MIME_262_april2007 - EXAM April 24th 2007 DURATION 3 HRS...

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Unformatted text preview: EXAM, April 24th, 2007 DURATION: 3 HRS Version A, 19 pages total CLOSED BOOK ALL Students must have a faculty standard calculator: CASIO fx-] 1 5, CASIO fic—991 , SHARP EL-520 or the SHARP EL-546. NON- MCGi“ ID ———— REGULATION CALCULATORS WILL BE REMOVED AND NO REPLACEMENT Name —— CALCULATORS WILL BE PROVIDED. McGill University Deptartment of Materials Engineering PROPERTIES OF MATERIALS IN ELECTRICAL ENGINEERING MID/[E262 FINAL EXAM Examiner: Prof. R.R. Chromik Date: Tuesday, April 24th, 2007 Associate Examiner: Prof. M. Pekguleryuz Time: 3 HRS Instructions 1. Read the instructions carefully. You are to complete all of the twenty questions in the exam booklet. Points are indicated for each question. 2. Put your name and ID# on this page. Put your NAME on pages 2-16. 3 Read each question completely before working on each part, (the parts may be interrelated). 4. Write your solutions in the space provided below the relevant question. Anything written outside the provided space will be ignored. 6. For questions requiring calculations, you must SHOW YOUR WORK to receive full credit. 7. Draw any diagrams as large as possible in the space provided. Label all diagrams, axes, curves etc. 9. A periodic table, the course concept map and a table of electromagnetic units are attached at the end of this examination book (pages i through iii). 10. The gas constant, R = 8.314 J/mol/K. Boltzmann’s constant, kb = 8.26x10'5 eV/K. ll. Avogadro’s number is 6.02x1023 12. e=2.71828 andn=3.l4159. 13. Electronic charge is 1.602xlO'19 C Name: MIME262, Version 7» 1. Conductivity & Semiconductors (30 pts). a) Calculate the density of Si in atoms/m3. The mass density of Si is 2.33 g/cm3. - b) The Si is doped with 1 phosphorous atom for every 1,000,000 Si atoms. Calculate the atomic concentration of P in this sample. State any assumptions you have made. 0) The conductivity of a semiconductor is typically determined from the equation below. Define each variable in this equation, including units. 0=nlelfle+plelflh Name: MIME262, Version A; d) A sample of Si, doped with the amount of phosphorous indicated in part (b), will be used for a new device developed by your company. Your colleague has measured a drift velocity of the charge carriers of 110 m/s when an electric field strength of 1.11 kV/m is applied. i. Determine the conductivity of the Si specimen, and ii. Identify the charge carriers (state your reasoning). — DO NOT WRITE BELOW THIS LINE ON THIS PAGE Name: MIME262, Version 7L 2. Energy Curves (20 pts) — For the graph below, energy is plotted versus interatomic separation (or bonding distance) for two materials (1 and 2). Discuss the properties of materials 1 and 2 and the graph including the following concepts: a) bond strength, b) mechanical properties, and 0) thermal expansion. energy atomic separation Name: MIME262, Version I 3. Copper-Nickel (30 pts) A copper nickel alloy is to be used for an electrical engineering application. The graph below shows its electrical properties as a function of temperature, at%Ni, and, in one case, deformation history. Answer the following questions, regarding these alloys. Temperature (°F) —400 —300 —200 —100 0 +100 Cu + 2.168l.%‘ Ni' Deformed r ’ /‘ Electrical resistivity (10"8 Q— m) —250 —200 —150 -—100 —50 0 +50 Temperature (O0) 21) Define pt, pi, and pd. Indicate for each how they contribute to the total resistivity of the deformed Cu + 1.12at% Ni alloy (i.e. what is the equation and what is the mechanism for each term?). Name: MIME262, Version 7» b) Rank the mechanical strengths of pure copper, Cu + 1.12 at% Ni and the deformed Cu + 1.12 at% Ni. If there are strengthening mechanisms at play, what are they, for which of the three materials are they active and how do they work? 0) A connection must be made at room temperature (25°C) with a wire 5.0 m long and a circular cross-section. The maximum rated current is 10 A. With a desired maximum voltage drop of 250 mV, calculate the minimum diameter of wires made from: “Pure” Cu, Cu + 1.12 at% Ni, deformed Cu + 1.12 at% Ni and Cu + 3.32 at% Ni. Name: MIME262, Version 7» 4. The mechanical engineer is on vacation (30 pts) - An electrical device you designed for your company is now at the final packaging stage. This step requires engineering decisions be made regarding bulk structural parts mounting the circuit to a frame. A bar in the frame is 1.6 cm long, with a circular cross-section 0.2 cm in diameter. This bar is fixed at both end and stress-free at 55°C. During operation, the temperature of the bar varies from -60°C to 205°C. Two materials are available, answer the following questions about them. Assume that the materials properties given in this table are iride endent of temperature. Material Yield Strength Elastic Modulus Fracture Toughness Linear CTE, 0L (MPa) (GPa) (MPa mm) ggflwoc Invar 260 140 140 Stainless 316 3 l0 193 a) What are the magnitude and type of stresses generated in the Invar and the 316 stainless steel at 205°C? b) What are the magnitude and type of stresses generated in the Invar and the 316 stainless steel at -60°C? 0) At the lower temperature limit, there are nearly plane-strain conditions. Calculate the maximum allowable flaw size for the two materials. Assume that the geometrical parameter, Y = l. Name: MIME262, Version 7» (1) Now, assume that the temperature will vary sinusoidally with time. What can you say about the thermomechanical fatigue of the two materials? e) Make a recommendation to your boss on what materials to use. Let him know why. — DO NOT WRITE BELOW THIS LINE ON THIS PAGE Name: MIME262, Version 9» 5. (20 pts) We learned a lot about atomic planes, Miller indices and planar density in the first half of the course. All three help us to understand crystal structure. Tie these three structural concepts (Where applicable) to these two properties: a) surface energy and b) plasticity. 6. (10 pts) What is piezoelectricity? What sort of material exhibits this effect? Give an example of one device each that makes use of the direct and the indirect piezoelectric effect. Name: MIME262, Version 9» 7. (10 pts) As microelectronic devices shrink, a constant issue is heat management. Power supplied to a chip will cause significant heat that needs to be conducted away from the temperature- sensitive semiconductor materials. What materials are good candidates for this application? Why? What is their mechanism for heat conduction? How is this mechanism different from other candidate materials? 8. (10 pts) What is the difference between low cycle fatigue and high cycle fatigue? 10 Name: MIME262, Version 7» 9. (10 pts) In general, why is fatigue important for engineering? Why is fatigue important for electrical engineers? 10. (20 pts) Draw the band structure of a metal (like Cu), a pure semiconductor and an insulator. Discuss how these diagrams explain the electrical behavior of the three materials, including the temperature dependence of their resistivity. s 11 Name: MIME262, Version 1 11. (10 pts) What does the mathematical expression below describe? What was it good for this semester? ex i p ka 12. (5 pts) What is a ceramic? 13. (5 pts) What is a metal? 14. (5 pts) What is a polymer? 12 Name: MIME262, Version 7» 15. (5 pts) What is a composite? 16. (20 pts) Describe the electron and hole motions in a p-n junction for forward and reverse biases. Explain rectification. How does the motion of the charge carriers lead to rectification? 13 Name: MIME262, Version 9» 17. (20 pts) Tensile stress versus strain curves are shown below for four common materials used in microelectronic packaging: a thermosetting polymer, cartridge brass, aluminum oxide and Pb-Sn solder. Each curve is labeled A thru D, and an ‘X’ marks where the specimen failed. a. Indicate which curve corresponds to which material. b. What is it about the structure of these materials that leads to these drastic differences in mechanical properties? Engineering stress Engineering strain 14 Name: MIME262, Version 9» 18. (10 pts) Ionic conductivity may be written in terms of a mobility of ions in a material, where the mobility, in, is given by the equation below. Define all of the variables, including units. _E1 6D] kb T “I 19. (20 pts) Discuss briefly at least four filnctions that an integrated circuit package has in connecting a Si device to the ‘outside world’. Highlight the importance of materials selection for these functions. 15 Name: MIME262, Version 9» 20. (10 pts) Explain the operation of a semiconductor laser. Use the electronic band structure to highlight your explanation. — DO NOT WRITE BELOW THIS LINE ON THIS PAGE 16 3.8a 8..mm$ .033 6:53 63va 899$ 5.5.3 5.5.3 803$ 603$ 63va mo.me 3.me 33$ 3 oz us. E“. m. 5 gm =6 .5 an. a: 3 an. E. 32564: m3 m? z: cor mm mm 3 mm mm 3 mm mm 6 om 3d: 89: mm.$_ 3.x: 3%: 8.8. amm— BS. and? 3.3: «Ni: 5.03 N33 5 mo E: 65.3 2.2a 3.255%... mEmem. :oEmcmF g AloE 9 39: 2:52. 8.3 om 53:5: o_E9< vm wmdom omKoN wméow .“Jflmmdow... 5.02 mom? NNNmF 8.8—. .m an. _.F .u: :< a .__ mo mm mm 5 Mom mm ms t. mu. mhémv whw: Nméz 3N: 3N3 mime a 5 a. man 5 cm me 3 t“ n— v 2 m .55: £5 awwomv Eng 9: m9 «9: 39: 8.08 mm— >> uh. _...” mu .2. mm mm nm em . $8.8. 8.x: Ems 03.8 83m VNNS 95.8 893 933 mv 3 9 fly 3. ov mm mm B o R mint. 5d? mmNmF .. m . wmmgvx. o Fwdh 9Vde mm mm 0mm mm www.mm. wmmdm omm. rm Nvmdm 8N? ommév whodw mmodn H _. .. w< 00 =0 _ o m...— :_2 no > E. om... 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This note was uploaded on 10/02/2010 for the course ENGINEERIN MIME 262 taught by Professor Chrimik during the Fall '10 term at McGill.

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MIME_262_april2007 - EXAM April 24th 2007 DURATION 3 HRS...

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