Thermal Modeling of Multi-Fin Field Effect Transistor Structure Using Proper Orthogonal Decomposition

Abstract

An approach is proposed to project thermal behavior in a semiconductor integrated-circuit structure onto a functional space based on the proper orthogonal decomposition (POD). The approach substantially reduces the numerical degrees of freedom (DOF) needed for thermal simulations and requires no assumptions about physical geometry, dimensions, or heat flow paths. The POD approach is applied to a multi-fin FinFET structure having heat sources driven by power pulse excitations with time shifts, width variations, and amplitude modulations. The POD models were compared with detailed numerical simulations (DNS) and it was shown that the POD approach provides thermal solutions that were as accurate and detailed as the DNS. It offers a reduction in numerical DOFs by nearly six orders of magnitude to capture the peak temperatures in multi-fin FinFETs.Index Terms-Compact thermal model (CTM), FinFET, proper orthogonal decomposition (POD), reduced-order model (ROM), thermal simulation.

Physics-informed reduced-order learning from the first principles for simulation of quantum nanostructures

“…This quantum POD-Galerkin model for a given in ( 9) is therefore constructed with the coefficients evaluated from (11) to (13) via its POD modes. After POD-Galerkin simulation using (9) to determine a , post processing is needed to calculate the WF from (6).…”

“…The concept of POD has been applied to many research areas including fluid dynamics, heat conduction, power distributions and some other problems governed by partial differential equations (PDEs) 3 – 6 , 17 – 23 . Many of these studies implemented machine learning, such as neural networks 17 , 18 or radial basis functions 19 , 20 , without incorporating the governing equation of the system.…”

“…An accurate prediction beyond the training conditions, including higher external field and larger internal potential in untrained quantum states, is also achieved. Comparison is also carried out between the physics-based learning and Fourier-based plane-wave approaches for a periodic case.In recent years, reduced order modeling techniques have been widely adopted to decrease the computational complexity in scientific and engineering problems [1][2][3][4][5][6][7][8][9][10][11][12] . Many of these techniques involve projecting the problem of interest onto a set of orthogonal basis functions to reduce the degrees of freedom (DoF) using the basis functions that are optimal for the problem.…”

“…Many of these techniques involve projecting the problem of interest onto a set of orthogonal basis functions to reduce the degrees of freedom (DoF) using the basis functions that are optimal for the problem. Proper orthogonal decomposition (POD) 13,14 is one of the such modeling techniques, where its basis functions (hereafter referred to as POD modes) are generated by maximizing the mean square inner product of each mode with the solution data for the problem [2][3][4][5][6][7] . The solution data used in the decomposition should incorporate as much as possible a realistic range of parametric variations for the problem.…”

“…In recent years, reduced order modeling techniques have been widely adopted to decrease the computational complexity in scientific and engineering problems [1][2][3][4][5][6][7][8][9][10][11][12] . Many of these techniques involve projecting the problem of interest onto a set of orthogonal basis functions to reduce the degrees of freedom (DoF) using the basis functions that are optimal for the problem.…”