Example 13.2: Screening effect of the electron cloud Consider the scattering of an electron by an ionized impurity atom in a semiconductor (see Sec. 13.3.4, case (ii)). Assume an exponential screening (due to the electron cloud) of the Coulomb potential and calculate the relaxation time τ.

[Hint: One can evaluate the integral



∞

0 sin αre−βrdr =

α

β2 + α2

, β>0, (13.69)

either by expressing sin αr in terms of exponentials, or by looking up a Table of Laplace Transforms].‡‡

‡‡See e.g. W. Magnus and F. Oberhettinger [40], p.125.