Effects of final-state interactions on modulation spectra of semiconductors

Abstract

Theories of modulation spectra are critically reviewed with particular attention paid to the effects of final-state interactions (exciton effects). These interactions lead to the formation of bound exciton states and also strongly correlate the motions of unbound electrons and holes, resulting in optical absorption spectra that diner significantly from the square-root shapes predicted by the one-electron, independent-particle model. The shapes of the absorption spectra depend sensitively on the Coulombic nature of the electron-hole interaction and cannot be reproduced with a short-ranged contact-exciton model of the final-state interaction. These well-known differences between the one-electron theory and the Elliott exciton theory of optical absorption are accentuated by differentiation, leading (in most cases) to enormous differences between the modulation spectra predicted by the two theories. Experimental data generally confirm the predictions of the exciton theory and lend support to the claim that the final-state interactions exert a dominant influence on the sizes and the shapes of modulation spectra. For example, virtually all structures in the modulation spectra of semiconductors are due to exciton effects and lie at energies displaced from the critical points of the interband densities of states. The very nature of modulation spectroscopy, which measures small differences between large numbers, puts severe demands on any quantitative theory of modulation lineshapes. To date, no theory has met those demands in the sense that the theory has been able to accurately describe a measured lineshape without resorting to the use of one or more adjustable parameters. A simple, qualitative description of final-state interaction effects on electroabsorption spectra is presented, and it is demonstrated that these effects manifest themselves in observed spectra. The excitonic theory of electroabsorption is valid in the limit of weak broadening, a situation rarely achieved experimentally. To reduce the importance of broadening processes, which are especially prominent in weak or zero fields, both modulation fields should be large and uniform.