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 10, 03 Feb 14
Chp. 01 Concentrations Nondegenerate Degenerate
Nondegenerate Intrinsic Contributed by
impurities Wanted impurities dopants Unwanted
impurities traps
Concentrations n
Effect of temperature
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Example Pr. 1.12
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Example Pr. 1.12
Need this
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Use
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General Info will use figure next slide to do
Pr. 1.12
Centripetal force Coulomb force
Average is defined as the harmonic mean not the
geometric mean. Used when E-field is present
P and B are shallow impurities in Si
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Tabulated can get EC ED _at_ 300 K from Sze Fig
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For P in Si EC ED 0.046 eV This is the
ionization energy Pr. 1.12 Given ionization
energy doesnt change as a function of T
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Have EC ED Need EF ED Note (EC ED)
(EC EF) EF ED Given ND 1016 cm-3
nondegenerate in Si Therefore use Sze (21)
Need NC _at_ 77K In App G NC _at_ 300K 2.8 x 1019
cm-3
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Use the ratio to something you know method
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Also kT at 77K
Plug and chug method
OR
Ratio to something you know method
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_at_ 77K 3.64 X 1018 cm-3
Thus far Sze (21)
Problem n ? ND 1016 cm-3 at 77K because not
all ND are ionized
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Important part NOT EQUAL
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Important step COMPARE
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Lecture 10, 03 Feb 14
Chp. 01 Concentrations Nondegenerate Degenerate
Nondegenerate Intrinsic Contributed by
impurities Wanted impurities dopants Unwanted
impurities traps
Concentrations n
Effect of temperature
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Summary concentration as a function of
temperature and dopingFor nondegenerate doping
(n-type Si shown in figure)
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Summary Freeze-out range concentration ?
partially ionized dopants
DONORS Neutral ND Electron occupies a local
energy level ED, h 1, gD 2 Ionized ND A
local energy level ED is empty and available
ACCEPTORS Neutral NA A local energy level EA is
empty and available Ionized NA- Electron
occupies a local energy level EA, h 1, gA 4

F(E) is probability of an electron occupying an
energy level E. If energy level E local level
ED (neutral ND) or local level EA (ionized NA-)
use
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Summary Intrinsic range concentration ?
partially ionized dopants
n
p
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Summary Saturation range concentration ? fully
ionized dopants AND some probability of
valence-to-conduction band transitions
Fully ionized dopants single doping n-type p
ni2/n, solve quadratic for n p-type n
ni2/p, solve quadratic for p
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Summary Intrinsic range concentration ? fully
ionized dopants AND high probability of
valence-to-conduction band transitions
n
pi ni
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Summary For all ranges Egap f(T) also f(P)
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Fig. 14 (a) Silicon (b not shown GaAs)
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Example
Sun-side for a LEO (low-earth orbit) satellite is
200oC 473 K. What doping concentrations cant
be used in Si electronics because all pn
junctions will act like intrinsic Si, causing
device inoperability?
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473 K
Answer n and p doping concentrations 1013 cm-3
and below cant be used.
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Lecture 10, 03 Feb 14
Chp. 01 Concentrations Nondegenerate Degenerate
Nondegenerate Intrinsic Contributed by
impurities Wanted impurities dopants Shallow
dopants Deep level dopants Unwanted impurities
traps
Concentrations n
Effect of temperature
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Donors and acceptors dont have to be
shallow. Many atoms can get into Si reason for
cleanrooms
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How to read graph
DONORS Neutral ND Electron occupies a local
energy level ED, h 1, gD 2 Ionized ND A
local energy level ED is empty and available
ACCEPTORS Neutral NA A local energy level EA is
empty and available Ionized NA- Electron
occupies a local energy level EA, h 1, gA 4

Above Ei read EC ED Below EI read EA - EV
Generally for single substitutional
impurities Donor Levels/two charge states ED
(neutral 0, positive 1) Acceptor levels/two
charge states EA (neutral 0, negative -1)
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Can have donor levels below Ei and acceptor
levels above Ei
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Pr. 1.16 (a) gold dopant/impurity Au
The acceptor level at EA-0.54 has two charge
states neutral 0 to start and -1 if it gets an
e-.
The donor level at ED-0.29 has two charge states
neutral 0 to start and 1 if it loses an e-
At start state of charge of the Au levels in
Si EA-.54 neutral 0 ED-.29 neutral 0
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Pr. 1.16 (a) Add neutral B to Au dopant/impurity
The acceptor level at EA-0.54 has two charge
states neutral 0 to start and -1 if it gets an
e-.
The donor level at ED-0.29 has two charge states
neutral 0 to start and 1 if it loses an e-
The acceptor level at EA-0.044 has two charge
states neutral 0 to start and -1 if it gets an
e-. It does get e- from the ED-0.29 donor level.
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Pr. 1.16 (a) After neutral B addition to Si with
Au dopant/impurities
The acceptor level at EA-0.54 is neutral 0 at
start and WHAT at finish
The donor level at ED-0.29 is neutral 0 at start
and WHAT at finish
The acceptor level at EA-0.44 is neutral 0 at
start and WHAT at finish
Neutrality is maintained overall.
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Pr. 1.16 (b) effect of Au impurities on electron
concentration n and hole concentration p, both
from Si
Consider what the acceptor level at EA-0.54 can
do with n from Si
Consider what he donor level at ED-0.29 can do
with p in Si
Result Si e- and holes that would have
participated in current I are both being tied up
(trapped) instead by the Au impurity levels.
They are NOT contributing to current I while they
are in traps.
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Effect on currents
1.5.4 Will show recombination and generation
due to deep level dopants has greatest effect on
ordinary current Ordinary current Current I is
in an assumed pn junction device
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1.5.4 Rate U is related to current I
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What is U Net transition rate driven by powerful
pn ni2 at thermal equilibrium
Fig 25 (a) matches Fig. 4 (b)
Note Recombining e- must have a momentum value
that matches the crystal momentum of the hole it
is dropping into. Direct bandgap OK all the
way to the valence band
Recombination with emission of photon Has a rate
Re
Generation with creation of e- hole pair Has a
rate Gthermal
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What is U Net transition rate driven by powerful
pn ni2 at thermal equilibrium
Fig 25 (a) matches Fig. 4 (b)
Recombination decreases both n and p by 1 Now pn
lt ni2 Think what if just recombination kept
going?
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What is U Net transition rate driven by powerful
pn ni2 at thermal equilibrium
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What is U Net transition rate driven by powerful
pn ni2 at thermal equilibrium
Fig 25 (a) matches Fig. 4 (b)
Recombination rate Re depends on having -
Concentration of electrons in EC, -
Concentration of holes in EV to take the e- -
Probability of spontaneous recombination Rec
Therefore Re Rec np Rec ni2
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What is U Net transition rate driven by powerful
pn ni2 at thermal equilibrium
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What is U Net transition rate driven by powerful
pn ni2 at thermal equilibrium
General
Specific
pn junction
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Evaluate U within 1 diffusion length of the
junction on the n-side of a pn junction
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Within 1 diffusion length Lp of the junction on
the n-side of a pn junction
Review For a pn junction with low level
injection Dp on n-side and Dn on p-side
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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