Thermodynamic design of energy models of semiconductor devices

Albinus, Günter; Gajewski, H.; Hünlich, Rolf

doi:10.1088/0951-7715/15/2/307

Cited by 67 publications

(82 citation statements)

References 20 publications

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“…The heat equation for the lattice temperature was derived from thermodynamic principles following [2,6] which guarantees conservation of the total energy. The source term in the heat equation contains energy relaxation, recombination heat, and radiation effects.…”

Section: Electro-thermal Couplingmentioning

confidence: 99%

“…Wachutka employed a thermodynamic approach to extend the drift-diffusion equations to the nonisothermal case [39]. Based on first principles of entropy maximization and partial local equilibrium, Albinus et al [2] derived nonisothermal carrier transport equations and included also carrier temperatures. Thermal effects in electric circuits were considered in [8,9].…”

mentioning

confidence: 99%

“…The heat equation for the lattice temperature is derived from thermodynamic principles following the approach of [2,6]. We adapt the free energy to the case of several temperatures and achieve a heat equation which guarantees energy conservation, i.e., the total energy is assumed to satisfy the balance equation…”

mentioning

confidence: 99%

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Self-heating in a coupled thermo-electric circuit-device model

Brunk

Jüngel

2010

J Comput Electron

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Abstract. The self-heating of a coupled thermo-electric circuit-semiconductor system is modeled and numerically simulated. The system consists of semiconductor devices, an electric network with resistors, capacitors, inductors, and voltage sources, and a thermal network. The flow of the charge carriers is described by the energy-transport equations coupled to a heat equation for the lattice temperature. The electric circuit is modeled by the network equations from modified nodal analysis coupled to a thermal network describing the evolution of the temperatures in the lumped and distributed circuit elements. The three subsystems are coupled through thermo-electric, electric circuit-device, and thermal network-device interface conditions. The resulting system of nonlinear partial differential-algebraic equations is discretized in time by the 2-stage backward difference formula and in space by a mixed finite-element method. Numerical simulations of a one-dimensional ballistic diode and a frequency multiplier circuit containing a pn-junction diode illustrate the heating of the semiconductor device and circuit resistors.Key words. Energy-transport equations, lattice heating, thermal network, circuit equations, mixed finite-element method, partial differential-algebraic equations.AMS subject classifications. 65L80, 65M60, 82D37.1. Introduction. Due to growing package densities, self-heating becomes more and more important in modern integrated circuits and power devices. Thermal effects may strongly influence the device behavior and even reduce its performance. In order to understand the influence of self-heating, power dissipation and temperature evolution have to be taken into account in the electric network models.In industrially used circuit simulators, complex semiconductor device models are usually substituted by circuits of basic network elements, resulting in simpler so-called compact models, and thermal effects are described heuristically by correction factors or simple heat models. In order to achieve accurate simulations of modern circuits, however, a very large number of circuit elements and a careful adjustment of a large number of parameters is needed. Therefore, it is preferable to model those devices which are critical for the parasitic effects by semiconductor transport equations and to include physical heat flow models.Beacuse of missing structural informations about the coupled device-circuit equations, first approaches to couple circuits and devices were based on a combination of device and circuit simulators as "black box" solvers [16] or on simple extensions of device simulators by more complex boundary conditions [26]. More recently, electric network models were coupled to semiconductor transport equations, such as driftdiffusion [34] or energy-transport models [11], leading to a coupled system of partial differential-algebraic equations. The work [11] includes temperature models for the

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Section: Electro-thermal Couplingmentioning

confidence: 99%

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confidence: 99%

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Self-heating in a coupled thermo-electric circuit-device model

Brunk

Jüngel

2010

J Comput Electron

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“…Physical parameters occurring in these equations depend on the device temperature T . Therefore, under nonisothermal conditions a balance equation for the density of total energy must be added, and a so called energy model arises (see [2,18]) . Finally, if incompletely ionized impurities (for example radiation induced traps or other deep recombination centers) are taken into account, we have to consider further continuity equations for the densities of (in general immobile) species X j , j = 1, .…”

Section: Model Equationsmentioning

confidence: 99%

“…Here j n , j p denote the particle flux densities of electrons and holes, R j1 , R j2 denote the reaction rates of the first and second reaction in (1) or in (2), respectively, while R 0 is the reaction rate of a (direct) electron-hole generation-recombination…”

Section: Model Equationsmentioning

confidence: 99%

Stationary energy models for semiconductor devices with incompletely ionized impurities

Glitzky¹,

Hünlich

2005

Z Angew Math Mech

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The paper deals with two‐dimensional stationary energy models for semiconductor devices, which contain incompletely ionized impurities. We reduce the problem to a strongly coupled nonlinear system of four equations, which is elliptic in nondegenerated states. Heterostructures as well as mixed boundary conditions have to be taken into account. For boundary data which are compatible with thermodynamic equilibrium there exists a thermodynamic equilibrium. Using regularity results for systems of strongly coupled linear elliptic differential equations with mixed boundary conditions and nonsmooth data and applying the Implicit Function Theorem we prove that in a suitable neighbourhood of such a thermodynamic equilibrium there exists a unique stationary solution, too.

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On thermodynamically consistent models and gradient structures for thermoplasticity

Mielke

2011

GAMM-Mitteilungen

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It is investigated in what sense thermoplasticity can be written as a generalized gradient system with respect to the total entropy and the entropy-production potential. The difficulty is that the quasistatic equilibrium equation for the elastic forces is obtained by minimizing the total energy and that this condition must be eliminated suitably. The subtle interplay between energy and entropy is treated via the formalism of GENERIC.

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Thermodynamic design of energy models of semiconductor devices

Cited by 67 publications

References 20 publications

Self-heating in a coupled thermo-electric circuit-device model

Self-heating in a coupled thermo-electric circuit-device model

Stationary energy models for semiconductor devices with incompletely ionized impurities

On thermodynamically consistent models and gradient structures for thermoplasticity

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