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Semi 4 Final Prob Sol 14
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Semi 4 Final Prob Sol 14
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Practice Test Papers 1 to 14 Sol
oooooooooooo
AccAud prob
acc aud
14.1
λ max
=
1.24
E g
(a) Si: λ max
µ m
=
(b) Ge: λ max
1.24 1.12 1.24
=
(c) GaAs: λ max
=
1.24 1.42
1.24
λ =
1.24 1.32
= 0.939 µ m
!" E = 1.90 e$# e$# 1.24 = 0.653 µ m λ = 1.90 _______________________________________
14.3
= ex'( − α d )
= 1 − 0.125 = 0.875 _______________________________________ ____________________________________ ___ 14.4
g ′ =
α I ( x )
hν
!" hν
1.24
λ =
= 1.3 e$#
1.3
= 0.95 µ m
!" siic!n: α ≅ 3 × 10 2 cm −1 *+en ,!" I ( x )
= 10
−2
-cm 2 # /e !bain
(3 ×10 )(10− ) (1.6 ×10 − )(1.3) 2
g ′ =
2
19
!" g ′ = 1.44 × 10 19 cm −3 s −1
*+e excess c!ncen"ai!n is
δ n !"
= g ′τ = (1.44 × 10 19 )(10 −6 ) 13
cm −3 _______________________________________ ____________________________________ ___
δ n
= 1.44 × 10
14.5
(a) λ =
1.24 1.65
= 0.752 µ m
(a) δ p
(i) "!m i%&"e 14.4# α ≅ 9 × 10 3 cm −1
I ν 0
"aci!n abs!"bed
1.24
= = 2.58 e$ λ 0.480 !" λ = 725 nm# 1.24 = 1.71 e$ E = 0.725 (b) !" E = 0.87 e$# e$# 1.24 1.24 = = 1.43 µ m λ = E 0.87 !" E = 1.32 e$# e$#
I ν ( d )
= ex' − ( 2.6 × 10 4 )( 0.80 ×10 −4 ) = 0.125
= 0.873 µ m
(a) !" λ = 480 nm# E =
(ii)
= 1.88 µ m
14.2
1.24
= 0.653 µ m
−1
= 1.11 µ m
0.66
=
1.90
(i) "!m i%&"e 14.4# α ≅ 2.6 ×10 4 cm
= 0.919 µ m 1.35 _______________________________________ (d) InP: λ max
1.24
(b) λ =
(ii)
I ν ( d ) I ν 0
g ′ =
= ex'( − α d )
= ex'[− (9 ×10 3 )()(1.2 × 10 −4 )] = 0.340 "aci!n abs!"bed = 1 − 0.34 = 0.66
= g ′τ p 0 ⇒ g ′ = 5 × 10 15 2 × 10
δ p τ p 0
= 2.5 × 10 22 cm −
3
−7
s
−1
!" hν
= 1.65 e$#
⇒ λ =
1.24 1.65
= 0.752 µ m
"!m i%&"e 14.4# α ≅ 9 × 10 3 cm −1
I ν 0
=
( g ′)() ( hν ) α
− ( )(1.65) 2.5 ×10 )(1.6 ×10 = 22
19
9 ×103
= 0.733 -cm 2
d 2 ( δ p n )
D p
dx 2
+ G L −
δ p n τ p
=0
!"
I ν ( d )
(b)
I ν 0
d 2 ( δ p n )
= 0.1 = ex'( − α d )
dx 2
[ (
0.1 = ex' − 9 ×10 d =
)( d ) ]
1 0.1
1 9 ×10
3
and +e %ene"ai!n "ae is
−4
= α Φ( x ) = α Φ O ex'( − α x )
G L
s! +e di,,e"enia e&ai!n bec!mes
14.6
1.24
λ =
E
=
1.24
d 2 ( δ p n )
= 0.886 µ m
1.40
(a)
d =
I ν 0 1
α
1 = 0.1
1 4.5 ×10
= 5.12 × 10
(b) d =
1 4.5 × 10
2
−3
2
cm =
1 0.1
)n
−
51 .2 µ m
1 0.3
)n
A x
D p
ex'( − α x )
*+en
− x α Φ Oτ p − = A ex' ⋅ ex'( − α x) 2 2 L p α L p − 1
= 0 # /e +ae d ( δ p n )
D p
GaAs: !" x = 1 µ m = 10 −4 cm# /e +ae 50 abs!"bed !" 50 "ansmied# +en
dx
x = 0
= sδ p n
x = 0
s! /e can /"ie δ p n
= 0.50 = ex'( − α x )
x = 0
= A −
α Φ Oτ p 2
2
α L p
−1
and
-e can /"ie
d ( δ p n )
1 1 = 1 ⋅ )n( 2 ) α = ⋅ )n x 0.5 10 − 4
dx
!"
α =
ΦO
α
Φ Oτ p ⋅ ex'( − α x ) 2 2 α L p − 1 As x → ∞ # δ p n = 0 s! +a B = 0 .
−3
14.7
I ( x ) I O
2
L p
=−
α
δ p n ( x )
cm = 26.8 µ m _______________________________________ = 2.68 × 10
δ p n
− x + B ex' + x = A ex' L p L p
δ p n ( x )
= 0.1 = ex'( − α d )
)n
−
*+e %ene"a s!&i!n is !, +e ,!"m
−1
I ν ( d )
2
dx
"!m i%&"e 14.4# α ≅ 4.5 × 10 2 cm
D p
D pτ p
L p =
/+e"e
G L
Φ( x ) = Φ O ex'( − α x )
cm = 2.56 µ m _______________________________________ = 2.56 × 10
L2 p
=−
*+e '+!!n ,&x in +e semic!nd&c!" is
)n
3
δ p n
−
x = 0
=
A − L p
+
Φ Oτ p 2 2 α L p − 1
α
2
*+en /e +ae 0.69 ×10 cm −1 4
*+is a&e c!""es'!nds ! λ = 0.75 µ m # E = 1.65 e$ _______________________________________ 14.8
*+e ambi'!a" "ans'!" e&ai!n ,!" min!"i ca""ie" +!es in sead sae is
−
AD p L p
+
Φ Oτ p D p sα Φ Oτ p = − sA 2 2 2 2 α L p − 1 α L p − 1
α
2
S!in% ,!" A# /e ,ind
A =
Φ Oτ p s + α D p ⋅ 2 2 s ( D L ) + α L p − 1 p p α
*+e s!&i!n can n!/ be /"ien as
δ p n ( x )
Φ Oτ p 2 2 α L p − 1 α
=
W + B sin+ + G Lτ n Ln S!in% ,!" B# /e !bain
s + α D p − x ex'( − α x ) × ⋅ ex' − s + ( D p L p ) L p _______________________________________ 14.9
B =
D n
-e +ae
d 2 (δ n p )
D n
dx 2
δ n p
+ G L −
Ln
=0
τ n
*+e s!&i!n is +en
!"
d (δ n p ) 2
dx 2
/+e"e Ln =
−
δ n p
=−
L2n
G L D n
D nτ n
=
x + B sin+ L + G Lτ n n !" s = ∞ a x = 0 means δ n p ( 0) = 0 .
*+en A x = W # d δ n p − Dn dx
= s o δ n p
W L n
c!s+
x =W
G Lτ n L n
W L n
sin+ B L n
W L n
c!s+
W BD n − L n L n
sin+
−3
cm
D D = eni2 n + p Ln N a L p N d −19
)(1.5 × 10 ) 10
2
−10
A
(a) I L = eG L AW -e ,ind
s! /e can /"ie
L n
!/ J S
= 8.950 × 10
+ G Lτ n D n
= 2.236 × 10
2
and
=−
= (10) (5 ×10 −7 )
25 10 × + 16 15 −3 −3 (5 ×10 )(10 ) ( 2.236 ×10 )(10 ) − J S = 1.790 ×10 10 Acm I S = AJ S = ( 5) (1.79 × 10 −10 )
x =W
W + B sin+ + G L τ n L n
dx
D pτ p 0
(
(W ) = −G Lτ n
d (δ n p )
=
= ( 25) (10 −6 ) = 5 ×10 −3 cm
= 1.6 × 10
!/ δ n p
Dnτ n 0
L p
⇒ A = −G Lτ n
x =W
14.10
x = A c!s+ L n
0 = A + G Lτ n
x sin+ B + L n
/+e"e B /as &s %ien. _______________________________________
Ln
x = G Lτ n 1 − c!s+ L n
δ n p ( x )
*+e %ene"a s!&i!n can be /"ien in +e ,!"m δ n p ( x )
W W + τ s o n c!s+ L − 1 L n n W W + c!s+ sin+ s o L n Ln
G L Ln sin+
W L n
c!s+
W = s o [ − G L τ n c!s+ Ln
(10 )(10 ) = ( 0.0259 ) )n = 0.6350 (1.5 ×10 ) 16
V bi
15
10
2
$
2 ∈ V W = s bi e
N a + N d N N a d
1. 2
2(11.7) (8.85 ×10 −14 )( 0.635) = −19 1.6 ×10
10 + 10 × 16 15 (10 )(10 ) 16
15
W =
1 2
= 120 × 10
9.508 ×10
−5
cm
(b)
= (1.6 ×10 −19 )(5 ×10 21 ) ( 5) (9.508×10 − = 0.380 A = 380 mA I V oc = V t )n1 + L I S
= 112 .75 mA P m = I mV m = (112.75 )( 0.412 ) = 46.5 m-
= I m R L ⇒ R L =
(d) V m
0.380 = ( 0.0259) )n 1 + −10 8.95 ×10 V oc = 0.5145 $ (c)
V oc V bi
=
0.5145 0.635
"!m P"!bem 14.10# I S
A
100 × 10
= 8.95 ×10 −10 A
I = V t )n1 + L I S
−3 10 ×10 = ( 0.0259) )n1 + −10 8.95 ×10
I = V t )n1 + L I S
−3
(i) V oc
= 8.95 ×10 −10
= 0.420 $
= 0.4847 $ V − 1 I = I L − I S ex' V t = 120 ×10
0.11275
(a)
120 ×10 −3 = ( 0.0259 ) )n1 + −10 8.95 ×10
0.412
14.12
14.11
(b)
I m
=
_______________________________________
_______________________________________
(a) V oc
V m
= 3.65 Ω
R L
= 0.810
"!m P"!bem 14.10# I S
−3
0.412 − (8.95 ×10 −10 ) ex' − 1 0.0259 ⇒ I m = 112.75 ×10 −3 A
*+en
I L
V = I L − I S ex' m − 1 V t
I m
= 1+
−3
V m
V t
(ii) 1 +
10 × 10
V m ex' V t
I L 1 = + I S
−3
8.95 × 10
−10 = 1.117 × 10
− 8.95 ×10
(c)
−10
V − 1 ex' V t
"ia and e""!"# V m !/
⇒ V = 0.4383 $ V m V m I L 1 + = + ex' 1 I S V t V t
= 1+
120 × 10
I m
8.95 × 10 −10
"ia and e""!"# V m !/
≅ 0.412 $
V = I L − I S ex' m − 1 V t = 10 × 10
−3
= 1.341 × 10
≅ 0.351 $
8
−3
0.351 − (8.95 ×10 −10 ) ex' − 1 0 . 0259 I m = 9.31× 10 −3 A = 9.31 mA
*+en
7
= I mV m = ( 9.31)( 0.351) = 3.27
P m m(b) (i)
J S
100 ×10 −3 = ( 0.0259) )n1 + −10 8.95 ×10
V oc
= 0.480 $ V m V m I L 1 + = + ex' 1 I S V t V t
(ii)
= 1+
100 ×10
−3
8.95 × 10
−10
= 100 × 10
8
I L
15
3.477 × 10
−1
0.891
10
16
3.478 × 10
−
0.950
10
17
3.484 × 10
−
1.01
10
18
3.539 × 10
−
J S
3.27
−3
/+e"e
= en
N d
τ p
D n τ n
+
18 5 ×10
−6
+
1
2
6 5 ×10
19
10
2
= 4.579 ×10 −12 A
-e +ae
V − I S ex' − 1 V t
1
D p
N d
τ p
I = 50 ×10
−3
V − ( 4.579 ×10 −12 )ex' − 1 V t
-e see +a /+en I = 0 #
V = V OC
= 0.599 $.
-e ,ind
/+ic+ bec!mes
J S
1 × N a
= (1.6 ×10 −19 )(1.8 ×10 6 ) 225 5 × 10 −8
+
−7
!"
30 ×10 = ( 0.0259) )n1 + J S J S
D p
= 2.289 ×10 −12 Acm
I = I L
J = V t )n1 + L J S
1 N a
1
/+ic+ bec!mes
I S
14.13
2 i
τ n
+
!"
= 11.7
_______________________________________
V OC
D n
= (1.6 ×10 −19 )(1.5 ×1010 )
1 × 16 3 ×10 J S
P m1
1 = eni2 N a
!"
= I mV m = ( 94.0) ( 0.407 ) = 38.3 38.3
1.07
= J L ⋅ A = ( 25 × 10 −3 )( 2) = 50 ×10 −3 A
−3
m-
10
J S
*+en
=
($)
-e +ae
0.407 − (8.95 × 10 ) ex' − 1 0.0259 −2 I m = 9.40 × 10 A = 94.0 mA
P m 2
V OC
(a)
≅ 0.407 $
−10
(c)
J S (Acm 2 )
N a (cm −3 )
V = I L − I S ex' m − 1 V t
P m
*+en
14.14
"ia and e""!"# V m !/
I m
6.708 ×10 4 = (5.184×10 − 7 ) + 1.183×10 −15 N a
_______________________________________
= 1.117 × 10
!"
1
7
10 19
5 × 10 −8
2
V ($) 0 0.1 0.2 0.3 0.4
I (mA) 50 50 50 50 49.98
0.45 0.50 0.55 0.57 0.59
49.84 48.89 42.36 33.46 14.19
P m m-
(b) *+e !a%e a +e maxim&m '!/e" '!in is ,!&nd ,"!m
(d) R L
→ (1.5)( 2.379 ) = 3.568 Ω
V
−12
3.568
10
= 1.092 × 10
A +is '!in# /e ,ind I m = 47.6 mA
!" P m
V = 180 × 10 −3 − ( 2 × 10 −9 ) ex' 0.0259
(c) -e +ae
I
=
I m
=
V
*+en I =
(a) V oc
V m
≅ 0.444 $
R L
=
0.444 3.568
= 0.1244 A
= (124.4 )( 0.444 ) = 55.2
14.16
= 24.8 mV
V = I L − I S ex' V t
m _______________________________________
= I mV m = ( 47.6)( 0.520 )
V = IR ⇒ R =
R L
P = IV
s! +e maxim&m '!/e" is
P m
V
"ia and e""!"# V
"ia and e""!"# V m = 0.520 $
= 2.379 Ω
0.169
!/
−3
4.58 ×10
I m
=
0.402
=
I =
50 ×10
V m
(c) R L
V m V m I L = + 1 1 + V ⋅ ex' V I S t t = 1+
= I m V m = (169 )( 0.402 ) = 67.9
= 0.5367 $ V m V m 1 + ex' V V t t
0.520 47.6 ×10 −3
100×10 −3 = ( 0.0259) )n1 + −10 10
(b)
!"
I L 1 = + I S
R = 10.9 Ω
= 1+
_______________________________________
100 ×10 10
14.15
(a) V oc
(b)
180×10 −3 = ( 0.0259) )n1 + −9 2 ×10
= 0.474 $ V m V m I 1 + ex' 1 + L = I S V t V t −3 180 ×10 = 1+ − 2 ×10 9
= 9 × 10
7
≅ 0.402 $
V ≅ I L − I S ex' m V t
0.402 = 180 × 10 −3 − ( 2 ×10 −9 ) ex' 0.0259 = 1.69 × 10
= 10
"ia and e""!"# V m *+en
−3
−10
9
≅ 0.461 $
0.461 = 100 ×10 −3 − (10 −10 ) ex' 0.0259
I m
= 9.463 × 10
−2
A = 94.63 mA
= I m V m = ( 94.63)( 0.461) = 43.62
P m m-
"ia and e""!"# V m
I m
−1
A = 169 mA
(c) n =
10
= 21.7 → n = 22 ces 0.461 (d) !/ V = ( 22 )( 0.461) = 10.14 $ P = IV 5.2
= I (10.14) ⇒ I = 0.5128 A
*+en n ′ =
0.5128 0.09463
= 5.42 → n′ = 6
(e) *+en I = ( 6 )( 0.09463)
= 0.5678 A
V
=
S! R L
=
10.14
= 17.86 Ω
*+en
I 0.5678 _______________________________________ 14.17
e x = 0 c!""es'!nd ! +e ed%e !, +e s'ace c+a"%e "e%i!n in +e ''e mae"ia. *+en in +e '"e%i!n
d (δ n p ) 2
D n
dx 2
+ G L −
δ n p τ n
=0
dx 2
−
δ n p
L2n
=−
G L D n
d (δ n p ) dx
2
−
2 n
L
=−
ΦO
α
D n
ex'( − α x )
− x + x δ n p ( x ) = A ex' L n + B ex' L n
Φ Oτ n ex'( − α x ) 2 α L n − 1 α
2
x → ∞
# δ n p
= 0 s! +a B = 0 .
*+en
− x α Φ Oτ n = A ex' − 2 2 ⋅ ex'( − α x ) L n α L n − 1 α Φ Oτ n -e as! +ae δ n p ( 0) = 0 = A − 2 2 # α L n − 1
δ n p ( x )
/+ic+ ieds α Φ Oτ n
A =
2
2
α L n
−1
-e +en !bain δ n p ( x )
=
1
Φ Oτ n − x α x − − ( ) ex' ex' 2 2 α L n − 1 L n Φ O is +e inciden ,&x a x = 0 . α
/+e"e _______________________________________ 14.18
!" 90 abs!"'i!n# /e +ae
Φ( x ) = ex'( − α x ) = 0.10 ΦO
2.3 µ
and ,!" hν *+en
x
m
= 2.0 e$# α ≅ 10 5 cm −
1
.
1 = 5 ⋅ )n (10) = 0.23 × 10 − 4 cm 10
!"
*+e %ene"a s!&i!n is !, +e ,!"m
As
= 10
1 = 4 ⋅ )n (10 ) = 2.3 × 10 − 4 cm 10
x =
δ n p
0.1
!"
= α Φ ( x ) = α Φ O ex'( − α x )
2
1
1 = ⋅ )n(10) α hν = 1.7 e$ # α ≅ 10 4 cm −
!" *+en
x
*+en /e +ae
−
x
/+e"e
G L
=
!"
!"
d 2 (δ n p )
ex'( + α x )
x =
0.23 µ
m _______________________________________
×
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