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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 sinav in: (es—3’7” We \poJK . ‘
g is We Sac} “M6 13700?“ : C0090 ‘” ‘09 (gilt3B AK _M\
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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%
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(e) Find the hole effective mass. _
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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.
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/0 (9&3 7* £04; KL ©4x<w 4. Short answer.
(3) Brieﬂy deﬁne the Fermi energy EF. we
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£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
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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, SWakk 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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 Spring '08
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