TY - JOUR

T1 - Simulation of THz Oscillations in Semiconductor Devices Based on Balance Equations

AU - Linn, Tobias

AU - Bittner, Kai

AU - Brachtendorf, Hans Georg

AU - Jungemann, Christoph

N1 - Publisher Copyright:
© 2020, The Author(s).

PY - 2020/10/1

Y1 - 2020/10/1

N2 - 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.

AB - 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.

KW - Hyperbolic Balance Laws

KW - Isothermal hydrodynamic model

KW - THz Oscillations in Semiconductors

KW - Well-balanced numerical Scheme

UR - http://www.scopus.com/inward/record.url?scp=85091268586&partnerID=8YFLogxK

U2 - 10.1007/s10915-020-01311-z

DO - 10.1007/s10915-020-01311-z

M3 - Article

C2 - 33029040

AN - SCOPUS:85091268586

SN - 0885-7474

VL - 85

SP - 6

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

IS - 1

M1 - 6

ER -