1. Title The Effect of Polyimide Fixation on Thermal Performance of GaAs Cantilever Based MEMS: A 3D Numerical Analysis with DEETEN Eduard Burian 1 and Tibor Lalinský 2 1 LOX Technologies, Bratislava, Slovakia, www.loxtec.com, mail@loxtec.com 2 Institute of Electrical Engineering of SAS, Bratislava, Slovakia, eleklali@savba.sk

2. Contents 1.Introduction 2.Basics of DEETEN 3.Studied MTC MEMS 4.Results of DEETEN Simulations 5.Conclusions

3. 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.

4. Basics of DEETEN D ifferential E quations E fficient T reatment by E liminative N esting is 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

5. 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

6. 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.

7.  example of domain structure by cantilever MTC simulation  upper level domains only Basics of DEETEN / 3D domain structure

8. 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 MTC two 1-2  m thin GaAs cantilevers with HFET heaters polyimide-enhanced mechanical stability 2. isolated membrane-like MTC GaAs “island” 1  m thin is floating on polyimide membrane Studied MTC MEMS / topologies Contact pad Cantilever pHEMT - Heater pHEMT–Temperature sensor Polyimide membrane

9.  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 256 3 =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 512 3 =134M points Studied MTC MEMS / simulation conditions

10. Polyimide-fixed cantilever beams: T MAX =9.96K Non-fixed cantilever beams: T MAX =10.11K Polyimide-induced degradation does not exceed 2% Heat dissipation through metallic leads results is ~40% Results of DEETEN simulations / cantilever MTC

11. Maximuim temperature in center: T MAX =16.76K Effective thermal resistance ~13K/mW Results of DEETEN simulations / membrane-like MTC

12. 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