Title

The Effect of Polyimide Fixation on Thermal Performance of GaAs Cantilever Based MEMS: A 3D Numerical Analysis with DEETEN

Eduard Burian1 and Tibor Lalinský2

1 LOX Technologies, Bratislava, Slovakia, www.loxtec.com, mail@loxtec.com2 Institute of Electrical Engineering of SAS, Bratislava, Slovakia, eleklali@savba.sk

Contents

1. Introduction2. Basics of DEETEN3. Studied MTC MEMS4. Results of DEETEN Simulations5. Conclusions

Introduction

In the first part of this presentation, we refer of a novel simulation technology DEETEN, of its principles and implementation for thermal analysis of micromechanical systems.

In the second part, we refer of results of DEETEN 3D thermal analysis of a GaAs Micromechanical Thermal Converter, particularly, to analysis of thermal effect of polyimide fixation of the cantilever beam of this MEMS.

Basics of DEETEN

Differential Equations Efficient Treatment by Eliminative Nestingis a novel software simulation technology capable of efficient multi-million-point 3D simulations on a conventional PC. It takes simple math of finite difference method and field relaxation algorithms together with modern software technologies to achieve impressive computational performance.

The efficiency and performance of DEETEN is achieved by:• recursive domain decomposition of simulation space• topology and field complexity is considered in created domain chain• multigrid capability, pre-computed field is smoothed on finer meshes• simple discretization algorithms based on finite differences method• solution to PDEs by field relaxation algorithms • computer-friendly (octree) domain structure defined by means of

OOP

Basics of DEETEN / the D10 domain

D10 domain consist of 10x10x10=1000 mesh points from those 8x8x8=512 points are inner 6x8x8=384 of the outer points contribute to solution of

PDEs in a parent domain, up to 8 smaller child domains can

exist the child domain is half the size of the parent domain inner volume of a child matches perfectly with one inner

parent octant domain chaining can go on till desired spatial resolution

is achieved

Basics of DEETEN / domain overlapping

Defined conditions assure that two neighboring child domains are overlapped so that a part of the boundary of one child domain covers with the first plane of inner points of the other, even in the case they have no common parent. Inner volumes of child domains, which never overlap, create a smooth simulation mesh necessary for sequential (domain-by-domain) treatment of PDEs.

example of domain structure by cantilever MTC simulation

upper level domains only

Basics of DEETEN / 3D domain structure

Micromechanical Thermal Converter (MTC) is being developed as key par of the Microwave Transmitted Power Sensor (MTPS) at Institute of Electrical Engineering of SAS. We studied two MTC topologies:

1. cantilever-based MTCtwo 1-2m thin GaAs cantilevers with

HFET heaterspolyimide-enhanced mechanical stability

2. isolated membrane-like MTCGaAs “island” 1m thin is floating

on polyimide membrane

Studied MTC MEMS / topologies

Contact pad

Cantilever

pHEMT - HeaterpHEMT–Temperature sensor

Polyimide membrane

Polyimide membrane

MEMS were kept in air and ambient temperature is 300K air thermal conductance is included into model power dissipation in a HFET heater is set to 1mW

Cantilever MTC: main domain dimensions 1.6x1.6x0.16mm domain level limit set to 5, i.e. spatial resolution 1:256 at

maximum typically 1500 domains were created, with 1.5M mesh points in comparison, regular rectangular mesh requires 2563=16.7M

points

Membrane-like MTC: main domain dimensions 1.0x1.0x0.1mm domain level limit set to 6, I.e. spatial resolution 1:512 at

maximum typically 2500 domains, 2.5M mesh points in comparison to regular rectangular mesh with 5123=134M

points

Studied MTC MEMS / simulation conditions

Polyimide-fixed cantilever beams: TMAX=9.96K

Non-fixed cantilever beams: TMAX=10.11K

Polyimide-induced degradation does not exceed 2% Heat dissipation through metallic leads results is ~40%

Results of DEETEN simulations / cantilever MTC

Maximuim temperature in center: TMAX=16.76K

Effective thermal resistance ~13K/mW

Results of DEETEN simulations / membrane-like MTC

In thermal investigations of two design of a MTC MEMS, DEETEN has been proven as viable and promising technology.

Joining advanced numerical methods for PDE solving with modern, object-oriented software technologies can substantially improve computational performance in electrophysical simulations.

Next plans: more detailed thermal investigation of MEMS details in 100-10nm range simulation of complex thermal, electronic and mechanic

phenomena integrated simulation & visualization environment

Conclusions