ELEC 3908, Physical Electronics, Lecture 12
pn Junction Reverse
Breakdown
Lecture Outline
• So far the diode model equation accuracy in forward and
reverse bias has been improved through incorporation of
more physical effects
• A new effect becomes important at higher values of
reverse bias, and is again not predicted by the model
equation
• This lecture describes impact ionization, a carrier
generating process which becomes more effective at higher
electric fields, and its application to reverse breakdown in
the pn-junction
• Last lecture’s results for increased electric field in reverse
bias are used in this lecture
ELEC 3908, Physical Electronics:
pn Junction Reverse Breakdown
Page 12-2
Measured Reverse Bias Characteristic
•
Measured characteristic shows
an abrupt increase in current
magnitude in reverse bias nothing in ideal diode model to
account for this
I D = I S (e qVD / nkT − 1)
ELEC 3908, Physical Electronics:
pn Junction Reverse Breakdown
Page 12-3
Reverse Bias - Applied Electric Field
•
•
•
Diagram to right shows junction
at equilibrium
Reverse bias raises potential of
n with respect to p
A reverse bias therefore creates
an electric field which adds to
the existing electric field in the
junction
ELEC 3908, Physical Electronics:
pn Junction Reverse Breakdown
Page 12-4
Reverse Bias Excess Charge Density
•
•
The extra electric field must be supported by an increased amount of
charge
The doping levels cannot change, therefore the extent of the depletion
region into each material must increase
ELEC 3908, Physical Electronics:
pn Junction Reverse Breakdown
Page 12-5
Reverse Bias Electric Field Distribution
•
•
The slope of the electric field distribution is ∝ ρ
Since doesn’t change, the slope of E is constant
•
The widening of the depletion region therefore corresponds to the
increased electric field
ELEC 3908, Physical Electronics:
pn Junction Reverse Breakdown
Page 12-6
Reverse Bias Potential Distribution
•
•
Potential is the -ve integral of electric field, so as electric field
increases the area, and hence the total potential drop, increases
This is consistent with the applied reverse bias potential causing the
increased electric field (E adds, and so does ψ)
ELEC 3908, Physical Electronics:
pn Junction Reverse Breakdown
Page 12-7
W and Edeplmax Field for Reverse Bias
• Because electric field and potential add to the existing built
in condition, the previous (equilibrium) equations for W
and Edeplmax can be modified by adding the reverse bias
potential to the built in potential
• Reverse bias VD is defined to be -ve, so subtract VD
W=
Edepl max
2ε Si ⎛ 1
1 ⎞
+
⎜
⎟ (Vbi − VD )
q ⎝ NA ND ⎠
2q ⎛ N D N A ⎞
=−
⎜
⎟ (Vbi − VD )
ε Si ⎝ N D + N A ⎠
ELEC 3908, Physical Electronics:
pn Junction Reverse Breakdown
Page 12-8
Impact Ionization
•
Impact ionization refers to the generation of an electron hole pair by a
collision between a free electron and another valence electron
ELEC 3908, Physical Electronics:
pn Junction Reverse Breakdown
Page 12-9
Avalanche Multiplication
•
•
When repeated impact ionization leads to the formation of many
electron hole pairs, avalanche breakdown occurs
Current becomes extremely sensitive to bias
ELEC 3908, Physical Electronics:
pn Junction Reverse Breakdown
Page 12-10
Ionization Probabilities
•
•
•
Process characterised in terms of ionization coefficients
Coefficient k is probability that carriers generated by impact ionization
at step k-1 will themselves generate further pairs by impact ionization
Probability*population is the expected value at step k:
nii1 = p1n ,
•
nii 2 = p 2 nii1 = p 2 p1n ,
nii3 = p 3 nii 2 = p 3 p 2 p1n , K
The total density is the original plus all generated by impact ionization
nii = n + nii1 + nii 2 + nii3 + K = n (1 + p1 + p 2 p1 + p 3 p 2 p1 + K )
•
Individual coefficients are sometimes used, but often all pk are
assumed equal to a value pii, so that
⎛ 1
nii = n 1 + p ii + p ii2 + p ii3 + K = n ⎜⎜
⎝ 1 − p ii
(
)
ELEC 3908, Physical Electronics:
pn Junction Reverse Breakdown
⎞
⎟⎟
⎠
Page 12-11
Multiplication Factor
•
The avalanche multiplication
factor is then defined as
1
M≡
1 − pii
•
For low ionization probability
pii, Mii ≈ 1, i.e. very little
multiplication
As pii increases, 1 - pii falls, and
Mii therefore increases
When pii approaches 1, Mii
becomes large - this is impact
ionization becoming quite
likely, therefore a large current
multiplication occurs
•
•
ELEC 3908, Physical Electronics:
pn Junction Reverse Breakdown
Page 12-12
Ionization Probability Model and VBR
• The probability(ies) pii is(are) very difficult to predict
• Widely used empirical model relates pii to the maximum
electric field in the junction and a critical field Ecrit
⎛E
depl max
⎜
pii ≈
⎜ Ecrit
⎝
⎞
⎟
⎟
⎠
3→ 6
• Breakdown defined as E → Ecrit, with pii → 1, M → ∞
• The corresponding breakdown voltage VBR is then
VBR
2
ε Si
E crit
= Vbi −
2q
⎛ 1
1 ⎞
⎜⎜
⎟⎟
+
⎝ ND NA ⎠
ELEC 3908, Physical Electronics:
pn Junction Reverse Breakdown
Page 12-13
Example 12.1: Ionization Probability
A diode has a saturation current of 3x10-10 A and an
ionization probability model exponent of 3. What
proportion of the critical field does the maximum depletion
field have to be in order to cause 10nA of reverse
breakdown current to flow through the junction?
ELEC 3908, Physical Electronics:
pn Junction Reverse Breakdown
Page 12-14
Example 12.1: Solution
• The reverse current of 10nA is larger than the saturation
current 4x10-10 by the multiplication factor Mii
10 × 10 −9
M ii =
.
−10 = 3333
3 × 10
• From this value, the ionization probability can be found as
1
M ii
M ii =
→ pii =
= 0.971
1 − pii
1 + M ii
• This corresponds to a maximum depletion electric field of
⎛E
depl max
pii = ⎜
⎜ Ecrit
⎝
3
⎞
⎟ → E
3
=
E
⋅
0.971 = 0.99 ⋅ Ecrit
depl max
crit
⎟
⎠
ELEC 3908, Physical Electronics:
pn Junction Reverse Breakdown
Page 12-15
Lecture Summary
• Impact ionization is a process in which carriers accelerated
by an electric field can generate electron hole pairs through
collision with valence band electrons
• For larger values of electric field, which are found in the
depletion region of the pn junction in reverse bias, impact
ionization can become significant enough to generate a
large number of carriers and cause considerable current
flow, contrary to the prediction of the ideal diode equation
• Reverse breakdown can be characterised by the reverse
bias required to cause a probability of impact ionization
close to 1, leading to a very large multiplication factor
ELEC 3908, Physical Electronics:
pn Junction Reverse Breakdown
Page 12-16