3080 Exam 1_Spring08

# 3080 Exam 1_Spring08 - ECE 3080 Semiconductor Devices...

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Unformatted text preview: ECE 3080 Semiconductor Devices Spring 2008 Dr. Klein Exam 1 (:jﬁﬁl Lot. Instructions: (I) 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 |05 minutes to work. Don‘t get hung up on one problem. Ifyou 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. PL"- 1. For this problem. the following identity may be useful: sin‘(x) = 0.5 * (I - 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? I {A s to o k gluti- 1K 1 C| gm bulk 9 l9 1:3) Scegmamylg git-m argrx i/q'iié AK [00K (42 1 ’ (.09 Q‘VL : L L l (“17’ “x low Ci 2 if : l.‘¥l‘l KT - (1.: 0.191% W? (b) Find the probabili f ﬁnding an elec ogﬂi the n = I state within 20 A of the center oflhe well. 0.3 m F g Q 2 g m 28"..«Z‘Ctrx\clg§ 2. Assume a material has conduction and valence bands given by amam)= BC + E. sin2 (kaiz) Emmk) = Ev cos2 (k 21/2) 9 Let a ~—~ 0.5 nm. a; = 2.1 cV.E1= 3 eV. and Ev = Low. (a) Roughly sketch the bandstructure (E vs. k) for both bands on the same set of axes. A ﬁx / .v ,4 (b) Find the longest wavelength of light that can be absorbed via an interband optical transition in this material. t/ 9 ; Ea, " Ev, 7’ "UV ' (c) Does this material have a direct or an indirect bandgap? 3 q, A nC/ﬂ. 5 of) (\$9 clan-mi“ P9. D ((1) Based on your answer to m, do you expect that this material will efﬁciently emit light? Brieﬂy explain the physical reason why or why not. %le<»- (mi) 'M‘l 7“ ( L g A :5 . av" A [A‘ag S m. “M U ~WJ\HM 1; S Fla-k 3-! (L \’ wk ‘ Cm (at, UMLHMVX ;/\ HMS 3.»\S\ ‘WNM (us) Find the hole effective mass. \ EVA: C..OSZ<_L(Q 0,9“,“5/2’ 9 gum; Zké‘ dé(w- bunk- @, L: O Tr "EELng gm LUSC?) How Clo M «9M [5,“ know “wig” k /_ . ,,., . a. 10 Pine, 52¢ Lang‘s; . '> JUN" h 1,. z Lye. '5 It“ Z: "Di t z. I, V" u>‘\ 3 a '" v’\_ (:3 L ’7 ,{V't\l 4,—- 3. A diode has a 'deplction region’, where we can approximate n = p m 0. Suppose a depletion region extending from x = 0 to x = W is uniformly doped with some constant acceptor concentration NA. Aswmc that the electrostatic potential (I) and the electric ﬁeld E are both zero at x = 0. Find 500 and qt(x) for 0 < x < W. {4 to use u EC»: (A; O U {)3 “’f M?" Mex ’1". ~ OQK<L~3 ; ix JFLJQ X” f I S M - Q '56:?» C” /0 \$83 :"sz’jw—EAEKL oéxéw l 1/ 4. Short answer. (8) Brieﬂy deﬁn the Fermi energy EF. A Gééyfiﬂ LJNLFQJ Q4; k?\$ («enough») a? Ea é (b) Brieﬂy deﬁne the intrinsic level El. As you know. it is nearly in the middle of the bandgap, but not exactly. Why not? E we new Q "we hub; Hi\ .| 'r. .-' i {93w Ln 3 w \~ Antacé. (6) Brieﬂy explain the density ofstates, g. What does it represent? { Ht; 14* gbkc‘s/GM K we“ WI\ 4 ‘i‘ ‘30th SW: ¢.-\.¢{'Qj {ALF-{Upk- m‘ bfoov\<£ E; (d) Brieﬂy explain the Auger recombination process. What happens in this process? A sketch might help. S (hr ‘x 1 2 a“! (no N) y ( txr[€, { a [c emu 9“ 5 m h: [VJ (1 4 3“ HIE-5 Eymﬂran 4 (no Muﬁ'ﬁm *0 e rid-L4” QKQLH'WX (6) Using the ﬁgure below. determine a semiconductor alloy that will have a bandgap of LB 6V. and can be grown on a GaAs substrate with a relativer small lattice mismatch. Provide the composition of this alloy in the standard notation. Bandeau {UV} Lattice Constant {A} Albany“; b“ 9- oc’ (Sc: 5211/; (Wig RS ...
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## This note was uploaded on 10/12/2010 for the course ECE 3080 taught by Professor Staff during the Spring '08 term at Georgia Tech.

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3080 Exam 1_Spring08 - ECE 3080 Semiconductor Devices...

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