Effect of electron-hole scattering on the current flow in semiconductors

Abstract

The effect of electron-hole scattering on transport in semiconductors has been considered from first principles. We conclude that the conventional equations for electron and hole currents are theoretically incorrect when electron-hole scattering is present. From thermodynamic considerations, we introduce the more general equations. A Boltzmann transport calculation including electron-hole scattering has been performed for Si. The key result is that the impact of electron-hole scattering depends primarily on the relative velocities of electrons and holes and therefore shows up differently in different device situations. Electron-hole scattering has the largest effect during conduction in high-level injection. This is because electrons and holes have net drift velocities in opposite directions. In contrast, electron-hole collisions have almost no effect on ambipolar diffusion because the carriers are moving in the same direction. Intermediate cases are also covered by this treatment. In low injection, electron-hole scattering serves to reduce the effective minority-carrier mobility. The degree of the reduction depends on whether the majority carriers are nearly static, as in diffusion situations, or whether they are flowing by drift, as in the Haynes–Shockley experiment.

Photoexcited carrier diffusion near a Si(111) surface: Non-negligible consequence of carrier-carrier scattering

“…3 Based on the reasoning that even though the initially fast moving electrons and slow moving holes tend to separate spatially, the separation quickly builds up an electric field between the opposite charges, which slows down the electrons and speeds up the holes to the same final speed. Consequently, electrons and holes diffuse at the same speed and carrier-carrier scattering is significantly reduced.…”

“…For example, it is well known both theoretically and experimentally that carrier mobility in semiconductor has strong density dependence, 4,5 which may well be true for ambipolar diffusion. However, totally different behaviors in carrier density dependence of ambipolar diffusivity have been predicted by theories, 2,3 which have yet to be confirmed by systematic experimental measurements.…”

“…2,3 However, even for the well-studied silicon, it is not well understood as to how these effects influence carrier transport properties such as diffusivity. For example, it is well known both theoretically and experimentally that carrier mobility in semiconductor has strong density dependence, 4,5 which may well be true for ambipolar diffusion.…”

Measuring photocarrier diffusivity near a Si(111) surface by reflective two-color transient grating scattering

“…14 In this case, theoretical calculation 15 based on the Einstein relation can account for the qualitative trend in Table I. However, Kane et al 16 have argued that electron-hole scattering should not affect the ambipolar diffusivity, since electrons and holes tend to move in pairs and not collide with each other. A calculation based on this assumption results in a less than 10% overall change in diffusivity, which is incompatible with the values in Table I.…”

Experiments on Minority Carrier Diffusion in Silicon: Contributions of Excitons

“…Their contributions in carrier transport have been discussed [3,4], but experiments on minority carrier diffusion including exciton contributions, especially at low temperatures (¡ 100K) had not been performed until now. There is also considerable discussion on Coulomb scattering effects in minority carrier mobility due to majority carrier flow [4,5,6], in Haynes-Shockley type experiments and in electron-hole plasma current transport, both effects must be considered. For minority carrier diffusion, matrix transport equations are not required, but in case of considerable exciton concentrations, a three-particle transport model is necessary [3].…”