Abstract
Instabilities of electron plasma waves in high-mobility semiconductor devices have recently attracted a lot of attention as a possible candidate for closing the THz gap. Conventional moments-based transport models usually neglect time derivatives in the constitutive equations for vectorial quantities, resulting in parabolic systems of partial differential equations (PDE). To describe plasma waves however, such time derivatives need to be included, resulting in hyperbolic rather than parabolic systems of PDEs; thus the fundamental nature of these equation systems is changed completely. Additional nonlinear terms render the existing numerical stabilization methods for semiconductor simulation practically useless. On the other hand there are plenty of numerical methods for hyperbolic systems of PDEs in the form of conservation laws. Standard numerical schemes for conservation laws, however, are often either incapable of correctly handling the large source terms present in semiconductor devices due to built-in electric fields, or rely heavily on variable transformations which are specific to the equation system at hand (e.g. the shallow water equations), and can not be generalized easily to different equations. In this paper we develop a novel well-balanced numerical scheme for hyperbolic systems of PDEs with source terms and apply it to a simple yet non-linear electron transport model.
Highlights
In recent years instabilities of electron plasma waves in high-electron-mobility transistors (HEMT) have attracted a lot of attention as a possible solution for closing the THz gap [4,7,8]
By using balance equations derived from the Boltzmann Transport Equation (BTE) together with appropriate closure relations, models of arbitrary complexity can be specified [1,11]
It should be noted that this model can only serve as a rough approximation and is not sophisticated enough to model transport in nanoscale devices [23], especially in the case of high mobilities, that are necessary for plasma waves
Summary
In recent years instabilities of electron plasma waves in high-electron-mobility transistors (HEMT) have attracted a lot of attention as a possible solution for closing the THz gap [4,7,8]. The standard DD model is not able to capture plasma wave effects, because the time derivative in the current constitutive equation is usually neglected [16]. It should be noted that this model can only serve as a rough approximation and is not sophisticated enough to model transport in nanoscale devices [23], especially in the case of high mobilities, that are necessary for plasma waves (quasi-ballistic transport) We chose this model because it is simple due to its inclusion of only two moments of the distribution function, while it still contains some non-linearity and can describe plasma instabilities [7]. This alleviates the development and validation of a suitable numerical solver,
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