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Unformatted text preview: Homework 0?
Sob’hom SQT CHAPTER 3 a
(a) See Fig. 310(a). (b) . EC 13v
C
(d) EC
Light W
ﬁ3v
O (f) See Fig. 3.15(a).
(g) See Fig. 3.150)).
(11) See Fig. 3.15(C) (C) Ec
iiv
0 130/4
0
c
( ) 13C
Thermal 5
energy
liv
O 32 (a) Given: Ud : 103 cm/sec
E : AWL : ZV/cm
[JD 2 Ud/8 = 500 cmZ/Vsec (b) (i) Lattice scattering
(ii) Ionized impurity scattering
(See the Relationship to Scattering discussion in Subsection 3.1.3.) (C_)}1inuinsic is higher than #heavily doped / . . v o .    o ' Reason: In inmnStc material the scattering 15 due excluswely t0 lattice scattenng. In
heavily doped materials, ionized impurity scattering is also important. The more
scattering there is, the lower the mobility. (d) Given N91 and NM >> ni, we know from Eqs. (3.8) that 1 1
p — —— ...n—type wafer l; p , — w W ...ptype wafer 2
qﬂnNot (#1pr A2 In most semiconductors including GaAs, ,ttn is greater than it for a given doping and system temperature. Since we are given N131 : NAg, taking tiie wafer temperatures to be the same. and with ,Lln > up, we conclude from the above equations that p(wafer 2} > p(wafer 1). Note that the conclusion here is consistent with Fig. 3.8(b). (e}DN=(kaq)ttn : (0.0259)(l300) = 33.7 cmz/sec a 1 (a) p = ...Eq.(3.8a)
QHnND
l
= w = 0.501 ohmcm it from Fig. 3.5(11)
(1.6 x10“19)(1248)(1016) i”
p 2: 0.5 ohnhcm ...by inspection from Fig. 3.8(a) (b) Since NA = ND , n = p : ni = 1010/cm2. Moreover, the total number of scattering
centers is ND + NA = 2 x 1015/cm3. Thus, from Fig. 3.5(a), ,un = 1165 cmZNsec, ,up = 419 ch/Vsec, and i 1
p _ (10.1“ +lup)ng _ (1.6x 1019)(1584){1010) = 3.95 X 105 ohmcm (c) Here n 2 p : n1: 10:0/cm3. With NA = 0 and ND 2 0, one has the maximum
possible carrier mobilities. From Fig. 3.5(a), unmax: 1358 cmE/V‘sec and tipmax :
461 cmZ/Vvsec. p : ——m~1— = ——————m1—_—— : 3.44 x 105 ohmcm
(101“ + ppm (1.6 x10'19)(1819)(1010) Because of the lower mobilities in compensated material, p(pan b) > p(p3rt c). (d) R = pm
p : RA/l = (500)(10*2)/(1) : Sohm—cm Since the bar is ntype, we conclude frorn Fig. 3.8(3) that ND 5 9 x 1014/c1n3. (e) For a sample where ND >> m, p = UCIiUnND Furthermore, since the sample is lightly
doped, lattice scattering will dominate and tin will decrease with increasing T. Fig. 3.73
conﬁrms the preceding observation. Thus, with p cc l/un, heating up the sample causes
the resistivity to increase. 3V7 212 _ . The briefexplanat'ion how one arrives at a given answer, an explanation applicable to all the
energy band diagrams, is given immediately below. Sketches indicating the gencrm’jbrm
of the expected answers follow the explanations. (a) for all cases. The semiconductor is concluded to be in equilibrium because the
Fermi level has the same energy value (it is constant) as a function of position. (b) Vvs. x has the same functional form as the "upside down" of E; (or E] or EV). The
sketches that follow were consmicted taking the arbitrary reference voltage to be V = 0 at I: O. (c) 8 vs. I is determined by simplyr noting the slope ofthe energy bands as a function of
posuton. (d) For electrons, PE : EC—EF and KB 2 EmEC; for holes PE : EPEV and KE : EWE. (e) The general carrier concentration variation with position can be deduced by noung
EF—Ei vs. x. Under equilibrium conditions, rt : niexp[(EF—E.)//<T] and
p : riiexp[(Ei—EF)/kT] if the semiconductor is nondegeneraie. (1) Since JNtdn’ft = gunng , the general variation of JNIdn'rt with position can be deduced by
conceptually fonning the product of the 8 vs. x dependence sketched in part (c) and the n
vs. I dependence sketched in pan (e). Under equilibrium conditions, JN = JNldrift + JNidiff = 0 Thus JNtdtrr = —JNtdrtn Diagram (3} Drift Diff Diagram (b) 316 Diagram {‘c) Diagram ((1) Diagram (e) Diagram (0 346 (a) One assumes the minority carrier drift current is negligible compared to the diffusion
current in deriving the equation; i.e., diffusion is taken to be the dominant mode of
minority carrier transport — hence the name DIFFUSION equation. (b) The equation is only valid for minority caniers. (c) The recombinationigeneration term appearing in the equation, namely —Anp/rn, is valid
only under lowlevel injection conditions. M ’0 ’0
._ __.L«‘ W120 lcm +31 (loge;
CLO f“ EVFNA / m I V? {H 300K .ow‘ {hﬁwﬁ 305a) Cm Book We limo!
NY '3— 116? U’ﬁeo C) ’l’mmtoblé CW1 {mejv OOBLICJIV]
From fo‘ft a) “Om/Mme, #LlfckVIESS {157/ +mw=003cwl
0““ R = 100m
L. ”am
R: 195 :> me £—
Wt w'flmmx
Rm , ft
W'fnmn
0,03
R , ﬂ; «— ﬂ" EM. : ‘Qnom Mj/ngﬂoﬁ
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R : ﬂmm L anal {QMRX'J M N
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1
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Sun/xi {our {7/ . __ , fnom U‘hﬂmm ‘ V “Rwy“ r helm {MU ' (Mammy —) Rmmﬂ 6?,3JLRIL
QR : , Mﬂm .\ MM Rhom fmm (NF‘Jmm J> QMax: MH' 23160, In +EV‘IM5 Qt +013rance 5 “H41 ’0 u) XIV/V1! ‘( .‘ LID/Tl) *_ (Qmin“RHOM)xw a ‘ ~32 13?
o ‘0 d ,— m 0 9 w ° 0
W 41W / (04305.5 1&Rmax*Rhom)X\Dop/O :+ “H.532, (WC/00,9 7%“ R \ ' ‘
\Qesb’Mﬂc: hummﬂ We Muck/x WOFSE W1 IC— ﬂaériwﬂl‘o” ’ «Hm m mm ,pgrm Mam {cm m
EOE ‘ﬁoOIKCJL EE3901 Semiconductor Devices A2000 (0 (ii) (iii) (M (V)
DOPING CARRIER I... ENERGY BAND DIAGRAM
D
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m3 hams El
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INTRINS IC
DEGEN
NONDEGEN MORE ON THE OTHER SIDE!!! EE3901 Semiconductor Devices A2000 (0 (ii) (iii) (M (V) DO P ING CARR]: ER
CONC l
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ENERGY BAND DIAGRAM
E E 2 (L131! NA ND H
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 Spring '09
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