Hydrodynamic electron-transport model: Nonparabolic corrections to the streaming terms

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Abstract
This paper presents a hydrodynamic model suitable for studying hot-electron transport in semiconducting materials with nonparabolic conduction bands. The model presented is based upon a unique derivation of the moments of the Boltzmann-transport equation for the streaming (collision-independent) terms. This derivation implements an efficient and compact mathematical formalism appropriate for electrons under the influence of high electric fields and nonstationary conditions. The theoretical investigation also introduces a distributional form with nonparabolic properties to precisely define the resulting nonparabolic streaming parameters. The final set of model equations is exhibited in a fashion to clearly show the correction factors to the more familiar hydrodynamic model applicable for the constant-effective-mass case. In general, the hydrodynamic (or conservation) model contains pure transport terms that are treated as being independent of the specific dissipation mechanisms and collision terms to directly account for the influence of scattering. Since the collision terms are almost always treated phenomenologically using a relaxation-time approximation, our formulation of the streaming terms should significantly improve the overall accuracy of the approach. In addition, this paper presents the results of an extensive investigation of the assumed ansatz distribution and resulting nonparabolic-model parameters using an elaborate Monte Carlo model. The Monte Carlo technique was used to generate comparison electron distributions and exact values for the nonparabolic transport parameters for stationary and nonstationary electronic structures. In all cases, excellent agreement was found between the Monte Carlo–calculated parameters and the derived nonparabolic-model terms. The Monte Carlo calculations also revealed that the ansatz distribution used in the derivation represented a significant improvement over the more familar displaced Maxwellian. Therefore, this model should prove very valuable for studying electronic-device structures operating under high-bias conditions.