Compact Dynamic Modeling for Fast Simulation of Nonlinear Heat Conduction in Ultra-Thin Chip Stacking Technology

Abstract

A novel nonlinear model order reduction method is proposed for constructing one-port dynamic compact models of nonlinear heat diffusion problems for ultra-thin chip stacking technology. The method leads to models of small state-space dimensions, which allow accurately reconstructing the whole time evolution of the temperature field due to an arbitrary power waveform of practical interest. The approach is also efficient, since the computational time/memory requirements for constructing each dynamic compact model is about one order of magnitude lower than that corresponding to a single 3-D finite element method transient simulation of a nonlinear problem. Index Terms-Dynamic compact thermal model (DCTM), nonlinear model order reduction (MOR), self-heating, thermal impedance, ultra-thin chip stacking (UTCS).

Bending induced electrical response variations in ultra-thin flexible chips and device modeling

“…In this regard, the nonlinear model order reduction method is useful as it constructs the one-port dynamic compact models of nonlinear heat diffusion in UTC stacking technology. 182 The method leads to models of small state-space dimensions and allows accurate reconstruction of the time evolution of temperature field due to an arbitrary power waveform of practical interest. This model has not been investigated for MOSFETs, but it helps us gather the information about the thermal behavior of UTCs.…”

Circuit-Based Electrothermal Simulation of Power Devices by an Ultrafast Nonlinear MOR Approach

“…. , M, with a chosen small M , using an extended version of the method presented in [21], as detailed hereinafter.…”

“…The most commonly adopted approach (due to its simple application) is based on the Kirchhoff's transformation [7], [19], [20], by which CTNs extracted assuming temperatureindependent thermal conductivities are extended to the nonlinear case. Unfortunately, this procedure in practice provides exact results only under steady-state conditions and considering a single material for the entire device, while introducing large inaccuracies in practical cases, as investigated by the Authors in [21]. Some attempts for a more accurate description of nonlinear thermal effects in power devices can be encountered in the recent literature.…”

“…The NCTN is obtained by extending the nonlinear MOR technique proposed in [21] so as to cover a much wider range of temperature; thus, accuracy is ensured in describing power devices operated under extremely harsh conditions (e.g., energy distribution, automotive, railway traction, aircraft, and spacecraft applications), for which a conventional linear ET analysis would provide an unacceptable underestimation of thermal issues. The resulting method, differently from previous techniques, does not need cumbersome measurements, costly 3-D numerical transient simulations of discretized nonlinear heat diffusion equations, or simplifying assumptions on the geometry of the domain, and can be effortlessly applied to any device category, including packages, for any input power profile (even for short huge-power pulses).…”

Effective Electrothermal Analysis of Electronic Devices and Systems with Parameterized Macromodeling

“…It is in principle possible to provide an a-posteriori correction by applying the Kirchhoff transformation [23] to the linear temperatures calculated by the TFB. However, this might lead to inaccurate results if exploited for dynamic simulations [24] or even for steady-state analyses in structures composed of multiple layers with a different temperature dependence of the thermal conductivity [25], [26]. The aforementioned approach is suited to perform fast and effective dynamic ET analyses of electronic systems, circuits, and multicellular / multifinger devices, as described for a case study in the following Section.…”