Lecture #17
OUTLINE
• pn junctions (cont’d)
– Reverse bias current
– Reverse-bias breakdown
Reading: Chapter 6.2
Spring 2007
EE130 Lecture 17, Slide 1
Carrier Concentration Profiles: Forward Bias
Spring 2007
EE130 Lecture 17, Slide 2
Carrier Concentration Profiles: Reverse Bias
– Depletion of minority carriers at edges of depletion region
– The only current which flows is due to drift of minority carriers
across the junction. This current is fed by diffusion of minority
carriers toward junction (supplied by thermal generation).
Spring 2007
EE130 Lecture 17, Slide 3
Alternative Derivation of Formula for I0
“Depletion approximation”:
• I0 represents the rate at which carriers are thermally
generated within a diffusion length of the depletion region:
n p ni / N A
n


t
n
n
-LN -x p  x  -x p
p
n / ND
p
 n  i
t
p
p
xn  x  xn  LP
2
2
Spring 2007
 ni 2 / N D 
 ni 2 / N A 

  qALP 
I 0  qALN 





n
p




EE130 Lecture 17, Slide 4
Junction Breakdown
I
Forward Current
VBR
V
R
Small leakage
Current
A
P N
(a)
R
3.7V
Zener diode
IC
(b)
A Zener diode is designed to operate in the breakdown mode.
Spring 2007
EE130 Lecture 17, Slide 5
Breakdown Voltage, VBR
• If the reverse bias voltage (-VA) is so large that the
peak electric field exceeds a critical value eCR, then
the junction will “break down” (i.e. large reverse
current will flow)
e
CR

2qN Vbi  VBR 
es
• Thus, the reverse bias at which breakdown occurs is
VBR 
Spring 2007
e se CR
2qN
2
 Vbi
EE130 Lecture 17, Slide 6
Avalanche Breakdown Mechanism
High E-field:
VBR 
e
CR
e se CR
2
if VBR >> Vbi
2qN
increases slightly with N:
For 1014 cm-3 < N < 1018 cm-3,
Small E-field:
Spring 2007
105 V/cm <
EE130 Lecture 17, Slide 7
e
CR
< 106 V/cm
Tunneling (Zener) Breakdown Mechanism
VA = 0:
Ec
Ev
Dominant breakdown
mechanism when both
sides of a junction are
very heavily doped.
VBR 
e
VA < 0:
Filled States -
Empty States
Ec
Ev
Spring 2007
CR
e se CR
2qN
2
 Vbi
 106 V/cm
Typically, VBR < 5 V
for Zener breakdown
EE130 Lecture 17, Slide 8
Empirical Observations of VBR
• VBR decreases with
increasing N
• VBR decreases with
decreasing EG
Spring 2007
EE130 Lecture 17, Slide 9
Breakdown Temperature Dependence
• For the avalanche mechanism:
– VBR increases with increasing T, because
the mean free path decreases
• For the tunneling mechanism:
– VBR decreases with increasing T, because
the flux of valence-band electrons available
for tunneling increases
Spring 2007
EE130 Lecture 17, Slide 10
Summary
•
•
The minority-carrier concentrations at the edges of
the depletion region change with the applied bias VA,
qVA / kT
e
by the factor
The diode saturation current I0 is dominated by the
term associated with the more lightly doped side:
 DP 

p+ n diode: I 0  I P ( xn )  qAni 
 LP N D 
2
 DN 

p n+ diode: I 0  I N ( x p )  qAni 
 LN N A 
I0 can be viewed as the drift current due to minority
carriers generated within a diffusion length of the
depletion region
2
•
Spring 2007
EE130 Lecture 17, Slide 11
Reverse-bias breakdown:
• If the peak electric field in the depletion region exceeds
a critical value eCR, then large reverse current will flow.
This happens at a large negative voltage, called the
2
“breakdown voltage”:
e s CR
VBR 
e
2qN
 Vbi
where N is the dopant concentration on the more lightly doped side
•
The dominant breakdown mechanism is
avalanche, if N < ~1018/cm3
tunneling, if N > ~1018/cm3
Spring 2007
EE130 Lecture 17, Slide 12
Deviations from the Ideal I-V Behavior
Forward-bias current
Spring 2007
Reverse-bias current
EE130 Lecture 17, Slide 13