Tamara Bechtold

Dynamic electro-thermal simulation of microsystems—a review

An overview of electro-thermal modeling of microsystems is presented. We consider the most important coupling between thermal and electrical phenomena, and then focus on the industrys central concern, that of Joule heating. A description of different solution approaches for the heat transfer partial differential equation, which constitutes the central part of electro-thermal simulation, is given. We briefly review the analytical solutions and consider further the numerical approaches, which are based on spatial discretization of the thermal domain. Lastly, we describe the final level of approximation, the dynamic compact thermal modeling. We emphasize the formal model order reduction methods, because they directly follow the spatial discretization, and thus preserve the investment into the finite element modeling.

Error indicators for fully automatic extraction of heat-transfer macromodels for MEMS

In this paper, we present three heuristic error indicators for the iterative model order reduction of electro-thermal MEMS models via the Arnoldi algorithm. Such error indicators help a designer to choose an optimal order of the reduced model, required to achieve a desired accuracy, and hence allow a completely automatic extraction of heat-transfer macromodels for MEMS. We first suggest a convergence criterion between two successive reduced models of order r and r + 1. We further propose to use a solution of the Lyapunov equations for reduced-order systems in each iteration, and alternatively to employ sequential model order reduction, which is based on consecutively applying Arnoldi and control-theory methods.

Efficient extraction of thin-film thermal parameters from numerical models via parametric model order reduction

In this paper we present a novel highly efficient approach to determine material properties from measurement results. We apply our method to thermal properties of thin-film multilayers with three different materials, amorphous silicon, silicon nitride and silicon oxide. The individual material properties are identified by solving an optimization problem. For this purpose, we build a parameterized reduced-order model from a finite element (FE) model and fit it to the measurement results. The use of parameterized reduced-order models within the optimization iterations speeds up the transient solution time by several orders of magnitude, while retaining almost the same precision as the full-scale model.

System-level Modeling of MEMS

System-level modeling of MEMS microelectromechanical systems comprises integrated approaches to simulate, understand, and optimize the performance of sensors, actuators, and microsystems, taking into account the intricacies of the interplay between mechanical and electrical properties, circuitry, packaging, and design considerations. Thereby, system-level modeling overcomes the limitations inherent to methods that focus only on one of these aspects and do not incorporate their mutual dependencies.

Model order reduction of 3D electro-thermal model for a novel micromachined hotplate gas sensor

In this paper we present an automatic, Arnoldi-based model order reduction of a 3D electro-thermal model for a novel sensor device. Model order reduction is essential for achieving a quickly evaluable, yet still accurate, macromodel of the device, needed for system-level simulation. We present below numerical simulation results of the full-scale finite element model and the compact-reduced order model, and show how the nonlinearities in the input function can be treated even with the linear reduction algorithm.

Connecting heat transfer macromodels for array MEMS structures

Different methodologies to extract a dynamic compact thermal model of a microelectronic or MEMS device have been developed in recent years. They include strategies based on data fitting, a time-constant spectrum, modal analysis and finally formal model reduction. Researchers seek compact thermal multiport representation for system level simulation. However, thermal flux is not lumped by nature as electrical flow and, as a matter of fact, there appears to be very few works on how to couple dynamic compact thermal models with each other. In the present work, we take a finite element model of a MOS-transistor-based microhotplate array made in ANSYS as a case study. We consider two available techniques to make the model reduction. First, we employ the block Arnoldi algorithm that makes model reduction of the whole array at once. Second, we use the modified Guyan algorithm for a single hotplate and couple reduced models via substructuring. We compare both techniques with each other and discuss the possibility of combining the best parts of the two approaches.

Computationally efficient and stable order reduction methods for a large-scale model of MEMS piezoelectric energy harvester

In this work, we present a computationally efficient model order reduction technique for a large-scale multiport model of piezoelectric energy harvester. This novel technique generates stable reduced order models. The method combines model reduction based on Krylov subspaces and a Schur complement transformation of the resulting system. We demonstrate an excellent match between the full-scale and the reduced order model during transient and harmonic simulation.

A two-sided Arnoldi algorithm with stopping criterion and MIMO selection procedure

In this paper we introduce a two-sided Arnoldi method for the reduction of high order linear systems and we propose useful extensions, first of all a stopping criterion to find a suitable order for the reduced model and secondly, a selection procedure to significantly improve the performance in the multi-input multi-output (MIMO) case. One application is in micro-electro-mechanical systems (MEMS). We consider a thermo-electric micro thruster model, and a comparison between the commonly used Arnoldi algorithm and the two-sided Arnoldi is performed.

Automatic order reduction of thermo-electric models for MEMS: Arnoldi versus Guyan

In this paper we present an automatic order reduction of a linear thermo-electric model describing a novel type of micropropulsion device. Model order reduction is essential to achieve easily to evaluate, yet accurate macromodel of the device. We present numerical simulation results of the full finite element model and the different reduced order models that describe the transient thermo-electric behaviour of the device. The advantages of an Arnoldi-algorithm-based model order reduction over a commercially available reduced order modeling after Guyan are shown.

SOLID PROPELLANT MICROTHRUSTER: THEORY OF OPERATION AND MODELLING STRATEGY

A modelling strategy for a microthruster array based on solid fuel is presented. We review the theory of operation of the microthruster that includes an electrothermal process, ignition, sustained combustion, membrane rupture and gas dynamics. The recommended level of theory is chosen to answer practical engineering questions, so as to make the recommended models feasible to develop and optimize. Special attention is paid to transferring the resulting models to existing software for electrical circuit simulation to permit the development of intelligent electrical driving circuits. The methods of automatic model reduction are presented and the most appropriate method for a microthruster array is chosen.