wavelength on both sides of each peak at which the intensity equals half the maximum. b. Record the wavelength at the left side and at the right side of each peak on your hard copy.
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7. Acquire absorption spectra: a. Place the cap over the spectrometer probe. Adjust the settings to minimize the noise of the dark spectrum. Then save the spectrum using Store Dark . b. Orient the spectrometer probe so that it is detecting the spectrum of a broad band white light source. Do not move the probe or the light for the remainder of the measurement. c. Adjust the settings to minimize the noise on the white light spectrum, then store it using Store Reference . d. Click on the Absorbance Mode icon . e. Place the sample with red quantum dots in front of the probe. Adjust the settings to minimize the noise, then save the spectrum. f. Acquire an absorption spectrum from the orange quantum dot sample. You may need to adjust the position and orientation of the sample to get a good spectrum. g. Overlay your absorption spectra in one window (see step 4) and print one copy for each person. 8. Measure the first absorption peak: a. Point and click with the mouse on the maximum of the lowest energy absorption peak for each spectrum and determine the wavelength. b. On your hard copy, label the wavelength of the lowest energy absorption peak for each spectrum.
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III. Analysis 1. Why do the quantum dot samples look different when illuminated with ultraviolet light compared to the room lights? 2. Attach a plot of the emission spectra from the UV lamp and the quantum dot samples with peak wavelengths and left and right side wavelengths marked as described in the Procedure section. Organize your data for each spectrum in a chart with the following columns: peak emission wavelength (nm), peak emission energy (eV), left and right side emission wavelengths (nm), left and right side emission energies (eV). 3. A quantum dot absorbs a UV photon of higher energy and emits a visible photon of lower energy. Assuming energy is conserved, what happens to the "missing" energy? 4. Construct a quantitative energy level diagram showing the electronic transitions that occurred in your quantum dot samples when excited by UV light. Put energy on the vertical axis and label the QD samples on the horizontal axis. Assign the ground state an energy of 0 eV. Electron transitions involving photons should be represented with solid arrows from one energy level to the other. All absorption arrows should start at the ground state and all emission arrows should end there. Represent any unobserved transitions with dotted arrows. 5. Plot peak emission energy vs. radius for the four quantum dot samples and attach your plot. The average radius for each dot as measured using TEM is: (red) 3.44 nm, (orange) 3.18 nm, (yellow) 2.60 nm, (green) 2.15 nm. Does emission energy increase or decrease with dot radius? Explain the trend. 6. Subtract the band gap energy for bulk CdSe from the peak emission energy for each quantum dot sample; the result is the confinement energy. Plot confinement energy vs. radius, using the radius data given in question 6. Using a spreadsheet or graphing program, fit a power law of the form y = Ax n where A and n are constants determined by the fit. Attach the plot to your report and include the equation. Does the power law exhibit the size dependence predicted by the particle-in-a-box model? 7. The width of an emission spectrum is primarily determined by size variation of the individual quantum dots within a sample. Using your power law fit from question 6 and the left and right side emission energies determined in question 2, estimate the variation in radius for each quantum dot sample. Report your data both in nm and atomic layers noting that the average CdSe atomic layer thickness is 0.36 nm. How well controlled is the growth process? 8. Attach your plot of absorption spectra, labeled as described in the Procedure section. Why does an absorption spectrum have a different shape than an emission spectrum for a particular quantum dot sample? What information does an absorption spectrum provide that an emission spectrum does not? 9. Calculate the energy of the lowest peak of the absorption spectrum and compare it to the energy at the peak of the emission spectrum for each quantum dot sample. Do the absorption and emission spectra for the same sample peak at the same energy? Do you expect them to? Why or why not?
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Giant Magnetoresistance
Vlad Prigiag, Ilya Krivorotov, Bob Buhrman, Monica Plisch
I. Introduction Giant magnetoresistance (GMR) was discovered in 1986 in magnetic multilayers. These structures had thin metallic layers that alternated magnetic and nonmagnetic materials, such as Fe (magnetic) and Cr (nonmagnetic) or Co (magnetic) and Cu (nonmagnetic). Magnetoresistance refers to the change in resistance as a magnetic field is applied, typically expressed as a percentage. Previous to the discovery of GMR, the largest known magnetoresistance values were a fraction of one percent. With the magnetic multilayer structures, resistance could decrease by more than 50% in a magnetic field. Even spin valves, which consist of only two magnetic layers separated by one nonmagnetic conductive layer, could achieve magnetoresistance values of greater than 10%. Due to the unprecedented large magnetoresistance values, this phenomenon was called "giant magnetoresistance." Within less than a decade, a very short time from discovery to market, GMR devices were incorporated into products as magnetic field sensors. Spin valves had a major impact on hard disk drives, since the large increase in the sensitivity allowed the magnetic bits on the hard drive to be much smaller, resulting in more compact high capacity drives. Spin valves are also being researched for potential application as bits in magnetic random access memory (MRAM). GMR originates from the fact that electrons have a magnetic moment called spin. Electrons in a magnetic material experience a different resistance depending on whether their spin is aligned parallel (up) or anti-parallel (down) to the magnetization of the material. This is a consequence of the different density of states for up- and down-spin electrons, and requires solid state physics for an explanation. Typically, up-spin electrons experience less scattering and therefore a lower resistance than down-spin electrons. A spin valve, which has two narrowly separated magnetic layers, will have a different resistance depending on whether the magnetizations of the two magnetic layers are parallel or anti-parallel to each other. When the layers are aligned parallel, the up-spin electrons can easily conduct through the entire material, resulting in a low resistance state. When the layers are anti-parallel, both up-spin and down-spin electrons scatter heavily at different parts of the spin valve, resulting in a state with an overall higher resistance. A simple model is shown below in Figure 1:
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Fig.1 Schematic of a Spin Valve with parallel and anti-parallel magnetization.
An equivalent resistor network model is shown below the diagrams of the spin valves. A spin parallel to the magnetization of a layer experiences a relatively low resistance of `r' and a spin anti-parallel to the layer experiences a relatively high resistance of `R'. The exact structure of the spin valve we will study in lab is shown in Figure 2. These samples make use of an anti-ferromagnetic pinning layer that makes it very difficult to flip the direction of the adjacent ferromagnetic layer, i.e. the `pinned' layer. The other ferromagnetic layer is the `free' layer, which requires a much lower field to change the direction of its magnetization. This arrangement makes it simple to achieve parallel and anti-parallel alignment of the two layers by flipping only the `free' layer.
Fig.2 Schematic of a Spin Valve
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It is important to mention that like any other magnetic system, a spin valve presents a hysteretic behavior. Hysteresis represents the history dependence of the behavior of physical systems. In a spin valve, when you cycle an applied magnetic field its magnetization goes through a hysteretic loop. As it can be observed in Figure 3, the magnetization curve as the field is ramped up is not the same as when the field is ramped down, this is because it takes certain amount of energy to restore a magnetized system to its original state.
Fig. 3 Magnetization Loop with Hysteresis
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II. Procedure A. Connect the circuit
1. Connect the power source to the proto-board. 2. Connect the yellow multimeter across the ceramic resistor, measure and record its resistance R, and keep it connected. 3. Connect the coil to the proto-board. B. Calibrate the electromagnet 1. Insert magnetic field probe so tip is in center of coil (electromagnet). 2. Record magnetic field in the center of the coil as a function of current through the coil (hint, what is the current through the resistor?) at over a wide range of current and magnetic field values. Note that the probe measures a field at no applied voltage highly dependent on its orientation (can you think of why?), make sure it remains in the same direction for the whole calibration. 3. The dial on the magnetic field probe has units of amperes. The probe is calibrated so that 1 A corresponds to 1 gauss. Record your magnetic field data in gauss. 4. Plot the magnetic field as a function of current through the coil. Using Excel find a linear fit to your data and record the equation so that you can determine the magnetic field in your coil for a given current through it. 5. Print one plot for each lab partner. C. Test run 1. Remove the magnetic field probe and insert the sample (spin valve) in the center of the coil. 2. Connect the spin valve leads to the orange multimeter and measure the resistance of the sample at no applied voltage.
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3. Increase the voltage of the power supply to the coil to its maximum setting. Note the resistance of your sample. Note the maximum current the power supply can generate through the coil. 4. Decrease the voltage of the power supply until you reach the minimum setting. Note the resistance of your sample. 5. Switch the leads on your power supply so that the current will run the opposite direction through the coil (this reverses the direction of the magnetic field). 6. Increase the voltage of the power supply to the coil to its maximum setting. Note the resistance of your sample. 7. Decrease the voltage of the power supply until you reach the minimum setting. Note the resistance of your sample. 8. Discuss the resistance data with your lab partner. At what point did the magnetic layers have their magnetizations in parallel alignment? Anti-parallel alignment? D. Measure magnetoresistance 1. Switch the leads on your power supply back to what they were at the start of your test run. 2. Based on the maximum current the power supply can generate through the coil, decide how much you will change the current between each data point. 3. Repeat the same sequence that you did for the test run (start from zero applied field, increase field, decrease field, switch leads, increase field, decrease field) while recording the resistance of your sample as a function of current through the coil at regular intervals. 4. Enter your data into a spreadsheet. Convert current through the coil to magnetic field in the coil. Plot resistance of your sample as a function of magnetic field separating the data for the ramp-up and ramp-down. Connect the data points with a line to better observe the hysteresis loop. 5. Print one copy of the data and one plot for each lab partner.
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III. Analysis 1. Attach the calibration plot for your electromagnet to your lab report. What is the equation to convert current to Gauss? 2. Attach the magnetoresistance plot for your sample to your lab report. Put arrows on your plot to indicate the direction of the field change for each segment. Label segments of your data where the magnetic layers have parallel alignment and where they have antiparallel alignment. 3. Why does the GMR curve differ for increasing applied magnetic field and decreasing applied magnetic field? 4. Calculate the giant magnetoresistance ratio for your sample by dividing the maximum change in resistance by the average resistance. How does it compare to a typical spin valve GMR of 5% for read heads? 5. Spin valves are used in read heads to sense the direction of magnetization of individual bits on hard disk drives. What is the minimum magnetic field a bit must exert on your spin valve to completely flip the free magnetic layer? What is the ratio of this switching field to the Earth's magnetic field? 6. Spin valves are also being developed for use as memory elements in magnetic random access memory (MRAM). The parallel and antiparallel states compose a two-state system that can encode "0" or "1." Describe how you would both read (i.e. detect the state) and write (i.e. change the state) to a spin valve memory element. 7. If your sample was missing the IrMn layer, would you still expect to see the GMR effect? Explain why or why not.
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APPENDIX A
Brief History of Solid State Electronics
In 1906 Lee de Forrest (1873-1961) invented the vacuum tube. From 1906-1956, the vacuum tube was the mainstay of electronic circuits. The tube that de Forrest invented, called the triode, has three elements, a cathode which emits electrons, a plate (anode) which collects the electrons, and a highly transparent mesh electrode (grid) placed between the cathode and anode. The vacuum tube was an electronic switch, with the grid voltage controlling the current through the tube. For the vacuum tube to operate, the cathode-grid-plate structure is placed into a glass envelope from which air is evacuated to a pressure one billionth or less of that of standard atmospheric pressure. Since vacuum tubes, transformers, and discrete electronic components were all fairly bulky, consumer electronics was limited to radio, TV sets, and HI FI systems. All of this equipment was large, heavy, and consumed a lot of power, on the order of 200 Watts. In the early days of commercial radio, when vacuum tube radio receivers were still fairly expensive, crystal set receivers were used by a large segment of the listening public. The crystals used in such sets were naturally occurring crystals of semiconducting material: galena (iron sulphide), fool's gold (iron pyrite), silicon, and germanium. The crystals were usually set in a small cup of solder and a thin wire, called a "cat's whisker" was moved around the crystal until a sensitive spot was found which would exhibit the required rectifying action. Rectification is the ability to pass current of only one polarity, i.e. one direction. Today such crystals are called point-contact diodes. Due to the erratic and unpredictable behavior of the crystal diodes, they were not used in the manufacture of radios. However, crystal radios are cheap and easy to build. Therefore, many people in the `20s and `30s who could not afford to buy radios built crystal sets. The large number of listeners using crystal radios contributed to the rapid expansion of radio stations in the `30s. In the late 1930s Russell Ohl, a staff scientist at Bell Laboratories, became fascinated by the erratic behavior of silicon and its then poorly understood ability to rectify alternating currents. He became convinced that the erratic behavior was due to impurities in the silicon, and not to any intrinsic property of silicon itself. By 1939 he succeeded in making crystals that were 99.8 % pure, and sure enough, the rectifying behavior of such pure crystals was much more reproducible. Ohl also discovered that there are two types of silicon, One type has a surplus of current carrying electrons (n-type) and the other a deficit (p-type). He also showed that this property was due to impurities in silicon and that it could be produced in the laboratory by introducing small amounts of certain atoms into the material. The introduction of impurities is called doping. Because of Ohl's work on silicon just prior to WW II, the Allies had much better crystal diodes than the Axis, and hence more sensitive radar receivers. Ohl's work on silicon however had far greater consequences in that it opened up Bell Laboratories to the idea that silicon diodes could replace vacuum tubes. Walter H. Brattain (1902-1987), also at Bell Laboratories, had been aware of Ohl's efforts to purify silicon, as well as his pioneering work on what today we call solar cells.
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Brattain was investigating how electrons behave on the surface of a semiconductor (Why does the "cat's whisker work only on certain parts of the crystal?). Brattain's work with silicon, and later with germanium, led to the invention of the point-contact-transistor with John Bardeen (1908-1991) and William Shockley (1910-1989). The most amazing thing was that a small piece of silicon, gold, and plastic was all that was needed to construct the first solid state amplifier in December of 1947. By 1958 the transistor was commonplace. The early point-junction-transistors were replaced by so called pn-junctions, and these could be fabricated easily and reliably. Transistors started to replace vacuum tubes in all electronics and the concept of making electronics small was born. However, transistors could not be made too small, since ultimately they had to be connected to wires and other electronic components. The size of transistors manufactured was essentially determined by how easily they could be handled and inserted into circuits by workers. At this point, people started to think about making the whole circuit, transistors, wires, resistors, capacitors, and inductors all in one package. If this could be done, then miniature circuits could be made, perhaps in only one operation. The idea occurred to Jack Kilby at Texas Instruments in the summer of 1958. People knew how to make transistors small, but the idea of making resistors and capacitors out of semiconductors had not been attempted. By mid September, Kilby had built a working circuit the size of a pencil point. Six months later, Texas Instruments filed a patent for the first "Solid Circuit". The idea that a whole circuit could be constructed on a small chip occurred independently and almost simultaneously to Robert Noyce, working at Fairchild Semiconductor, a company that was just starting up. In this way the integrated circuit was born. Much of what we think of now as nanotechnology started with the invention of the transistor in 1947 and the integrated circuit in 1958. Rapid progress was made in the five decades following these inventions in miniaturizing circuit components and building ever more powerful circuits. At the time of this writing, state of the art processors in personal computers contain several hundred million transistors within an area of approximately one square inch. This means that each transistor has been shrunk so that a thin layer called the "gate dielectric" is 1.4 nm thick; this is only 5 or 6 atomic layers of silicon dioxide! The "gate length" of each transistor, the distance over which current is switched on and off, is 60 nm or less. The fabrication tools and techniques that have been developed to build such tiny devices form the basis of our tool set for working in nanotechnology today.
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APPENDIX B
How Does a Crystal Radio Work?
To understand how a crystal radio works, it is important to first review AM radio. "AM" stands for Amplitude Modulation. An electromagnetic wave with frequency 540 kHz to 1600 kHz, called the "carrier signal," has its amplitude modulated according to the audio signal to be transmitted (voice, music, etc.). The amplitude modulation occurs at much lower frequencies than the carrier signal, usually within the range that can be heard by the human ear, 20 Hz to 20 kHz. For example, to transmit a pure tone such as the sine wave shown in the top part of the Fig. 1, the amplitude of the carrier signal would be modulated as shown in the bottom part of Fig. 1.
Figure 1. Amplitude modulation of a carrier signal. Each AM station broadcasts at a different carrier frequency. An antenna positioned on the roof of Ward Lab detects the broadcast electromagnetic waves of all the AM stations in the area. Therefore, the first task of the radio is to select the carrier signal of just one station and reject the carrier signals of all other stations. The coil and the capacitor connected in parallel with it form a "band-pass filter." Such a filter passes a small range of frequencies and attenuates all others. The inductance of the coil and the capacitance of the capacitor determine what frequency is passed without attenuation. In the radio you built, moving the slider arm changes the inductance of the coil by lengthening or shortening it. This allows you to adjust the frequency that is passed by the filter so that you can tune the radio to your favorite station. Next, the signal is "rectified," meaning that only the positive part of the signal is kept. Rectification is necessary for extracting the audio signal from the carrier signal III
(explained in the next paragraph). The diode in your radio acts to rectify the signal. Diodes allow current to pass through only in one direction and not the other. In a simple radio of the 1920's and 1930's, a chunk of semiconductor crystal contacted by a sharp metal wire or "cat's whisker" formed the rectifying device; hence the name "crystal radio." The top half of Fig. 2 shows a rectified version of the signal from Fig. 1. In the final stage of signal processing, a "low-pass filter" averages the rectified signal. Note that the average of the signal before rectification is zero. After rectification, the averaged signal is proportional to the amplitude, as shown in the bottom part of Fig. 2. The low-pass filter, consisting of a resistor and a capacitor, passes only frequencies below a threshold frequency determined by the resistance and capacitance of these components. The crystal radio you built has low-pass filter with a threshold lower than the range of possible carrier frequencies and higher than the range of audio frequencies. Therefore, the filter will pass the low frequency modulation of the carrier signal, but not the carrier signal itself.
Figure 2. Rectified signal (top) and signal after low-pass filter (bottom). The recovered audio signal then goes to the earphone. The earphone uses a piezoelectric device to convert the electrical signal back into sound. The main component is a metal disk coated with piezoelectric material that shrinks and expands as the voltage of the signal varies. This causes the disk to vibrate and generate sound waves that reach your ear. No additional power is needed to operate the crystal radio. The broadcast signal drives the circuit as described above. However, this means that the volume cannot be adjusted and is entirely dependent on local signal strength. In Ithaca, you will be able to tune in two AM stations: 870 WHCU (talk radio) and 1470 WTKO (oldies).
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APPENDIX C
Reading Resistor and Capacitor Values
Most small resistors are color coded to indicate the value of their resistance. There are usually 4 colored bands on a resistor close to one end. The first two bands indicate a two digit number, the third band indicates a power of 10 multiplier, and the fourth indicates the tolerance. The color code: color black brown red orange yellow green blue violet gray white gold silver digit 0 1 2 3 4 5 6 7 8 9 multiplier 100 101 102 103 104 105 106 107 108 109 10-1 10-2 tolerance 2% 5% 10%
For example, if you have a resistor coded gold/red/violet/yellow, you should realize that you must turn it around, since gold is not a valid digit. You will also notice that the yellow band is closer to one end than gold is to the other, another clue to start with the other end.
Yellow Red Gold Violet
So make that yellow/violet/red/gold. Therefore, the two digits are 4 and 7, the power of ten of is 2 and the tolerance is 5%. This indicates a resistance value of 47102 = 4700 = 4.7 k. The tolerance is 5% meaning that the actual resistance may be 5% greater or less than 4.7 k if you measure it with a multimeter. Note that the interpretation of the significant digits and power of 10 are similar to, but not the same as, scientific notation in that the decimal point is after the first two digits, not between them.
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Capacitors work in a similar way; however, numbers are used rather than colored bands to indicate capacitance values. Capacitance is assumed to be in picofarads or pF. For example, "103" stamped on a capacitor indicates a capacitance of 10 10 3 pF = 0.01F.
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APPENDIX D
Physical Vapor Deposition
Making thin, uniform films of materials is a basic task in nanoscale science and engineering. Three physical methods of depositing thin films are described below. Evaporation The simplest way to make a thin film is to evaporate material in vacuum and allow its vapor to deposit on a substrate. A "boat" typically made of tungsten, which has a high melting point, has a little dimple into which the material to be evaporated is placed. The boat is heated in vacuum to a high enough temperature so that the vapor pressure of the evaporated material is appreciable, and the vapor is allowed to condense on a "cold" substrate. "E-beam" evaporation is a variation in which electrons are accelerated and directed at the target material, causing it to heat up. This technique allows more precise control of deposition rates and film composition. Molecular beam epitaxy (MBE) Thin layers of materials can be made by a sophisticated beam evaporation system shown schematically in the figure at right. Three or more crucibles containing material to be evaporated can be maintained at different temperatures. Shutters are opened or closed for an appropriate interval of time to allow vapors of different materials or combinations of materials to be deposited on a substrate that is at a controlled temperature. Sputtering In sputtering, atoms are removed from one surface by energetic ion bombardment and allowed to collect on another surface. Noble gas ions, typically argon, are used to bombard the surface of the material from which one wishes to make a thin film. Incident ions with large kinetic energy collide with surface atoms and give them VII
enough kinetic energy to leave the surface and travel to the substrate. It is somewhat like shooting cannon balls at a cement wall causing chunks to fly off. Eventually the sputtered atoms accumulate in a layer on the substrate, forming a thin film. Quartz crystal monitor A quartz crystal thickness monitor is frequently used to determine film growth rate and instantaneous thickness in physical vapor deposition processes. In our lab, a quartz crystal sensor is positioned near the Si substrate so that Al atoms also condense on the surface of the quartz crystal. The increase in the mass of the sensor is converted to a film thickness by the electronic control unit. The deposition of the Al film is stopped once it reaches the desired thickness, as displayed by the control unit. When electrically energized, quartz crystals resonate or produce an alternating electrical current at a stable, well-defined frequency. This is the basis of their use in timepieces. There are two quartz crystals in the crystal monitor, one in the sensor and one in the control unit. The control unit counts the number of oscillations per second from each crystal and determines the difference. The initial frequency difference before the film is deposited can be stored by the control unit and used to "zero" the readout. As the evaporation proceeds, the substrate and the sensor (usually positioned the same distance from the source) are coated with atoms. The coating increases the mass of the sensor, which causes the frequency of its crystal to decrease. Meanwhile, the frequency of the crystal inside the control unit remains unchanged. The control unit compares current frequency difference to the initial frequency difference, and computes the increase in mass of the sensor. Using information already programmed into the instrument, including the exposed area of the sensor crystal and the density of the deposited film, the control unit computes and displays the thickness of the material deposited on the sensor. The quartz crystal thickness monitor has the advantage of allowing the evaporation process to be controlled in real time. However, it is typically not as accurate as instruments that directly measure film thickness, such as a surface profilometer or an atomic force microscope. For example, variations in deposition conditions can cause a change in film density, which affects the accuracy of the thickness determined by the crystal monitor.
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APPENDIX E
Evaporation Procedure
crystal substrate monitor
vent valve evaporation boat 220V current control cold trap gate valve diffusion pump
thermocouple (TC) gauge (>10-3 Torr) ion gauge (<10-3 Torr)
vent valve roughing valve TC gauge exhaust
foreline valve
mechanical (rotary) pump
Pre-pump down 1. Put on gloves for work inside the chamber 2. Place Al source in W boat. 3. Put shielding tube over boat to prevent excess deposition on glass cylinder. 4. Clip substrate on substrate holder. 5. Put glass cylinder on Al base and center it (make sure seals are clean). 6. Put implosion shield over glass cylinder. 7. Put Al top on glass cylinder and center it. 8. Put substrate holder on Al top and center it. 9. Attach coaxial cable to crystal monitor. 10. Close chamber vent valve. 11. Turn on power strip for gauges and sensors. Pump down A: if chamber and pumps at atmospheric pressure 1. 2. 3. 4. 5. Turn on cooling water for diffusion pump. Make sure gate valve is closed. Open foreline and roughing valves. Check that hood is on to exhaust rotary pump fumes. Close vent valve on foreline.
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6. Plug in rotary pump to turn it on. 7. When thermocouple gauges both read < 50 mTorr, close roughing valve, turn on both diffusion pump switches, and press black interlock button on same panel. Check that lights are on for both switches. 8. Add liquid nitrogen to cold trap. When trap is full and the diffusion pump has been on for 20 minutes, then open gate valve if chamber is <50 mTorr. (If needed, first close foreline valve and open roughing valve to get chamber pressure below 50 mTorr. Then reclose roughing valve and reopen foreline valve.) 9. Wait 5 minutes after the thermocouple gauge reads 0 mTorr, then turn on the ion gauge. Push "Standby" to turn on, then push "Emis.". Ion gauge should glow. Pump down B: if diffusion and rotary pumps on, chamber at atmospheric pressure 1. Close foreline valve. 2. Open roughing valve. 3. When thermocouple gauge on chamber reads below 1000 mTorr, close roughing valve. 4. Open foreline valve. 5. Open gate valve. 6. When thermocouple gauge reads 0 mTorr, then turn on the ion gauge. Push "Standby" to turn on, then push "Emis." Ion gauge should glow. Evaporate 1. When the pressure is below 1.010-5 Torr, it is OK to evaporate Al. 2. Turn on the power to crystal monitor by pressing "Power". 3. Check film settings by pressing "PG" key. Page 4-7 in the manual contains settings for bulk density and z-ratio. Enter new values if needed using the "E" key to scroll down and the numerical keypad for entry. 4. Hit "zero" to zero film thickness. 5. Check that the "front" boat is selected. 6. Check that the transformer dial on the lowest panel is set to the position of the black arrow. 7. Make sure the current dial on the second lowest panel is at its lowest setting. Turn on the power switch. 8. Press "start" on the crystal monitor. 9. Slowly turn up the current until the boat is glowing and the Al begins to melt. 10. Turn down the current so that the Al melts slowly. 11. Gradually turn up the current to about 100A to get an evaporation rate of 10--20 /sec. 12. Turn the current to zero when desired film thickness is reached. 13. Turn off crystal monitor and power to boat. Vent A: leave pumps running, vent chamber only 1. Wait 5 minutes for boat to cool. 2. Turn off the ion gauge. 3. Close the gate valve.
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4. Open chamber vent valve. Vent B: vent chamber and pumps 1. Wait 5 minutes for filament to cool. 2. Turn off the ion gauge. 3. Close the gate valve. 4. Turn off diffusion pump (both switches). 5. Open chamber vent valve. 6. Close foreline valve. 7. Turn off mechanical pump. 8. Open mechanical pump vent valve. 9. Open roughing valve. 10. After the diffusion pump has been off for 20 minutes, turn off cooling water Post-vent 1. 2. 3. 4. 5. Disconnect crystal monitor cable. Remove substrate Remove Al top and glass cylinder and place carefully on table. Wipe Al from the glass with cleaning fluid and clean wipe. Place glass cylinder, Al top and substrate holder back on chamber.
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APPENDIX F
Vacuum Pumps
There are two types of vacuum pumps used in the evaporator system, a mechanical (or rotary vane) pump and a diffusion pump. Initially, the mechanical pump is used to "rough out" the main vacuum chamber, or pump it down to a pressure of 50 mTorr (atmospheric pressure is 760 Torr). At that pressure, the diffusion pump is turned on and pumps the chamber down into "the sixes" or on the order of 10-6 Torr for evaporation. The mechanical pump "backs" the diffusion pump, or removes the exhaust of the diffusion pump so that it can function properly. Mechanical Pumps The operation of the mechanical pump is shown below. The pump has a chamber and an off-axis cylinder that rotates inside. There are two vanes that are spring-loaded such that they maintain contact with the wall of the chamber as the cylinder rotates. Pump oil seals any small gap between the vanes and the cylinder wall. At the start of the cycle, the vane marked P is near the intake port. As the cylinder rotates clockwise, gas flows into the region behind P until this region is isolated from the intake port as shown in (c). As the cylinder advances further, the gas is expelled through the exhaust port. In this way, air is continually removed from any volume connected to the intake port.
(a) (b)
(c)
(d)
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Diffusion Pumps There are no moving parts in a diffusion pump, the heart of which is a tree-like structure called the "multistage jet assembly" (see diagram below). A heater at the bottom of the pump boils the pump oil, and vapors travel upward inside the jet assembly. The vapors are then accelerated out and downward through jet nozzles toward the outer walls of the pump. The outer wall of the pump is cooled with cooling water, so that when the vapors strike the wall they condense and return to the bottom of the pump, completing the cycle. Gas molecules from the chamber diffuse into the pump at the inlet (top). The high-speed oil jets collide with gas molecules and direct them downward into the bottom of the pump, where they are exhausted by a mechanical pump (attached at "Foreline pump connection"). Diffusion pumps can achieve pressures of 10-8 Torr. Diffusion of the pump oil into the vacuum chamber can be prevented by placing a "cold trap" or a liquid nitrogen cooled baffle between the pump and the vacuum chamber. This is done on our system. Molecules that strike the surface of the baffle freeze to it and stay in the trap as long as it is supplied with liquid nitrogen.
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APPENDIX G
Introduction to the Atomic Force Microscope
Since the beginning of the 17th century, physicists and others have extended the capability of humans to see small objects with microscopes. By the 18th century, instrumentation technology had reached a fundamental limit, diffraction. Lenses that used light could not image objects smaller than the wavelength of light, or a fraction of a micron (10-6 m). In the 20th century, the limitations of the light were overcome with the invention of the transmission electron microscope. Electrons instead of photons were used to probe specimens and magnetic and electric lenses where used to focus the beam of electrons. Eventually in the best microscopes objects smaller than 0.2 nm could be imaged, approximately the distance between individual atoms. However, there were limitations to this technique as well. The electrons that were transmitted through the sample often damaged it, especially biological materials. The sample needed to be cut in a thin enough cross-section to allow electrons through, making preparation challenging. The electron beam could only operate in an ultra-high vacuum. Despite these limitations, it was and still is an outstanding tool for the study of the structure of many types of materials. The first imaging tool used to study the surface, or topography, of a material was the scanning electron microscope. A focused beam of high energy (~10 keV) electrons is scanned over the surface of an object. The number and angle of electrons ejected from the surface were used to assemble an image that appears three-dimensional. Again there were limitations. Non-conducting samples had to be coated with a thin layer of metal, which could obscure some features and modify the sample. Resolution was limited due to scattering of electrons just below the surface of the sample. The scanning tunneling microscope invented in the early 1980's was the first instrument that could probe a surface with atomic resolution. A very sharp tip held very close (~ 1 nm) from a surface allowed a tunneling current to flow between them when a voltage was applied. Since the magnitude of the tunneling current is very sensitive to tip-sample separation, this current could be used to image the surface topography on an atomic scale. This technique is limited to conducting surfaces and to maintain surface cleanliness an ultra-high vacuum is often required. Shortly after the invention of the scanning tunneling microscope, a new microscope called the atomic force microscope was developed. It uses a very fine-tipped probe to gently touch a surface. By measuring how much the tip moves up or down while dragging it across the surface, an image can be formed with near-atomic resolution. Its simplicity allows a wide range of materials to be studied, since it works in air and requires no special sample preparation. It even allows biological molecules to be imaged in aqueous solution, which is their natural environment. The atomic force microscope has become a very versatile tool in several fields of science and engineering.
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The basic premise of an AFM can be seen in the diagram below:
Source: PROBING BIOMOLECULES WITH THE ATOMIC FORCE MICROSCOPE. Helen G. Hansma, Department of Physics, University of California, Santa Barbara, CA 931106 http://www.physics.ucsb.edu/%7Ehhansma/afm-acs_news.htm
How the AFM works: 1. Tip--The tip at the end of the cantilever is the part of the AFM that actually contacts the sample. It is the key to horizontal resolution; tips with a smaller radius of curvature have better resolution. They are typically made by patterning and etching silicon, which can produce tips with a 5-10 nm radius. 2. Cantilever--The cantilever is like a diving board with a very small spring constant. This allows the very sharp tip at the end of it to contact the sample without dislodging atoms. The cantilever bends in proportion to the force between the tip and the sample. 3. Laser--In the AFM the laser shines down on the cantilever and reflects from the top surface. As tip moves up and down, the laser reflects at different angles from the cantilever. This causes the position of the laser to rise and fall on the segmented photodiode, a position-sensitive detector, allowing topographic information to be gathered. 4. Piezo scanner--The end of the cantilever is attached to a piezoelectric material that changes slightly with an applied voltage. The piezo tube scans the tip over the sample, and the tip rises or falls based on the topography of the sample. Typically, the AFM is operated in constant force mode, so that the tip adjusts up and down while scanning over the surface to maintain constant force. This is accomplished by contracting and extending the piezo in order to keep the position of the laser constant on the photodiode.
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APPENDIX H
Catalyst Synthesis
Catalyst Materials: o o o o 45 mg of Alumina Nanoparticles 60 mg Iron Nitrate (Fe(NO3)39H2O) 3 mg Molybdenyl Acetylacetonate (MoO2 (acac)2) (chemical is air sensitive) 45 ml Methanol
Equipment Needed: o o o o o o o o o Sonicator Magnetic Stirrer Stirring Bars Balance Weighing Paper Nitrile Gloves Glass Pipettes 50ml glass vial Parafilm
Safety Measures: 1. Always wear suitable protective clothing and gloves. 2. Handle substances carefully. 3. Keep an organized working space. 4. For all chemicals remember to: o Not breathe the vapors. o Not get in eyes, on skin or on clothing. o Avoid prolonged or repeated exposure. o Keep away from combustible materials, heat, sparks and open flame (only Methanol and Iron Nitrate are flammable). 5. Aluminum Oxide is a very light powder, be careful when handling it to avoid skin and eye contact. For more information refer to the MSDS sheets in the laboratory. Synthesis: 1. Rinse glass vial with a little bit of methanol. Dispose the methanol down the drain with plenty of water. Dry vial with compressed air tank (if available). 2. Pour 45ml of methanol in vial, close cap. 3. Use a new film of weighing paper and a new pipette to scoop out and measure each substance.
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4. Each time flush away any leftover powder down the drain with plenty of water. Rinse the weighing paper and dispose in trash container. 5. Place a film of weighing paper inside the balance and calibrate. 6. Scoop out 60mg of Iron Nitrate with clean pipette and place in vial. 7. Place a new film of weighing paper on balance and calibrate. Then, using a new pipette, scoop out 3mg of Molybdenyl Acetylacetonate and place it in vial. 8. Repeat step 7 with 45mg of Alumina nanoparticles. 9. When all substances are in vial, drop in the magnetic stirring tablet and place on magnetic stirrer for 24 hours. First, be sure to label the vial since you'll be leaving it on the stirrer for a long time. 10. After stirring is done, sonicate the solution for 1 hour. WARNING: DON'T put your fingers in the water tank while sonicator is ON. Make sure the water in the sonicator tank covers all of the substance in the vial before starting it. 11. When sonicating is finished, turn sonicator OFF and then remove vial. 12. Wrap cap with parafilm to avoid evaporation.
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APPENDIX I
Abbreviated Version of Software Help for WSxM
GENERAL
Information Basic image information.
Recalibrate Allows recalibration of x, y and z dimensions. Useful when WSxM does not read dimensions correctly from original data file.
Show Scale Bar, Edit Scale Bar
QUANTITATIVE ANALYSIS
Profile Profile curve of transversal cut across image. 1) Select image, 2) Click icon, 3) Left-click and drag, 4) Right-click to apply, 5) Click on profile window to get the following options: Reset: Restore Original Curve Reverse: Invert Y-axis of the graph. Smooth: Average current values. Fit Line: Fit curve to a line and subtract, brings out features. Measure Point: Display point values in Status Bar: (Z-coord., Profile line-coord.). Measure Distance: Display distance between two points. 1) Click and drag crosses to select distance, 2) Status Bar displays horizontal and vertical distances between two points.
Multiple Profile Find same profile curve on multiple images. Useful to compare the effect of filters and other modifications on an image. 1) Select image, 2) Click icon, 3) Select other images, 4) Left-Click on main image and drag, 4) Right-click to apply.
ANALYSIS OF PERIODIC IMAGES
Fast Fourier Transform To find periodic structure and/or remove unwanted frequencies or noise. 1) Select Window (ellipse or rectangle), 2) Click Filter, 3) Select Areas on Bottom-Right image by leftclicking and dragging, 4) Right click to apply.
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2D Cross Correlation The higher the value, the more similar the two images are. Good when dealing with thermal drift to calculate the distance the point has moved. 1) Select first image, 2) Click on icon and 3) Select second image.
Lattice Create a new layer over an image, usually a periodic atomic pattern (e.g. graphite hexagonal lattice). 1) Select image, 2) Click icon, - Preset lattice: hexagon, nxn (for Si 111), square. - User defined: 1) Tick vector checkbox, 2) Select 3 points by left-clicking, 1st click is the common origin for other two points; lattice displays in green lines, 3) Adjust vectors with V1/V2 length (nm) and V1/V2 angles. - Correct: Corrects distortion to enable a better fit. 1) Left click to select all similar vertex points associated with a pattern, 2) Right click to correct. 3) Click OK to apply.
VIEWING IMAGES
2D Displays top view of image.
3D View, 3D Settings Displays 3D view of image; adjusts 3D view settings.
Zoom, Multiple Dynamic Zoom Zoom in; zoom into same region of up to 4 images. 1) Select images, 2) set X and Y apertures of zoom region, 3) click on recalculate Max and Min to find hidden features in images.
BASIC IMAGE MANIPULATION
Duplicate Image
Z Reverse Negative of image, data multiplied by -1.
Mirror Reflect image with respect to Y-axis.
Rotate 90 90 CW rotation about Z-axis.
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Rotate Angle Rotate by any angle. 1) Select image, 2) Click icon, 3) Select Horizontal or vertical, 4) Select new X or Y axis by left-clicking and dragging to create a line, release. - Rotating by an angle not multiple of 90 will place zeros in points not representing data points.
BRING OUT FEATURES
Lut Command, Lut Settings Command Change color gradient. Sometimes new palettes bring out features that were not nvisible with other color gradients. 1) Select image, 2) Click icon, - Useful Palettes: ThermicHot.lut, Flag.lut, AEP.lut 3) Select preset palette, or 4) Create own color table by modifying brightness, contrast, continuous or discrete modes, 5) Save color table in Lut file format, 6) Click OK to apply.
Z-Scale Control Useful to bring out low features when high features are present in the image. 1) Select image, 2) Click icon, 3) Rescale max value to a lower value to find low features or 4) Click Automatic.
Derivative Calculates derivative along the X-axis, good to find borders. 1) Select image, 2) Click icon.
Cosine Calculates cosine of angle between slope of image and Z-axis, good to find borders. 1) Select image, 2) Click icon.
Equalize Select range of heights to enhance contrast, features lower than left limit will be raised to left edge min height; features higher than right limit will be lowered to right edge max height. 1) Select image, 2) Click Icon, 3) Left-click for left-edge, 3) Right-click for right edge.
Contour Plot, Contour Plot Settings Contour plot of the image, brings out `invisible' features. 1) Select Image, 2) Click Icon, 3) Select number of contours, 4) Ok to apply.
TILT CORRECTIONS
Plane Global Corrects any tilt due to tip-surface angle, applied to whole image. 1) Select image, 2) Click icon to apply.
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Plane Local Same as global, but applied to local planes. 1) Select image, 2) Click icon, 3) Left-click and drag to select as many planes as you want, 4) Right click to apply.
Find 2nd Fits local planes to parabolic surface, then subtracts from whole image. 1) Select image, 2) Click icon., 3) Left-click and drag to select as many planes as you want, 4) Right click to apply.
CLEAN UP IMAGE
Flatten Removes low frequency noise (seen as random darker lines along Y-direction). 1) Select image, 2) Click icon. - Simple Flatten: Removes a function from each line, Offset (average), Line or Parabola. - Discard Regions: Avoid flattening features you want to highlight. 1) Create, 2) Left-click and drag, 3) Right click. Select as many regions as you wish, 4) Apply. - Path Selection: Lines that connect top with bottom of image, 1 line subtracts avg. of values crossed by path, 2 lines subtract a plane and 3 lines subtract a parabola. 1) Path1-Create, 2) Drag mouse to bottom of image through area to calculate function to remove, 3) Left-click at bottom of image. Create up to 3 paths. 4) Apply.
Popcorn Removes peaks, by finding average of heights of whole image and subtracting. 1) Select image, 2) Click icon. - Cutoff: Max height distance from average. - Correlation: Global use whole image to do average, Local use separate regions, take local averages and filter individually; apply to XY Squares or lines in X or Y direction. - Number: of points affected by filter. 3) Apply.
Remove Lines Delete bad scan lines. 1) Select image, 2) Click icon. - Removing Style: -Average, interpolates 2 closest `good lines', -Set zero, replaces with zeros (black lines). - No. of lines to be removed. - 1st line: type or drag cursor to left of image. 3) Apply.
Spot Removal Cleans noise (peaks) locally, remove unwanted high points in image. 1) Select image, 2) Click icon, - Options: Copy, region into memory, Paste, copied region into selected region, Medium, replaces region with average value and Smooth, replaces each point with average of neighbors. - Cutoff: for Medium, max height distance from average value allowed. - Source Aperture %: size of selected region. - Zoom Aperture %: size of region in zoom frame. 3) Apply.
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SMOOTHING DATA
Redimension Change number of columns and rows in image, maintains original ratio.
Smooth Removes high frequency components, replaces each point with neighbors average.
EXTRA STUFF
Tip/Sample Dilation Simulates the effect of a finite sized tip on an image. Tip used follows the equation: Z = aX^2 +bY^2. 1) Select image, 2) Click icon, X and Y Tip Radius: radius along X or Y direction in nm, 3) Click Dilate to apply.
Y Average Profile curve of averages of all horizontal lines.
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APPENDIX J
Brief Introduction to Quantum Mechanical Tunneling
The scanning tunneling microscope (STM) is based on a quantum mechanical phenomenon known as tunneling. In tunneling, a particle, in this case an electron, can jump from one location to another without spending any time in between. A diagram about tunneling can be seen in the figure to the right. If a particle is incident upon a barrier in our everyday macroscopic world, it will always reflect from the barrier. In other words, its probability of reflecting from the barrier R is always R = 1. In the microscopic world of quantum mechanics, a particle will not necessarily reflect; rather, it has some probability T of tunneling through the barrier. The probability of reflecting from the barrier R is less than one. R and T are related by:
Potential Energy
e-
Position
eClassical
R e-
e- T Quantum
R+T = 1
The probability of transmission, or tunneling, is
T e-w
Where is a constant that depends on the energy of the particle and the barrier, and w is the width of the barrier.
A particle incident on a barrier. In the macroscopic world it always reflects. In quantum mechanics, it can be transmitted with probability T, or reflected with probability R.
The exponential dependence on distance is what makes the STM such a sensitive instrument for exploring surfaces. If the tip contains one atom that is slightly closer to the surface than the other atoms, most of the tunneling current will flow through that one atom. The sensitive tunneling current allows the STM to have ~0.01 nm resolution vertically and atomic (~0.2 nm) resolution horizontally. Electrons are allowed to be in either the STM tip or the sample. The space between the two is a barrier. However, if the distance between the two is small enough, electrons will tunnel from one to the other. If no voltage is applied between the tip and the sample, electrons will tunnel back and forth with equal probability and no net current will flow. However if a voltage is applied, electrons will prefer to tunnel from the lower voltage to the higher one.
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APPENDIX K
Brief Introduction to Fourier Transforms
This is a basic conceptual introduction to the fourier transform (FT), which can be useful in understanding the FFT data processing step for removing noise from images. The idea behind the FT is that any signal can be written as the sum of sine waves, with each frequency sine wave having its own amplitude. The FT signal is the amplitude corresponding to each frequency. For example: Signal y = sin(x) Plot of signal
1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 0 2 4 6 8 10 12 14
Fourier Transform
Signal Strength
2 1 1 2
frequency
3
1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 0 2 4 6 8 10 12 14
Signal Strength
y = sin(2x)
2 1 1 2
frequency
3
2.5 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 -2.5 0 2 4 6 8 10 12 14
Signal Strength
y = sin(3x) + 2sin(x)
2 1 1 2
frequency
3
In WsXM, the software goes through the image and breaks it into sine waves (in the case of a spatial image the `frequency' has units of 1/length) and maps the amplitude of each sine component. Since the image is two dimensional, the FT is also two dimensional. Features with regular spacing will appear much brighter than those without regular spacing. You can choose to keep only those signals with a specific frequency by selecting them on the FT. Since graphite has a regular structure that repeats spatially, this is a good strategy. Such frequency filtering tends to remove noise, which appears at all frequencies. Additional information on Fourier transforms http://www.med.harvard.edu/JPNM/physics/didactics/improc/intro/fourier1.html http://www.cs.unm.edu/~brayer/vision/fourier.html http://online.redwoods.cc.ca.us/instruct/darnold/laproj/Fall98/KrisCrg/Fourier.pdf
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APPENDIX L
LT1007 Operational Amplifier Specification Sheet
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APPENDIX M
The Particle in a Box Model
Understanding the size-dependent frequency of light emission from quantum dots requires the wave description of matter, specifically, of the electrons inside the quantum dot. The one-dimensional "particle in a box" model is useful for gaining some insight. After this model is introduced, a discussion of how it applies to the quantum dot follows. Picture a particle such as an electron bouncing around inside a one-dimensional box of length L. However, the "correct" picture in modern physics is that of an electron wave reflecting back and forth from the walls of the box. The wave is a probability wave, and the square of the amplitude at any location gives the probability of finding the electron there. The addition of reflected traveling waves sets up a standing wave. The waves must have a node at the edges of the box (since the electron cannot escape the box and its probability must go to zero at the edge), so only certain wavelengths fit inside. Analogous to a wave on a string that is clamped at both ends, the size of the dot determines the characteristic wavelengths of the electrons that can exist inside of it.
n =
2L n = 1, 2, 3, ... n h nh = pn = n 2 L p nh = 2m 8mL2
2 2 2
E4
E3 E2 E1 L
E=
The diagram above shows how the wavelength of the electron wavefunction depends on the size of a one-dimensional "box" of length L. The allowed wavefunctions have wavelengths that are half-integer multiples of L, and each allowed state can be labeled according to the number of half-wavelengths n that it contains. Using the De Broglie relationship, p = h , the momentum p of the particle can be calculated from its wavelength. Finally, the kinetic energy E = p 2 2m of each allowed state n for the electron can be computed. Notice that the energy of the electron states varies inversely as L2. Therefore, as the box gets smaller, the energy for each state increases.
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The one-dimensional model of a particle in a box can easily be extended to a threedimensional box, which is somewhat more relevant to describing the behavior of quantum dots. In three dimensions the energy of the particle (an electron) becomes
E= h2 n2 m2 l 2 + , + 8m L2 L2y L2 z x
which is a sum of the individual energies along the three orthogonal directions. n, m, and l can all take on integer values greater than or equal to one, and Lx, Ly and Lz are the dimensions of the box in the x, y, and z directions. Notice that the energy of the particle still depends on the inverse square of the box's dimensions. While the particle-in-a-box model cannot be perfectly applied to quantum dots, it is a good first approximation and can be used to gain some insight into their behavior. One important feature of the particle-in-a-box model is "confinement energy." Notice that the lowest possible energy for the particle is not zero; rather, it is E1 = h 8mL2 , which increases with decreasing size. The confinement energy is observed in quantum dots through an increase in the energy of the band gap. The band gap for bulk CdSe at 300 K is Eg = 1.74 eV. As you will measure in the lab, the energy of the band gap is greater for CdSe quantum dots. The confinement energy for the quantum dot sample is equal to the band gap energy minus 1.74 eV. A second important feature of the particle-in-a-box model is that the energy spectrum is discrete rather than continuous. Only certain energies are allowed for the particle. This also begins to happen in quantum dots; the density of states gets peaked at certain energies. This can be observed in the absorption spectrum.
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