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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
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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) ($9 clanmi“ P9. D
((1) Based on your answer to m, do you expect that this material will efﬁciently emit
light? Brieﬂy explain the physical reason why or why not. %le<» (mi) 'M‘l 7“ ( L g A :5 . av" A [A‘ag S m. “M U ~WJ\HM 1; S Flak 3! (L \’ wk ‘
Cm (at, UMLHMVX ;/\ HMS 3.»\S\ ‘WNM (us) Find the hole effective mass. \ EVA: C..OSZ<_L(Q 0,9“,“5/2’
9 gum; Zké‘ dé(w bunk @, L: O Tr "EELng gm LUSC?) How Clo M «9M [5,“ know “wig” k /_ . ,,., . a.
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4,— 3. A diode has a 'deplction region’, where we can approximate n = p m 0. Suppose a
depletion region extending from x = 0 to x = W is uniformly doped with some constant acceptor concentration NA. Aswmc that the electrostatic potential (I) and the electric ﬁeld
E are both zero at x = 0. Find 500 and qt(x) for 0 < x < W. {4 to use u
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1/ 4. Short answer.
(8) Brieﬂy deﬁn the Fermi energy EF. A Gééyfiﬂ LJNLFQJ Q4; k?$ («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“ HIE5 Eymﬂran 4 (no Muﬁ'ﬁm *0
e ridL4” 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.
 Spring '08
 Staff

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