Asymptotic solution details for Boltzmann equation for a hole has a uniform electric field
n + - n = 0
Steps to solve Boltzmann equation <ref name="Huxley"> Huxley, L. G. H. Leonard George Holden, The diffusion and drift of electrons in gases, John Wiley and sons, 1974 , call number QC793.5.E628 H89 </ref>
for the previous equation let consider the asymptotic solution has the form:
In spherical coordinates:
which is symmetric in direction.
Assumingthe solution of the zenith angle direction is the Legendre polynomial, and can be written as:
The modified Bessel functions, first and second kind, are the solutions for the previous equation but the boundary conditions determines which one to use, in this case , , and as . so only the modified Bessel of second kind K_k are the non-zaro terms. so the the general solution for the equation can be written as :
The general form of the previous equation and its solution are defined as the following:
whereand are the modified Bessel of the first and the second kind.
The previous solution bcan be written as
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