ECE 875:
Electronic Devices
Prof. Virginia Ayres
Electrical & Computer Engineering
Michigan State University
ayresv@msu.edu
Lecture 11, 04 Feb 14
Chp. 01 – Chp. 02
Net transition rate U for:
Direct bandgap materials
Indirect bandgap materials
Deep level dopants/traps
Effect on Idiode: Review of low and high level injection:
Low level injection: pn junction without light
High level injection pn junction with light
Effect on Idiode: examples
VM Ayres, ECE875, S14
Direct bandgap material: band-to-band transitions in GaAs:
Recombination rate Re
EC
(photon or other)
EV
Generation rate Gth
Definition of net transition rate U:
U = Re – Gth
Averaged over a long time:
U = Re – Gth = 0
However: over short time(s) t:
U = Re – Gth > 0
OR
U = Re – Gth < 0
VM Ayres, ECE875, S14
Looking at the Recombination rate Re:
Re = Rec np = if mass actions holds: Rec ni2
- Concentration n of electrons in EC,
- Concentration p of holes in EV to take the e- Probability of spontaneous recombination Re
Looking at the Generation rate Gth:
Rec ni2 – Gth = 0
=> Gth = Rec ni2
Therefore: net transition rate U can be written:
U = Rec(pn – ni2) = Re – Gth
Expect: U = 0 but over short time(s) t, it can be > OR < 0
U < 0 drives recombination
U > 0 drives generation
When this matters: in transient situations when you try to turn a device
ON of OFF. We will consider this in the context of turning a diode (pn
junction ON, then OFF.
VM Ayres, ECE875, S14
Direct bandgap material: band-to-band transitions in GaAs:
Recombination rate Re
EC
(photon or other)
EV
Generation rate Gth
The net transition rate U
(# transitions / Vol s) is:
U = Rec(pn – ni2) = Re – Gth
Rec ≈ 10-10 cm3/s
VM Ayres, ECE875, S14
Indirect bandgap material: band-to-band transitions in Si:
EC
or
Et (ED or EA)
EV
Note:
Recombining
e- must have
a momentum
value that
matches the
crystal
momentum of
the hole it is
dropping into.
Indirect
bandgap =
can’t get a
match with
the valence
band
VM Ayres, ECE875, S14
Indirect bandgap material: band-to-band transitions in Si:
Two step process via an impurity energy level Et :
Recombination rate 01 Re01
EC
(other or photon)
Generation
rate 01 Gth01
or
Et (ED or EA)
Recombination rate 02 Re02
Generation
rate 02 Gth02
(other or photon)
EV
VM Ayres, ECE875, S14
Lecture 09:
Neutral ND
Electron occupies a local energy
level ED
Note: e- must be in local
neighborhood. Likelihood of
“capture” described by a capture
cross section sn: cm2
Ionized NAElectron occupies a local energy level
EA
Note: e- must be in local neighborhood.
Likelihood of “capture” described by a
capture cross section sn: cm2
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Lecture 09:
Ionized ND+
Local energy level ED is empty and
available
“capture” of a hole described by a
capture cross section sp: cm2
Neutral NA
Local energy level EA is empty and
available
“capture” of a hole described by a
capture cross section sp: cm2
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Recombination via a trap:
An e- drops into an acceptor impurity at Et creating an A- level. Then a hole
migrates into one of the nearby trap bonds. e- and hole interact and
annihilate.
EC
sn
sp
Non-radiative transitions
Et
EV
OR:
A hole migrates into a bond at Et creating an acceptor level. Then an edrops into the acceptor level at Et and annihilates the hole
sn and sp are electron and hole capture cross sections, roughly how good is
the trap at attracting e- or holes into the Et level.
VM Ayres, ECE875, S14
Net transition rate U in Indirect bandgap material:
band-to-band transitions in Si:
Recombination rate 01 Re01
EC
(other or photon)
Generation
rate 01 Gth01
or
Et (ED or EA)
Recombination rate 02 Re02
Generation
rate 02 Gth02
(other or photon)
EV
The net transition rate U (#transition/s) is:
U = Rec(pn – ni2) = Re – Gth
SLOWER: Rec ≈ 10-15 cm3/s
MORE COMPLICATED: Rec
VM Ayres, ECE875, S14
Rec
What temperature is it and what does the
crystal E-k environment look like:
vth = ✔3kT/m*
What’s the concentration
of traps Nt
U
What’s the likelihood of an available e- in EC/hole in EV
What’s the likelihood that Et already has an e- /a hole in it
VM Ayres, ECE875, S14
U
Sign of (pn – ni2) determine whether there is net recombination or net
generation going on:
pn < ni2
-
generation increases p and n
pn > ni2
+
recombination decreases p and n
VM Ayres, ECE875, S14
U
Net transition rate U is highest when denominator is smallest:
Et = Ei
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Net transition rate U is highest when denominator is smallest: Et = Ei
The Et = 0.54 eV level in Au is an efficient trap in Si that can be used for
recombination and generation that creates and maintain ni at a given
temperature.
kT
P and B are not.
VM Ayres, ECE875, S14
Useful trick from Units:
U
Therefore: time = Nt
|U|
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How deep level traps in Si influence applications:
1. Chp. 01. No E-field  electrons and holes do random motion. Note that
Dp and Dn in our discussions are in the neutral regions of the pn junction
device. Role of efficient mid-gap traps like Au in Si: maintain ni at a given kT.
One question to ask (Prs. 1.25-28): how much time is needed to achieve this
goal.
2. Chp 02: E-field in depletion region W. Deep level traps are a reservoir of
electrons and holes. When the number of carriers decreases in W during
change to OFF reverse bias, traps release carriers, so get opposing
generation current. When number of carriers increases in W during change
to ON forward bias, traps recombine out the attempt to re-establish the
diode current, so get opposing recombination current.
VM Ayres, ECE875, S14
Lecture 11, 04 Feb 14
Chp. 01 – Chp. 02
Net transition rate U for:
Direct bandgap materials
Indirect bandgap materials
Deep level dopants/traps
Effect on Idiode: Review of low and high level injection:
Low level injection: pn junction without light
High level injection pn junction with light
Effect on Idiode: examples
VM Ayres, ECE875, S14
Review:
a pn junction operating in forward bias:
Assume: nondegenerate doping with T such that saturation range
operation is occurring:
pp0 ≈ NAnn0 ≈ ND+
Lp
np0 ≈ ni2/p=NA-
Ln
pn0 ≈ ni2/n=ND+
excess holes: Dp
electrons: Dn
VM Ayres, ECE875, S14
Review:
Low level injection:
pp0 ≈ NAnn0 ≈ ND+
Minority carrier pn0 < Dp < majority carrier nn0
Minority carrier np0 < Dn
< majority carrier pp0
Lp
np0 ≈ ni2/p=NA-
Ln
pn0 ≈ ni2/n=ND+
excess holes: Dp
electrons: Dn
VM Ayres, ECE875, S14
Review:
High level injection: requires external energy: e.g., laser light in W:
Dn = Dp
Dn > majority carrier pp0
Dp > majority carrier nn0
pp0 ≈ NAnn0 ≈ ND+
Lp
np0 ≈ ni2/p=NA-
Ln
pn0 ≈ ni2/n=ND+
excess holes: Dp
electrons: Dn
VM Ayres, ECE875, S14
Evaluate U: within 1 diffusion length of the junction.
Example: on the n-side of a pn junction:
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Evaluate U: within 1 diffusion length of the junction.
Example: on the n-side of a pn junction:
Low level injection in an indirect bandgap material:
Assume: Et = Ei. Then:
Proportional to trap
concentration
because most
carriers pass
through trap
COMPARE: Low level injection in a direct bandgap material:
Proportional to carrier
concentration from
host material doping
High level injection (with laser light) in an indirect bandgap material:
Proportional to trap
concentration
because most
carriers pass
through trap
COMPARE: High level injection (with laser light) in a direct bandgap
material:
Proportional to
light-generated
carrier
concentration