Calculation of knock-on sputtering cross sections

Abstract

Electrons in a TEM can be energetic enough to remove atoms from the exit surface of a sample. The probability of a collision imparting enough energy to dislodge an atom from the surface is expressed in terms of a cross-section which depends on the nuclear charge, the atomic mass, surface binding energy, and incident electron kinetic energy. McKinley and Feshbach have given an asymptotic relation for the Mott cross-section which has been widely used in studies of this process. However the expression is accurate only for low Z, and low incident electron energies (see Figure 1). Since modem TEMs often have accelerating voltages up to 300 or 400kV and occasionally over 1MV the assumption of low incident electron energies is not valid and the restriction to low Z is prohibitive.We have developed a program to evaluate numerically the total Mott cross-section. This program uses an algorithm like that described by Doggett and Spencer to evaluate two conditionally convergent Legendre series.