Chapter 18s - 1 – – – – – – 2 • Micro Electro...

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Unformatted text preview: 1 – – – – – – 2 • Micro Electro Mechanical Systems – A new technology for producing superminiature mechanical devices motors and sensors . – Silicon devices • mass produced like integrated circuits www.memx.com mems.colorado.edu/c1.gen.intro/mems.shtml • MEMS device used as a sensor: – Becomes integral part of an integrated circuit – Programmed to make decisions based on conditions sensed 3 • An array of 256 microscopic mirrors. Each mirror is the size of the head of a pin. The mirrors tilt to steer lightwave signals from one optical fibre to another. • • Bell Labs 4 Scanning electron microscope images of an IC Al Si (doped) 0.5 mm An elemental distribution map showing location of Si: 45 m Si shows up as light regions. An elemental distribution map showing location of Al Al shows up as light regions. Fig. (a), (b), (c) from Fig. 18.0, Callister 6e. 5 From Fig. 18.25, Callister 6e. (Fig. 18.25 is courtesy Nick Gonzales, National Semiconductor Corp., West Jordan, UT.) • V IR – V volts J/C – I Amperes C/s – R ohms V/A • RA l OR VA Il Schematic diagram for measuring electrical resistivity • Conductivity, σ reciprocal of resistivity : 1 Units: (Ω‐m)‐1 • Current density, J: J • Electric field, E: Distance between two points V l • – – • – – •e.g. fuel cells 9 • Electronic conduction exists in: – Conductors – Semiconductors – Insulating • Conductivity is dependent on: – – – – The number of electrons available to conduct Electron states/ levels with respect to energy How electrons fill orbital's in an atom band structure Principles of quantum mechanics not covered in course • Pauli exclusion principle – Each electron occupies an independent state • At relatively large separation distance, each atom is independent of all the others: – Individual atomic energy levels/ orbital state – Individual electron configuration • When atoms are brought to close proximity: – Electrons are acted upon by electrons and nuclei of adjacent atoms – Atomic states may split into a series of closely spaced electron states in the solid electron energy band – Extent of splitting depends on interatomic separation distance – Gaps may exist between adjacent bands • Energy band gaps Electron states dependent on interatomic separation distance Displays how energy band structure at equilibrium separation is formed Conventional representation of electron energy band structure for a solid material at the equilibrium interatomic separation distance • Whether or not a material is a conductor or an insulator depends on the outermost shell of its atoms. –There are four main possibilities 0 K : 3 eV >3eV Metals insulators semiconductor s • • • 14 Fermi energy EF energy of the last highest filled state at 0 K If a band is partially full or bands overlap conductor If the valence band is full and the conduction band is empty insulator or semiconductor • Only electrons with energies greater than the Fermi energy may be acted on and accelerated in the presence of an electric field – Free electrons • When the temperature is above 0 K – thermal promotion • Holes: – Found in semiconductors and insulators – Energies less then Ef – Participate in the conduction process Electroluminescence EL is an optical and electrical phenomenon in which a material emits light in response to an electric current passing through it or to a strong electric field; it is the result of a recombination of electrons and holes in a material usually a semiconductor . • Electrons are excited into one of the empty and available energy states above Ef • Vacant energy states adjacent to the highest filled state at Ef , therefore little energy is required to promote electrons to empty states – Electric field is sufficient energy • – g – g • – – • Number of excited electrons into the conduction band depends on Eg and temperature – Eg σ at a given T – Semi‐conductors: narrow band gap – Insulators: relatively wide band gap • • When an electric field is applied, free electrons accelerate in the opposite direction to the field No interaction between accelerating electrons and atoms in a crystal lattice – So why does current reach a constant value when the field is applied and not continuously increase with time? • Frictional forces counter this acceleration, which are a result of scattering electrons by imperfections in the crystal lattice including: – – – – – Impurity atoms Vacancies Interstitial atoms Dislocations Thermal vibrations • Scattering: – Electron loses kinetic energy – Electron changes direction of motion – Resistance to passage of electric current • Net electron motion created in opposite direction to the field dQ – Flow of charge electronic dt current, I • Drift velocity: average electron velocity in the opposite direction of the electric field vd e E Electron mobility, e Units: m2/V‐s • • – – – How will heating / cooling change the resistance of a metallic wire? • Turning on the heat gun will increase the resistance of the wire • Immersing the wire in dry ice will lower its resistance 22 Ag > Cu 2 Al too expensive • We can process Cu to have very low impurity levels especially when it comes to oxygen . – Oxygen‐free high‐conductivity OFHC Cu. Sometimes higher strength is needed. Eg. High power electromagnets Lorenz force . • Pure alloys are very soft. – • We can strengthen pure materials by “cold working” them or adding solutes or particles. – Particles have the least effect on conductivity. Eg. Cu‐Be Cu‐Ag laminates 23 total t i d Represent thermal, impurity and deformation resistivity contributions Influence of each resistance variable on three copper‐ nickel alloys • t 0 aT Material constant Influence of temperature • As T , n ... • … but e and this dominates when it comes to temperature dependence. • The net result: E 0K T>0 K aT for T > ‐200oC EF EF N(E) 26 • Concentration is in terms of atomic fraction at%/100 • A is a composition‐independent constant – a function of both the impurity and host metals i Ac i (1 ci ) Room‐temperature electrical resistivity versus composition for copper‐nickel alloys • sSi 410‐4 Wm ‐1 sCu 6 107 Wm ‐1 They have unique properties due to doping solute additions) 29 • • • • • – Positively charged relative to the electron 1.602x10‐19C a vacant electron state in the valence bond – creation of electron‐hole pairs • – – 3 3 • n | e | e p | e | h • n | e | (e h ) Pure Si - no excitation Pure Si - after excitation Pure Si - after excitation 32 electrons and holes move in response to the electric field • • Just how many electrons and holes does an intrinsic semiconductor have? Consider Silicon see Table 18.2 – At room temperature: s 410‐4 W m ‐1 e 0.14 m2/V‐s mh 0.05 m2/V‐s – What is n and p? n p e e h 1.33 1016 / m 3 – How many electrons per atom is this? Electrons / atom electrons / volume volume / atom n W Note: here 1.331016 8.45 10‐29 represents the atomic volume 1.12 10‐12 So only one in every 1012 atoms contributes an electron‐hole pair to the conduction process. 33 • You only need an impurity concentration of 10‐12 to alter the intrinsic behavior of a semiconductor – The semiconductor industry is dependent on ultra‐high purity Si • Commercial semiconductors are all extrinsic – But the doping is intentional, not random impurities • It’s not practical to get a purity of 10‐12 – Typically impurity concentration 10‐9 – You need sufficient deliberate additions to overcome this • Excess electrons / holes are created by: – Aliovalent solutes e.g. P, B in Si – Dangling bonds e.g. dislocations, grain boundaries 34 • Excess electrons are loosely bound (weak electrostatic attraction) therefore easy to promote to conduction band • electron binding energy corresponds to the energy required to excite the electron from an impurity state to a state within the conduction band (ED) • Excess electrons sit in a donor state located close to the top of the band gap • ED Eg band gap energy • typically ED 0.1 eV, cf. Eg 1.1 eV, Si • At room temperature, many donor electrons are promoted. – Very few electron‐hole pairs – n p – Called an n‐type semiconductor • Position of donor state is a function of both temperature and donor concentration n | e | e Electrons are the majority carriers only electron mobility is taken into consideration 36 • Dopant atoms are added • One of the covalent bonds around each dopant atom is deficient in an electron – leaves an empty hole that an electron can move in to – Introduces an energy level acceptor state just above the valence band • When an electron fills the acceptor state, a hole is left in the valence band • At room temperature many acceptor states are filled • p n therefore only hole mobility is taken into account p | e | h • • • – – – ‐28 3 23 3 16 3 ‐5 Compare with: Impurity level for semiconductor grade Si 10‐9 38 • Increase in thermal energy allows electrons to excite to conduction band intrinsic carrier concentration increases Intrinsic carrier concentration vs. Temperature logarithmic •Intrinsic excitations are insignificant in relation to the extrinsic donor excitations until very high temperatures Saturation Eg n no exp 2kT Intrinsic semiconductor ED n nDo exp kT E p p Ao exp A kT n‐type extrinsic semiconductor p‐type extrinsic semiconductor **At high temperatures the behaviour of the material becomes intrinsic** ( E g / 2) n no exp kT Eg ln(n) ln(no ) 2kT Eg 1 log(n) log(no ) 2.3(2k ) T bm x y 41 • Much steeper T‐dependence for intrinsic region Eg EA . • Small saturation region. • s nearly constant near room temperature. • ALS – The extrinsic s decreases at higher temperatures – WHY? – Answer: • Consider the effect of mobility on temperature. • Increased scattering due to thermal fluctuations. P‐type Si, doped with B 42 43 p | e | h • Dopant Content below : – Concentrations 1020 m‐3 carrier mobility is as its max – Mobility decreases with increasing impurity content • Temperature above : – enhanced thermal scattering of carriers – Concentrations 1020 m‐3 dependence on temperature is independent of dopant concentration Mostly beyond the scope of this course • p‐ and n‐type regions in contact – The simplest case is p‐n junction Bias Forward • Each device is a single crystal • The behavior of the junction depends on the direction of the bias voltage – Forward bias low resistance – Reverse bias insulator • Rectifier Reverse 45 • • • Explain why the p‐n junction behaves as an insulator under reverse bias. What about forward bias? Answer: Electrons and holes leave the region near the junction – There is no source to create new defects there – Depleted region behaves as an intrinsic semiconductor i.e. drops by about 107x • For forward bias: – Electron‐hole recombination's occur at the interfaces – New electrons and holes are injected into the device at the end contacts > 100 V 46 Extra P + + + + + + + + + + + + + + + + + + + + n P ++++ -++++ ---++++ ---++++ ---++++ e.g. Si doped with B e.g. Si doped with P P ++++ ++++ ++++ ++++ ++++ n P ++++ ++++ ++++ ++++ ++++ P + + + + + + + + + + + + + + + n P ------ ------ + + + + + + + + + + + + + + + + Conductive 47 Non‐conductive Extra 48 Extra 49 50 Most ceramics and polymers are insulator • Compare doped Si, s~1000 W‐m ‐1 pure Cu, s~6107 W‐m ‐1 • Some ceramics are semiconductors at high T • Few polymers are excellent conductors • – e.g. polypyrrole, polyaniline s up to 1.5 107 W‐m ‐1 – Complex mechanism involving doping, orientation to alter band structure 51 • • • • • • 52 1. Consider a boron doped (p‐type) semiconductor. It is well‐known that the conductivity vs. T curve of such a semiconductor will have three regions; freeze‐out region (low T), the saturation region (intermediate T) and intrinsic region (high T). Estimate the temperature at which the saturation zone ends and the intrinsic zone begins given that the concentration of boron is 1020 /m3, Eacceptor is 0.01 eV/atom, Egap is 1.6 eV/atom, the number of electrons in the valance band at 0 K is 1030/m3, the mobility of electrons is 0.14m2 /V ‐ s and that of holes is 0.05m2 /V ‐ s . a) 273 K b) 328 K c) 380 K d) 401 K e) 280 K 2. A one meter long stainless steel wire has electrical conductivity of 0.200x107 (ohm‐m)‐1, and end‐to‐end resistance of 10.0 ohms. What is the diameter of the wire? a) 0.126 mm b) 0.252 mm c) 0.396 mm d) 0.505 mm e) 0.936 mm 3. According to Matthiessen’s rule the conductivity of a metal decreases with: (i) Increasing temperature (ii) increasing impurity content (iii) increasing number of dislocations a) i only b) ii only c) i and ii only d) i, ii and iii 4. Selenium Se is a group VI element i.e. two columns to the right of Silicon on the periodic table . An extrinsic semiconductor is produced by doping Silicon Si with 1020 Selenium atoms per m3. Assuming saturation, calculate the conductivity of the extrinsic semiconductor. Assume that the mobility of holes is equal to μh 0.05 m2/ V‐s and that the mobility of electrons is equal to μe 0.14 m2/ V‐s . a b c d 0.000448 Ω m 4.48 Ω m 1 0.0052 Ω m 1 0.52 Ω m 1 1 ...
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