Ideal Diode I-V characteristic
ECE 663
Real Diode I-V characteristic
ECE 663
Real Diode – Forward Bias (semi-log scale)
ECE 663
Real Diode – Reverse Bias
ECE 663
What’s wrong with this picture?
• Forward Bias
–
–
–
–
For V < 0.35 volts slope is kT/2q
For 0.35V < V < 0.7volts, slope is kT/q
For V > 0.7 volts, slope less than kT/q (V~Vbi)
I0 ~10-14A from intercept of semi-log plot in FB
ECE 663
What’s wrong with this picture?
• Reverse Bias
– Current ~103 times larger than FB I0
– Reverse current doesn’t saturate
– Breakdown – large current above Vbd
• Avalanche breakdown
• Zener (tunneling) process
ECE 663
Reverse Bias Avalanche Breakdown
Depletion width larger
than mean free path
lots of collisions
ECE 663
Avalanching
• Minority carriers accelerated by electric field in depletion
region
• The average energy lost per collision goes up as E field
(voltage) goes up (v = E )
• At some critical field (Ec), the average energy lost per
collision will be enough to “ionize” lattice atoms – knock out
more carriers
• Those carriers will also be accelerated by E>Ec and make
more carriers when they collide, etc…….
• Many collisions=huge multiplication in number of carriers=
avalanche breakdown
ECE 663
Max. Field
NAxp = NDxn
= WD/(NA-1 + ND-1)
Kse0Em = -qNAxp = -qNDxn
= -qWD/(NA-1 + ND-1)
Vbi = ½|Em|WD
Doping
Charge
Density
Electric
Field
Electrostatic
Potential
ECE 663
Maximum Field
Em = 2qVbi/kse0(NA-1+ND-1)
ECE 663
Avalanching
Vbi  VA  Vbi  VBR  VBR
Ec 
2
N A ND
2q
VBR 
K S e 0 N A  ND 
N A  ND
 VBR 
N A ND
VBR 
1
NB
One-sided junctions
ECE 663
Experimental Data on VBR
VBR 
1
NB
0.75
ECE 663
Zener Breakdown - Tunneling
Barrier must be thin:
depletion is narrow
doping on both sides
must be large
 2K S e 0 N A  ND 

Vbi  Vappl 
W 
ND N A
 q

Must have empty states
to tunnel into 
Vbi + VBR > EG/q
ECE 663
1
2
Zener diode I-V characteristic
ECE 663
Reverse bias R-G in the depletion region
n
 qA 
dx
 x t thermal
R G
xn
IR G
p
ECE 663
R-G Current
• In depletion region we don’t have low level injection because
number of carriers is small and injected carriers is large
np  ni2
n

t thermal
 p (n  n1 )   p ( p  p1 )
R G
np  ni2
 qA 
dx
 x  p (n  n1 )   p ( p  p1 )
xn
IR G
p
But, in depletion n,p  0
ECE 663




2
x
 ni
qAni
1


 qA 
dx  qAWni

W
p1 
 n1
2 0
 x  p n1   n p1



n
 pn

n

i
i 
n
IR G
p
p1  1
1  n1
 0    p   n    p   n 
2  ni
ni  2
But
 2K e N  ND 
Vbi  Vappl 
W  S 0 A
ND N A
 q

IR G 
Vreverse_ bias 1/ 2
0
1
2
Reverse bias current=lifetime
measurement
ECE 663
Forward Bias R-G
ECE 663
Forward Bias R-G current
np  ni2
 qA 
dx
 x  p (n  n1 )   p ( p  p1 )
xn
IR G
p
n and p cannot be neglected in the depletion region in FB so
the integral is not so easy as in RB.
pn nn  pn 0 nn 0e qV / kT  ni2e qV / kT
n1  p1  ni
n   p  0
ni2 e qV / kT  1
 qA 
dx
 x  0 (nn  pn  2ni )
xn
IR G
p
Estimate value of integral using maximum value of integrand = constant
ECE 663
Forward Bias R-G current
ni2 e qV / kT  1
 qA 
dx
 x  0 (nn  pn  2ni )
xn
IR G
p
Integrand maximum when n + p is minimum or n = p
nn pn  ni2e qV / kT
nn  pn  nn pn  ni e qV / 2kT
x
ni2 e qV / kT  1
 qA
 dx
qV / 2 kT
qV / 2 kT
 0 (ni e
 ni e
 2ni )  x
n
IR G
IR G
ni e qV / kT  1 W
 qA
2 0 (e qV / 2kT  1)
IR G
qAniW qV / 2kT

e
2 0
p
ECE 663
Ideality factor
I  I0e
qV / kT
ECE 663
Forward Bias with High Currents: High Level injection
np = ni2eqV/kT
n ~ p ≈ nieqV/2kT
Use in boundary condition
Forward Bias with High Currents: Series Resistance
I = I0[eqV/kT-1]
I = I0[eq(V-IRs)/kT-1]
ECE 663
Real Diode I-V curve summary
A.
B.
C.
D.
E.
Breakdown (VB~1/NB)
R-G RB (I~V)
R-G FB (slope~q/2kT)
High Level Inj.(slope ~ q/2kT)
Series Resistance – slope over
ECE 663
Narrow Base P-N junction Diode
P-side
N-side
np
pn
Lp
Ln
xp
xn
What happens if the diode is smaller than the minority carrier diffusion
length(s)?
Diffusion lengths can be 20-30 microns
ECE 663
dpn qDp pn 0 qV / kT
e  1
J p  qDp

dx
Wn
Similarly for Jn
qDn n p 0 qV / kT
e  1
Jn 
Wp
ECE 663
Total diode current
Jtotal
 qDn np 0 qDp pn 0  qV / kT
e
 Jn  J p  

 1

Wn 
 Wp
Compare to result from wide base ideal diode:
 qDn n p 0 qDp pn 0  qV / kT
e
J  

 1

Lp 
 Ln
 Replace minority carrier diffusion length with diode width
Ln  Wp
Lp  Wn
ECE 663
Charge control methodology
• Analyze by examining injected minority carrier charge:
• e.g. electrons injected into p side of FB diode
np
x  x / L
qV / kT
n p  n p  n p 0  n p 0 e
 1e
p
n
Ln  Dn  n
x
•
Total negative charge on p-side:
xp
 xp
Qtotal negative   n p ( x )dx  q  A

ECE 663
Charge control method
• Approximate total charge by diffusion length times charge
at boundary of QN-depletion regions:
Qtotalnegative  Ln np0 e qV / kT  1  q  A
• Non-equilibrium injected electrons with average lifetime of
n
• Recombination Rate=charge/time=current
 Ln n p 0  qV / kT
In  Q /  n  qA
 1  J n A
e
 n 

 Ln n p 0  qV / kT
Jn  q 
 1
e
 n 
ECE 663
Charge control
but
Dn  n
Ln
Dn
Dn
Dn




n
n
n
Dn  n Ln
 Dn np 0  qV / kT
Jn  q 
 1
e
 Ln 
Similarly for holes on the n-side:
 Dp pn 0  qV / kT
e
J p  q 
 1

 Lp 
ECE 663
Total current:
 Dn np 0 Dp pn 0  qV / kT
e
J  Jn  J p  q 

 1

Lp 
 Ln
• Same result as before but we didn’t have to solve the
minority carrier diffusion equations
• Stored charge and recombination = current needed to
resupply
ECE 663