Electrostatically driven vacuum-encapsulated polysilicon resonators part I. design and fabrication

Basic design issues and a fabrication process based on surface-micromachining techniques for electrostatically driven vacuum-encapsulated polysilicon resonators are presented. A novel freeze-drying method that does not require vacuum equipment is presented. Reactive sealing with LPCVD silicon nitride is used to create the evacuated cavity, resulting in cavity pressures close to the deposition pressure. Design issues regarding choice of materials, technology and layout are discussed. First experimental results, including an admittance plot of the one-port resonator and a plot indicating the dependence of the Q-factor on the resonator geometry and ambient pressure, are presented

Static and dynamic aspects of an air gap capacitor

This paper deals with the theory of an air-gap capacitor used as a micromechanical resonator. Both static and dynamic aspects are discussed. A single-element approach for the electrostatic excitation and capacitive detection of the vibrational motion of the resonators is described. The non-linear character of the electrostatic force is accounted for in the static analysis. The behaviour of the air-gap capacitor is modelled as a lumped spring-mass system and its limitations are discussed. Also an equivalent electrical one-port network is derived, which can be used in a circuit simulation to account for the mechanical behaviour of the resonator. The results obtained from the spring-mass system are compared with the results obtained from a more elaborate numerical analysis of the air-gap capacitor. The lumped spring-mass system is adequate for modelling the air-gap capacitor

Nonlinearity and hysteresis of resonant strain gauges

Nonlinearity and hysteresis effects of electrostatically activated, voltage driven resonant microbridges have been studied theoretically and experimentally. It is shown, that, in order to avoid vibration instability and hysteresis to occur, the choices of the ax. and d.c. driving voltages and of the quality factor of a resonator, with a given geometry and choice of materials, are limited by a hysteresis criterion. The limiting conditions are also formulated as hysteresis-free design rules. An expression for the maximum attainable figure of merit is also given. Experimental results, as obtained from electrostatically driven vacuum-encapsulated polysilicon microbridges, are presented and show good agreement with the theory

Stiction of surface micromachined structures after rinsing and drying: model and investigation of adhesion mechanisms

The mechanisms causing stiction of polysilicon structures fabricated by surface micromachining techniques have been investigated. It is found that during drying from rinse liquids attractive dynamic capillary forces are responsible for bringing micromechanical structures into contact with the underlying substrate. Measured adhesion energies of sticking microbridges indicate that van der Waals forces are responsible for the stiction of hydrophobic surfaces and that hydrogen bridging is an additional adhesion mechanism for hydrophilic surfaces. Methods to reduce the stiction problem are indicated

Design considerations for micromechanical sensors using encapsulated built-in resonant strain gauges

This paper describes the various design aspects for micromechanical sensors consisting of a structure with encapsulated built-in resonant strain gauges. Analytical models are used to investigate the effect of device parameters on the behaviour of a pressure sensor and a force sensor. The analyses indicate that the sealing cap can have a strong degrading effect on the device performance if the thicknesses of the cap and of the supporting structure are of the same order of magnitude. A novel design, employing bossed structures, is described, which reduces the design complexity and virtually eliminates the influence of the cap on the sensitivity of the sensor

A differential resonator design using a bossed structure for applications in mechanical sensors

Theory and experimental results are presented of a differential resonator design employing a bossed structure for applications in mechanical sensors. The effects of residual strain, temperature and mechanical load on the resonance frequency are investigated. Mismatches in the resonators are accounted for in the analysis, resulting in a predicted temperature dependence of the offset and of the sensitivity. Experimental data obtained from a macroscopic brass model, mounted on a steel bar and applied as a force sensor, are given. Compared to a design employing a single resonator, the measurements indicate a doubling in force sensitivity and a reduction of both the intrinsic temperature dependence and of the differential thermal expansion effects. The results of this research are directly applicable to micromachined structures in silicon

Active vibration control using mechanical and electrical analogies

Mechanical-electrical analogous circuit models are widely used in electromechanical system design as they represent the function of a coupled electrical and mechanical system using an equivalent electrical system. This research uses electrical circuits to establish a discussion of simple active vibration control principles using two scenarios: an active vibration isolation system and an active dynamic vibration absorber (DVA) using a voice coil motor (VCM) actuator. Active control laws such as gain scheduling are intuitively explained using circuit analysis techniques. Active vibration control approaches are typically constraint by electrical power requirements. The electrical analogous is a fast approach for specifying power requirements on the experimental test platform which is based on a vibration shaker that provides the based excitation required for the single Degree- of-Freedom (1DoF) vibration model under study

Electrostatically driven vacuum-encapsulated polysilicon resonators part II. theory and performance

In this paper, the design, modelling and performance characteristics of electrostatically driven vacuum-encapsulated polysilicon resonators are addressed. A one-port configuration is preferably employed for excitation and detection of the vibration. Mechanical instability (pull-in) is discussed on the basis of the energy minimum principle. An expression for the pull-in voltage of a beam is given. The electromechanical behaviour in a limited frequency regime around the fundamental resonance is accurately modelled by an electric circuit consisting of a (static) capacitor shunted by a series (dynamic) RLC branch. The d.c. bias dependence of the circuit components and of the series resonance frequency has been experimentally investigated and is compared with the theory. The large-amplitude behaviour is discussed as well. The plate modulus and residual strain of boron-doped polysilicon are estimated from the resonance frequencies of microbridges of varying lengths. The feasibility of their application as resonant strain gauges is investigated. The 210 m long beams typically have an unloaded fundamental frequency of 324 kHz, a gauge factor of 2400 and an uncompensated temperature coefficient of -135 ppm 0C-1

0-Level packaging techniques for flip-chip mounted MMICs

Currently, the thin film microwave multi-chip module (MCM) technology offers many benefits for a compact, lightweight and low cost integration of RF and microwave circuits [see Carchon et al (1)]. This technology allows the realisation of low loss transmission lines with a variety of characteristic impedances (between 10 and 100 Ohm) up to the higher mm-wave frequencies (>50 GHz). The technology also allows mounting active circuits (such as MMICs) by e.g. flip-chip technology. However, when placing different functions closely together, an adequate shielding and also mechanical protection of the active dies may be required. For this purpose, we developed a wafer level (called 0- level) package concept using micromachined cavities to realise versatile, microwave compatible protection and shielding structures on the thin film substrate. 0-level packaging refers to packaging before separation of the dies of the thin film integration substrate. In order to illustrate this concept and the benefits in real microwave functions, the realisation of a Ka-band LNA module, including 0-level package, bias circuits and RF feedthrough structures is discussed in this contribution

Micro resonant force gauges

A review of micro resonant force gauges is presented. A theoretical description is given of gauges operating in a flexural mode of vibration, including a discussion of non-linear effects. Gauge factor and quality factor are defined and their relevance is discussed. Performance issues such as sensitivity, stability and resolution are addressed. Design aspects, including the means for excitation and detection of the vibration, and examples of silicon microfabrication technologies are described