Semiconductor Device Physics
Lecture 8
Dr.-Ing. Erwin Sitompul
President University
http://zitompul.wordpress.com
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Erwin Sitompul
SDP 8/1
Chapter 6
pn Junction Diodes: I-V Characteristics
Qualitative Derivation
Majority
carriers
Majority
carriers
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Chapter 6
pn Junction Diodes: I-V Characteristics
Current Flow in a pn Junction Diode
 When a forward bias (VA > 0) is applied, the potential barrier to
diffusion across the junction is reduced.
 Minority carriers are “injected” into the quasi-neutral regions
 Δnp > 0, Δpn > 0.
 Minority carriers diffuse in the quasi-neutral regions,
recombining with majority carriers.
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Erwin Sitompul
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Chapter 6
pn Junction Diodes: I-V Characteristics
Ideal Diode: Assumptions
 Steady-state conditions.
 Non-degenerately doped step junction.
 One-dimensional diode.
 Low-level injection conditions prevail in the quasi-neutral
regions.
 No processes other than drift, diffusion, and thermal R–G take
place inside the diode.
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Erwin Sitompul
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Chapter 6
pn Junction Diodes: I-V Characteristics
Current Flow in a pn Junction Diode
 Current density J = JN(x) + JP(x)
dn
d (n)
J N ( x)  qn nE  qDN
 q n nE  qDN
dx
dx
dp
d (p )
J P ( x)  qp pE  qDP
 q p pE  qDP
dx
dx
 JN(x) and JP(x) may vary with position, but J is constant
throughout the diode.
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Erwin Sitompul
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Chapter 6
pn Junction Diodes: I-V Characteristics
Carrier Concentrations at –xp, xn
 Consider the equilibrium carrier concentrations at VA = 0:
p-side
n-side
pp0 ( xp )  N A
nn0 ( xn )  N D
ni2
np0 ( xp ) 
NA
ni2
pn0 ( xn ) 
ND
 If low-level injection conditions prevail in the quasi-neutral
regions when VA  0, then:
pp ( xp )  NA
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nn ( xn )  ND
Erwin Sitompul
SDP 8/6
Chapter 6
pn Junction Diodes: I-V Characteristics
“Law of the Junction”
 The voltage VA applied to a pn junction falls mostly across
the depletion region (assuming that low-level injection
conditions prevail in the quasi-neutral regions).
 Two quasi-Fermi levels is drawn in the depletion region:
p  ni e( Ei  FP ) kT
n  ni e( FN  Ei ) kT
np  ni2e( Ei  FP ) kT e( FN  Ei ) kT
 ni2e( FN  FP ) kT
np  ni2eqVA
kT
for  xp  x  xn
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Chapter 6
pn Junction Diodes: I-V Characteristics
Excess Carrier Concentrations at –xp, xn
p-side
n-side
nn ( xn )  ND
pp ( xp )  NA
ni2 e qVA
pn ( xn ) 
ND
2 qVA kT
i
ne
np ( xp ) 
NA
 np0 e
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 pn0 e qVA
qVA kT
ni2 qVA
np ( xp ) 
(e
NA
kT
kT
 1)
ni2 qVA
pn ( xn ) 
(e
ND
Erwin Sitompul
kT
kT
SDP 8/8
 1)
Chapter 6
pn Junction Diodes: I-V Characteristics
Example: Carrier Injection
 A pn junction has NA=1018 cm–3 and ND=1016 cm–3. The
applied voltage is 0.6 V.
a) What are the minority carrier concentrations at the
depletion-region edges?
np (xp )  np0eqVA
pn ( xn )  pn0eqVA
kT
kT
 100  e0.6 0.02586  1.192 1012 cm3
 104  e0.6 0.02586  1.192 1014 cm3
b) What are the excess minority carrier concentrations?
np (xp )  np (xp )  np0  1.192 1012 100  1.192 1012 cm3
pn ( xn )  pn ( xn )  pn0  1.192 1014 104  1.192 1014 cm3
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Chapter 6
pn Junction Diodes: I-V Characteristics
Excess Carrier Distribution
 From the minority carrier
diffusion equation,
d 2 pn pn
0  DP

,
2
dx
p
x  0
 We have the following
boundary conditions:
pn ( xn )  pn0 (eqVA
pn ()  0
kT
1)
 For simplicity, we develop a
new coordinate system:
x
0
0
 Then, the solution is given
by:
 x LP
x LP
pn ( x)  Ae

A
e
1
2
for x  0
LP  DP p
• LP : hole minority
carrier diffusion length
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x
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SDP 8/10
Chapter 6
pn Junction Diodes: I-V Characteristics
Excess Carrier Distribution
 x '/ LP
x '/ LP
pn ( x)  Ae

A
e
1
2
 New boundary conditions
pn ( x  0)  pn0 (eqVA
pn ( x  )  0
kT
1)
 From the x’ → ∞, A2  0
From the x’ → 0, A1  pn0 (e
qVA / kT
1)
 x LP
 Therefore
qVA

pn ( x )  pn0 (e
kT
1)e
 Similarly,
np ( x)  np0 (eqVA
kT
1)ex LN , x  0
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Erwin Sitompul
, x  0
SDP 8/11
Chapter 6
pn Junction Diodes: I-V Characteristics
pn Diode I–V Characteristic
n-side
d pn ( x)
DP
J P ( x)  qDP
q
pn0 (eqVA
dx
LP
d np ( x)
DN
q
np0 (eqVA
p-side J N ( x)  qDN
dx
LN
J  JN
x  xp
 JP
x  xn
 JN
x 0
 JP
 DN
DP  qVA
J  qn 

 (e
 LN N A LP N D 
2
i
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Erwin Sitompul
kT
kT
kT
 1)e x LP
 1)e x LN
x 0
 1)
SDP 8/12
Chapter 6
pn Junction Diodes: I-V Characteristics
pn Diode I–V Characteristic
 DN
DP  qVA
I  AJ  Aqn 

 (e
 LN N A LP N D 
2
i
I  I 0 (e
 1)
DP 
2  DN
I 0  Aqni 


 LN N A LP N D 
qVA kT
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kT
 1)
• Shockley Equation,
for ideal diode
• I0 can be viewed as the drift
current due to minority
carriers generated within the
diffusion lengths of the
depletion region
Erwin Sitompul
SDP 8/13
Chapter 6
pn Junction Diodes: I-V Characteristics
Diode Saturation Current I0
 DP
DN 
I 0  Aqni 


L
N
L
N
N A 
 P D
2
 I0 can vary by orders of magnitude, depending on the
semiconductor material, due to ni2 factor.
 In an asymmetrically doped pn junction, the term associated
with the more heavily doped side is negligible.
 If the p side is much more heavily doped,
 DP 
I 0  Aqni 

L
N
 P D
2
 If the n side is much more heavily doped,
 DN 
I 0  Aqni 

L
N
 N A
2
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Chapter 6
pn Junction Diodes: I-V Characteristics
Diode Carrier Currents
• Total current density is
constant inside the diode
• Negligible thermal R-G
J  J N  JP
throughout depletion region
 dJN/dx = dJP/dx = 0
J N (  xp  x  xn )  J N ( xp )
J P ( xp  x  xn )  J P ( xn )
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Chapter 6
pn Junction Diodes: I-V Characteristics
Carrier Concentration: Forward Bias
 Law of the Junction
np  ni2eqVA
kT
 Low level injection
conditions
pp0
nn0
pp  N A
nn  N D
pn0
np0
Excess minority
carriers
np ( x)  np0 (e
qVA kT
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 x LN
1)e
Erwin Sitompul
Excess minority
carriers
pn ( x)  pn0 (eqVA
kT
SDP 8/16
1)e x LP
Chapter 6
pn Junction Diodes: I-V Characteristics
Carrier Concentration: Reverse Bias
 Deficit of minority carriers near the depletion region.
 Depletion region acts like a “sink”, draining carriers from the
adjacent quasineutral regions
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Chapter 6
pn Junction Diodes: I-V Characteristics
Deviations from the Ideal I-V Behavior
 Si pn-junction Diode, 300 K.
Forward-bias current
Reverse-bias current
“Slope over”
No saturation
“Breakdown”
Smaller slope
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Chapter 6
pn Junction Diodes: I-V Characteristics
Empirical Observations of VBR
 VBR decreases with
increasing N,
1
VBR  0.75
NB
 VBR decreases with
decreasing EG.
• VBR : breakdown voltage
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Dominant breakdown
mechanism is tunneling
Erwin Sitompul
SDP 8/19
Chapter 6
pn Junction Diodes: I-V Characteristics
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” and large reverse current will flow
ECR
2q  N A N D 


 Vbi  VBR 
S  NA  ND 
• At breakdown, VA=–VBR
 Thus, the reverse bias at which breakdown occurs is
VBR 
 SECR 2  N A  N D 

  Vbi
2q  N A N D 
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Chapter 6
pn Junction Diodes: I-V Characteristics
Breakdown Mechanism: Avalanching
High E-field:
High energy, enabling
impact ionization which
causing avalanche, at
doping level N < 1018 cm–3
E
2
CR
Small E-field:
2q  N A N D 


 VBR
S  NA  ND 
• ECR : critical electric field
in the depletion region
Low energy, causing
lattice vibration and
localized heating
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Chapter 6
pn Junction Diodes: I-V Characteristics
Breakdown Mechanism: Zener Process
 Zener process is the tunneling
mechanism in a reverse-biased diode.
 Energy barrier is higher than the
kinetic energy of the particle
 The particle energy remains
constant during the tunneling
process
 Barrier must be thin  dominant
breakdown mechanism when both
junction sides are heavily doped
 Typically, Zener process dominates
when VBR < 4.5V in Si at 300 K and
N > 1018 cm–3.
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Chapter 6
pn Junction Diodes: I-V Characteristics
Effect of R–G in Depletion Region
 R–G in the depletion region contributes an additional
component of diode current IR–G.
n
 qA 
dx
t thermal
 xp
xn
I R-G
R G
 The net generation rate is given by
np  ni 2
n

t thermal
 p (n  n1 )   n ( p  p1 )
R-G
( ET  Ei ) kT
n1  nie
p1  ni e( Ei ET ) kT
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• ET: trap-state energy level
Erwin Sitompul
SDP 8/23
Chapter 6
pn Junction Diodes: I-V Characteristics
Effect of R–G in Depletion Region
 Continuing,
np  ni 2
 qA 
dx
 (n  n1 )   n ( p  p1 )
 xp p
xn
I R-G
 For reverse bias, with the
carrier concentrations n and p
being negligible,
• Reverse biases with
VA< – few kT/q
I R-G
qAnW
i

2 0
p 
1 n
where  0   p 1   n 1 
2  ni
ni 
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Chapter 6
pn Junction Diodes: I-V Characteristics
Effect of R–G in Depletion Region
 Continuing,
np  ni 2
 qA 
dx
 (n  n1 )   n ( p  p1 )
 xp p
xn
I R-G
 For forward bias, the carrier
concentrations n and p cannot
be neglected,
qVA
IR-G  qAnWe
i
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Erwin Sitompul
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Chapter 6
pn Junction Diodes: I-V Characteristics
Effect of R–G in Depletion Region
I  I DIFF  I R G
Diffusion, ideal diode
I DIFF
I R-G
 DN
DP  qVA
 Aqn 

 (e
 LN N A LP N D 
2
i
kT
qVA kT
qAnW
(
e
 1)
i

2 0  V  V  n p
1  bi A
eqVA

kT q 2 0

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Erwin Sitompul
 1)

2 kT



SDP 8/26
Chapter 6
pn Junction Diodes: I-V Characteristics
Effect of Series Resistance
VJ  VA  IRS
q (VA  IRS ) kT
I  I 0e
 I 0eqVJ
kT
, VA  Vbi
Voltage drop,
significant for high I
RS can be determined
experimentally
V  IRS
slope=RS
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Chapter 6
pn Junction Diodes: I-V Characteristics
Effect of High-Level Injection
 As VA increases and about to reach Vbi, the side of the junction
which is more lightly doped will eventually reach high-level
injection:
nn  nn0
(for a p+n junction)
pp  pp0
(for a pn+ junction)
 This means that the minority carrier concentration approaches
the majority doping concentration.
 Then, the majority carrier concentration must increase to
maintain the neutrality.
 This majority-carrier diffusion current reduces the diode current
from the ideal.
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Chapter 6
pn Junction Diodes: I-V Characteristics
High-Level Injection Effect
Perturbation of both
minority and majority carrier
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Chapter 6
pn Junction Diodes: I-V Characteristics
Summary
Deviations from ideal I-V
Forward-bias current
Reverse-bias current
Due to high-level injection
and series resistance in
quasineutral regions
Due to thermal recombination
in depletion region
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Erwin Sitompul
Due to thermal generation in
depletion region
Due to avalanching and
Zener process
SDP 8/30
Chapter 5
pn Junction Electrostatics
Homework
 This time no homework. Prepare well for Quiz 2.
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