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

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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.