Thermal compact models for electronic systems

The goal of this research is to develop a Dynamic Compact Thermal Model (DCTM) of electronic packages. The general objectives of thermal modeling are to increase the accuracy of electrical analysis by taking the effect of temperature variation into consideration, predicting the reliability of the product, and acquiring the information which is necessary to design the cooling system in order to enhance the performance of the electronic systems. The project is focused on generating the dynamic compact thermal model of electronic packages so that the transient thermal behaviors of the package could be predicted fast and accurately. The approach proposed by DELPHI consortium (a collaborative European project) for static compact thermal model generation is extended in this work to generate the dynamic compact model of a BGA package represented by a RC network or admittance matrix. Two steps performed as the methodology of dynamic compact model generation in this work are: 1- A static compact thermal model of BGA package is generated and validated from the static thermal simulation and 2- A RC network is proposed as the contribution of this work and calculated by optimization as the dynamic compact thermal model of the package using the data of transient simualtion. The size of the proposed RC network then is optimized by eliminating some capacitors from the original RC network and validated by comparing its output to the ouptut of finite element simulation. COMSOL©, a Finite element analysis tool is used for thermal simulation and detailed steady state and transient model generation. The optimization algorithm implemented for both static and dynamic compact model generation is Nelder-Mead multidimensional optimization which is realized by MATLAB© programming. The obtained results from the compact models for both static and dynamic analysis of the BGA package are in agreement with the detailed thermal model results and with the available results in literature.

The construction and usage of compact thermal models (CTMs), for the thermal analysis as well as the design of cooling devices for electronic systems, are reviewed. These models have many advantages over the so called detailed models based on 3D simulations, mainly being a convenient and simple quantitative description of the modeled object, when constructional details are either unavailable or too detailed to be of use at the desired level of analysis. However, CTMs have manifested some deficiencies in many cases, in particular, multiple chip modules (MCM) and stacked dies. The opposite approach, detailed modeling, is more reliable, although extremely heavy. A new approach is proposed that solves this dilemma by bridging the gap between compact and detailed models. While retaining all advantages of CTMs, i.e., having a limited number of degrees of freedom and not requiring detailed constructional features, it can attain any required precision level depending on the degree of complexity adopted. It gives reliable results covering all operating conditions including MCM and stacked dies. Moreover, it gives access to data on surface temperature gradients that were never obtained before by compact models and are highly important for reliability issues.

The paper presents a compact thermal model of an electronic component enclosed in a D2Pak case.The model includes convection cooling and is compared to a linear model with isothermal boundary condition.The model presented is a static model.

Compact Modeling of Physical Mechanisms Present in the Weak Breakdown Regime of Advanced Si and SiGe Bipolar Transistors

Temperature control of the new-generation integrated multicore system is challenging. This is because the leakage power, which is significant in modern systems, is nonlinearly related to temperature, resulting in a complex nonlinear control problem in thermal management. In this article, a new dynamic thermal management (DTM) method with compact piecewise linear (PWL) model based predictive control is proposed to solve the nonlinear control problem. First, a compact PWL thermal model, which takes dynamic power as input, is built by combining multiple local compact linear thermal models expanded at several Taylor expansion points. These local compact linear thermal models are obtained by sampling-based model order reduction with high accuracy. Their Taylor expansion points are selected by a systematic scheme, which exploits the thermal behavior property of the multicore chips. Based on the compact PWL thermal model, a new predictive control method is proposed to compute the future power recommendation for DTM. By approximating the nonlinearity accurately with the compact PWL thermal model and being equipped with predictive control technique, the new DTM achieves an overall high quality temperature management with smooth and accurate temperature tracking. Experimental results show that the new method outperforms the linear model predictive control based method and the echo state network based predictive thermal management method in temperature management quality with lower computing overhead.

Large progress has been realized in modeling conduction heat transfer problems over the past decade by the introduction of high performance compact thermal models (CTMs) mainly developed for thermal design of complicated electronic systems. The objective of this paper is to generalize these advances to convective heat transfer. A new convective CTM is proposed, which offers many advantages over the traditional approach using the heat transfer coefficient (HTC). The latter is simply a zeroth order CTM. The HTC is quite handy and simple, but with unpredictable errors. It can be suitable for hand calculations of simple systems giving rather crude estimates. For a higher precision, users have no other option than time consuming 3D simulations. For large systems, in terms of number of components, 3D simulations can be rapidly impractical. The CTM bridges the gap between both approaches going gradually from “HTC” levels (low precision and calculations time) at the zeroth order, to 3D simulation precision and computing time levels at large orders. Fortunately, like for conduction, a CTM of order of few tens quickly approaches 3D simulation precision levels, while keeping computation time significantly lower than 3D simulation. Moreover, the CTM approach solves conjugate heat transfer problems in a quite elegant way. A “black box” model, developed for fluid domain alone, can be easily combined with classical CTM conduction models to generate good precision predictions for any combination of fluid/solid domains.

A novel approach for extracting dynamic compact thermal models from nonlinear heat diffusion equations, which take into account the temperature dependence of thermal properties, is presented. In such Model Order Reduction method, the nonlinear heat diffusion equation is projected onto the space spanned by a few terms in the Volterra's series expansion of the solution. Such projection is performed by a novel structure-preserving hyper-reduction algorithm. The resulting method is very efficient, and can lead to very accurate compact thermal models, with unprecedented levels of simplicity. Moreover such models can be extracted for practically any regular temperature dependence of heat capacity, thermal conductivity and heat exchange coefficients. The method has been validated through the analysis of a complex ultra thin stacked chip module.

PurposeThe purpose of this paper is to develop a dynamic compact thermal model (DCTM) of electronic packages. This model is a necessary tool for rapid thermal analysis of the systems which we exposed to boundary condition variation and/or power switching mode such as mobile systems and battery powered systems.Design/methodology/approachThe methodology of compact model generation used was based on generating the transient dynamic detailed finite element thermal model of a package, designing a resistor/capacitor network topology representative of the dynamic detailed model, calculating the resistors'/capacitors' value by optimization method and validation efforts. The method is demonstrated for a ball grid array (BGA) package, a commonly used modern electronic package.FindingsBased on the obtained results, it can be concluded that the dynamic thermal behavior of a BGA package can be accurately described by a generated dynamic compact model in terms of predicted junction temperature response and heat flux of the desired locations of the package.Originality/valueThis model is capable of calculating the temperatures and heat fluxes at desired locations which can help the designer to perform the thermal analysis much faster and easier with the required accuracy.

A methodology is presented for development of compact thermal models for a family of electronic packages, ceramic pin grid arrays (CPGA), in a form compatible with computational fluid dynamics (CFD) codes. A compact model of a CPGA was created and its performance investigated in numerical wind tunnel tests. The results were compared with a detailed CFD model of the package previously validated with experimental results available in the literature. The CFD compact model was able to predict the junction temperatures within 5% of those calculated by the detailed model for flow velocities ranging from 0 to 5 m/s (0 to 1000 ft/min) and three different heat sink configurations. The effects of coarsening the grid were also investigated and the results show that the compact model predicts the junction temperature accurately, whereas the detailed model increasingly loses accuracy as the grid is coarsened.

In this article, we propose a new behavioral thermal modeling method for fast building performance analysis, which is critical for energy-efficient smart building control and management. The new approach is based on two recurrent neutral network architecture to obtain the compact nonlinear thermal models for complicated building. We start with a more realistic building simulation program, EnergyPlus, from Department of Energy, to model some practical buildings such as office buildings and data centers. EnergyPlus can model the various time-series inputs to a building such as ambient temperature, heating, ventilation, and air-conditioning (HVAC) inputs, power consumption of electronic equipment, lighting and number of occupants in a room sampled in each hour and produce resulting temperature traces of zones (rooms). In this work, we apply two recurrent neural network (RNN) architectures to build the non-linear compact thermal model of the building: one is non-linear state-space RNN architecture (NLSS), which has global feedbacks, and the other one is Elman's RNN architecture (ELNN), which has local feedbacks in each layer. We give a simple formula to calculate the RNN layer number, layer size to configure RNN architecture to avoid overfitting and underfitting problems. A cross-validation based training technique is further applied to improve predictable accuracy of models. Experimental results from a case study of three buildings show that ELNN and NLSS can both build very accurate building thermal models for the 2-zone and 5-zone building cases: both of them have average errors from around 1% to 1.5% for the two buildings. For the more complex 6-zone building case, ELNN outperforms NLSS with maximum errors 16% against 23%. But both methods have 2.2% average errors.

In this paper it is shown how parametric dynamic compact thermal models can be exploited for the calibration of detailed thermal models of electronic components and packages. A constrained least square fit of the thermal response of a parametric dynamic compact thermal model, having as parameters the material thermal properties and geometrical details to be calibrated, onto the measured temperature response is performed. Numerical results show that the use of parametric dynamic compact thermal models instead of detailed compact thermal models, in conjunction with an optimization algorithm solving the constrained least square problem, can reduce the computational time for calibration by more than two orders of magnitude.

Compact thermal models (CTMs) are simplified multi-nodal thermal resistor network representations of the detailed material and geometric structure of the electronic package. CTMs predict the thermal response of the package, in various environments, to within an accuracy of 2%. The junction temperature of the package is typically obtained by solving the linear algebraic network equations of the CTM, with the heat transfer to the ambience modeled by a convection coefficient obtained from handbooks, assuming identical ambient conditions imposed on all nodal surfaces. This approach may give misleading results as the ambience at each nodal surface can differ depending on the cooling flow patterns at that surface. In this work, a methodology is presented where the network equations of the CTM are integrated into the governing fluid flow and energy equations solved by computational fluid dynamics (CFD). The CTM+CFD approach predicts a significantly (20–30%) higher junction temperature as compared to the conventional CTM network solver method, even when the convection coefficient used in the latter case is obtained more accurately from CFD, rather than from handbook correlations. It is also found that CFD computations assuming uniform flux at the package surfaces (and ignoring the internal resistance of the package) vastly under-predict the junction temperature. The new approach offers a promising alternative for electronic package thermal design and is highly advantageous where the internal geometric and material configurations are not known due to proprietary concerns.

It is shown how the objective function optimization approach fails in the construction of boundary condition independent compact thermal models of complex Systems On Silicon in which more than two powers are allowed to arbitrarily change. For such applications a novel matrix reduction approach is shown to lead to the efficient construction of accurate boundary condition independent compact thermal models whichever is the number of independent heat sources. Such matrix reduction approach is implemented in the FANTASTIC BCI software tool which is allow to analyze state-of-the art industrial applications.

Innovative methodology to extract dynamic compact thermal models: Application to power devices

Compact thermal models (CTMs) are used to evaluate thermal characteristics of critical electronic chip packages under several hypothetical design and usage scenarios. In order to ensure that CTMs accurately estimate thermal response, an appropriate set of model parameters must first be selected. The challenge arising in this paper is to glean a set of parameters that best describes the performance of CTM over a set of test conditions. We examine a non-convex optimisation formulation for this parameter estimation problem, and derive the first exact optimisation algorithm for the problem using a continuous version of the reformulation-linearisation technique. We provide experimental results on real data to demonstrate the applicability of our approach.