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From Global Balance to Local Non-Equilibrium
masses of Silicon according to the crystal direction. The relaxation time
is taken to be constant in (6.73). We may roughly estimate its value
τ = 5 × 10 – 14 s : this corresponds to an average electron mobility of
about 0.145 m ⁄ Vs , as is the case for low–doped silicon.
2
6.3 From Global Balance to Local Non-Equilibrium
The route from global to local equilibrium and further through different
length scales is best explained in the schematic diagram of Figure 6.7.
Level Description
Global balance Macromodel
Continuity
Local balance
equations
Length scale
Kinetics Boltzmann
equation
Quantum Schrödinger
mechanics equation
Figure 6.7. This diagram compares the transport theory levels with their respective equa-
tions. The ordering of the levels follow the applicable length scale.
Semiconductors for Micro and Nanosystem Technology 219
