Numerical modelling of microscale heat conduction effects in electronic package for different thermal boundary conditions
05 Dec 2000-pp 53-59
TL;DR: In this article, a two-phase lag model is used to bring in the non-Fourier effects to analyze microelectronic devices and a numerical solution procedure based on the finite element method and fourth order Runge-Kutta time marching procedure has been employed for the spatial and temporal discretisations respectively.
Abstract: The reduction of semiconductor device size to the submicrometer range leads to unique electrical and thermal phenomena. The Fourier conduction effect was not enough to explain the phenomena and we need to bring in nonFourier conduction effects to analyse microelectronic devices. A two-phase lag model is used here to bring in the nonFourier effects. A numerical solution procedure based on the finite element method and fourth order Runge-Kutta time marching procedure has been employed for the spatial and temporal discretisations respectively. The predicted results for different boundary conditions clearly capture thermal wave-like and pure diffusion type phenomena in the appropriate range of time lag values. In electronic packaging, the microscale heat conduction must be considered in view of higher heat fluxes encountered recently, especially when we deal with transient heat transfer. A two dimensional case is considered as a first step. The results are encouraging.
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TL;DR: In this paper, the Fourier and non-Fourier equations are reduced to a system of linear differential equations, respectively, using finite element method and then solved with AWE, which is at least three orders faster in terms of computational time as compared to conventional iterative solvers.
30 citations
TL;DR: The non-Fourier heat conduction has been investigated where the maximum likelihood and Tikhonov regularization technique were used successfully to predict the accurate and stable temperature responses without the loss of initial nonlinear/high frequency response.
Abstract: Non-Fourier heat conduction model with dual phase lag wave-diffusion model was analyzed by using well-conditioned asymptotic wave evaluation (WCAWE) and finite element method (FEM). The non-Fourier heat conduction has been investigated where the maximum likelihood (ML) and Tikhonov regularization technique were used successfully to predict the accurate and stable temperature responses without the loss of initial nonlinear/high frequency response. To reduce the increased computational time by Tikhonov WCAWE using ML (TWCAWE-ML), another well-conditioned scheme, called mass effect (ME) T-WCAWE, is introduced. TWCAWE with ME (TWCAWE-ME) showed more stable and accurate temperature spectrum in comparison to asymptotic wave evaluation (AWE) and also partial Pade AWE without sacrificing the computational time. However, the TWCAWE-ML remains as the most stable and hence accurate model to analyze the fast transient thermal analysis of non-Fourier heat conduction model.
4 citations
Cites background from "Numerical modelling of microscale h..."
...whereχT stands for finite relaxation time for electron phonon and χq represents finite thermal wave speed [5]....
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TL;DR: In this article, the thermal response of an infinitely extended shape memory alloy thin film is investigated. But the results of the analysis are limited to the case of a single SMA layer and are not applicable to other SMA layers.
Abstract: This paper reports a study of the thermal response of an infinitely extended shape memory alloy thin film. Motivated by experiments reported in the literature about SMA thin films on a silicon substrate, the thin film is taken to have three layers from the bottom to the top – an amorphous layer, a non-transforming austenitic layer and a transforming SMA layer. The boundary conditions are taken to be adiabatic and convective at the bottom of the film and the top
respectively. The material properties of the transforming layer (thermal conductivity, electrical resistivity and specific heat) are taken to evolve hysteretically with temperature, commencing from an initial room temperature
state of martensite. All the results are presented in non-dimensional form. The steady state results are compared with
an analytical solution. The computations of the transient response are carried out with ANSYS. The thermal response of the 3-layer model is compared with that of a 1-layer model (where the entire film is a SMA
transforming layer) and it is seen that the the temperature of the top surface for the 3-layer model is higher than that
of the 1-layer model. It is also seen that the evolution of the specific heat has the least effect whereas the evolution
of the electrical resistivity has the most effect on the thermal response of the 3-layer model. The thermal response of the infinitely extended films provides a benchmark against which the response of finite sized films can be assessed.
4 citations
Cites background from "Numerical modelling of microscale h..."
...[6] modeled the microscale heat conduction effect in electric package numerically for different thermal boundary conditions, Al-Nimr et al....
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...Furthermore, thermal modeling of the thin films has been studied and published by various researchers [3-8]....
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TL;DR: In this paper, the thermal response of a shape memory alloy (SMA) thin film during a complete cycle of heating and cooling is computationally addressed in this communication, and a comparison is made between the cyclic response time of a an SMA unit cell and an Ovonic unit memory (OUM) cell.
Abstract: With a view toward contributing to the state of the art in the research on shape memory alloy memory storage devices, the thermal response of a shape memory alloy (SMA) thin film during a complete cycle of heating and cooling is computationally addressed in this communication. The ultimate objective is to provide a better understanding of shape memory alloys within the context of the characteristics of thermally activated phase-transforming materials as candidate materials for memory devices. In this study, the effect of the current density, thickness of the SMA thin film, convection and boundary conditions on the transformation of the SMA thin film are investigated. In particular, we study the effect of pulse heating as that is important for memory devices. A comparison is made between the cyclic response time of a an SMA unit cell and an Ovonic unit memory (OUM) cell. The total cycle time for the SMA cell and the OUM cell is 0.7 and 60 ns, respectively. The total energy consumption per cycle for the SMA cell and the OUM cell is 0.441 and 37.8 pJ, respectively. While the response of the SMA cell is almost two orders of magnitude better than the OUM cell, we want to strike a cautionary note that the results for the SMA cell are computational and those for the OUM cell are experimental in nature. Regardless, we hope that the outcomes for the SMA cell will provide some motivation for research in SMA-based memory devices.
3 citations
TL;DR: In this paper, the authors investigated the thermal response of shape memory alloy (SMA) island structures and showed that a reduced inter-island spacing results in lower heat losses to the substrate, and that a heterogeneous microstructure has a minimal effect on the thermal field.
Abstract: The thermal response of periodic, shape memory alloy (SMA) island structures is addressed in this paper. Incorporated into the thermal modeling are several ingredients that are encountered at length scales typical to micron-sized thin films: (i) the microstructure may be heterogeneous, e.g., there may be a mix of an amorphous layer, a non-transforming crystalline layer and a crystalline layer that does undergo phase transformation; (ii) given the typical large surface-to-volume ratios and the attendant thermal losses to the environment, the strength of the heat source as well as its duration during a martensite to austenite transformation become very important. These issues, especially the latter, are investigated for a range of periodic structures with different spacings including the limiting structures of vanishing inter-island spacing on the one hand (infinitely extended thin film) and infinite inter-island spacing on the other (isolated islands). It is seen that a reduced inter-island spacing results in lower heat losses to the substrate, that a heterogeneous microstructure has a minimal effect on the thermal field, and that there appears to be a threshold in the strength of the heat source (represented by a current density, if the heat source is electrical in origin) above which the reduction in the heating time does not improve substantially. Interestingly, the evolution of martensite volume fraction with respect to time seems to be insensitive to the thickness of the film undergoing transformation to austenite.
2 citations
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TL;DR: In this paper, a generalized macroscopic model is introduced in treating the transient heat conduction problems in finite rigid slabs irradiated by short pulse lasers, and the analytical solution is derived by using Greens function method and finite integral transform technique.
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TL;DR: In this paper, a hyperbolic equation based on a wave model has been used to predict the rapid transient heat conduction in IC chips and the peak temperature, spatial difference, and time variation of temperature, which are critical to thermal reliability of the chip, are given and compared with that obtained from the Fourier equation.
Abstract: Instead of the classic Fourier equation based on diffusion, a hyperbolic equation based on a wave model has been used to predict the rapid transient heat conduction in IC chips. The peak temperature, spatial difference, and time variation of temperature, which are critical to thermal reliability of the chip, are given and compared with that obtained from the Fourier equation. Analytical and numerical results show that non-Fourier effects, including the higher peak temperature and thermal stress, greater temperature difference between components, and stronger thermal noise, are significant to IC chip reliability.
29 citations
TL;DR: In this article, a two phase lag model for conduction has been proposed, which accounts for the finite propagation speed of a thermal wave and the equilibration time between the electrons and lattice.
Abstract: Non-Fourier microscale effects are significant during the rapid heating of metallic substrates. Recently, a two phase lag model for conduction has been proposed, which accounts for the finite propagation speed of a thermal wave and the equilibration time between the electrons and lattice. Available closed-form solutions for the dual phase lag model are found to be very different for apparently similar boundary conditions. In this study, the origin of the discrepancy in the available analytical results has been identified as the sensitivity of the predicted solution to the way of implementing the surface boundary condition. A numerical solution procedure based on the finite element method and fourth-order Runge?Kutta time marching procedure has been employed for the spatial and temporal discretisations, respectively. The predicted results for different boundary conditions clearly capture thermal wavelike and pure diffusion-type phenomena in the appropriate range of time lag values. Application of the two p...
26 citations