# Solution details

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# asymptotic solution details for Boltzmann equation for a hole has a uniform electric field

n + - n = 0

## Steps to solve Boltzmann equation

for the previous equation let consider the asymptotic solution has the form:

so

where

and

In spherical coordinates:

which is symmetric in direction.

Assuming the solution of the zenith angle direction is the Legendre polynomial, and can be written as:

and

so,

The modified Bessel functions, first I_k and second kind K_k, are the solution for the previous equation but the boundary conditions determines which one to use, in this case , , and as . so