ece 606 key equations5
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8/18/2019 ECE 606 Key Equations5
http://slidepdf.com/reader/full/ece-606-key-equations5 1/3
"#"$%&% '()*+, -&./.
!"!#$%$& ()* !+,-./012 3405 )6-7 89
'()*+, -&./01)2 34+567)89: ;4)54< =+*><)6*7?
:;*2/<-= <012.-1.2& '*@*A8+ B! C /&&DE! =1.055!10
"34J-s[ ]
N C = 3.23!10
19cm
-3
m0 = 9.109 !10
"31 kg[ ] N V = 1.83!10
19cm
-3
k B = 1.380 !10
"23J/K[ ]
ni = 1!10
10cm
-3
q =1.602!10
"19C[ ]
! 0 = 8.854 "10
#14F/cm[ ]
0*@@<) F+5*A<6G BH2@E IH2@J KH2@L MH2@N
O+,@< P<7Q<<+ 7Q8 (@1+<6G cos! =
h1h2 + k
1k 2 + l
1l 2
h1
2+ k
1
2+ l
1
2h2
2+ k
2
2+ l
2
2
'(1A*+, P<7Q<<+ 7Q8 (@1+<6G d = 1!
N = a h2+ k
2+ l
2
R*9< *+5<(<+5<+7 Q1>< <STG!!
2
2m0
"2# x( )" x
2 +U x( )# x( ) = E # x( ) ! x,t ( ) =" x( )e# i$ t
d 2! x( )dx
2 + k
2! x( ) = 0 k
2=
2m0
!2
E !U 0
"# $% ! x( ) = Ae± ikx
F+U*+*7< S41+749 Q<@@ 8U Q*57H: VG ! n =
!2k n
2
2m* =
!2n2"
2
2m*W
2 " C .: -: /: W
089<+749 8(<)178)G ˆ p ! !
i
"
" x "+<),? 8(<)178)G ˆ E = !
!
i
"
"t
;@1+< Q1><G ! x,t ( ) = ei ±kx"# t ( )
089<+749 8U (@1+< Q1><G p = !k
>)12/.* 04 2.-.)2 /1 ?#2@-<)&
.XG N k dk = 2! L 2" ( )dk = L " ( )dk
-XG N k d
2k = 2 ! A 2" ( )
2#$%
&'(d
2k = A 2"
2( )d 2k
/XG N k d 3k =2! " 8#
3( )d 3k = " 4# 3( )d 3k
>)12/.* 04 2.-.)2 /1 )1)5A* B1P8>< 7H< P87789 8U 7H< A8+54A7*8+ P1+5EG
.XG D1 D( E ) =
1
! !
2m D
*
E " E C
-XG D2 D
( E ) =m D
*
! !2
/XG D
3 D E ( ) =
m D
*( )3/2
2 E ! E C
( )"
2!
3
8/18/2019 ECE 606 Key Equations5
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"#"$%&% '()*+, -&./-
Y<)9* U4+A7*8+G f E ( ) =1
1+ e E ! E F ( ) k BT
!=)<.501 B)12/./)2& B ! F
= E F " E
C ( ) k BT EG
.XGn L
= N C
F !1/2
" F ( ) 9
$.
N
C
=
1
!
2m D
*k BT
! 9
$.
-XG nS = N
C F
0 !
F ( ) 9$- N
C =
m D
*k BT
! !2
"
# $%
& '
9$-
/XG n = N C F
1/2 !
F ( ) 9$/ N
C =
1
4
2m D
*k BT
! !2
"
# $%
& '
3/2
9$/
YX F+7<,)1@G F j !
F ( ) =1
" ( j +1)
! jd !
1+ e!#!
F
0
$
% Y8) " 1+ *+7<,<)G ! (n) = n"1( )!
Y8) +8+$*+7<,<) "G ! 1/ 2
( )= " 1+5 ! p +1
( )= p! p
( )
C@-<) <;-5A) 1),.5-=/.*G p ! n + N D+
! N A!
= 0
N D+
N D=
1
1+ g De E F ! E D( ) k BT
N A
!
N A=
1
1+ g Ae E A! E F ( ) k BT
D)<07E/1-./01&
Z15*17*><G R Rad = B np ! ni
2( ) O4,<)G R Aug = C nn np ! ni
2( )+ C p p np ! ni
2( )
'Z[G ! "n
"t SRH
= ! " p
"t SRH
= RSRH =
np! ni
2( )
# p n + n1( )+# n p+ p1( )
",55)1. )+,-./012G J n = nµ
n
dF n
dx J
n = nqµ
nE
x + qD
n
dn
dx D
n µ
n = k
BT q
J p = pµ
p
dF p
dx J
p = pqµ
pE
x ! qD
p
dp
dx D
p µ
p = k
BT q
C)7/<01B,<.05 !+,-./012&
!n!t
= "# i
!
J n
"q$ % &
' ( ) +Gn " Rn 0*+8)*7? #1))*<) X*UU46*8+ "S147*8+
! p!t
= "# i
!
J p
q$ % &
' ( ) +G p " R p !" p
!t = D p
!2" p
dx2 # "
p
$ p
+G L
0 = !" i #
!
E ( )+ $
L p = D
p! p
>/0B) !+,-./01G I D = qA
ni
2 D
n
N A L
n
+
ni
2 D
p
N D L
p
!
" #
$
% & e
qV A/k BT '1( ) B@8+,E
8/18/2019 ECE 606 Key Equations5
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"#"$%&% '()*+, -&.//
I D = qA
ni
2 Dn
N AW
P
+
ni
2 D
p
N DW
N
!
" #
$
% & e
qV A/k BT '1( ) B6H8)7E
F/@0=-5 .5-12/2.052&
! = I C I B
= N DE
N AB
Dn
D p
W E
W B
gm = ! I C
!V BE
= I C
k BT q( )
! = I En
I Ep + I En=
1
1+W
B
W E
niE
2
niB
2
N AB
N DE
I Cn
=! T I En
" I C
! T "1#
1
2
W B
Ln
$ % &
' ( )
2
I C =!
dc I E
! dc
=! T " !
dc =
" dc
1#" dc
t t =
W B
2
2 Dn
f T max =
1
2! t t
GHC !=)<.502.-./<2&
X<(@<7*8+ A8+5*7*8+6 B($7?(< 64P67)17<EG 0 <! S < 2!
F ! F =
k BT
qln
N A
ni
" # $
% & '
W D =
2! S " 0# S
qN A
E S =
2qN A! S
" s# 0 Q B = !qN AW D "
S ( ) Q B ! S ( ) = " 2q# s$ 0 N A! S
\17< >8@71,< >6T 64)U1A< (87<+7*1@ )<@17*8+G
!V G =" S #Q
S
" S ( )C
ox
C ox =! ox" 0 t ox QS ! S ( ) =Qn ! S ( )+Q B ! S ( )
Qn !
S ( ) = " # Si
k B
T n B
eq! S /2k BT
F+><)6*8+ A8+5*7*8+6G
W T =
2K S ! 0
qN A
2" F
#
$%
&
'(
1/2
!V G = 2" F #Q B
2" F ( )+Qn
C ox
!V T = 2" F #
Q B 2" F ( )
C ox
Qn = !C ox V G !V T ( )
GHC IJ <;-5-<.)5/2./<2 32+,-5) =-K9&
I D
=
W µ nC
ox
LV G !V
T ( )V
D !V D
2
2
"
#$
%
&' 0 !V
D <V
Dsat V
G !V
T
I D
=
W µ nC
ox
2 LV G !V
T ( )
2
V D !V
Dsat V
G !V
T