Invited lectures > Invited Lecture 2

MEMS: FIELD MODELS AND OPTIMAL DESIGN

P. Di Barba, S. Wiak

The invited lecture presents the same-title monograph in press by Springer, which covers a broad overview of methods of both analysis and synthesis of Micro Electro Mechanical Systems (MEMS) and devices./br In particular, the MEMS devices the various case studies are focused on, are analyzed by means of distributed models (i.e. field models) which allow to represent the physical layer i.e. the internal reality which takes place within materials forming the device. In contrast, the traditional approach to analysis is based on lumped-parameter models (i.e. circuit models), which rely on the assumption of disregarding space effects. This twofold approach and its implications at the computing level is described. Following the field model approach, an overview of electrostatics, magnetostatics and steady-state conduction is presented, respectively. Methods to simulate the mechanical effects which take place in the field, i.e. forces and torques of electromagnetic origin acting on a structure, are accordingly illustrated. In turn, an introduction to multiphysics problems is developed as well. On the other hand, the lumped parameter approach is also exploited: the integral parameters characterizing a MEMS device (e.g. the equivalent capacitance), can be reliably computed just starting from field analyses; accordingly, the field-circuit approach is proven and discussed. If simulating a device by solving an analysis problem gives a fundamental information about its behavior, the design of MEMS is the main computational challenge which arises nowadays, in particular, the automated design optimization. In fact, the industrial designers are more and more involved in solving synthesis problems based on procedures of automated optimal design which are, in turn, based on analysis problems. This is the rationale behind Chapter 10 and Chapter 11: in the former, definitions and properties of synthesis (or inverse) problems are summarized and a few regularization methods are presented, while in the latter methods for the automated optimal design are presented and discussed. Because numerical methods have to follow the ongoing technological trend, which is more and more oriented towards Nano Electro Mechanical Systems (NEMS), a selection of NEMS devices is presented; accordingly, it is shown how they can be still modelled by means of numerical methods used for MEMS. A categorization commonly accepted of MEMS devices is based on the inherent actuation principle. In fact, there are many principles of actuation, among the others electrical, magnetic, thermal, fluidic and chemical actuation. Each kind of actuation presents advantages and drawbacks; MEMS devices characterized by electrical, thermal and magnetic actuation are treated.

Electrical actuation is the most common and the oldest one. In fact, capacitive transduction, coupled with the electrostatic actuation, is used for many applications like e.g. pressure sensors, micromotors, accelerometers, gyroscopes and energy harvesters. In particular, pressure sensors became the first mass-produced MEMS device around 1995. On the other hand, electrostatic micromotors were the first devices to be designed and prototyped, exploiting the Silicon integrated technology as early as the late eighties of last century. In the lecture the thermal actuation is presented as coupled with the electrical actuation, i.e. the conduction current heats a structural component of the device thanks to the Joule effect; then, the gradient of temperature gives rise to a strain and, finally, to a displacement. This kind of electro-thermo-elastic device is significant from the point of view of complex models, because of the three coupled fields. Finally, magnetic actuation is considered due to its many advantages. Among the others, low voltages are needed for power supply and, hence, the power consumption is low; moreover, they are simple to control because of their linear response to the input signal. Even if they appear not to be used very extensively, they fill some important niches in mechatronics e.g. for those applications that need large force densities and broad strokes. Following the three actuation types, examples of MEMS devices like micromotors, accelerometers, micromirrors and actuators of various shapes are analyzed by means of field models. In turn, the same devices are considered from the viewpoint of automated optimal design and solved by means of recently proposed optimization algorithms.