Formation and propagation of shock waves in the conduction channel of a field-effect-transistor structure

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Abstract
We consider the evolution of a nonuniform initial electron-density distribution in the conduction channel of a field-effect-transistor structure using a hydrodynamic description which is a reasonable approximation for devices with high electron densities and short gate lengths. We show that nonlinear terms in the hydrodynamic equations may lead to the formation of the shock waves in the quasi-two-dimensional electron gas in the conduction channel, and study how their propagation is affected by the boundary conditions on the source and drain sides of the channel. For the time-independent boundary conditions considered in this work, nonlinear effects such as shocks will decay with time as energy is dissipated at the shock front. However, these examples will help us to understand nonlinear effects in the response of two-dimensional electron gas to high-frequency signals. In that situation the nonlinear waves will persist even when dissipation is significant.