semiconductor device physics lecture 8 pn junction diodes: i-v characteristics dr. gaurav trivedi,...
TRANSCRIPT
Semiconductor Device Physics
Lecture 8PN Junction Diodes: I-V Characteristics
Dr. Gaurav Trivedi,EEE Department,
IIT Guwahati
Empirical Observations of VBR
Dominant breakdown mechanism is tunneling
BR 0.75B
1 V
N
• VBR : breakdown voltage
VBR decreases with increasing N,
VBR decreases with decreasing EG.
Charge Control Approach
P
n p n n
( )
n P np( )
1J
x J x x
dqA p dx A d qA p dx
dt
J
P
P n
( )
P P P n
( )
( ) ( )J
J x
A d A A x
J J J
P PP n
p
( )dQ Q
A xdt
J 0 In steady state
QP QP
Integrating over the n quasineutral region (after all terms multiplied by Adx),
Furthermore, in a p+n junction,
So:
P n( )A x J0
Charge Control Approach
NN p
n
( )Q
I x
P PP n
p
( ) 0dQ Q
A xdt
J
In steady state, we can calculate pn junction current in two ways: From slopes of Δnp(–xp) and Δpn(xn) From steady-state charges QN and QP stored in each “excess minority charge
distribution”
Therefore,
Similarly,
PP n P n
p
( ) ( )Q
A x I x
J
Charge Control Approach
N p( ) 0x J
P PDIFF
p
dQ Qi
dt
DIFF P n( )xJ J
0 In steady state
Moreover, in a p+n junction:
Narrow-Base Diode
0x 0 x
cxnx
n-side contact
cx
Narrow-base diode: a diode where the width of the quasineutral region on the lightly doped side of the junction is on the order of or less than one diffusion length.
px
Narrow-Base Diode I–V
An n0( 0) ( 1)qV kTp x p e
P Pn 1 2( ) x L x Lp x Ae A e
A
c P c P
n0 1 2
1 2
( 1)
0
qV kT
x L x L
p e A A
Ae A e
We have the following boundary conditions:
n c( ) 0p x x
Then, the solution is of the form:
Applying the boundary conditions, we have:
Narrow-Base Diode I–V
cc P cc P
A
cc P cc P
( ) ( )/
n n0 c( ) ( 1) , 0x x L x x L
qV kTx L x L
e ep x p e x x
e e
A c Pn n0 c
c P
sinh ( )( ) ( 1) , 0
sinhqV kT x x L
p x p e x xx L
Solving for A1 and A2, and substituting back:
Note that sinh( ) , cosh( )2 2
e e e e
The solution can be written more compactly as
Narrow-Base Diode I–V
A c Pn n0
c P
( )( ) ( 1)qV kT x x L
p x p ex L
An n0
c
( ) ( 1) 1qV kT xp x p e
x
With decrease base width, xc’0:
02
0
limsinh( )
lim cosh( ) 12
• Δpn is a linear function of x due to negligible thermal R–G in region much shorter than one diffusion length• JP is constant
• This approximation can be derived using Taylor series approximation
Narrow-Base Diode I–V
Because , then
A P c PP P n0
c P
1 cosh ( ) ( 1)
sinhqV kT L x x L
qD p ex L
J
nP P
( )p xqD
x
J
A
2c PP i
DIFF PP D c P
cosh( )( 0) ( 1)
sinh( )qV kT x LD n
I A x qA eL N x L
J
2c PP i
0P D c P
cosh( )
sinh( )
x LD nI qA
L N x L
ADIFF 0 ( 1)qV kTI I e
Then, for a p+n junction:
Narrow-Base Diode I–V
2 2P i P P i
0P D c c D
D n L D nI qA qA
L N x x N
2c P
c P
( )1
2( )
x L
x L
If xc’ << LP,
02
0
limsinh( )
lim cosh( ) 12
c PP
c
( )
2
x LL
x
P
c
L
x
c P
c P
cosh( )
sinh( )
x L
x L
Resulting
Increase of reverse bias means• Increase of reverse current• Increase of depletion width• Decrease of quasineutral region xc’=xc–xn
Wide-Base Diode
A c Pn n0
c P
sinh ( ) /( ) ( 1)
sinh /qV kT x x L
p x p ex L
c P c P
A
c P c P
( ) ( )
n n0( ) ( 1)x x L x x L
qV kTx L x L
e ep x p e
e e
A Pn n0( ) ( 1)qV kT x Lp x p e e Back to ideal
diode solution
Rewriting the general solution for carrier excess,
For the case of wide-base diode (xc’>> LP),
pc P c PP
A
c P c P
// //
n0 ( 1)x Lx L x Lx L
qV kTx L x L
e e e ep e
e e
Wide-Base Diode
A
2c PP i
DIFFP D c P
cosh( )( 1)
sinh( )qV kT x LD n
I qA eL N x L
A
2P i
DIFFP D
( 1)qV kTD nI qA e
L N Back to ideal
diode solution
Rewriting the general solution for diffusion current,
For the case of wide-base diode (xc’>> LP),
lim sinh( )2
lim cosh( )2
e
e
Small-Signal Diode Biasing
V0 << VA
RS : serial resistance
C : capacitanceG :
conductanceY : admittance
When reversed-biased, a pn junction diode becomes functionally equivalent to a capacitor, whose capacitance decreases as the reverse bias increases.
Biasing additional a.c. signal va can be viewed as a small oscillation of the depletion width about the steady state value.
Y G j C
Total pn Junction Capacitance
DCD
IC
kT q
sJC A
W
Junction / depletion capacitance,
due to variation of depletion charges
i
J DC C C av
1R G
Diffusion capacitance,due to variation of stored minority charges in the quasineutral regions
Minority carrier
lifetime
• CJ dominates at low forward biases, reverse biases.• CD dominates at moderate to high forward biases.