From SOI to Abstract Electric-Thermal-1D Multiscale Modeling for First Order Thermal Effects

Bartel, Andreas; Günther, Michael

doi:10.1076/mcmd.9.1.25.16517

Cited by 5 publications

(6 citation statements)

References 13 publications

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“…is given in terms of (y 1 , y 2 ) ≡ (P C u,  L ) by the equations (3.1b) for the algebraic network part. Identity (6.2) shows that the quadratic part of y B P y is controlled by the voltage drops over resistors, that is, by |P R u| 2 , where P R = Id − Q R , and Q R denotes the orthogonal projector onto the kernel of A R . On its turn, |P R u| 2 is controlled by the differential node potentials y 1 if we demand ker A R ⊂ ker A C .…”

Section: A Priori Estimatesmentioning

confidence: 99%

“…In chip design, PDAE models have been successfully used in refined network modeling: since spatial dimensions of semiconductor technology shrink steadily, former secondary effects tend to influence or even conduct the general behavior of the electric networks. Therefore hyperbolic PDAE models [6] are introduced to incorporate transmission line effects to the description of highly integrated circuits of extremely fast clock rate, whereas the inclusion of thermal effects in SOI circuits constitutes a parabolic PDAE system [2]. A third example is given by taking into account the distributed nature of semiconductor devices.…”

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confidence: 99%

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Parabolic Differential-Algebraic Models in Electrical Network Design

Alì¹,

Bartel²,

Günther³

2005

Multiscale Model. Simul.

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In refined network analysis, a compact network model is combined with distributed models for semiconductor devices in a multidimensional approach. For linear RLC networks containing diodes as distributed devices, we construct a mathematical model that joins the differentialalgebraic initial-value problem for the electric circuit with parabolic-elliptic boundary value problems modeling the diodes. For this mixed initial-boundary value problem of partial differential-algebraic equations a first existence and uniqueness result is given and its asymptotic behavior is discussed.

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Section: A Priori Estimatesmentioning

confidence: 99%

mentioning

confidence: 99%

Parabolic Differential-Algebraic Models in Electrical Network Design

Alì¹,

Bartel²,

Günther³

2005

Multiscale Model. Simul.

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“…In this section we describe the thermal network based on the model of [7,9]. The thermal network describes how the heat is evolving in the semiconductor-circuit topology.…”

Section: Thermal Network Modelingmentioning

confidence: 99%

“…The numerical results seem to indicate, at least for the presented circuit, that the index of the system does not increase even for the fully coupled model. Future work may be concerned with circuit-device systems containing several devices and the simulation of MOS transistors in several space dimensions [21] and silicon-on-insulator (SOI) structures [9].…”

Section: Electro-thermal Couplingmentioning

confidence: 99%

“…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]. Furthermore, an energy-transport model taking into account the heat transfer between the devices and the circuit was proposed in [3].…”

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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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