Modellierung, Simulation und Optimierung integrierter Schaltkreise

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

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 (nonlinear) 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

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

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.Comment: 26 pages, 7 figure

An experimental assessment of computational fluid dynamics predictive accuracy for electronic component operational temperature

Ever-rising Integrated Circuit (IC) power dissipation, combined with reducing product development cycles times, have placed increasing reliance on the use of Computational Fluid Dynamics (CFD) software for the thermal analysis of electronic equipment. In this study, predictive accuracy is assessed for board-mounted electronic component heat transfer using both a CFD code dedicated to the thermal analysis of electronics, Flotherm, and a general-purpose CFD code, Fluent. Using Flotherm, turbulent flow modelling approaches typically employed for the analysis of electronics cooling, namely algebraic mixing length and two-equation high-Reynolds number k-e models, are assessed. As shown, such models are not specific for the analysis of forced airflows over populated electronic boards, which are typically classified as low-Reynolds number flows. The potential for improved predictive accuracy is evaluated using candidate turbulent flow models more suited to such flows, namely a one-equation SpalartAllmaras model, two-layer zonal model and two equation SST k-co model, all implemented in Fluent. Numerical predictions are compared with experimental benchmark data for a range of componentboard topologies generating different airflow phenomena and varying degrees of component thermal interaction. Test case complexity is incremented in controlled steps, from single board-mounted components in free convection, to forced air-cooled, multi-component board configurations. Apart from the prediction of component operational temperature, the application of CFD analysis to the design of electronic component reliability screens and convective solder reflow temperature profiles is also investigated. Benchmark criteria are based on component junction temperature and component-board surface temperature profiles, measured using thermal test chips and infrared thermography respectively. This data is supplemented by experimental visualisations of the forced airflows over the boards, which are used to help assess predictive accuracy. Component numerical modelling is based on nominal package dimensions and material thermal properties. To eliminate potential numerical modelling uncertainties, both the test component geometry and structural integrity are assessed using destructive and non-destructive testing. While detailed component modelling provides the à priori junction temperature predictions, the capability of compact thermal models to predict multi-mode component heat transfer is also assessed. In free convection, component junction temperature predictions for an in-line array of fifteen boardmounted components are within ±5°C or 7% of measurement. Predictive accuracy decays up to ±20°C or 35% in forced airflows using the k-e flow model. Furthermore, neither the laminar or k-e turbulent flow model accurately resolve the complete flow fields over the boards, suggesting the need for a turbulence model capable of modelling transition. Using a k-co model, significant improvements in junction temperature prediction accuracy are obtained, which are associated with improved prediction of both board leading edge heat transfer and component thermal interaction. Whereas with the k-e flow model, prediction accuracy would only be sufficient for the early to intermediate phase of a thermal design process, the use of the k-co model would enable parametric analysis of product thermal performance to be undertaken with greater confidence. Such models would also permit the generation of more accurate temperature boundary conditions for use in Physics-of-Failure (PoF) based component reliability prediction methods. The case is therefore made for vendors of CFD codes dedicated to the thermal analysis of electronics to consider the adoption of eddy viscosity turbulence models more suited to the analysis of component heat transfer. While this study ultimately highlights that electronic component operational temperature needs to be experimentally measured to quality product thermal performance and reliability, the use of such flow models would help reduce the current dependency on experimental prototyping. This would not only enhance the potential of CFD as a design tool, but also its capability to provide detailed insight into complex multi-mode heat transfer, that would otherwise be difficult to characterise experimentally

Simulation of hot carriers in semiconductor devices

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1995.Includes bibliographical references (p. 109-113).by Khalid Rahmat.Ph.D

Simulation of hot carriers in semiconductor devices

Includes bibliographical references (p. 109-113).Supported by the U.S. Navy. N00174-93-C-0035Khalid Rahmat

SCEE 2008 book of abstracts : the 7th International Conference on Scientific Computing in Electrical Engineering (SCEE 2008), September 28 – October 3, 2008, Helsinki University of Technology, Espoo, Finland

This report contains abstracts of presentations given at the SCEE 2008 conference.reviewe