ECE 875: Electronic Devices

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ECE 875Electronic Devices

• Prof. Virginia Ayres
• Electrical Computer Engineering
• Michigan State University
• ayresv_at_msu.edu

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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
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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 gt
0 OR U Re Gth lt 0
VM Ayres, ECE875, S14
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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 gt 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 gt OR lt
0 U lt 0 drives recombination U gt 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
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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
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Indirect bandgap material band-to-band
transitions in Si
EC
Note Recombining e- must have a momentum value
that matches the crystal momentum of the hole it
is dropping into. Indirect bandgap cant get a
match with the valence band
or
Et (ED or EA)
EV
VM Ayres, ECE875, S14
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Indirect bandgap material band-to-band
transitions in SiTwo 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
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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 NA- Electron occupies a local energy
level EA Note e- must be in local neighborhood.
Likelihood of capture described by a capture
cross section sn cm2
VM Ayres, ECE875, S14
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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
VM Ayres, ECE875, S14
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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
Non-radiative transitions
Et
sp
EV
OR A hole migrates into a bond at Et creating an
acceptor level. Then an e- drops 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
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Net transition rate U in Indirect bandgap
materialband-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
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Rec
What temperature is it and what does the crystal
E-k environment look like vth ?3kT/m
Whats the concentration of traps Nt
U
Whats the likelihood of an available e- in
EC/hole in EV
Whats the likelihood that Et already has an e-
/a hole in it
VM Ayres, ECE875, S14
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U
Sign of (pn ni2) determine whether there is net
recombination or net generation going on pn lt
ni2 - generation increases p and n pn gt
ni2 recombination decreases p and n
VM Ayres, ECE875, S14
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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. P and B are
not.
kT
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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
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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
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Reviewa pn junction operating in forward bias
Assume nondegenerate doping with T such that
saturation range operation is occurring
pp0 NA-
nn0 ND
pn0 ni2/nND
Lp
np0 ni2/pNA-
Ln
excess holes Dp
electrons Dn
VM Ayres, ECE875, S14
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ReviewLow level injection
pp0 NA-
nn0 ND
Minority carrier pn0 lt Dp lt majority carrier nn0
Minority carrier np0 lt Dn lt majority carrier pp0
pn0 ni2/nND
Lp
np0 ni2/pNA-
Ln
excess holes Dp
electrons Dn
VM Ayres, ECE875, S14
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ReviewHigh level injection requires external
energy e.g., laser light in W
Dn Dp
Dp gt majority carrier nn0
Dn gt majority carrier pp0
pp0 NA-
nn0 ND
pn0 ni2/nND
Lp
np0 ni2/pNA-
Ln
excess holes Dp
electrons Dn
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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
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Low level injection in an indirect bandgap
material
Assume Et Ei. Then
Proportional to trap concentration because most
carriers pass through trap
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COMPARE Low level injection in a direct bandgap
material
Proportional to carrier concentration from host
material doping
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High level injection (with laser light) in an
indirect bandgap material
Proportional to trap concentration because most
carriers pass through trap
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COMPARE High level injection (with laser light)
in a direct bandgap material
Proportional to light-generated carrier
concentration