Theory of valence-band Auger line shapes: Ideal Si (111), (100), and (110)

We report independent-electron model calculations of the $L_{2,3}VV$ and $L_1{L}_{2,3}V$ Auger line shapes for ideal Si (111), (100), and (110) surfaces and compare the results to data of Houston, Lagally, and Moore. For the $L_{2,3}VV$ transitions, agreement between experiment and theory is excellent, in contrast to poor agreement between experiment and the self-fold of the occupied Si density of states; this result shows that matrix-element angular momentum dependence and not many-electron effects cause the latter discrepancy. For the $L_1{L}_{2,3}V$ lines our calculated results are less satisfactory. We suggest that the disagreement between theory and data for these "Coster-Kronig" transitions is due to the difficulty of calculating accurate Auger matrix elements at low energies and, perhaps, to the use of "ideal" (i.e., unreconstructed) surface geometries in modeling actual Si surfaces.