[...]... that u(t) = 1 for t ≥ 0 and u(t) = 0 for t < 0 Step response is the system response to a step input 3a 6 Fabrication and Design of Resonant Microdevices Figure 1.3 Amplitude and phase responses of two resonators with quality factors of 5 and 25 and identical resonant frequencies of ω0 = 1000 rad/sec Figure 1.4 The step response of a resonator with a Q of 25 and resonant frequency of ω0 = 1000 rad/sec... William Andrew Inc 1 2 Fabrication and Design of Resonant Microdevices Figure 1.1 Amplitude response of a system with multiple resonant frequencies infamous example of destructive effects of resonance at large scales To avoid such disasters, the structural designers try to damp the resonant response of the system by including proper energy dissipating mechanisms in the design Common examples of resonance... and the height differences across the wafer, a doping step to adjust electrical properties or for film thickness adjustments, and bonding of wafers and substrates to other substrates 2.1 Material Selection The first step when designing a process flow for fabrication of a micromachined device is to choose the structural and other materials which c 2008 William Andrew Inc 9 10 Fabrication and Design of Resonant. .. Design of Resonant Microdevices a micromachined resonator after a number of cycles, or damp the resonator response to unacceptable levels References 1 M Elwenspoek and R Wiegerink, Mechanical microsensors, Springer-Verlag, Berlin, Germany, 2001 2 M.J Madou, Fundamentals of microfabrication: the science of miniaturization, 2nd edn., CRC Press, Boca Raton, USA, 2002 3 S.D Senturia, Microsystem design, ... (i.e., imaginary part of system poles for ζ = 0), ω0 , of a second order 1 Natural frequencies are also the eigenvalues of the characteristic equation of the system for a higher order device when its operation is approximated as that of a second order device over a limited bandwidth 2 Or 4 Fabrication and Design of Resonant Microdevices system is: 1− ωr = ω0 1 2Q2 (1.5) Most micromachined resonators... Failure of resonant systems is often a result of imperfections (i.e., defects) in the structural materials Micromachined devices are significantly less prone to these imperfections thanks to their small dimensions and the random scatter of such defects across the bulk of the material Nevertheless, a material defect can prevent the resonator from operating, cause permanent failure of 8 Fabrication and Design. .. [10] [11] [11] [11] [11] [11] [11] References Table 2.1 Properties of Materials Commonly Used in Fabrication of MEMS Resonators at 300 K Applications nomenclature: 1: Structural; 2: Transduction; 3: Sacrificial; 4: Dielectric; 5: Coating; 6: Electrical routing; and 7: Etch mask 2: Microfabrication 11 12 Fabrication and Design of Resonant Microdevices there are several applications which require the devices... 2000 2 Microfabrication Dimensions of micromachined devices generally fall in the 100 nm to 10 mm range Although some micromachined structures could be produced by precision machining techniques, the associated cost and low throughput of precision machining techniques prohibits commercial applications of such techniques Instead, fabrication of MEMS mainly relies on the technologies inherited from microelectronic... Introduction Microengineering refers to the practice and technology of making three dimensional structures and devices with dimensions on the order of less than a micrometre to a few millimetres Micromachining is the name for the techniques used to produce the structures and moving parts of microengineered devices Microelectromechanical Systems (MEMS) contain tiny mechanical elements that are often produced... circuits and microwave cavities Unwanted electrical resonance is the cause of ringing in the step response of electrical systems and in some cases may lead to instabilities 1.2 Frequency and Time Response of Resonators An example of the amplitude response of an underdamped system (to be defined shortly) with multiple resonant frequencies is shown in Fig 1.1 The resonance behaviour of a system around its resonant . FABRICATION AND DESIGN OF RESONANT MICRODEVICES MICRO & NANO TECHNOLOGIES Series Editor: Jeremy Ramsden Professor of Nanotechnology Microsystems and Nanotechnology Centre, Department of. Inc. 1 2 Fabrication and Design of Resonant Microdevices Figure 1.1 Amplitude response of a system with multiple resonant frequencies. infamous example of destructive effects of resonance at large. the present range of their sizes probably represents the optimal endpoint of a compromise between adequate performance and acceptable cost. The latter depends not only on the direct costs of making