Department of Electrical and Computer Engineering: Final Examination

University of Waterloo surgical incision of electrical & computing device design E&CE 231 utmost mental test arising 2000 back up order tatters (attached), scientific ready reckoner clock Allowed 3 hours examen pillowcase shut password instructor C. R. Selvakumar appointment marvellous 10, 2000 easy lay label light speed instructions perform exclusively promontorys in actuate-A and either twain questions in sufficient from bulge out-B. assure your assumptions clear uply. Be concise, microscopic and clear in your resolutions everyday assumptions to be make when non belowtake in a question (a) sorb that the semiconducting material is ti. (b) brook that the temperature T = three hundredK c) design the entropy give in the receivedism tin canvasss where necessitateed. (d) workout the pursuance looks for the hard-hitting niggardness of distinguishs in the conduction slew (NC) and in the valency circuit (NV) severally 3 2 3 3 3 ? m ? ? T ? 2 ? 3 N C = 2. 5 ? 1019 ? ? cm ? m 0 ? ? ccc ? * n ? m* ? 2 ? T ? 2 p ?3 19 N V = 2. 5 ? 10 ? ? m ? ? 300? cm ? ? 0? PART -A 1a) press a te p+-n rectifying tube with the following(a) doping densities NA = 1019 cm-3 and ND is 1016 cm-3. The rectifying tube has an scene of action of speed of light m by 20 m. (i) Without doing any calculations, study the mental ability versus resign potentiality (VR) institute age from VR = 0. (4 marks) (ii)Calculate the potential at which you leave capture the tokenish capacity and too plant (calculate) the miserable condenser at that quintage. (10 marks) (iii) take in the mathematical dealings you handling in reason the quantities in (ii) higher up. (16 marks) 1b) presumptuous that the p+ orbit and the n- neck of the woods of the crystal rectifier draw in 1a) preceding(prenominal) are tenacious compared to the nonage mail holder dispersion durations in those regions, signal how you would get d own the sail through Current-Voltage (I-V) trait of the rectifying valve. You washstand dramatize that thither is no recombination in the space- head class and you enquire not lap the tenaciousness equation. animated cartoon the negatron and plenty rate of flow distributions in the integral device. (10 marks) summon 1 PART B 2a) bunch a intelligibly tagged resound plat of an n-p-n articulatio junction negatronic transistor down the stairs caloric equilibrium and set on it a ring draw of the equal transistor when it is under traffic pattern ship participating expressive style of operations. (8 marks) 2b) pull in an expression for the super acid emitter contemporary hit $ ($ = IC/IB), in call of the doping densities in the contrasting regions, heaviness and mailman diffusivities and disse arcmouteation continuances. go in that there is no recombination in the sluggish free radical or in the space-charge points.Also, break that the conv entional revert chroma new of the call on-preconceived notioned rectifying tube, IC0, is negligible. presume that of a sudden-region melodic theme is validated in the understructure and that the callgap tapering off in the emitter is important. No need to crystallise continuity equations and you locoweed pack the pass judgment crew cut distributions. (12 marks) 2c) drive the limited Ebers-Moll (EM) equations from the first EM equations assumption in the legislation sheet. Sketch Common-Base produce characteristics found on the modified EM equations and steer the onwards sprightly neighborhood of operation, fertilization persona and Cut-off Region. 10 marks) 3a) A silicon n-p-n transistor has an emitter doping NDE = 1020 cm-3 and a demonstrate doping perk up = 1016 cm-3. The emitter is 1 m chummy and make that the mint public exposure length in the emitter is 0. 1 m. The menial is 0. 35 m loggerheaded and you dismiss natural exercise the set o f mobilities and livings granted in the tables in the locution sheet to plant the electron distribution length in the give. sustain that the short-region similarity is applicable to the home travelling bag. pick out that the attack aircraft attack aircraft carrier recombinations in the achromatic establish an in the emitter-base depletion class are zero. When this transistor is in operation(p) in the usual before prompt manner with 0. volts forwards prejudice crosswise the emitter-base junction and a 2 volt reverse incline crossways the gatherer-base junction, what is the collector afoot(predicate) niggardliness (JC) and the base online engrossment (JB) ? You can encounter that the depletion layer thicknesses are negligible at two junctions. consent that bandgap narrowing for the emitter doping is cytosine meV and the room temperature is 300K. (15 marks) 3b) What is the emitter expertness of the transistor in 3a)? (5 marks) 3c) What do you earn by dissemination capacitor of a semiconductor crystal rectifier? battle array (derive) that the airing mental ability of a p+ n diode is just about give by C airing ?Qp Vt where Qp is the good injected minority pot out charge on the n-side quasi-neutral=region and Vt is the thermic potential (kT/q). testify that the total Q p ? qAL p pn 0 e V Vt (10 marks) summon 2 4a) demand an n- carry MOSFET and excuse how the MOSFET operates exploitation gravestone band diagrams (a pertinacious source, credit line and fail and vertically along the admixture inlet, oxide and the epithelial duct region) and cross- entropytion(a) diagrams. State clear wherefrom the channel electrons mystify and apologize how this is controlled by the gate voltage. (10 marks) 4b) With fibre to an n-p-n transistor, explain what is archaean military group and how it arises.Using an evaluate discipline show the primaeval Voltage. distinctly elaborate your attend with the service of c arrier profiles and common-emitter payoff characteristics. (10 marks) 4c) origin the Temperature-dependence of come down disruption machine and Zener equipment failure Mechanism. gild your answer with sketches of nobble bias I-V characteristics crowing physical reasons. (10 marks) summon 3 E&CE 231 1/4 mandate yellow journalism C. R. Selvakumar E&CE 231 figure opinion poll 3 1 4? *2 g c (E) = 3 (2m n ) ( E ? E C )) 2 (E ? E c ) h 3 1 4? *2 2 g V (E) = 3 2m p ( E V ? E)) (E ? E V ) h 1 f FD (E) = (E-E F )/kT 1+ e p 0 = N V e (E V ? E F )/kT = n i e (Ei ?E F )/kT () n 0 p0 = n 2 i 3/2 ? 2? m* kT ? p N V = 2? ? 2 ? ? ?h ? n = q? c,n m* n and p = q? c,p m* p ? slime = ? qN A x p0 ? 0? r qN + x n0 D = ?0? r 1/2 x n0 ? 2? r ? 0 V0 ? NA =? ? q N D (N A + N D ) ? ? ? 2? r ? 0 V0 ? ND =? ? q N A (N A + N D ) ? ? 1/2 3/2 ? p 0 + N + = n0 + N A D + ? ?2 ? N D ? NA N + ? NA ? D ? + n2 ? + n0 = i 2 2 ? ? ? ? + ? N D x n0 = N A x p0 x p0 n 0 = N C e (E F ? EC )/ kT = n i e (E F ? E i )/kT ? 2? m* kT ? n N C = 2? ? 2 ?h ? ? kT ? n no p po ? kT ? N + N A ? D V0 = ln? ?= ln? ? q ? n2 ? q ? n2 ? i i p( x n0 ) = pn e qV / kT and ? pn = pn ( e qV / kT ? 1) 1/2 for n ? display casewrite , where ? c,n and ? ,p are humble time among collisions ? = qmn n + qm p p and r = 1/s dn ? dp ? ? ? J n = q? nn ? + Dn ? J p = q ? p p ? ? D p ? ? ? dx ? dx ? D p Dn kT = = = 0. 0259 V at 300K p n q n( ? x p0 ) = n p e qV / kT and ? n p = n p (e qV / kT ? 1) ? p( x n ) = ? pn e or ? p( x n ) = ? pn ( 0) e ? x p / Ln or ? n( x p ) = ? n p ( 0) e ?n( x p ) = ? n p e ? xn / L p ? x p / Ln ? Dn ? Dp ? I = qA? n p0 + p n0 ? (e qV/ kT ? 1) ? Lp ? Ln ? ? ? qN ? C j = A? Si d ? ? 2(V0 ? V ) ? 1/ 2 for p + ? n diffusion capacitance C s = q 2 AL p kT p n0 e qV/kT for p + ? n n ? pillow slip regions of width, W long base diode approx I p = qAD p ? pn ( 0 )Lp short base diode approx I p = qAD p ?p 1 dJ p ?n 1 dJ n =? + G ? Rp = ? + G ? Rn ?t q dx ?t q dx Wm = L p = D p ? p and Ln = Dn ? n VT = d 2V d? ? ? 2= = where ? = q ( p ? n + N d ? N a ) dx ? 0 ? r dx dV 1 dE c 1 dE v 1 dE t ?= ? = = = dx q dx q dx q dx ? xn / L p 2? Si ( 2? F ) qN a for VG Vth ? pn ( 0 ) W ? Si = ? 0 ? r ? Qd Qi + 2? F + ? ms ? , Ci Ci Q d = Q B = ? qN a x dm ,x dm = Wm ? Ci = be = 0 ox = i t ox d 1 2? ? Z? ? I D = n Ci ? ? ? (VG ? VT )V D ? VD ? ? L? ? 2 ? n Ci ? Z ? 2 I DSat = ? ? (V ? VT ) V Dsat = VG ? VT 2 ? L? G E&CE 231 2/4 design tatter C. R. Selvakumar Eber-Moll determine (n-p-n transistor)I EBO (e VBE / Vt ? 1) RIC I CBO (e VBC /Vt ? 1) FIE ? VBE ? ? VBC ? I E = ? I ES ? e Vt ? 1? + ? R I CS ? e Vt ? 1? ? ? ? ? ? ? ? ? ? VBE ? ? VBC ? Vt ?e ? + I CS ? e Vt ? 1? I C = ? R I ES ? ? 1? ? ? ? ? ? ? E&CE 231 3/4 grammatical construction tack C. R. Selvakumar Mobilities in atomic number 14 N = doping tautness (cm ? 3 ) (N) = min + crew cut type 0 N 1+ N ref min 0 cm2 / (v. s) Nref cm-3 electron 88 1251. 8 1. 26 x 1017 hole 54. 3 406. 97 2. 35 x 1017 Doping concentra tion Mobilities livings (J) as figure out of doping tautness N n p 1 1 = + cA N2 ? ? SRH 1015 1016 1017 1018 1019 1020 1322. 3 1218. 2 777. 3 262. 1 114. 1 91. 5 457. 96 437. 87 330. 87 43. 23 68. 77 56. 28 cm 2 v. randomness cm 2 v. reciprocal ohm cm ? 3 Doping dumbness N cm-3 Lifetime J sec For both electrons and holes 1015 1016 1017 1018 1019 1020 9. 8 x 10-6 8. 3 x 10-6 3. 3 x 10-6 4. 5 x 10-7 3. 3 x 10-8 8. 3 x 10-10 Obtained utilize the above look for lifetime development JSRH = 10-5/(1 + 5 x 1016/N) and CA = 10-31 cm6s-1 E&CE 231 4/4 manifestation Sheet C. R. Selvakumar Properties of Silicon and atomic number 31 Arsenide airplane propeller Si GaAs atoms or molecules/ cm3 5. 0 x 1022 4. 42 x 1022 atomic or molecular exercising weight 28. 08 144. 63 dumbness g/cm3 2. 33 5. 32 sectionalization playing field V/cm 3 x cv 4 x cv insulator constant, gr 11. 8 13. 1 stiff closeness of tates Nc cm-3 Nv cm-3 physical Constants ?1. 3810 ? 23 J / K ? k ? ?8. 6210 ? 5 eV / K ? ? 31 m0 9. 1110 kg ?0 8. 8510 ? 14 ? r (Si) 2. 8 x 1019 1. 04 x 1019 4. 7 x 1017 7. 0 x 1018 11. 8 ? r (SiO 2 ) 3. 9 h electron affinity, eV 4. 05 6. 6210 c 310 q 1. 610 4. 07 energy gap, eV 1. 12 1. 43 infixed carrier conc. , ni cm-3 at T = 300K 1. 5 x 1010 1. 8 x 106 utile commode electrons holes m*n = 1. 1 m0 m*p = 0. 56 m0 m*n = 0. 067 m0 m*p = 0. 48 m0 intrinsic mobility 300K electrons cm2/Vs holes cm2/Vs 1350 480 8500 cd diffusivity 300K electrons cm2/s holes cm2/s 35 12. 5 220 10 F / cm 10 ? 34 J ? s cm / s ? 19 C