The effect of excitons on apparent band gap narrowing and transport in semiconductors

Abstract

The interactions between electrons and holes are known to alter the energy levels in semiconductors. At high carrier densities, these interactions produce extended states that can be described by a carrier-induced band gap narrowing. Below the Mott density, this description is no longer valid and electron-hole interactions produce localized excitonic states. Excitons in Si have been thoroughly studied at low temperatures but they are usually ignored in semiconductor device operation. We have performed an analysis of the thermodynamics of excitons in Si below the Mott transition and find that the presence of excitons is expected to be significant at certain carrier densities, especially at 77 K. The electrical properties of semiconductors containing excitons are described and contrasted with the situation above the Mott transition where the conventional rigid band gap narrowing of extended states is valid. There are two key results. First, excitons mimic a rigid band gap narrowing in that they lead to an increase in the carrier density at a given voltage level. This occurs because as electrons occupy the excitonic states, the total electron density increases without increasing the density of electrons in the extended conduction band states. Second, excitons affect device transport and the result is different from the rigid band gap narrowing case. Since excitons can be mobile, they can contribute to diffusion. Because they are neutral, however, they cannot contribute to drift currents. In the extreme limit that all the carriers exist as excitons, there will be a finite ambipolar diffusion constant, but the conductivity mobility will drop to zero. Such an outcome is not possible within the framework of conventional device modeling. The necessary modifications are discussed.