Theory of Auger Neutralization of Ions at the Surface of a Diamond-Type Semiconductor

Abstract

The two-electron, Auger-type transitions which occur when an ion of sufficiently large ionization energy is neutralized at the atomically clean surface of a diamond-type semiconductor are discussed. Consideration of the basic elements of the problem leads to a computing program which enables one to calculate the total electron yield and kinetic energy distribution of ejected electrons in terms of a number of parameters. It is possible to account for the experimental results for singly-charged noble gas ions incident on the (111) faces of Si and Ge and the (100) face of Si. The fit of theory to experiment is unique in its principal features yielding numerical results concerning: (1) the state density function for the valence bands of Si and Ge, (2) the energy dependence of the matrix element as it is determined by symmetry of the valence band wave functions, (3) the effective ionization energy near the solid surface, (4) energy broadening, and (5) electron escape over the surface barrier. Over-all width of the valence band is found to be 14-16 ev for both Si and Ge. Width of the degenerate $p$ bands is 5.1 ev in Si, 4.3 ev in Ge. The matrix element for $p$-type valence electrons is 0.3 times that for $s$-type valence electrons. Effective ionization energy is 2.2 ev less than the free-space value for 10-ev ${\mathrm{He}}^{+}$ ions and decreases linearly with ion velocity. Energy broadening is small for 10-ev ions and increases approximately linearly with ion velocity. Probability of electron escape is several times that predicted for an isotropic distribution of excited electrons incident on a plane surface barrier. A general theory of Auger neutralization is given in which the conclusions of the fit to experiment are interpreted. Investigation of the matrix element as a Coulomb interaction integral involving wave functions whose general characteristics are known but which are not explicitly evaluated leads to an understanding of its principal dependences on energy and angle.