ece3080_old_exam1_solutions

ece3080_old_exam1_solutions - ECE 3080 Semiconductor...

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Unformatted text preview: ECE 3080 Semiconductor Devices Spring 2008 Dr. Klein Exam 1 SM‘DWQ Instructions: (1) Closed book, closed notes. You are only permitted a calculator and a writing instrument. (2) Show all work to receive full credit. Proctor will provide additional paper on request. (3) You have 105 minutes to work. Don’t get hung up on one problem. lfyou get stuck, move on and come back later. (4) Each problem is worth 20 points. (5) Circle, box, or otherwise indicate your final answer. (6) Answers must be legible. (7) Calculate numerical values where possible. 1M 1. For this problem, the followin§ identity may be useful: sin (x) = 0.5 * (1 — cos(2 x)) (a) For a silicon quantum well of width W = 100 A, find the proper normalization constant C; for the lowest (n = 1) conduction band bound state in the well. em m sin-av in: (es—3’7” We \poJK . ‘ g is We Sac} “M6 13700?“ : C0090 ‘” ‘09 (gilt-3B AK _M\ c} r 1 HM . 1‘; Z we HAT- C :0 wmév H’\ v \ ‘2) __ . .l i. (b) Find the probabilit of finding an elee o in the n = 1 state within 20 A of the center ofthe well. O.fi m I" 5% Q: g zwcwg dxé ZS 2. Assume a material has conduction and valence bands given by Emma) = BC + El sin? (k a I 2) Evamk) = Ev cos2 (k 3,12) Let a = 0.5 nm, EC = 2.1 eV, E] = 3 eV, and Ev = l.OeV. (a) Roughly sketch the bandstructure (E vs. k) for both bands on the same set of axes. A / (In) Find the longest wavelength of light that can be absorbed Via an interband Optical transition in this material. 0 gram :‘ EL "- Ev 1 \«lflv (0) Does this material have a direct or an indirect bandgap? é QLQEQCXI 9 0 (d) Based on your answer to N, do you expect that this material will efficiently emit light? Briefly explain the physical reason why or why not. .5 eg' «Q, Min 43K— ané. (IVE—"Q 9% Wu: W\Jrv\~\ L, a $2 Max: u -~1'\~ \OD'AA- ’_;> We ~ MOMMHW‘ (Di/\o’rorx CW [at umk'oeh in H“; Jfl‘yxsi‘ih‘hfl (e) Find the hole effective mass. _ EM: QM) Cesium cam/a3 PWW}: Zlé’ défw- QA‘ Q LL: 0 g L?) weciebmk—e 2m -2: 239m *9 la. #53, “Lwii %SECOSZ(€B “‘ §macgsg 8. L2, : 0 919m at FAVE“ an} 1 * J71“ " W . z w» 5. wig. * genera kg 39 V 10 3. A diode has a ‘depietion region”, where we can approximate n = p = 0. Suppose a depletion region extending from x = 0 to x = W is uniformly doped with some constant acceptor concentration NA. Assume that the electrostatic potential (p and the electric field E are both zero atx=0. Find E(x) and (p(x) for0<x<W. @ COCK: 03;; 0 E01; 03:“ O V End K ther I W 49 ='-* 80 Keen. M o : :- Ci'M.__“* 04X<VQ /0 kegox d Tif— : r E K " 1 S «W —-= -~ Voltaire“ /0 (9&3 7* £04; KL ©4x<w 4. Short answer. (3) Briefly define the Fermi energy EF. we 6 94 £964 2, A Gig—Ia; Mg 660‘03‘0} 8F. :3 (b) Briefly define the intrinsic level Ei. As you know, it is nearly in the middle of the bandgap, but not exactly. Why not? lg w EI— \ “week; we ii aw [fliéw’r' deed- Q N 0% mm; m meme 0L 6G K Lav-9L Al :- (3; , ‘bo‘t' (143‘ 4 MU dedfi‘c’fi (c) Briefly explain the density of states, g. What does it represent? / é 30$ ‘5 W a? gbgg/Qol X eweréj LA (“Jet L. AWUBK $50M, SWa-kk m beLNKCK/ E: in Z/ \_ ((1) Briefly explain the Auger recombination process. Whathappens in this process? A sketch might help. 5 : Z eiachro n3 4 t k 0 [EL [ Mac/Wan m 4m [no {a 4 W534 (6) Using the figure below, determine a semiconductor alloy that will have a bandgap of 1.8 eV, and can be grown on a GaAs substrate with a relatively small lattice mismatch. Provide the composition of this alloy in the standard notation. Bandgap (at!) {uni} umuagmm 52 5,4 5.6 5.8 5.9 8,2 5.4 8.8 Lattice constant {A} MUM“; Ql A19 °r 9“ firing (figs RS ...
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ece3080_old_exam1_solutions - ECE 3080 Semiconductor...

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