Chapter 11comsizo.com.br/resolucoes/semisolex11.pdf · Semiconductor Physics and Devices: Basic...
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Semiconductor Physics and Devices: Basic Principles, 3 rd edition Chapter 11 Solutions Manual Exercise Solutions 163 Chapter 11 Exercise Solutions E11.1 (a) φ fp x x V = = ( ) F H G I K J 0 0259 3 10 15 10 0 376 16 10 . ln . . x x x x dT = ( ) ( ) R S T U V W − − 4 117 885 10 0 376 16 10 3 10 14 19 16 12 . . . . / b g b gb g or x m dT = 0 180 . µ (b) φ fp x V = = ( ) F H G I K J 0 0259 10 15 10 0 288 15 10 . ln . . x x x dT = ( ) ( ) R S T U V W − − 4 117 885 10 0 288 16 10 10 14 19 15 12 . . . . / b g b gb g or x m dT = 0 863 . µ E11.2 φ fn x x V = = ( ) F H G I K J 0 0259 8 10 15 10 0 342 15 10 . ln . . x x x x dT = ( ) ( ) R S T U V W − − 4 117 885 10 0 342 16 10 8 10 14 19 15 12 . . . . / b g b gb g or x m dT = 0 333 . µ E11.3 φ fp x x V = = ( ) F H G I K J 0 0259 3 10 15 10 0 376 16 10 . ln . . φ φ χ φ ms m g fp E e = ′− ′+ + F H G I K J 2 = − + + ( ) 3 20 3 25 0 555 0 376 . . . . or φ ms V =−0 981 . E11.4 φ fp V = 0 376 . φ ms =− + ⇒ ( ) 0 555 0 376 . . φ ms V =−0 931 . E11.5 φ fp V = 0 376 . φ ms = − ⇒ ( ) 0 555 0 376 . . φ ms V =+0 179 . E11.6 From E11.3, φ ms V =−0 981 . C t x x x F cm ox ox ox = ∈ = = ( ) − − − 39 885 10 200 10 173 10 14 8 7 2 . . . / b g Then V Q C x x x FB ms ss ox = − ′ =− − − − φ 0 981 16 10 8 10 173 10 19 10 7 . . . b gb g or V V FB =−106 . E11.7 From E11.4, φ ms V =−0 931 . V x x x FB =− − − − 0 931 16 10 8 10 173 10 19 10 7 . . . b gb g or V V FB =−1 01 . E11.8 From E11.5, φ ms V =+0 179 . V x x x FB =+ − − − 0 179 16 10 8 10 173 10 19 10 7 . . . b gb g or V V FB =+0 105 . E11.9 From E11.3, φ ms =−0 981 . V and φ fp V = 0 376 . x x x x m dT = = ( ) ( ) R S T U V W − − 4 117 885 10 0 376 16 10 3 10 018 14 19 16 . . . . . b g b gb g µ Now ′ = ( ) − − Q x x x SD max . . 16 10 3 10 018 10 19 16 4 b gb gb g or ′ = ( ) − Q x C cm SD max . / 8 64 10 8 2 From Equation [11.27b]
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Transcript of Chapter 11comsizo.com.br/resolucoes/semisolex11.pdf · Semiconductor Physics and Devices: Basic...
Semiconductor Physics and Devices: Basic Principles, 3rd edition Chapter 11 Solutions Manual Exercise Solutions
163
Chapter 11 Exercise Solutions E11.1
(a) φ fp
x
xV= =( ) FHG
IKJ0 0259
3 10
15 100 376
16
10. ln
..
xx
x xdT =( ) ( )RST
UVW−
−
4 11 7 8 85 10 0 376
1 6 10 3 10
14
19 16
1 2. . .
.
/b gb gb g
or x mdT = 0 180. µ
(b) φ fp xV= =( ) FHG
IKJ0 0259
10
15 100 288
15
10. ln
..
xx
xdT =( ) ( )RST
UVW−
−
4 11 7 8 85 10 0 288
1 6 10 10
14
19 15
1 2. . .
.
/b gb gb g
or x mdT = 0 863. µ
E11.2
φ fn
x
xV= =( ) FHG
IKJ0 0259
8 10
15 100 342
15
10. ln
..
xx
x xdT =( ) ( )RST
UVW−
−
4 11 7 8 85 10 0 342
1 6 10 8 10
14
19 15
1 2. . .
.
/b gb gb g
or x mdT = 0 333. µ
E11.3
φ fp
x
xV= =( ) FHG
IKJ0 0259
3 10
15 100 376
16
10. ln
..
φ φ χ φms m
g
fp
E
e= ′ − ′ + +FHG
IKJ2
= − + +( )3 20 3 25 0 555 0 376. . . . or φ ms V= −0 981.
E11.4 φ fp V= 0 376.
φ ms = − + ⇒( )0 555 0 376. . φ ms V= −0 931.
E11.5 φ fp V= 0 376.
φ ms = − ⇒( )0 555 0 376. . φ ms V= +0 179.
E11.6 From E11.3, φ ms V= −0 981.
Ct
x
xx F cmox
ox
ox
=∈
= =( ) −
−
−3 9 8 85 10
200 101 73 10
14
8
7 2. .
. /b g
Then
VQ
C
x x
xFB msss
ox
= −′
= − −−
−φ 0 981
1 6 10 8 10
1 73 10
19 10
7.
.
.
b gb g
or V VFB = −1 06.
E11.7 From E11.4, φ ms V= −0 931.
Vx x
xFB = − −−
−0 931
1 6 10 8 10
1 73 10
19 10
7.
.
.
b gb g
or V VFB = −1 01.
E11.8 From E11.5, φ ms V= +0 179.
Vx x
xFB = + −−
−0 179
1 6 10 8 10
1 73 10
19 10
7.
.
.
b gb g
or V VFB = +0 105.
E11.9 From E11.3, φ ms = −0 981. V and φ fp V= 0 376.
xx
x xmdT = =
( ) ( )RSTUVW
−
−
4 11 7 8 85 10 0 376
1 6 10 3 100 18
14
19 16
. . .
..
b gb gb g µ
Now ′ =( ) − −Q x x xSD max . .16 10 3 10 018 1019 16 4b gb gb g or ′ =( ) −Q x C cmSD max . /8 64 10 8 2 From Equation [11.27b]
Semiconductor Physics and Devices: Basic Principles, 3rd edition Chapter 11 Solutions Manual Exercise Solutions
164
V x xTN = −− −8 64 10 10 16 108 11 19. .b gb g
× − +−
−( )FHG
IKJ ( )250 10
3 9 8 85 100 981 2 0 376
8
14
x
x. .. .b g
or V VTN = +0 281.
E11.10 From Figure 11.15, φ ms V= +0 97.
φ fn xV= =( ) FHG
IKJ0 0259
10
15 100 288
15
10. ln
..
xx
xmdT = =
( ) ( )RSTUVW
−
−
4 11 7 8 85 10 0 288
1 6 10 100 863
14
19 15
1 2. . .
..
/b gb gb g µ
Then ′ =( ) − −Q x xSD max . .16 10 10 0 863 1019 15 4b gb gb g or ′ =( ) −Q x C cmSD max . /1 38 10 8 2 Also ′ = =− −Q x x x C cmss 8 10 16 10 128 1010 19 8 2b gb g. . / Now, from Equation [11.28] V x xTP = − −− −138 10 128 108 8. .b g × + −
−
−( )FHG
IKJ ( )220 10
3 9 8 85 100 97 2 0 288
8
14
x
x. .. .b g
or V VTP = +0 224.
E11.11 By trial and error, let N x cmd = −4 1016 3 , then φ fn = 0 383. , φ ms ≅ 1 07. ,
′ =( ) −Q xSD max 1 10 7 and V VTP = −0 405. which is between the limits
specified. E11.12
′
=
∈
+ ∈ ∈∈
=
+∈
∈
FHGIKJ
C
C
t x
t
t
t xox
ox
ox ox s dT
ox
ox
ox
oxox
s
dT
min a f
or
′
=
+∈
∈FHGIKJFHGIKJ
C
C xt
ox ox
s
dT
ox
min 1
1
From E11.9, x mdT = 0 18. µ Then
′
=
+
⇒FH IKFHG
IKJ
−
−
C
C x
xox
min
.
.
.
1
13 9
11 7
0 18 10
250 10
4
8
′
=C
Cox
min .0 294
Also
′
=
+∈
∈
∈FHGIKJFHGIKJFH IKFHGIKJ
C
C
t
kT
e eN
FB
ox ox
s ox
s
a
1
11
=
+ FH IKFH IK( )( )
−
−
−
1
13 9
11 7
1
220 10
0 0259 11 7 8 85 10
1 6 10 3 108
14
19 16
.
.
. . .
.x
x
x x
b gb gb g
or
′
=C
CFB
ox
0 736.
E11.13
Ct
x
xoxox
ox
=∈
= ⇒( ) −
−
3 9 8 85 10
200 10
14
8
. .b g
C x F cmox = −1 73 10 7 2. / Now
IW
LC V VD n ox GS TN= −F
HIK
1
22µ a f
= −FH IK( ) −50
2650 1 73 10 0 47 2. .x VGSb ga f
or
I x VD GS= −−2.81 10 0 43 2b ga f. Then V V I mAGS D= ⇒ =1 1 01.
V V I mAGS D= ⇒ =2 7.19
V V I mAGS D= ⇒ =3 19
Semiconductor Physics and Devices: Basic Principles, 3rd edition Chapter 11 Solutions Manual Exercise Solutions
165
E11.14
IW
LC V VD n ox GS TN= −FH IK
1
22µ a f
Now
100 10650 1 73 10
21 75 0 46
7
2xW
L
x−
−
= −FHIK
( )( )
.. .
b g
which yields
W
LFH IK = 0 976.
E11.15
Ct
x
xx F cmox
ox
ox
=∈
= =( ) −
−
−3 9 8 85 10
220 10157 10
14
8
7 2. .
. /b g
I x VD SG= −FH IK( ) −60
2310 157 10 0 47 2. .b ga f
or
I x VD SG= −−1 46 10 0 43 2. .a f Then V V I mASG D= ⇒ =1 0 526.
V V I mASG D= ⇒ =15 1 77. .
V V I mASG D= ⇒ =2 3 74.
E11.16
200 10310
2157 10 1 25 0 46 7 2x
W
Lx− −= −FH IKFH IK ( ). . .b g
which yields
W
LFH IK = 114.
E11.17 (a)
Ct
x
xx F cmox
ox
ox
=∈
= =( ) −
−
−3 9 8 85 10
200 101 73 10
14
8
7 2. .
. /b g
Now
γ =∈2e N
Cs a
ox
=− −
−
( )2 1 6 10 11 7 8 85 10 10
1 73 10
19 14 16 1 2
7
. . .
.
/x x
x
b g b gb g
or γ = 0 333 1 2. /V
(b) φ fp xV= =( ) FHG
IKJ0 0259
10
15 100 347
16
10. ln
..
(i)
∆V = + −( ) ( )( ) ( )0 333 2 0 347 1 2 0 347. . .
or ∆V V= 0 156. (ii)
∆V = + −( ) ( ) ( )0 333 2 0 347 2 2 0 347. . .
or ∆V V= 0 269.
E11.18 C x V cmox = −1 73 10 7 2. / (a)
γ =− −
−
( )2 1 6 10 11 7 8 85 10 10
1 73 10
19 14 15 1 2
7
. . .
.
/x x
x
b g b gb g
or γ = 0 105 1 2. /V
(b) φ fp xV= =( ) FHG
IKJ0 0259
10
15 100 288
15
10. ln
..
(i)
∆V = + −( ) ( ) ( )0 105 2 0 288 1 2 0 288. . .
or ∆V V= 0 052. (ii)
∆V = + −( ) ( ) ( )0 105 2 0 288 2 2 0 288. . .
or ∆V V= 0 0888.
E11.19 C x V cmox = −1 73 10 7 2. /
gW
LC V Vm n ox GS T= −FH IK µ a f
= −( )( ) ( )−20 400 173 10 2.5 0 47. .xb g or g mA Vm = 2.91 /
Semiconductor Physics and Devices: Basic Principles, 3rd edition Chapter 11 Solutions Manual Exercise Solutions
166
Now
C
Cg RM
gdT
m L= + = + ( )( )1 1 2.91 100
or
C
CM
gdT
= 292
E11.20
fV V
LTn GS T=
−µ
π
a f2 2
=−( )( )
−
400 2.5 0 4
2 0 5 10 4 2
.
.π xb g
or f GHzT = 53 5.
