Contractor: Stanford University
Agreement Number: F30602-96-2-0308
Project Number: HJ1500-3221-0599
DARPA Order Number: N-7-0504/AO E117/12
Contract Period: September 13, 1996 - September 12, 1999
Sponsor: Department of the Air Force
Technical POC: Robert W. Dutton
2) APPROACH:
a) enhanced gridding capabilities compatible with VLSI TCAD.
b) object-oriented design of layered access to model definition
that allows fast prototyping of new and realistic physical
and constitutive models.
c) enhanced element technology for discretization of multi-physics
system of equations.
d) fully-integrated MEMS fabrication and device simulation
with detailed material and stress analyses monitored by
the test MEMS structure discussed below.
e) development of lumped models for specific MEMS applications
of interest to DARPA.
3) PROGRESS:
Nonlinear dynamic lumped models of MEMS microwave switches have been formulated and successfully applied to analyses of transient characteristics and geometrical scaling. Physical effects including electrostatic, bending, stretching, residual stress, inertia, squeeze film damping, Van der Waals forces and contact have been accounted for. The assumptions in the lumped model are compared with the quasi-2D simulations, where the deformed beam is discretized with areal correction and each discrete element is assumed to have vertical motion only. The comparison has clearly demonstrated that the two-lump model is accurate for geometrical scaling, and has shown how intelligence can be extracted from a lower level model.
The complexity and dimension of a MEMS device is usually much larger than the electronic device. In addition to model hierarchy (e.x., inclusion of different moments in hydrodynamics and mechanics), geometry hierarchy (e.x., full-3D, membrane, quasi-3D, beam, 2D, quasi-2D and lumps) is also critical for accurate and efficient prototyping of the MEMS systems. Commercial tools such as MEM-CAD from Microcosm, COMCO from Computational Mechanics and SOLIDIS from ETH have been evaluated, and MEM-CAD is in the purchasing process. The commercial tools will not be used as development platform, but for identifying established approaches and validating computation.
Adaptive gridding of the level-set method for simulation of thin-film fabrication has been investigated. It is clearly identified that to account for the residual stress effect during growth, the quad/oct tree adaptation scheme is much better than the traditional thin-tube one. Examples of tracing stress gradients in isotropic-elastic material deposition have been benchmarked for computation and memory-usage efficiency.
Develop extraction schemes of materials properties using in-situ test MEMS structures, in combination with the CAD tools developed above, to support predictive modeling. The scope of material characterization includes the use of multilayer and graded structures, and reliability issues such as fracture and fatigue. This closed-loop process of test structures, simulation and extraction/validation of models is the key link between groups in CAD/Material Science/MEMS developers.
2) APPROACH:
a) mechanical characterization of MEMS materials with dependencies
on processing and microstructure.
b) reliability study including fracture and fatigue.
c) feedback to the constitutive models in the FEM-based solver in
Task 1.
3) PROGRESS:
A new technique for determining the Possion's ratio of crystalline thin films based on x-ray measurements of interplanar spacings of a film under different stress conditions is being developed. The primary advantage of the x-ray technique is that it does not require any micromachining steps. Results are applicable to MEMS structures because elastic behavior is generally not microstructure dependent. Films for testing have been fabricated, and initial trials are under way. Results may be compared to the plain-strain bulge test technique for verification, if necessary.
The torsional fatigue subtask has been reactivated. As a long term goal studies tying torsional fatigue mechanisms and microstructure will identify certain key microstructural parameters that affect MEMS performance. Our calculations indicate that scaling up Al torsional members from the size typical of micromirror structures should bring the strains into the regime known to cause rapid fatigue failure in bulk Al. Because of the difficulties involved in fabricating torsional test structures, uniaxial test structures are being investigated.
As part of the joint effort related to new in-situ test structures, we have identified several possible structures for measuring residual stress that represent significant improvements over current structures. We are modeling a cantilever variant and a membrane variant to determine feasibility.
Design and implementation of MEMS structures for in-situ materials parameter extraction (mentioned above), which will be applicable to MEMS devices of interest to DARPA. The experimental measurements made with these structures will facilitate the critical evaluation of models, parameters and overall simulation accuracy for MEMS devices. The geometry and process flow design will support not only the application side (such as micromachined RF switches) but also the underlying need to quantify and understand MEMS device limits resulting from materials and process dependences.
2) APPROACH:
a) design and implementation of in-situ test structures.
b) design and implementation of example prototype MEMS device.
c) measurement, parameter extraction, modeling and testing.
3) PROGRESS:
Before embarking on the detailed analysis and design of test structures, a thorough review of the background literature was completed. Having surveyed the available literature, several conclusions were drawn regarding the best test structure designs. Uniform stress measurements using simple dimensional change of cantilevers seem impractical due to measurement limitations, and will be pursued only as a side-line. Doubly-constrained cantilevers and "Guckel rings" are adequate for approximate quantitation of compressive and tensile stresses, respectively, but do not provide information about stress gradients in the direction orthogonal to the wafer surface (vertical) which are critical to surface micromachined structures. Measurements of the curvature of released/relaxed thin-film regions can, with certain assumptions, be used to estimate the sign and magnitude of vertical gradients. Archimedean spirals have been used by others for this purpose, but measurement of curvature, radial shrinkage and free-end rotation are relatively difficult to accomplish accurately.
The preferred measurement technique is the use of released, singly-supported cantilevers to measure both stress gradients and Young's modulus. We are undertaking the design of a system that can, using a laser, thermally excite such a beam into mechanical resonance and determine its natural resonant frequency (in vacuum, to eliminate squeeze-film damping effects). A separate laser interferometer will be used to measure deflection of the cantilever's free end to provide the amplitude information for the measurements. In another mode of operation, the laser interferometer can be scanned along the length of such a cantilever and measure its curvature relative to a parallel scan of the bare wafer surface nearby (using digital subtraction to null any unwanted tilt of the substrate). We anticipate that this approach, in combination with other test structures that will also be developed, should provide accurate, run-to-run parameters for modeling.