Carrier scattering and ballistic transport

1. Carrier Scattering in Bulk Semiconductor Devices
Arpan Deyasi
RCCIIT, Kolkata
09-01-2022 Arpan Deyasi, Kolkata, India 1
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2. Carrier-carrier Scattering in Heavily Doped Semiconductor
Important in heavily doped semiconductors where impact ionization and Auger
processes are significant
scattering relaxation time
c c
t t th
1
N v
−
 =

Nt = density of total scattering centres
σt= total scattering cross section
vth = average thermal velocity
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3. Scattering from Ionized Impurity
Scattering of electrons by an ionized shallow donor impurity
Ni = density of ionized donor impurity
i
2
i
1 N

 
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4. Scattering from Neutral Impurity
We only consider elastic scattering
n
ni
1
N
 

Nn = density of neutral impurity
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5. Scattering from Dipoles
When acceptor and donor atoms in semiconductors are close together, they may
scatter electrons as a dipole instead of as individual monopoles.
Qd = is the dipole moment
N = the density of the dipoles
2
dipole 2
d
N
q

 
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6. Scattering from Acoustic Phonons: Deformation Potential
The acoustic-mode lattice vibrations induce changes in lattice spacing, which
induces a local fluctuation in the bandgap. The potential resulting from this
fluctuation is called the deformation potential.
1
dp 2
1
C
E
 
C1 = longitudinal elastic constant
E1 = deformation potential constant
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7. Scattering from Acoustic Phonons: Piezoelectric Potential
For polar semiconductors, bonds are partially ionic and the unit cell does not possess
inversion symmetry. A strain-induced electric field can be generated due to the
piezoelectric effect. The piezoelectric potential is thus generated by the acoustic-
mode lattice vibrations.
pp 2
P

 
P= piezoelectric coefficient
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8. Optical Phonon Scattering — Polar
Scattering from dipole moments formed by the interaction of the ionic charges
on atoms with optical-mode lattice vibrations is called the polar optical-mode
scattering process. This scattering mechanism is the dominant process in
semiconductors at a high temperature or a high electric field.
po
po
po
T Tpo
exp 1
T T
T
 
   
 
− 
 
 
   
 
 
 
 
 
Tpo = energy of longitudinal optical phonon
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9. Optical Phonon Scattering — Nonpolar
optical phonon modes produce fluctuations in the bandgap similar to those
produced by the acoustic phonon modes. Electrons are scattered by the deformation
potential produced by the optical phonon modes. This type of scattering is called
nonpolar scattering.
npo
0
1
D
 
D0 = deformation potential
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10. Scattering from Dislocations
Charge carriers (both electrons and holes) can be scattered from dislocations in
semiconductors. Dislocations may be considered as a line charge, and scattering
can be viewed as scattering from ionized impurity centres.
dis
d
1
N v
 
v = electron velocity
Nd = dislocation density
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What is Ballistic Transport?
When mean free path of carriers is longer than the dimension of the medium
through which they travel, then the corresponding carrier transport is defined
as ballistic in nature
L
 
When it occurs?
When carriers are moving under very high electric field with velocities than
the equilibrium thermal velocity
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Ballistic Effect
Carriers experiencing ballistic transport are free from scattering
Carrier motion is altered when only they collide with outer walls
Insignificant generation of heat owing to absence of electron-phonon interaction
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Where it is valid?
The model is valid in mesoscopic regime (between microscopic and atomic scale)
Mobility expression under Ballistic transport
bt *
th
2qL
m v
 =

B
th *
3k T
v
m
=
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Difference with Diffusive transport
Diffusive Transport Ballistic Transport
Phase incoherent Phase coherent
No size quantization Size quantization
No single electron charging effect Single electron charging effect
No spin effect Spin effect
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