Module 2 lecture 4

1. Semi-classical Bulk
Transport
Qualitative Model
Charge Transport in the Bulk of a Large Semiconductor
NAME: B.WARUN KUMAR
REGISTER NO. 17D113

2. Balances in the bulk of a Large Semiconductor
under Equilibrium
CARRIER BALANCE:
The statement that

3. Equilibrium value of Wn denoted as Wn0
 ENERGY BALANCE: No net flow of energy of any sort
 KE density of electrons(Wn)
 KE density of holes
 Energy density of phonons
 Energy density of photons in the semiconductor
 Energy density in the ambient

4.  To estimate the carrier motion, in general, carrier, momentum and energy, all
three balances need to be considered.
 However, momentum balance considerations are sufficient to identify the various
carrier transport mechanisms.
 Net e- flow or momentum from 1 to 2 due to imbalances in momentum density
because of:
n1 > n2 (diffusion) or
v1 > v2 due to
Ψ2 > Ψ1 (drift) or
T1 > T2 (thermoelectric current)

5. Saturation of e- Flow or momentum or velocity at
High Driving Forces
 Equilibrium High Driving Force
 (nmnv)1 = (nmnv)2 = nmnvth In the limiting case,
(nmnv)2 reduced to zero,
cannot go negative
(nmnv)1 doubled to 2nmnvth

6. Quasi-Equilibrium or Ohmic Regime of the Carrier Velocity versus
Driving Force Curve
Momentum balance:
 Carrier gain a momentum
density, p = n0F𝜏M0,

p ∝ F
 v = p!(n0mn)
 F ∝ ∇Ψ ,∇p,∇n,∇TL
 v versus ∇Ψ,∇p, ∇n, ∇TL
 is linear and currents
from

7. ENERGY BALANCE:
Carrier gain an energy
density = n0v.F𝜏E0 << Wn0
Wn ≈ Wn0
≈Energy density of phonons
≈Energy density of ambient
Negligible net flow of energy from carriers to phonons to
ambient
Scattering rate is unaffected, i.e. 𝜏M ≈ 𝜏MO , 𝜏E ≈ 𝜏E0

8. Non-Equilibrium or Velocity Saturated Regime of the Carrier
Velocity versus Driving Force Curve
Carrier balance:
G= g0 ,r = r0, › › n = n0
(Many not hold for very high f, e.G. Impact g at high e can increase g
and so

9. Momentum balance:
Carrier gain a momentum
density, p = n0F𝜏M0, where
𝜏M< 𝜏MO since 𝜏M decrease as energy
increase
p versus F tend to saturate
v = p/(n0mn)
F ∝ ∇Ψ ,∇p,∇n,∇TL
v versus ∇Ψ,∇p, ∇n, ∇TL also tends
to saturate .

10. Net flow of energy from carriers to phonons to ambient
Much change in Scattering rate is unaffected, i.e. 𝜏M and 𝜏E differ
very much 𝜏MO and 𝜏E0 due to increase in Wn
 ENERGY BALANCE:
 Carrier gain an energy
density = n0v.F𝜏E0 >> Wn0
Wn ≈ Wn0 + n0v.F𝜏E0 ≈ nv.F𝜏E
≈Energy density of phonons
≈Energy density of ambient

11. Analog illustrating Energy Balance Between Carriers and Phonons
 Liquid from the tap > Energy input from driving forces
 Height of the liquid > Energy density
 Holes in the bucket > phonon scattering

12. Concept of Carrier Temperature, Tc