Analysis of Temperature-dependent Residual Stress Gradients in Cmos Micromachined Structures

In this paper, we present a technique to analyze variation of structural curl with temperature due to residual stress gradients in multilayer CMOS microstructures. Analytic equations verified by finite element analysis (FEA) and experiment are used as a basis for a FEA technique to predict residual stress dependent curl in an arbitrary device. A parameter extraction method based on measurement of tip deflection with temperature is proposed to extract the simulation parameters. Simple beam test structures composed of all metal-dielectric combinations possible in the Hewlett Packard 3-meta l 0 .5μm n-wel l CMOS process are experimentally characterized. This information is used to obtain the characteristic temperature at which the beam has no vertical displacement and the stresses in each layer is zero. The thermal coefficient of expansion (TCE) for each layer is extracted using the rate of change of tip deflection with temperature. The characteristic temperature and TCE are inserted in FEA for prediction of structural curl with temperature. This predictive technique has been demonstrated for a curl-matched CMOS accelerometer. INTRODUCTION CMOS surface-micromachining technology through conventional CMOS processing integrates circuits with mechanical structures at low cost. It provides an ability to place multiple isolated conductors in microstructures for novel capacitive sensing. The multilayer structural material, composed of metal layers with interleaved dielectric layers, exhibits residual stress gradients that induce structural curling. Stress in each layer is a function of temperature due to the differences in the TCE of the layers. This variation of structural curling leads to variation of sensitivity of lateral capacitive sensors, as the coupling area between adjacent electrodes changes. Curl-matching techniques have been used to minimize the effect of these variations[1]. To design and verify matched curl in structures it is imperative to predict structural curl variation due to temperature. The analysis of temperature-dependent curl for CMOS micromachined beams extends Timoshenko’s treatment of thermal bimorphs[2][3] and results in equations describing the beam tip deflection with temperature. The residual stress effects in each layer are represented by a characteristic temperature at which the beam is completely flat. The TCE values for each material are extracted experimentally from the measured rate of change of tip deflection with temperature. The material properties and the characteristic temperature are used in a FEA to predict curling of arbitrary CMOS surface-micromachined structures. CMOS MICROMACHINING PROCESS The devices described in this paper have been fabricated in the high-aspect-ratio CMOS micromachining process developed at Carnegie Mellon University [4]. The process flow, shown in Figure 1, enables fabrication of micromachined structures in a standard 0.5μm 3-metal CMOS process. The conventional CMOS process is followed by an anisotropic reactive-ion etch (RIE) with CHF3 and O2 to etch away oxide not covered by any of the metal layers, resulting in high aspect ratio vertical sidewalls. An isotropic RIE (using SF6 and O2) then removes the underlying silicon, thus releasing the microstructure. THERMAL MULTIMORPH ANALYSIS A CMOS micromachined structure can be designed with any of the metal layers as the top metal mask leading to numerous choices for the design of each element of a device. Figure 1: Schematic of the process for micromachined structures in standard CMOS. (a)