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Unformatted text preview: ﬂax/2713100123 5"” Sea/73’0“" 55. Electron mobility in copper. (a) Using ”all?
me 0': tc withe x 5.8 x 10784111 ,nc =8.45>< 1028 1.111113 ,iqe ~ 1.602x 10 19c, andme x
9 11 x 10““ kg, the mean free time between coliisions can be found as ta 2 2. 44 x 10 14s
The electron mobility in copper at room temperature can be caiculated as Iq etcl _(1 6.02 x 1019)(2 44 x 1014) m 911 X 10;“ ~ 4.28 x 10—3 m2 — (v — s)"
e Me: which 18 the same as 115 2 42 8 cm2 (V— s) 1 .Note from Problem 59 that the electron mobiiities 1n
silicon and germanium at 300K are 1118:1450 cmz‘1(Vs) and 1118:3900 cmZ—(Vs)1respectively
which are much higher than the electron mobility 1n copper. (b) Using the electron mobility value we found in part (a) along with I — l A, A: «(0. 5 x 10"3)2
m2, and or: 5.8 x 1078 Sm ,the average drift velocity of the electrons can be calculated as J I (4.28 x 103)(1) ode11 E=11 ”=11 ——:~:—————~—————————29.41x 10—51114"!
8 '30 340 «(0.5 x10‘3)2(5.8 x 107) 59. Intrinsic semiconductor. (a) For silicon, the intrinsic carrier concentration N15. and the conduc
tivity 013i are given by 1..124(1602x10 19) "3
We =1/(2. 8 x 1019)(1. 04 x 10 9)e 211‘a'axwﬁxs‘m) ~ 6.13 x 109 cm dig; zl‘IelUJ'e + .U'p)Ni
~1602 x 10"9(1450+450)(6. 13 x 109)_~187 x 10 43 —m and respectively.
(b) Similarly, for germanium, the intrinsic carrier concentration N10: and the conductivity ”is:
can be calculated as 0.6611.602x10—‘9) 13 _3
N15"1/(104 x 1019)(6 x 101% Tush—W moo) ~ 2.25 x 10 cm Jim, =QeKIJe + pp)Ni
21.602 x 10—19(3900 +1900)(2.25 x 1013) 2 2.09 S—m and vi H1WMﬂNﬁana‘ﬁmmmuuthi MnrwNthvmm‘zxtmﬂ WWWmmmmq 512. A silicon resistor. Since Np 2 Nﬂ = 1016 cm“3 >> Ne = Nf/N , the resistance of of this ptyge
silicon sample can be approximately written as g ' z axis4 —~——————~2m———*——————————~=18x103
_ 0A '" lqelaprA 1.602 x 1019 x 101'5 x 2.5 x 2.5 x104”? R from which we solve for hp cu. 444 cmZ—(V~s)“‘. 516. Diffused IC resistor. (a) The sheet resistance of the diffused pty'pe IC resistor with differential
thickness aim and conductivity 0(a) can be written as l (1qu z: cr(:c)d:e Noting that these differential resistances are connected in parallel, it is more convenient to ﬁnd
the total sheet resistance using differential sheet conductance given by 1
dGSq 3 m; = O'(£L')d33 The total sheet conductance can be found by adding (i.e., integrating) the sheet conductances of
the differential resistors as t
0 Therefore, the total sheet resistance follows as (b) Since the conductivity of the p—type layer decreases linearly from 0(32 = 0) = cm and 0(3; =
t) = 01 << (70, the conductivity expression can be written as 01$): (01 :00) x+aoszc+oro where K = (0; ~— mﬂ/t. The sheet resistance can be found by integrating this expression as t —l
Rag = [f (KID + O‘o)d:r:l
0 {real —1
”1‘00 2 = t + t _(Ug+0“1)t _ O'ot since 0; << 09. (c) Assuming the conductivity expression to be 0(3) = 096“"3
0'] << 00, the sheet resistance for this case can be evaluated as qu =[/:oroe_”d:c] 14
=[(—°'°:i“)lll _[“°‘Oe_at +00] 4 a a, and noting that 0(t) = age—“t = a 00‘01 do 52.1. Resistance of a hemispherical conductor. Using the result of Example 54, the resistance of
the hemispherical conductor buried in the earth is I 1 1 R 2 = W N
2mm 271' x 10‘4 x 12.5 x 10‘2 m 12'7 k9 527. Leaky capacitor. As discussed in Section 5.6, at the interface between lossy dielectrics, the
current boundary condition [5.7] is in general incompatible with the electrostatic boundary con—
dition concerning the continuity of the normal component of electric ﬂux density, unless a surface charge layer is assumed to exist. (a) At steady—state, the eiectric ﬁeld between the plates must
satisfy the following conditions: E1d+E2d=Vo
V~JmO —> J1n=J2n —> 01E1=02E2 . V'D=P "—’ Ps=ﬁzE26131
so thatwehave and E2 = (b) The answer to this part is actually worked out at the end of Section 5.6.2; we have 0'2 0'1
P3 = (61“ — 62) E2 = (61* €2—) E:
a] 02 (02 ) 0: Vo aim—6102170
psm —————————— e;——ez ——«
0’1 01+02d 01+0'2 d 01' mwwuwmtxw WwIwWrﬂ'rmwxxmw emumimwvwmvmwmmmwmwwmmwmwwmwmmmpmm )sw’kwmfamwln» u u M ‘ 3: m wmmmmmtw
1 c m mmmmm WWW WWWmmmwwvmwwwmwstwwwmmWmmmwememmm I x
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 Summer '08
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