Lecture #18
OUTLINE
• pn junctions (cont’d)
– Deviations from the ideal I-V
 R-G current
 series resistance
 high-level injection
– Narrow-base diode
Reading: Chapter 6.2, 6.3
Spring 2007
EE130 Lecture 18, Slide 1
Effect of R-G in Depletion Region
• The net generation rate is given by
ni  np
p n


t t τ p (n  n1 )  τ n ( p  p1 )
2
where n1  ni e ( ET  Ei ) / kT and p1  ni e ( Ei  ET ) / kT
ET  trap - state energy level
• R-G in the depletion region contributes an
additional component of diode current IR-G
I R G
Spring 2007
p
 qA
dx
 x p t
R G
xn
EE130 Lecture 18, Slide 2
• For reverse bias greater than several kT/q,
I R G
qAniW
1  n1
p1 

where τ 0   τ p  τ n 
2τ 0
2  ni
ni 
I
n
Ip
Spring 2007
EE130 Lecture 18, Slide 3
• For forward biases,
I R G  qAniWe qVA / 2 kT
In
Ip
Spring 2007
EE130 Lecture 18, Slide 4
Effect of Series Resistance
Spring 2007
EE130 Lecture 18, Slide 5
High-Level Injection Effect
• As VA increases, the side of the junction
which is more lightly doped will eventually
reach HLI:
nn  nno
(p+n junction)
or
p p  p po (n+p junction)
 significant gradient in majority-carrier profile
Majority-carrier diffusion current reduces the diode
current from the ideal
Spring 2007
EE130 Lecture 18, Slide 6
Summary: Deviations from Ideal I-V
Forward-bias current
Spring 2007
Reverse-bias current
EE130 Lecture 18, Slide 7
Derivation of Narrow-Base Diode I-V
• We have the following boundary conditions:
pn ( x'  xc ' )  0
pn ( xn )  pno (e qVA / kT  1)
• With the following coordinate system:
NEW:
x'
0
0
x' '
x' c
• Then, the solution is of the form:
p ( x)  A1e
Spring 2007
x / L p
 A2 e
EE130 Lecture 18, Slide 8
 x / L p
Applying the boundary conditions, we have:
pn (0)  A1  A2
0  A1e
Therefore
xc' / L p
 A2 e
 xc' / L p
 e xc  x ' / LP  e  xc  x ' / LP
 1)
 e xc' / LP  e  xc' / LP

'
pn ( x' )  pn 0 (e
Note that
sinh   
pn ( x' )  pn 0 (e
Spring 2007
qVA / kT
qVA / kT
e e 
2
'

, 0  x'  xc'


so that

 , 0  x'  x
  
 sinh xc'  x' / LP
 1)
'
sinh
x
c / LP

EE130 Lecture 18, Slide 9
'
c
Excess Carrier Profiles: Limiting Cases
Long base (xc’):
pn ( x' )  pn 0 (e
Spring 2007
qVA / kT
 pn 0 (e
qVA / kT
 pn 0 (e
qVA / kT
 e x  x ' / L  e  x  x ' / L 


'
c
 1)


 1)e
P
e
e
 1)


'
c
xc' / LP
xc' / LP
 x '/ L p
EE130 Lecture 18, Slide 10
e
e
e
 x '/ L p
xc' / LP
P
 xc' / LP
e
e
 xc' / LP
 xc' / LP


e
x '/ L p




Narrow base (xc’0):
pn ( x' )  pn 0 (e
 p n 0 (e
qVA / kT
qVA / kT


 
  
 sinh xc'  x' / LP
 1)
'
sinh
x
c / LP


 xc'  x' / LP 

x' 
qVA / kT
  pn 0 (e
 1)
 1)1  ' 
'
 xc / LP 
 xc 
pn is a linear function of x
 Jp is constant (no recombination)
Spring 2007
EE130 Lecture 18, Slide 11
cosh  
pn ( x)
J P   qD p
x

J P  qD p pn 0 e
qVA / kT
 1



  L cosh xc  x  / LP 
1  P

sinh  xc / LP 





• For a p+n junction, then:
I  AJ P
 I 0 (e qVA
where
Spring 2007
x  0
kT
D p ni2 qVA
 qA
(e
LP N D
 1)
I  qA
'
0
e e 
2


DP ni 2 cosh xc' / LP
LP N D sinh xc' / LP


EE130 Lecture 18, Slide 12
kT
cosh xc / LP 
 1)
sinh xc / LP 
Note: sinh     as   0 and cosh   1   2 as   0
• If xc’ << LP:
2


cosh  xc / LP  1   xc / LP 
LP


xc / LP 
sinh  xc / LP 
xc
D p ni2
I 0  qA
LP N D
Spring 2007
D p ni2
 LP 
   qA
xc N D
 xc 
EE130 Lecture 18, Slide 13
Narrow (Short) Base Diode I-V Equation
Let WN  width of n - type region
WP  width of p - type region
and WN  WN  xn  LP
WP  WP  x p  LN
Then,
 DP
DN  qVA / kT
qVA / kT
I  qAni 

e
1  I0 e
1

WN N D WP N A 
2
Spring 2007

EE130 Lecture 18, Slide 14



Summary: Current Flow in pn Junctions
• The diode current is dominated by the term
associated with the more lightly doped side:
p+n diode:
2  DP 

qAni 
LP N D 

I 0  I P ( xn ) 
DP 
2

qAni 
 WN N D 
pn+ diode: I 0  I N ( x p ) 

2 D
qAni  N 
 LN N A 

2  DN

qAni 
 WP N A 
long n  side
short n  side
long p  side
short p  side
i.e. current flowing across junction is dominated by
carriers injected from the more heavily doped side
Spring 2007
EE130 Lecture 18, Slide 15