Prof. Yo-Sep Min Electronic Materials: Semiconductor Physics & Devices Chapt. 6 - Lec 14-1
Ideal diode I-V characteristics
)1(/
0 kTqVAeII
kt/qfew if AV kTqVAeII /
0
AVkT
qII 0lnln
Prof. Yo-Sep Min Electronic Materials: Semiconductor Physics & Devices Chapt. 6 - Lec 14-2
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
Prof. Yo-Sep Min Electronic Materials: Semiconductor Physics & Devices Chapt. 6 - Lec 14-3
Deviations from the ideal
breakdown
AI ideal
14
,0 10
AVkT
qII 0lnln
Prof. Yo-Sep Min Electronic Materials: Semiconductor Physics & Devices Chapt. 6 - Lec 14-4
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
BRN
V
where NB is the doping on the lightly doped side.
Prof. Yo-Sep Min Electronic Materials: Semiconductor Physics & Devices Chapt. 6 - Lec 14-5
Reverse-bias breakdown
eV Si G, 12.1V
eV Ge G, 66.0V
eV GaAs G, 42.1V
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”
Prof. Yo-Sep Min Electronic Materials: Semiconductor Physics & Devices Chapt. 6 - Lec 14-6
Reverse-bias breakdown: avalanching
BRA VV
BRA VV
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
IM
Prof. Yo-Sep Min Electronic Materials: Semiconductor Physics & Devices Chapt. 6 - Lec 14-7
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
Abi
DA
DA VVNN
NN
qW
Prof. Yo-Sep Min Electronic Materials: Semiconductor Physics & Devices Chapt. 6 - Lec 14-8
Avalanching v.s. Zener process
q
EV G
BR
4 when Zener breakdown
q
EV
q
E GBR
G 64 when Both avalanche and Zener
q
EV G
BR
6 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
EG6
q
EG4
VBR
cf
Prof. Yo-Sep Min Electronic Materials: Semiconductor Physics & Devices Chapt. 6 - Lec 14-9
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.
Prof. Yo-Sep Min Electronic Materials: Semiconductor Physics & Devices Chapt. 6 - Lec 14-10
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
Prof. Yo-Sep Min Electronic Materials: Semiconductor Physics & Devices Chapt. 6 - Lec 14-11
Series resistance at high VA
When 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
SAJ IRVV
)1(/
0 kTqVAeII
biA VV
kTqVJeII /
0kTIRVq SAeI /)(
0
SIRV SJA IRVVV
Prof. Yo-Sep Min Electronic Materials: Semiconductor Physics & Devices Chapt. 6 - Lec 14-12
High-level injection at high VA
The 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.
Prof. Yo-Sep Min Electronic Materials: Semiconductor Physics & Devices Chapt. 6 - Lec 14-13
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
Prof. Yo-Sep Min Electronic Materials: Semiconductor Physics & Devices Chapt. 6 - Lec 14-14
Announcements
• Next lecture: p. 477 ~ 487
• Homework: 6.2, 6.10, 6.18, 6.20
