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EE130/230A Discussion 3
Peng Zheng
Conductivity of a Semiconductor
EE130/230A Fall 2013
n [qtmn / mn*] is the electron mobility p [qtmp / mp*] is the hole mobility
tmn ≡ average time between electron scattering eventstmp ≡ average time between hole scattering events
Mobility Dependence on DopingCarrier mobilities in Si at 300K
Lecture 4, Slide 3EE130/230A Fall 2013
Mobility Dependence on Temperature
impurityphonon 111
Lecture 4, Slide 4EE130/230A Fall 2013
Resistivity Dependence on Doping
Lecture 4, Slide 5
For n-type material:
nqn 1
For p-type material:
pqp 1
Note: This plot (for Si) does not apply to compensated material (doped with both acceptors and donors).
EE130/230A Fall 2013
R.F. Pierret, Semiconductor Fundamentals, Figure 3.8
Recombination-Generation (R-G) of Carriers in Silicon
EE130/230A Fall 2013
Recombination Processes
Direct R-G Center Auger
Recombination in Si is primarily via R-G centersLecture 5, Slide 7EE130/230A Fall 2013
R.F. Pierret, Semiconductor Fundamentals, Figure 3.15
Net Recombination Rate (General Case)
For arbitrary injection levels, the net rate of carrier recombination is:
kTEEi
kTEEi
np
i
TiiT enpenn
ppnn
npn
t
p
t
n
/)(1
/)(1
11
2
and where
)()(
Lecture 5, Slide 8EE130/230A Fall 2013
Electrostatics (Step PN Junction)
Band diagram:
Electrostatic potential:
Electric field:
)(1
refc EEq
V
dx
xdVx
)()(
dx
dE
qx c1)(
electrostatic potential V(x)
electric field ɛ(x)
potential energy PE(x)
kinetic energy KE(x)
Carrier concentration
Electron drift-current density and the electron diffusion-current density
x
x
x
x
x
x
kTEEnn iFi /)(exp
kTEEnp Fii /)(exp
nqJ ndriftN
)()( xJxJ NdriftNdiff