Two-dimensional simulation of thermal runaway in a nonplanar GTO-thyristor

Brand, H.; Selberherr, S.

doi:10.1109/16.477772

Cited by 7 publications

(9 citation statements)

References 23 publications

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“…(c) Correction factor (32) that quantifies the deviation of the Fermi-Dirac integrals from the exponential function. The non-degenerate limit corresponds to γ (η) ≡ 1. namics [9][10][11][12][13][14]. The model equations read:…”

Section: The Non-isothermal Drift-diffusion System Using the Kelvin Fmentioning

confidence: 99%

“…It can be derived from, e. g., the Debye model for the free phonon gas [64]. The Coulomb interaction energy f Coul must be modeled such that the state equations (5) follow consistently from solving the defining relations for the quasi-Fermi energies (11) for the carrier densities. In order to supplement the "missing" electrostatic contributions in Eq.…”

Section: Kelvin Formula For the Seebeck Coefficientmentioning

confidence: 99%

“…The last line in Eq. ( 20) is a purely transient contribution, that has been discussed by several authors [9][10][11][12]25]. In simulation practice, this term is often neglected, since estimations show that it is negligible in comparison with the other self-heating sources, see Refs.…”

Section: Heat Generation Ratementioning

confidence: 99%

“…The numerical simulation of semiconductor devices showing strong self-heating and thermoelectric effects requires a thermodynamically consistent modeling approach, that describes the coupled charge carrier and heat transport processes. In the context of semiconductor device simulation, the non-isothermal drift-diffusion system [9][10][11][12][13][14] has become the standard model for the self-consistent description of electro-thermal transport phenomena. This is a system of four partial differential equations, which couples the semiconductor device equations [15,16] to a (lattice) heat flow equation for the temperature distribution in the device.…”

Section: Introductionmentioning

confidence: 99%

“…In this section we briefly review the non-isothermal drift-diffusion system, which provides a self-consistent description of the coupled electro-thermal transport processes in semiconductor devices. The model has been extensively studied by several authors from the perspective of physical kinetics or phenomenological non-equilibrium thermody- namics [9][10][11][12][13][14]. The model equations read:…”

Section: Introductionmentioning

confidence: 99%

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Generalized Scharfetter–Gummel schemes for electro-thermal transport in degenerate semiconductors using the Kelvin formula for the Seebeck coefficient

Kantner

2020

Journal of Computational Physics

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Many challenges faced in today's semiconductor devices are related to self-heating phenomena. The optimization of device designs can be assisted by numerical simulations using the non-isothermal drift-diffusion system, where the magnitude of the thermoelectric cross effects is controlled by the Seebeck coefficient. We show that the model equations take a remarkably simple form when assuming the so-called Kelvin formula for the Seebeck coefficient. The corresponding heat generation rate involves exactly the three classically known self-heating effects, namely Joule, recombination and Thomson-Peltier heating, without any further (transient) contributions. Moreover, the thermal driving force in the electrical current density expressions can be entirely absorbed in the diffusion coefficient via a generalized Einstein relation. The efficient numerical simulation relies on an accurate and robust discretization technique for the fluxes (finite volume Scharfetter-Gummel method), which allows to cope with the typically stiff solutions of the semiconductor device equations. We derive two non-isothermal generalizations of the Scharfetter-Gummel scheme for degenerate semiconductors (Fermi-Dirac statistics) obeying the Kelvin formula. The approaches differ in the treatment of degeneration effects: The first is based on an approximation of the discrete generalized Einstein relation implying a specifically modified thermal voltage, whereas the second scheme follows the conventionally used approach employing a modified electric field. We present a detailed analysis and comparison of both schemes, indicating a superior performance of the modified thermal voltage scheme.

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