POD-based thermal model for FinFET IC structure

Abstract

A reduced basis element method is presented based on proper orthogonal decomposition (POD) to develop thermal models for FinFET devices and integrated circuits. The POD approach is able to substantially reduce numerical degrees of freedom (DOF) while offering spatial thermal solution as detailed as detailed numerical simulation. The POD thermal models for the selected FinFET blocks can be stored in a library for constructing a larger circuit structure. This study demonstrates that, using the developed approach, an accurate thermal model for a multi-block FinFET structure can be developed to capture all the hot spots in the structure with a reduction in DOFs by nearly 6 orders of magnitude, compared to DNS.

Benchmarking of Machine Learning Methods for Multiscale Thermal Simulation of Integrated Circuits

“…The next step is determining the POD coefficients from Eq.1. One way of doing this is, is by Galerkin projection [3], [25], [36]. This requires solving a system of coupled ordinary differential equations, formed by the heat equation projected on the orthonormal basis.…”

“…This is an important drawback for the interpretability of the model. On the other side of the spectrum, there are the white box ML methods [25] that contain physical information or governing equations about the system. These typically contain much less trainable parameters and are easier to interpret, making them closely related to traditional statistics and not only ML.…”

“…Proper Orthogonal Decomposition (POD) combined with Radial Basis Functions (RBF) is one example of a ML method that uses classical statistical tools. In this approach the fundamental behaviour or patterns (POD modes) are retrieved from the training dataset as a first step [25]. [20], [22] [3]* [25]* [37] [21], [24], [28], [29] Subsequently combining the POD modes allows for the prediction of new data points.…”

“…In this approach the fundamental behaviour or patterns (POD modes) are retrieved from the training dataset as a first step [25]. [20], [22] [3]* [25]* [37] [21], [24], [28], [29] Subsequently combining the POD modes allows for the prediction of new data points. It is a black box method in the sense that no physical information or governing equations are used during the model training.…”

Multitimescale Thermal Network Model of Power Devices Based on POD Algorithm

“…It is integrated into circuit simulators used and extracts the dominant patterns , while preserving as much key features of high-dimensional data sets as possible, to generate low-dimensional data. This enables reduced computational complexity by compressing data in thermal analysis, as was successfully demonstrated in other fields, such as analyzing heat transfer in fluid flow [21,22], coupling the POD method with the finite element method (FEM) to solve heat transfer problems [23], combining the POD algorithm with the meshless method to improve the efficiency of solving heat transfer problems [24], solving the inverse problem of heat transfer problems [25], and, in addition, is able to analyze the thermal characteristics of integrated circuits [26][27][28].…”