Extrinsic Semiconductors Carrier Transporthadley/psd/lectures17/oct25.pdf · 2017-10-27 ·...
Transcript of Extrinsic Semiconductors Carrier Transporthadley/psd/lectures17/oct25.pdf · 2017-10-27 ·...
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Institute of Solid State PhysicsTechnische Universität Graz
Extrinsic Semiconductors
Carrier Transport
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http://www.synopsys.com
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Donors
Five valence electrons: P, As
States are added in the band gap just below the conduction band
Ec
Eg
Ev
ED
n-type: n ~ ND Many more electrons in the conduction band than holes in the valence band.
majority carriers: electrons; minority carriers: holes
D(E)
EF(T=0)
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Acceptors
Three valence electrons: B, Al, Ga
States are added in the band gap just above the valence band
Ec
Eg
Ev
EA
p-type: p ~ NA Many more holes in the valence band than electrons in the conduction band.
majority carriers: holes; minority carriers: electrons
EF(T=0)
D(E)
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Donor and Acceptor Energies
Energy below the conduction band Energy above the valence band
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B Dk T E
Temperature dependence
200
K
1000
KIntrinsic
Extrinsic p NA
Freeze-out
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exp gi v c
B
En N N
k T
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n-type
For n-type, n ~ density of donors, p = ni
2 /n
n-type ND > NA, p ~ 0
exp F cD c
B
E En N Nk T
ln cF c B
D
NE E k TN
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p-type
For p-type, p ~ density of acceptors, n = ni
2/p
p-type NA > ND, n ~ 0
exp v FA v
B
E Ep N Nk T
ln vF v B
A
NE E k TN
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Intrinsic / Extrinsic
Intrinsic: n = p
Conductivity strongly temperature dependent near room temperature
Extrinsic: n ≠ p
Conductivity almost temperature independent at room temperature
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exp2
gi v c
B
En N N
k T
Intrinsic semiconductors
intrinsicextrinsic
freeze-out
1/T
log 1
0(n i
) cm
-3
GaAs
Si
Ge
300 K
Extrinsic semiconductors
At high temperatures, extrinsic semiconductors have the same temperature dependence as intrinsic semiconductors.
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Why dope with donors AND acceptors?
collector base emitter
n pn+
lightly doped p substrate
Bipolar transistor
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MOSFET
Bipolar Junction Transistor
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Ionized donors and acceptors
For Ev + 3kBT < EF < Ec- 3kBT Boltzmann approximation
1 4exp
AA
A F
B
NNE E
k T
1 2exp
DD
F D
B
NNE E
k T
4 for materials with light holes and heavy holes (Si)2 otherwise
Mostly, ND+ = ND and NA
- = NA
ND = donor density cm-3 ND+ = ionized donor density cm-3
NA = donor density cm-3 NA- = ionized donor density cm-3
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Charge neutrality
n + NA- = p + ND
+
Carrier concentration vs. Fermi energy
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Calculating EF(T) numerically
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http://lamp.tu-graz.ac.at/~hadley/psd/L4/eftplot.html
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degenerately doped semiconductor
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Degenerate semiconductor
Heavily doped semiconductors are called degenerately doped
ND > 0.1 Nc -> EF in the conduction bandNA > 0.1 Nv -> EF in the valence band
Heavy doping narrows the band gap
The Boltzmann approximation is not valid
Degenerate semiconductors = metal
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Institute of Solid State Physics
Carrier Transport Technische Universität Graz
Ballistic transportDriftDiffusionGeneration and recombinationThe continuity equationHigh field effects
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Ballistic transport
dvF ma eE mdt
Electrons moving in an electric field follow parabolic trajectories like a ball in a gravitational field.
0eEtv vm
2
0 02eEtx v t x
m
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Classical equipartition:
At 300 K, vth ~ 107 cm/s.
Drift
2 312 2th Bmv k T
mean free path: = vthsc ~ 10 nm ~ 200 atoms
The electrons scatter and change direction after a time sc.
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Drift (diffusive transport)
<v0> = 0 <t - t0> = sc
* *sc
deE eEvm m v
, , d n n d p pv E v E drift velocity:
* * dvF eE m a mdt
0 0* ( )eEv v t tm
t0
t+t0v0
v
time between two collisions
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for Si: n = 1500 cm2/Vsp = 450 cm2/Vs
Drift
For E = 1000 V/cm vd = 106 cm/s
, , d n n d p pv E v E drift velocity:
* *sce e
m m v
, , d n d p n pj nev pev ne pe E E
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Drift
, , d n n d p pv E v E , , d n d p n pj nev pev ne pe E E
Solid state electronic devices, Streetman and B
anerjee