А Р

I X

ANSWERS ТО SELECTED PROBLEMS

Chapter 1

LI {a) 4 atoms, (h) 2 atoms, (c) 8 atoms

L3 {a) 52.4 percent, (h) 14 percent, (c) 68 percent, [d) 34 percent

1.5 (a) 2.36 A, {b) 5 X 10 atoms/cm

L7 ib) a = 2.8 A, (c) 2.28 x 10- cm - for both Na and CI, № 2.21 gmW

L9 (a) 3.31 X lO * atoms/cm-; Same for A atoms and В atoms, (b) Same as (й). (с) Same material.

ЫЗ {a) 5.63 A, Ф) 3.98 A, (c) 3.25 A

1.15 {a) 6.78 X 10 cm--, {b) 9.59 x 10 cm-\

(r)7.83 X 10 cm-

L17 2 X 10 cm-

1.19 ia) 4 X 10 percent, (b) 2 x 10 percent 1.21 cl = 1.94\ n\ cm ord/oo = 146

Chapter 2

2.5 2.7

л = 0.254 m (gold), X = 0.654 цт (cesium)

3- 0.01727 eV, P = 7.1 X 10- kg-m/s, л = 93.3 A

(a)E = IA4 X JO eV, p = 1.82 X lO- kg-m/s, Л = 364 A

(b) p = 5.3 X 10- kg-m/s, i; = 5.82 X 10 cm/s, £ = 9.64 x 10 eV

(a) Д/? = 1.054 X 10- kgm/s

(/7) Д£; = 0.198 eV

2.13 {a) Ap = 8.78 x 10 kg-m/s

ib) AE = 4.82 X 10- eV

2Л5 {a)Ap= 1.054 x lO kgm/s

2.11

2.17 A= 1, or Л =+1,-L-hy.-7

2.19 (a) P = 0.393, (/;) P = 0.239, (c) P = 0.865

2.21 Ф л) = A expl - j {kx -\-cot)] where it = 6.27 x 10** m and CO = 2.28 x 10 rad/s

2.23 (a) £] = 0.261 eV, £3 = 1.04 eV,

{b)X= ].59pm

2.25 £i = 2.06 X !0 eV (neutron), £1 - 3.76 X 10 eV (electron)

2.29 (b) (i) A£ = 3.85 X JO-- cV, (п)АЕ = 2Ав X 10- cV

2.31 (й)Р = 0.118 percent,

(/?) P = 1.9 x 10- percent

2.33 (a) Г = 0.138,(7) T 1.27 X 10--

2.38 El = -13-58 eV, E. = -3.395 eV, £3 = -L51 eV, £4 = -0.849 eV

Chapter 3

3.9 (a)AE 0.488 eV, (i?) A£ = 1.87 eV, (c) AE = 3.83 eV, (d) AE = 6.27 eV

3.11 (a) AE = 0.638 eV, (b) AE = 2.36 eV, (c) Д£ = 4.73 eV, (d) AE 7,39 eV

3.13 m* (A) < m (Б)

3.15 A, B: velocity = - x; C, D: velocity = +x; B, C: positive mass; A, D: negative mass

3.17 A: m/mo = 0.476; B: m/mo = 0.0953

3.23 g = 3.28 x 10

3.25 ( )At £ , =0;

0.05 eV,>, = 1.71 X 10- cm- eV

ih) At = 6.6 X 10

O.lOeV, g, = 2.41 X I0- cm- eV

r-l .

0.15 eV, gr = 2.% X 10 cm еУ- 0.20еЧ, = 3.41 X 10 cm eV ,

(h)At E g =0,

-0.05 eV, g, = 0.637 x 10 cm- еУ- -O.lOeYg, =0.901 X 10 cm-eV-; -0.15 еЧ, = 1.10 X 101 cm-- eV ; -00.20 eV, g, = 1.27 X 10- cm еУ-

3.29 (a) f{E) = 0.269, (b) 1 - /(£) = 0.269

3.31 (a) 1 - /(£) = 0.269,

(b) 1 -/(£):= 6.69 X 10-

(c) 1 - /(£) = 4.54 X 10- 3.37 ia) f{E) = 6.43 x 10- percent,

(b) /(£) = 4.53 percent, (c) Г 756 К

3.39 ( )For £ = £ /(£) =9.3 X 10-

For £ = £2, 1 ~ /(£) = 1.78 X 10-i\

(b) For £ = £ /(£) = 8.45 x 10 ; For£ = £2, 1 -/(£) = 1.96 x 10-

3.43 Г 461 К

Chapter 4

4.1 (a) ni = 7.68 X 10 cm-; 2.38 x 10- cm-; 9.74 X 10 cm-,

(b)ni = 2.16 X 10** cm--; 8.60 x 10 cm- 3.82 X 10 cm-\

{c)n, = 1.38 cm- 3.28 x 10 cm-;

4.8 4Л0

5.72 X 10 cm- kT

{a)E = E, + -

(b)E = E -

= 47.5

En - £midgap = -0.0128 eV (Si) Efi - £rnidg.p = -0.0077 eV (Ge) Efi - £midg.p = +0.038 eV (GaAs) 4.12 Efi - £ijgp = -8.51 meV, -17.0meV, -25.5 meV

4.17 Г] 104 A, £ = 0.0053 eV

4.19 = 2.13 X 10- cm-,/7o = 2.27 x 10 cm-

4.21 E, -Ef = 0.88 eV, 0 = 4.9 x 10 cm-

4.23 (fl) = 1.33 X 10 cm-,

Ф) Ep, - Ef = 0.207 eV,

(c) For (fl) По 2.44 cm -; For(;?)fi[, = 8.09 X 10 cm

4.25 £,- -Ef = -0.034 eV

4.27 (fl) o = 2.45 X 10

/0 =9.12 X 10 cm--

4.29

4.31

4.33

4.35 4.41

4.43

4.45 4.49 4.51

(fl) =2.95 X 10*3 cm, 0 = F95 X 10* ст--,(/?)ло = 5 x 10 cm- = 1.15 X 10* cm

(fl)f7o = 2 X 10* cm--. A) = F125 x 10 cm Ф) = 10 cm, 0 = 2.25 x 10 cm-\ (c) Ли = Po = rtf = 1-5 X 10** cm .

{d)p = 1.0 X 10* cm 0 = 5.66 X 10 cm

{е)щ = 1.49 X 10 cm-3 Po =4.89 X 10 cm-3 (fl) p type, Ф) Si: po = 1.5 x 10*3 -з^ 0 = 1.5 X 10 cm-3, Ge: Po = 3.26 X 10 cm--\ 0 = 1.77 X 10 cm-, GaAs:

= 8.04 x 10 cm-

Po = 1.5 X 10* cm-3, 0 = 0.216 cm

0 = 1.125 X 10 cm--, n-type

(fl) n type; 0 = 10 cm-, Po = 2.25 X 10 cm-, ф) p-type; Po = 2.8x10

Г = 200 К = Ef, - Ef = 0.1855 eV Г = 400 К = En - Ef ОтШ eV 7 = 600 К = Ef, - Ef 0.000674 eV

Г 762 К

Л^ = 1.2 x 10** cm- (fl) Ef - Ef, = 0.2877 eV, Ф) Efi - Er = 0.2877 eV, (c) For (fl)

2.25 X 10 cm

0.1291 eV,

ф}по = 1.87 X 10 cm Po = 9.20 X 10 cm--

0 = 10 cm-3, For(/;)/io 4.53 (fl) Ef - Ef, = 0.3056 eV, Ф) EFi - Ef= 0.3473 eV, (c) Ef = Efi , {d) Efi ~ Ef = (e) Ef - EFi = 0.0024 eV 4.55 p type, Efi - E 0.3294 eV

Chapter 5

5.1 {a) no = 10* cm-, Po = 3.24 x 10 cm-

Ф) p 7500 cmVV-s so

7 = 120 A/cm ic) (i) po = 10 cm-,

/70 = 3.24 X lO-cm-3;

(ii) pp 310cmA-s

so J = 4.96 A/cm

(a) I = 0.44 mA, ф) I - 4.4 mA,

(c) For (fl) Vd = 5.5 X lO* cm/s. For Ф) ?v = 5.5 X 10 cm/s

{a) fi = 3333 cmW-s,

Ф) v,i = 2.4 X 10 cm/s

(fl)cr; = 4.39 X 10 * (Q-cm) ,

ф)а{ = 1.03 X lO- (Q-cm)-*

5.11

5.13 5.17 5.19 5.23 5.25

5.27

i(300 K) = 3.91 X 10 cm- E. = 1.122 eV; rt,(500K) =2.27 X 10 cm-\ a(500 K) = 5.81 X 10-- (fi-cm)-i

(a)Nd=9.26 X 10- cm-\

(b) p(200 K) 2.7 Q-cm, p 9.64 Q-cm

(a) Г = 5.6 X 10-* еЧ (b) T 5.6 x IQ- eV p - 316cm/V-s Д = 167 cm/V-s / = 18 mA J = 16A/cm2

J, = 3.41 exp

V22.5

A/cm

5.29 (a) Jhijf = 1,6 exp

AJcnr,

W.,/ = 4.8- 1.6 exp

A/cm\

(c)E =

5.31 {a)n = hf exp

1 - exp y-j V/cm 0.4-2.5 X lOjcl

(h) J = -5.79 X 10-* exp

Г0.4-2.5 X lOr

5.33 5.35

5.39 5.41

5.43

0.0259

(0 JAx = 0) = -2.95 X 10 A/cm\ 00 Jnix = 5 pm) = -23.7 A/cm

N{x) = A exp {-ax) where Of = 3.86 X 10- cm

(a) = 2.19 mV, (b) E =0.219 V/cm

ia) p type, ib) p = 8.08 x 10 cm-\

{b) = 387 cmVV-s

{a) n type, (b) n 8.68 x 10 cm-\

(c) p = 8182cm-/V-s,

(d) p = 0.88 Q-cm

Chapter 6

6Л = 5 X 10 cm- s- 6.3 (a) r o = 8.89 X 10 s.

-3 -1

6.7 6.9

{b)G= 1.125 X 10 cm-s (c)G = R 1.125 X 10 cm s 3E

-5 .,-1

= -2 X 10 cm- s

D = 58.4 cm/s, p = -868 cmVV-s, T o 54 s, tpo = 24/xs

6.11 6.13 6.15

6.17

6.19

G =8 + 0.114(1 -€i>),TVi = 10- s / = (54 + 2.206-) mA, r,o = 3 x I0- s

(a) = 4.44 x 10,

(b) г^,o = 2.25 x 10- s

( )ForO < / < 2 X 10-

Sn =10 (\- -/- 0) where т„о = 10- s:

For? > Г = 2 X 10-

a = 0.865 X 10* exp ~

(й)п/,о = 2.25 X 10 cm\ (b)Sn(0) - = 2.25 X 10 cm-

(c) Sn

6.25 For-L < jt < +L,5p (5L - jc);

2D,

For L < л < 3L, 6p -(3L - л);

6.29

6.31

6.33

6.37

For-3L <x <:-LJp= -{3L+x)

Ef - En = 0.3498 eV, En - Erp = 0.2877 eV Sn=8p = 5x 10 cm--\

(a) Ef - Ep = 0.0025 eV, {b) En - Erp = 0.5632 eV (a)Sp = 5 X 10-cm\

(b) Ef, - En =0.1505 eV

/? 1

{a) For n-type, -- =

= 10 S-

6.39

(h) For mtrinsic, - =---

Sn tpq + t o

= 1.67 X 10 s-, R 1

(c) For p-type, = - = 2 X 10

osinhL(W-.r)/LJ

(й) 5л = ~------ ,

sinhliy/LJ

0 - 10 cm- and L = 35.4 дт.

6.41

ib)Sn = 10-(l-)

For-W < < 0, G

Sn = Trf (- - 2М/X + 2W); 2D

ForO <x <W,Sn = (IV -Jc)

Chapter 7

7.1 (й) For /Vj = 10* cm; (0 Уы = 0.575 V, iii) 0635 V, (ш) 0.695 V, (zV) 0.754 V,

Ф) For /V = 10 cm (/) 0.754 V, m 0.814 V, (iii) 0.874 V, (iv) 0.933 V

7.11 7.13

7.17

7.19 7.21

7.23 7.25 7.27

7.29

7.33 7.35

(a) n side, Er - £// = 03294 eV; p side. En - E = 0.4070 eV

(h) Vbi 0.3294 + 0.4070 = 0.7364 V

(c) Vb, = 0.7363 V

(d) x = 0.426 дт, x, = 0.0213 дт, EJ = 3.29 X 10 V/cm

(b) (n region), no = Ki = 8.43 x 10 (p region), /?o = Ki = 9.97 x 10** cm (r) = 0.690 V

(a) Vb. = 0.635 V, (/;) x = 0.864 /xm, xp = 0.0864 дт,

(d) En;,xl = 1-34 x 10 V/cm

(a) Vbi = 0.8556 V, (/;) T = 302.4 К

(a) Vi,i = 0.456 V, (b) x = 2.43 x 10 cm,

{c)xp = 2.43 X 10-3 j

(d) E I = 3.75 X 10- V/cm

(a) Vbi = 0.856 V,

(h) =0.301 X 10- cm,

(c)E = 3.89 X 10- V/cm,

(d) С = 3.44 pF

(a) Neglecting change in Vi , 41.4 percent increase; {b) 17.95 mV increase

(fl)V,=73V,0)y/,=7.18V,

(c) Vfi = 0.570 V Vf,2 = 18.6 V

N,i = 3.24 X 10 cm

(a) 14, = 0.557 V, ib) xj. = 5.32 x lO * cm,

= 2.66 X 10- cm, (c) Vr = 70.3 V

(a) (0 С = 1.14 pF, (ii) С = 0.521 pF, (iii) С = 0.389 pF; (b) (i) С = 3.69 pF, (ii) С = 1.74 pF, (iii) С = 1.31 pF

(a) E{x = 0) = 7.73 x 10 V/cm,

ic) Vf, = 23.2 V

a = 1.1 X 10- cm-*

Chapter 8

8.1 (a)60mV, (b) 120 mV

8.5 (a)

7,1 + jp

l+(2.04)(/V,/W

8.7 8.9

KJKi =0.083

/ = 2.91 X 10- A, (a) I = 6.55 дА, {b)I = -2.91 nA

(й) V = 4.02 x Ю--* A,

да/ 0 =6.74 X 10-- A,

8.13 8.15 8.18 8,20

8.23

8.25 8.27 8.29 8.31

8.33

8.39 8.41 8.43 8.45 8.47 8.49 8.51

(c) /7 = 3,42 X 10** cm-

(d) / = 3.43 X 10- A

(a) Va = 0.253 V, (b) V, = 0.635 V £ 2 0.769 eV T; , 519 к

For 300 K, Vd = 0.60 V; For 310 K,

Vd = 0.5827 V; For 320 K, Vd = 0.5653 V

For 10 kHz, Z = 25.9 - j0.0814; For 100 kHz, Z = 25.9 - 7O.8I4; For 1 MHz, Z = 23.6 - У7.41; For 10 MHz, Z = 2.38 - 77.49

tp = 1.3 X 10- s; С/ = 2.5 x 10- F

(й) = 72.3 Q, / = 1.38 mA

V, = 0.443 V

js = 8.57 X 10-** A/cm,

7g = 1.93 X lO- A/cm

(a) For K, = 0.3 V, / = 7.96 x 10- A;

For K, = 0.5 V, / = 3.36 X 10- A

Vn = 0.548 V

Vf, = 19,9 V Vr = 5.54 V V;, 15 V

fn/Ir = 1.1ЕЬ/Г;,()

W = 61.9 A

3 X 10= cm-\ Л = 1.99 x 10- cm

0.65

Chapter 9

9.1 (c) = 0.206 V, Фво = 0.27 V,

Vbi = 0.064 V, E , = 1.41 X 10 V/cm, (J) фв, = 0.55 V, En,ax I = 3.26 X 10- V/cm

9.3 (a) Фво = 1.03 V, (b) ф„ = 0.058 V,

(с) Vbi = 0,972 V, (d) = 0.416 дт,

(e) E,

2.87 X 10- V/cm

9.5 9,7

(a) С = 4.75 pF, (b) С = 15 pF (я) Vft, = 0.334 Ч .Yj = 0.211 дт.

-mux

= 3.26 X 10 V/cm,

(/?) = 20 mV, л- , = 0.307 x 10- cm, (c)E,n.J = 1Л6Х 10- V/cm, Аф = 37,8 mV, = 0.163 x 10- cm 9.9 (a) Vbi = 0.812 V, jTj = 0.153 д(n.

I Em

9.11

= 1.06 X lO- V/cm, да = 7.47 V

(a) фв) = 1.13 V, да 0 = 0.858 V,

(с) фви = 0.43 V, фв = 0.733 V 9.13 (а) ф„ = 0.206 V, да Vb, = 0.684 V,

9.15 9.17

9.21

(c)JsT = 13 x 10 А/ст\ {d) К = 0.488 V

(й) = 0.603 v, {h) A = 18 mV

Vb, = 0.474 X ia) = 1.52 x Ш A, (b) Ir2 = 1.86 x 10- A

For Schottky diode, Kj = 0,467 V; for pn diode, = 0.705 V

(a) For Schottky diode, / 0.5 x 10 A; for pn diode, / = 1.02 x 10- A; (b) for Schottky diode, = 0,239 V; for pn diode, V =0.519 V

9.25 9.27

(b) Nd = 1 -24 x 10 cm \ (c) 0.20 V Ф) фво = Фп =0Л38 V

Chapter 10

10.3 (a) Is = 3.2 x 104 A; ф) (i) ic = 7.75 дА,

Ш) ic = 0.368 mA, (/7/) /V = 17.5 mA 10.5 {a) /3 = 85, a = 0.9884, ir 516 fiA\ Ф) j6J = 53, a = 0.9815, Ie = 2.70 mA Ф) Ic = 4.7 mA

10.7 10.9

10.11

10.15

10.17

10.19 10.21

10.23 (a) (/)

(a) pTf) = 4.5 x 10 cm

Пво = 2.25 X 10 cm \

peo = 2.25 x 10 cm~

ф)пв(0) = 6М x 10 cm-\

PtiO) = 1.36 x 10 cm-

Assume ехр(Ув£/У,) coshl/L), ia) 09950, ih) 0.648, (c) 9.08 x 10 *

(c) ForxB <Ln, jixb )/y(0) = 1; Foyxb = Lb = 10 дт,

7(jCfi)/i(0) = 0.648

(a) Vcb = 0.70 V, (b) VecX) = 0.05 V,

(t0 3.41 x 10 holes/cm-,

(d) 8.82 X 10 electrons/cm-VcB = 0.48 V

(a) Ic = 17.4 pA, (b) a = 0,9067, Ic = 1.36 mA, ic) Ic = 19.4 pA

y{B) , Л^йо Oe Xb

(ii)

у{Л) yiC)

Nc Db

= \:ib)ii) У (A) r(a)

ar(C)

-1>

о(т(Л) 2 Lb

changes in space charge width.

; ic) neglect

HB) SiA)

Ло exp

edbribo Xb

10.25 10.27

10.29 10.35

10.39 10.41

10.43 10.45

10.47 10.53

5(C)

Ло exp

ервпви Xb

(d) Device С

Ф) /с - 1.19 mA, /£ = 0.829 mA

(a) 8 =

ib)fi =

{ -Vbe 1 + 15.38expf-

Ь

1 -Ь

0518

, (с) for Vbe < 0,4 V,

recombination factor will be the limiting factor in current gain,

ia) Xb 0.742 дт, (b) Ь = 0.9999994

ia) K4 = 47.8 V, ib) = 33.4 V, ic) Va = 19.0 V

(a) R = 893 ф) V = 8.93 mV, (c) 70.8 percent

. . kT

(a)E = -

(с) Total solution is

-\- пц (0) exp(-Ax)

ep E

where A

пя(0) =

) ep,\

Nb(0) \ V, J ep E

BVcBo = 221 V, Nc - 1,5 x 10 cm-\ Xc = 6.75 pm

ia) Vpt = 295 V; however, junction breakdown for these doping concentrations is V 70 V, so punchthrough will not be reached.

(a) I в = 0.105 mA, ib) = 11-9 дА, ic) I в = 10.14 дА

fr = 509 MHz

Chapter 11

11.1 (a) p type, inversion; Ф) p type, depletion;

(f) p type, accumulation; (d) n type, inversion 11,3 ia) By trial and error,

Nd = 3.27 X 10- cm-\

ih) 0, = -0.518 V

11.5 ia) N = 4.98 x 10 cm- {b) cannot use p+ poly gate, (c) Nd = 3.43 x 10 cm

11.7 Q,Je= 1.2 x 10 cm-

11.9 Vp = -1.44 + фп,., (a) Vp = -1.76 V,

ib) Vtp =-1.11 V, (c) Vtp = -0.592 V

11.11 11.13 11.15 11.21

11.23

11.27

By trial and error, N = 1.71 x 10 cm (a) Vfb = -\-52 V, (b) Vr = -0.764 V ib) ф„,. = - Ll 1 V, ic) Vj- = +0.0012 V

ia) Cox = 8.63 X 10- F/cm, Ср=ЪЛ2 10- F/cm C; = 0.797 X 10- F/cm C(inv) = Q,

ib) Same as (a) except C(inv) (c) Vtp = -0.989 V {a)AVfB =-1.74 V, ф) A Vfb = -0.869 V, a) AVfB = -1.16 V {a) n type, и = 345 A,

11.31

11.37 11.39 11.41 11.43 11.47

ic) e;. = 1-875 x 10 cm {d)cfb = 156pF VsG = 1 V, /л (sat) = 0.00592 inA; Vsc = 3 V, J(saO = 0.716 mA; V-f; = 5 Ч /л (sat) = 2.61 mA 0.2 V, д = 342 cm/V-s (Д) W/JL = 14.7, (b) W/L = 25.7 (a) g f = 0.148 mS, ib) g , , = 0.947 mS Vbs = 1.92 V

ia) It =5M GHz, ib) fj = LO GHz

Chapter 12

12.1 b = 10-*-exp

(2.\)vJ

Jr = a0)lo,

P = h- Vj;;;for =0.5 V,

lo = 9.83 pA, h = 9.83 дА,

P = 49.2 д\У; for Vf; = 0.7 V,

lo = 0.388 nA, It = 0.388 mA,

P = 1.94 mW; for Vas = 0.9 V,

I о = 15.4 nA, It = 15.4 mA, P = 77 mW

12.3 (a) AVos = 1 V, AL = 0.0451 дт; AVoi- = 3 V, AL = 0.122 дт; AVos = 5 V, AL = 0.188 дт; Ф)Е= 1.88 дт

12.7 (a) Assume ViJi(sat) = 1 V; then

L = 3 дт => Es,i = 3.33 x lO V/cm

L = 1 дт=Е,,= 10 V/cm

L = 0.5 дт = E,at = 2x10 V/cm

(&) Assume д^, = 500 cin-/V-s, L = 3 дт V = 1,67 X 10* cm/s

12.17 12.23 12.27 12.31 12.33

12.35

12.37

L = 1 дт V = 5 X 10 cm/s

L < 0.5 дт =v iO cm/s 12.13 ia) Both bias conditions, fp kit),

ib) FkP 12.15 ia)ii) I о = 1.764 mA;

07) I о = 0.807 mA:

ib) ii) P = 8.82 mW, (/7) P = 2.42 mW;

ic) current: 0.457; power: 0-274 L = 1.59 дт AVr = +0.118 V (fl)V5o = 15V,(;7)Vc=5V L = 0.844 дт

(я) Vr = -0.478 V, (ip) implant acceptors, Di =4.25 X 10 cm- (a)Vr = -0.624 V, ib) implant acceptors, Dl = 4.37 X 10 cm- (c) Vt = 1.24 V ia) Vr = -1.53 V; enhancement PMOS, (b) implant acceptors, Dl =4.13 X 10- cm- 12.39 AVy=-2.09 V

Chapter 13

13.3 ia) Vp = 4.91 V, ib) for V = 1 Y (/) a - h = 02\5 дт, iii) a - h= 0.0653 дт, (/77) a -h - -0.045 дт (zero depletion width)

ia) Vpo = 15.5 V, ib) Vcs = -4-66 V (fl) Vpo = 1-863 V, Vp =0.511 V; ib)ii)a-h =4.45 X 10- cm, iii)a-h = 1.70 X 10- cm (fl) For Vos = 0, Vos = -1.125 V;

ib) For Vos = 1 V, Vcs = -0.125 V Vcs = 0, = 0.523 X 10--; Vg.s = -0-53 V, g = 0.236 X 10-; Vcs - -E06 V, g, = 0

13.13 , .v(niax) =1.31 mS/mm

13.15 (fl) Vpo = 2.59 V, Vr = -1.78 V,

ib) depletion mode 13.17 Vos = 0, fl - /г = 0.716 дm;

Vos = 2V,a-h= 0.545 дт;

Vos = 5 V, fl - /7 = 0.410 дт 13.19 Nj 5.45 X 10* cm- 13.21 (fl) V, =0.612 V, V,4j = 2.47 V,

Vr = -1.86 V, Vzjs4sat) = 0.858 V,

(b) add donors, = 1.64 x 10* cm ;

13.5 13.7

13.9

13.11

Vbi = 0.628 Ч Vf = -3.87 V,

V4sat) = 2-87 V 13.23 (n) W = 26A дт; (b) for Vcs = OA V,

>, = 78.8 дА; for Vcs = 0-65 Ч

/о i (sat) = 0.56 mA 13.29 (a) With vek>city saturation,

(sat) = 4.86 mA; without velocity

saturation, /iji(sat) =18.2 mA 13.31 (a) и = 20 ps, (b) td = 20 ps 13.33 (a) g , = 2.82 mS, (b) = 88.7

(c) L = 0.67 дт 13.35 ia) fr = 155 GHz, (/?) fj = 15.9 GHz 13.37 ia) g /W = 502 mS/mm,

[h) bi (sat)/W = 537 mA/mm

Chapter 14

14.1 {a)X=\,24/E

(0£=0.66= a= 1.88 дт

(ii) E = 1.12 л = 1.11 дт

(iii) E=\A2X= 0.873 дт (h) (OA = 570 nm= £ = 2.18eV

14.3 14.5 14.11

14.13

14.15

( ) л = 700 nni £ = 1.77 eV Sn gr = 1.44 x 10 cm (a) X = 1.98 дт, (b) x = 0.41 дт и = 500 mA, V , = 0.577 V, / , = 478.3 mA, R = 276 mW

For/zv - 1.7 eV, x = 2.3 дт; ¥orhv 2.0 eV, x = 0.23 дт

(a) Sp = Sn = 10 cm-\

(b) Aa = 1.32 x 10- (Q-cm) ,

(c) = 0.66 mA, (d) Vp =4.13

14.17

14.19

(a) Ju = 9.92 mA/cm,

(/?) Jl = 0.528 A/cm-

W = 1 дт 7/, =4.15 mA,

W \Opm= Jl = 15.2 mA,

14.21 14.23

W = 100 дт Л = 16 mA,

0.625 < Л < 0.871 дт

(a) 8.83 percent, (b) 5.95 percent

Chapter 15

15.1 /с =5.33 a

15.7 Vc с = 25 v

15.9 (a) h = 1-84 a, h = 1.66 a, h = 1-51 a;

Pi = 6.09 W, P2 = 5.48 W, P3 = 4.98 W

(b)L =2.16 a, a = 1.08 a, h = 1.77 a;

P] = 8.38 W, Pn = 4.19 W, P3 = 6.85 W 15.11 (h)

(i) Vgs--S у I о = 0.25 a, Vns = 37.5 v,

P = 9.38 W

(/0 Vt;5 = 6 v, /£> = 1.0 a, V/,i = 30 v, P = 30 W

(iii) Vcs = 7 v, Iiy = 2.25 a, V. = 17.5 v, P = 39.4 W

(/v) Vcs = 8 v, Ь = 4.0 a, Vps = 2.92 v, P = 11.7 W

(v) Vas = 9 v, = 6.25 a, Vos = 1-88 v, P = 11-7 W

z,. J Incase-ашЬ 15.15 c.se b =4C/W