Ideal diode I-V characteristics )
1
(
/0
I e
qVA kTI
ifVA few kt/qI I
0e
qVA /kT
VAkT I q
I ln 0 ln
Ideal diode equation: assumptions
– The diode is being operated under steady state conditions
– A non-degenerately doped step junction models the doping profile
– The diode is one-dimensional
– Low-level injection prevails in the quasi-neutral regions – There are no processes other than drift, diffusion, and
thermal R-G taking place inside the diode, specifically, GL=0
Deviations from the ideal
breakdown
A I0,ideal 1014
VA
kT I q
I ln 0 ln
Reverse-bias breakdown
Although referred to as “breakdown”, it is a completely reversible process. no damage in the diode.
Breakdown voltage (VBR): the absolute value of the reverse voltage where the current goes off to infinity.
Practical VBR measurements typically quote the voltage where the current exceeds a preselected value such as 1 μA or 1 m A.
At a given doping, VBR tends to increase with EG.
For p+n or pn+ junctions, the VBR is roughly described by
75 . 0
1
B
BR N
V
where NB is the doping on the lightly doped side.
Reverse-bias breakdown
Si eV
G, 1.12 V
Ge eV
G, 0.66 V
GaAs eV
G, 1.42 V
Breakdown is directly related to the failure of the “no other processes” assumption in the ideal diodes.
In fact, two “other processes” can cause the breakdown current. “avalanche” and “Zener process”
Reverse-bias breakdown: avalanching
BR
A V
V
BR
A V
V
Energy-losing collisions with the lattice
lattice vibration
localized heating that is readily dissipated
Impact ionization
the added and original carriers make additional collision
carrier multiplication
avalanching
mean free path = ~10-6 cm
median depletion width = ~10-4 cm
Multiplication factor
0 reverse
I M I
Reverse-bias breakdown: Zener process
Zener process is the name given to the occurrence of “Band- to-band tunneling” in a reverse-biased diode.
From filled state to empty state Narrow barrier width (< ~10 nm)
Tunneling of electrons in V.B. to C.B.
at the same energy
The Zener process is important only in diodes which are heavily doped on both sides of the junction due to the narrow W.
) 2 (
A bi D
A D
A V V
N N
N N
W q
Avalanching v.s. Zener process
q VBR 4EG
when Zener breakdown
q V E
q
E G
BR
G 6
4
when Both avalanche and Zener
q VBR 6EG
when avalanche breakdown
Avalanche breakdown: higher VBR at higher Temp.
Zener breakdown: lower VBR at higher Temp.
Zener breakdown Both avalanche and Zener
avalanche breakdown
q EG 6
q EG 4
VBR
cf
The thermal R-G current
The “extra” current from the ideal at small forward biases and all reverse biases before the breakdown arises from thermal R- G processes in the depletion region.
The thermal R-G current
reverse forward
Thermal generation in the depletion region
Thermal recombination in the depletion region The slope for the forward thermal R-G current: q/2kT
Series resistance at high V
AWhen VA approaches Vbi, the assumption that all of the VA is dropped across the depletion region becomes questionable.
At current levels where IRs becomes comparable to VA, the applied voltage drop is reduced to
Junction voltage
Series resistance
S A
J V IR
V
) 1
( /
0
I eqVA kT I
bi
A V
V
kT qVJ
e I
I 0 /
kT IR
V
q A S
e
I0 ( )/
IRS
V
S
J
A V IR
V
V
High-level injection at high V
AThe low-level injection assumption begins to fail when the minority
carrier concentration approaches the doping concentration.
An analysis of high-level injection
leads to a predicted slope of q/2kT in a semi-log plot of the forward I-V
curve.
The enhanced carrier concentrations can reduce the observed series
resistance.
Avalanching and/or Zener process
Thermal generation In the depletion region
Thermal recombination in the depletion region
Ideal region (q/kT slope)
High-level injection (q/2kT slope) Series resistance
Announcements
• Next lecture: p. 477 ~ 487
• Homework: 6.2, 6.10, 6.18, 6.20
