Distortion of the core exciton by the swift electron and plasmon wake in spatially resolved electron-energy-loss scattering

Abstract

Soft-x-ray-core to conduction-band absorption edges obtained by spatially resolved electron-energy-loss spectroscopy are systematically different from those obtained by x-ray-absorption or partial photo- yield techniques. I discuss here a hypothesis as to why this should be the case, and give a theoretical framework that explains the results. The Elliott theory for excitonic distortion of an absorption edge is modified to include the swift electron and its associated charge-density wake for electron-energy-loss scattering. Using a simple model potential in parabolic coordinates, Elliott’s effective-mass Schrödinger equation is solvable for envelope functions which describe the occupation of excited crystal Bloch states. A perturbation approach is then used to include important features of the wake which are not reproduced well in the analytically solvable model. The fleeting presence of the swift electron significantly affects the excitonic distortion when the exciton is weakly bound. In addition, the trailing charge-density wake anisotropically distorts the final-state envelope function. The excited state is found to extend several tens of nanometers behind the swift electron. Comparisons with experiment are shown for diamond, crystalline silicon, and silicon dioxide core edges.