Numerical simulation of a polysilicon thermal flexure actuator

 An electrothermal equation of a polysilicon thermal flexure actuator is presented, which takes heat conduction, air convection and radiation into account. A numerical method is developed to solve the equation. The deflection model based on the matrix displacement method, i.e. finite element method (FEM) in structural mechanics, is given. It transforms deflection equations into a matrix and is easy to calculate numerically. Simulation results for the actuator with typical dimensions are presented. Discussions are finally given. Received: 28 April 2000/Accepted: 9 January 2001     

Thermally driven phase-change microactuation

This paper describes a microactuation scheme based on thermally driven liquid-vapor phase-change in a partially filled sealed cavity. A test structure for studying this system has been designed and fabricated. The cavity is 900 μm by 900 μm by 300 μm in size with a thin, 600 μm by 800 μm grid-shaped heater located on the floor of the cavity and elevated approximately 8 μm above it. The heater is composed of open diamond-shaped unit cells defined by 12-μm-wide, 3-μm-thick bulk-silicon beams, giving an overall electrical heater resistance of 3-10 Ω. Using methanol as the cavity fluid with partial filling, drive levels of 10 mW sustain a 1.2-Atm pressure rise within the cavity. Real-time measurements demonstrate a pressure response time on the order of 100 ms for an input power of 100 mW. Simulated pressure response calculations indicate the potential for an optimized response time on the order of 40 ms at this power level     

Surface-tension-driven microactuation based on continuouselectrowetting

This paper describes the first microelectromechanical systems (MEMS) demonstration device that adopts surface tension as the driving force. A liquid-metal droplet can be driven in an electrolyte-filled capillary by locally modifying the surface tension with electric potential. We explore this so-called continuous electrowetting phenomenon for MEMS and present crucial design and fabrication technology that reduce the surface-tension-driving principle, inherently powerful in microscale, into practice. The key issues that are identified and investigated include the problem of material compatibility, electrode polarization, and electrolysis, as well as the micromachining process. Based on the results from the initial test devices and the design concept for a long-range movement of the liquid-metal droplet, we demonstrate a liquid micromotor, an electrolyte and liquid-metal droplets rotating along a microchannel loop. Smooth and wear-free rotation of the liquid system is shown at a speed of ~40 mm/s (or 420 r/min along a 2-mm loop) with a driving voltage of only 2.8 V and little power consumption (10-100 μW)     

Surface topography evolution and fatigue fracture in polysilicon MEMS structures

This paper presents the results of an experimental study of the micromechanisms of surface topography evolution and fatigue fracture in polysilicon MEMS structures. The initial stages of fatigue are shown to be associated with stress-assisted surface topography evolution and the thickening of SiO/sub 2/ layers that form on the unpassivated polysilicon surfaces and crack/notch faces. The differences in surface topography and oxide thickness are characterized as functions of fatigue cycling before discussing the micromechanisms of fatigue fracture.     

耐高温多晶硅应变计

介绍了一种适用于特殊环境进行高温测量的多晶硅应变计的原理、设计、制作工艺及粘贴方法。它的特点是耐高温 (可用在温度达 2 5 0℃的环境中 )、体积小、安装方便。该种应变计已用于检测电站锅炉焊缝的牢固程度 ,在实际应用中性能较好     

Optimization of temperature of polysilicon rods

The problem of synthesis of optimal control for temperature of polysilicon rods is solved taking heat emission into account. A method of dynamic programming for linear systems with distributed parameters (SDP), a modified performance criterion, and a moderated form of solution to the functional Bellman equations for SDP are used. The obtained control algorithms for polysilicon were numerically realized earlier.     

Thermal conductivity of doped polysilicon layers

The thermal conductivities of doped polysilicon layers depend on grain size and on the concentration and type of dopant atoms. Previous studies showed that layer processing conditions strongly influence the thermal conductivity, but the effects of grain size and dopant concentration were not investigated in detail. The current study provides thermal conductivity measurements for low-pressure chemical-vapor deposition (LPCVD) polysilicon layers of thickness near 1 μm doped with boron and phosphorus at concentrations between 2.0×10¹⁸ cm^-3 and 4.1×10¹⁹ cm^-3 for temperatures from 20 K to 320 K. The data show strongly reduced thermal conductivity values at all temperatures compared to similarly doped single-crystal silicon layers, which indicates that grain boundary scattering dominates the thermal resistance. A thermal conductivity model based on the Boltzmann transport equation reveals that phonon transmission through the grains is high, which accounts for the large phonon mean free paths at low temperatures. Algebraic expressions relating thermal conductivity to grain size and dopant concentration are provided for room temperature. The present results are important for the design of MEMS devices in which heat transfer in polysilicon is important     

Magnetic bubble memory structures for relational database management systems

Recently the concept of using magnetic bubble technology to store data and to perform logical operations has received considerable attention. By exploiting this hardware approach for relational database management systems, we introduce an efficient support for records permutation, sorting and searching for data. Actually these are substantial operations in relational data models.The organization of a relational data model in a magnetic bubbie memory is straightforward. In such systems the memory consists of loops, where each loop is capable of holding one record. Under the control of a switch, a loop can circulate the records or can hold them in position. However, as the number of switches in the memory system increases, the number of control lines becomes large and the model structure may lose its practical significance.In this investigation three different models of bubble memories are applied to a simple relational database example. The two basic operations of permuting records and searching for data are emphasized. For these models, some theoretical features, the essential characteristics and their applicability are pointed out.     

Rapid thermal annealing of polysilicon thin films

In comparison with conventional heat treatment, high-temperature rapid thermal annealing (RTA) in a radio frequency (RF) induction-heated system can reduce or eliminate residual stresses in thin films in a few seconds. In this work, changes in the stress level due to the RTA of polycrystalline silicon thin films were studied as a function of annealing time and temperature. The corresponding variations in the microstructure and surface layer of the thin films were experimentally investigated by a variety of analytical tools. The results suggest that the residual stress evolution during annealing is dominated by two mechanisms: 1) microstructure variations of the polysilicon thin film and 2) effects of a surface layer formed during the heat treatment. The fact that the microstructure changes are more pronounced in samples after conventional heat treatment implies that the effects of the formed surface layer may dominate the final state of the residual stress in the thin film     

Fracture strength of polysilicon at stress concentrations

Mechanical design of MEMS requires the ability to predict the strength of load-carrying components with stress concentrations. The majority of these microdevices are made of brittle materials such as polysilicon, which exhibit higher fracture strengths when smaller volumes or areas are involved. A review of the literature shows that the fracture strength of polysilicon increases as tensile specimens get smaller. Very limited results show that fracture strengths at stress concentrations are larger. This paper examines the capability of Weibull statistics to predict such localized strengths and proposes a methodology for design. Fracture loads were measured for three shapes of polysilicon tensile specimens - with uniform cross-section, with a central hole, and with symmetric double notches. All specimens were 3.5 /spl mu/m thick with gross widths of either 20 or 50 /spl mu/m. A total of 226 measurements were made to generate statistically significant information. Local stresses were computed at the stress concentrations, and the fracture strengths there were approximately 90% larger than would be predicted if there were no size effect (2600 MPa versus 1400 MPa). Predictions based on mean values are inadequate, but Weibull statistics are quite successful. One can predict the fracture strength of the four shapes with stress concentrations to within /spl plusmn/10% from the fracture strengths of the smooth uniaxial specimens. The specimens and test methods are described and the Weibull approach is reviewed and summarized. The CARES/Life probabilistic reliability program developed by NASA and a finite element analysis of the stress concentrations are required for complete analysis. Incorporating all this into a design methodology shows that one can take "baseline" material properties from uniaxial tensile tests and predict the overall strength of complicated components. This is commensurate with traditional mechanical design, but with the addition of Weibull statistics.     

Controlled stepwise motion in polysilicon microstructures

This paper presents a polysilicon slider and a rotor capable of stepwise motion. These devices were fabricated on a silicon wafer with surface micromachine technology. The proportional relation between the velocity of motion and the frequency of the applied pulse was experimentally confirmed. The peak value of the applied pulse determines the step length. The step values observed were in the range of 10-30 nm for a bushing height of 1.0 μm and of 40-80 nm for a bushing height of 2.0 μm depending on the peak voltage of the applied pulse     

A HARPSS polysilicon vibrating ring gyroscope

This paper presents the design, fabrication, and testing of an 80-μm-thick, 1.1 mm in diameter high aspect-ratio (20:1) polysilicon ring gyroscope (PRG). The vibrating ring gyroscope was fabricated through the high aspect-ratio combined poly and single-crystal silicon MEMS technology (HARPSS). This all-silicon single-wafer technology is capable of producing electrically isolated vertical electrodes as tall as the main body structure (50 to 100's (μm tall)) with various size air-gaps ranging from submicron to tens of microns. A detailed analysis has been performed to determine the overall sensitivity of the vibrating ring gyroscope and identify its scaling limits. An open-loop sensitivity of 200 μV/deg/s in a dynamic range of ±250 deg/s was measured under low vacuum level for a prototype device tested in hybrid format. The resolution for a PRG with a quality factor (Q) of 1200, drive amplitude of 0.15 μm, and sense node parasitic capacitances of 2 pF was measured to be less than 1 deg/s in 1 Hz bandwidth, limited by the noise from the circuitry. Elimination of the parasitic capacitances and improvement in the quality factor of the ring structure are expected to reduce the resolution to 0.01 deg/s/(Hz)^0.5     

Determination of the growth strain of LPCVD polysilicon

This work presents a semi-empirical procedure for determining the through-the-thickness variation of the eigenstrain (eigenstrain is a generic term for any inelastic strain, including plastic strain, free thermal expansion, phase transformation, etc.) that develops during the growth of thin polysilicon films formed using low-pressure chemical vapor deposition (LPCVD). This variation is assumed to depend on the polysilicon microstructure and deposition conditions, but not on the characteristics of the (single crystal silicon) substrate. The procedure involves the use of an elastic laminated plate model to determine the eigenstrain distribution that predicts the experimentally measured substrate curvatures. In comparison to the "shaving method" presented by A.Ni et al., which relies on incremental etching of a single specimen, an alternative experimental procedure is followed to measure the substrate curvatures of a series of different thickness films. While being significantly more time-consuming, the alternative procedure was expected to lead to improved predictions of the eigenstrain distribution, as it avoids the nonuniform film thicknesses produced by the etching procedure. However, a comparison of the curvature histories measured using the two approaches demonstrates that, as long as sufficiently small increments are used in the shaving method, then the improvement is insignificant. This suggests that the plasma etching does not alter the polysilicon's intrinsic growth strain, and that the etch rate nonuniformities across the substrate are small. The eigenstrain distributions could be used, in conjunction with structural mechanics models, to design multilayered polysilicon devices with prescribed curvatures.     

Quality factor in trench-refilled polysilicon beam resonators

In this paper, thermoelastic damping (TED) in trench-refilled (TR) polysilicon microelectromechanical beam resonators is studied as a mechanism for limiting quality factor (Q) at low frequencies. An approximate model based on Zener's theory is developed and verified by numerical simulations in FEMLAB. According to the proposed model a double-dip characteristic is expected for the quality factor versus frequency curve of TR beam resonators. To verify the model experimentally, equal-width TR micro-resonators are fabricated in different length to cover a broad range of frequencies. Frequency response of these devices agrees well with our model. By using the theoretical and numerical models developed in this paper, an upper bound for the quality factor in TR beam resonators or any similar structure such as TR polysilicon gyros can be predicted.     

Comprehensive static characterization of vertical electrostaticallyactuated polysilicon beams

This article unifies two parameter-extraction methods to generate a consistent simulation model calibrated to multi-user microelectromechanical systems processes (MUMPS). The simulation model is calibrated to optical (buckling amplitude) and electrical (pull-in voltage) measurements concurrently, not independently, thus increasing confidence in the extracted parameters. A simulation-based model consisting of geometrical and material property information precludes the need for ad hoc parametric adjustments and simplifying assumptions. The calibration steps consist of identifying relevant simulation model parameters, designing suitable test structures, measuring geometry, then extracting parameters using detailed, yet fast electromechanical simulations, and finally extrapolating the behavior of an actual complex device. This article targets electrostatically actuated beams fabricated in the Poly1 layer, although the model parameters can be used to simulate other devices     

Electrothermal properties and modeling of polysilicon microthermal actuators

This work addresses a range of issues on modeling electrothermal microactuators, including the physics of temperature dependent material properties and Finite Element Analysis (FEA) modeling techniques. Electrical and thermal conductivity are a nonlinear function of temperature that can be explained with electron and phonon transport models, respectively. Parametric forms of these equations are developed for polysilicon and a technique to extract these parameters from experimental data is given. A modeling technique to capture the convective and conductive cooling effects on a thermal actuator in air is then presented. Using this modeling technique and the established polysilicon material properties, simulation results are compared with measured actuator responses. Both static and transient analyzes have been performed on two styles of actuators and the results compare well with measured data.     

Microfabrication using one-step LPCVD porous polysilicon films

A simple, one-step LPCVD process was recently reported to allow the repeatable fabrication of polycrystalline silicon (polysilicon) thin films containing through-pores measuring 10-50 nm in diameter, as-deposited, with no additional processing steps required. This paper describes methods for using this one-step porous polysilicon material to quickly and easily fabricate structures of interest to MEMS designers. Among the structures presented are hermetically sealed diaphragms, hollow tube and shell structures, substrate-aligned membranes over one square centimeter in area ("supermembranes"), and permeable fluidic microchannels on silicon and quartz substrates.     

Mechanical characterization of polysilicon through on-chip tensile tests

Two new types of on-chip tests have been designed in order to evaluate the elastic Young modulus and the fracture strength of polysilicon used in microelectromechanical systems (MEMS). The former is a pure tension test, while the latter is a single-edge-notched tension test. The actuation in both tests is obtained by means of an ad hoc designed layout of parallel plates capacitors applying sufficiently high forces to reach significant strains in the tensile specimens and complete failure of the notched specimens. The pure tension tests on 20 specimens showed a low dispersion and gave a Young modulus for the polysilicon of 143 GPa. A total of 92 notched specimens were tested up to failure. The experimental results, supported by finite-element simulations, gave a value of the maximum stress for the notched specimens in the range 4144-4568 MPa.     

Multimode digital control of a suspended polysilicon microstructure

Digital control of a suspended 350 μm×380 μm×1.6 μm-thick surface-micromachined polysilicon plate is demonstrated in three degrees of freedom, with application to multimode accelerometers, vibratory rate gyroscopes, and actively positioned micromirrors. Plate displacement about the 2.2 μm nominal position above the substrate is measured with shielded capacitive sensors connected to CMOS buffer circuits fabricated adjacent to the microstructure. Four micromechanical sigma-delta loops are used to control eight electrostatic actuators that drive the plate vertically (z) and in out-of-plane rotation (&thetas; and φ). Resonant frequencies are 2.7 kHz for the &thetas; rotational mode and 3.7 kHz for both z and φ modes. The system is evaluated using a mixed mechanical/electromechanical/circuit simulation in SPICE. Closed-loop transient simulation of a 150-Hz square-wave position input signal is in good agreement with experimental results. Squeeze-film damping limits the plate slew rate to 0.83 mm/s in air. Position is controlled to within ±25 mm, being limited by quantization noise at the 50 kHz sampling rate     

Surface micromachined polysilicon heart cell force transducer

A microelectromechanical systems (MEMS) force transducer system, with a volume less than 1 mm³ millimeter, has been developed to measure forces generated by living heart muscle cells. Cell attachment and measurement of contractile forces have been demonstrated with a commercially fabricated surface-micromachined hinged polysilicon device. Two freestanding polysilicon clamps, each suspended by a pair of microbeams, hold each end of a heart cell. When the cell contracts, the beam bend and force is determined from the measured deflection and the spring constant in the beams. The average maximal force over seven contractile experiments using a calcium solution stimulus was F_max =12.6±4.66 μN. Normalizing to a cross-sectional area, F _max/area was 23.7±8.6 mN/mm². These force data were also correlated to optically imaged striation pattern periodicity. Intermediate forces were also measured in response to a calcium solution gradient and showed similar behavior to those measured in other laboratories. This MEMS force transducer demonstrates the feasibility of higher fidelity measurements from muscle cells and, thus, an improved understanding of the mechanisms of muscle contraction