Microtransducer CAD

Modeling and simulation collectively describe the complex process of constructing models of a device, process, or system, and subsequently imitating its function on a computer [1].

In contrast to very large scale integrated (VLSI) devices, microtransducers have relatively large dimensions and are not in the race to push the limits of feature size into the submicron regime. Thus with microtransducers, it is reasonable to assume a static picture for electrical transport in the device, whereby the mobile charge carriers are in equilibrium with the host lattice. This permits the use of the classical model comprising Poisson’s equation, which relates the electrostatic potential and space charge in the device, and the electron and hole continuity equations, which account for charge conservation, with current density relations based on the drift-diffusion formulation. Effects of non-static transport have become very important in VLSI devices where the active device dimensions are reaching scales (nm) where the carrier transit time becomes comparable to the collision time.

The model equations and boundary conditions reviewed in the preceding chapter describe electrical transport in semiconductor microtransducers in the absence of external fields. As summarized in Sect. 2.7, external fields appreciably alter carrier transport by introducing asymmetries in device operation. For example, radiation alters the generation-recombination rate, and hence, the electrical carrier transport in a semiconductor by virtue of its wavelength- and material-dependent absorption. In this chapter, we review the physical effects induced by radiant signals along with associated model equations relevant to simulation and subsequent optimization of optical microtransducers.

The domain of magnetic signals ranges from the very weak biomagnetic fields (∼ 10 fT) to the very high fields associated with superconducting coils (∼ 10 T) (see [1–6]). As a measure of the field strength H, we use the related magnetic induction B whose unit is 1 tesla = 1 Vs/m² and is related to the field strength as: B = μ₀ H in vacuum, where μ₀ is the free space permeability. In this very large span of over 15 orders of magnitude in field strength, the lower limit of field strengths (< 1 μT) requires relatively sophisticated detection devices and techniques [4], such as the flux-gate magnetometer, fiber optic magnetometer, nuclear magnetic resonance, and the superconducting quantum interference device, while the higher field strengths can be resolved by semiconductor magnetic sensors. Our discussion on the modeling issues will be restricted to the latter. Here, the signals are associated with geomagnetism (30–60 μT), magnetic storage media (∼ 1 mT), permanent magnets for contactless sensing (5–100 mT), and current carrying conductors (∼1 mT at 10 A) [6]. These signals lend themselves to two categories of direct and indirect applications [1–3]. Direct applications include measurement of the geomagnetic field, reading of magnetic storage media, identification of magnetic patterns in cards and banknotes, and control of magnetic apparatus. In indirect applications, a non-magnetic signal is detected via the magnetic field which is used as an intermediate carrier. Examples include voltage-free current detection and watt-hour meters, and contactless sensors, based on mechanical displacement of a permanent magnet, for detection of linear or angular displacement and velocity.

Physical properties of semiconductor materials and devices are sensitive to variations in temperature, whether generated from the ambient or internally in a device or integrated circuit (IC). While the variations in temperature associated with the ambient can be treated as uniform (isothermal) relative to device dimensions, internal heat generation is highly localized giving rise to a temperature gradient, which constitutes a non-isothermal signal. Various methods can be employed for detection of thermal signals. For measurement of ambient temperature, we can employ the highly predictable and stable temperature dependence of the base-emitter voltage V _BE of a bipolar junction transistor. Together with co-integrated biasing, signal correction, and amplification circuitry, they provide an output voltage or current that is proportional to absolute temperature (PTAT) [1, 2]. On-chip temperature gradients or non-isothermal signals transduced by physical signals, not necessarily from the thermal domain (see [3, 4]), can be detected using thermoelectric or thermoresistive effects. Our discussion of modeling issues will be restricted to non-isothermal signals and related microtransducers; models pertinent to isothermal signals are reviewed in Chapt. 2.

Simulation of the static and dynamic behavior of solid structural and fluid mechanical variables, e.g., stress, strain, strain-rate, displacement, force, and velocity, is critical to the design and analysis of microsensors and microactuators in the mechanical domain. For example, in Chapt. 6, we saw how electrical transport is modified by piezoresistance. This, in addition to deflection-induced capacitance change, can be effectively utilized for conversion of signals from the mechanical to the electrical domain. Alternatively, as we will see in Chapt. 8, a micromechanical structure subject to an electrical, thermal, magnetic, or mechanical excitation signal, gives rise to micro-actuation in the mechanical domain. In this chapter, we deal with model equations and constitutive relations relevant to: simulation of mechanical (e.g., pressure) microsensors; computation of velocity profiles relevant to flow microsensors (needed in Chapt. 5) and selected microfluidic systems; computation of mechanical stresses induced by packaging or encapsulation of microtransducers or integrated circuits (needed in Chapt. 6); and simulation of mechanical microactuators, including fluidic damping effects (needed in Chapt. 8).

Microactuators are miniaturized output transducers which convert an electrical input signal into a non-electrical output signal in the radiant, magnetic, thermal, mechanical, or chemical domains [1, 2]. Integrated silicon microactuators are realized using integrated circuit (IC) micro-fabrication techniques coupled with application-specific thin film deposition and micromachining technologies [3–11]. Central to current research is microactuation in the mechanical domain. Mechanical microactuators are three-dimensional structures with physical dimensions ranging from micrometers to millimeters. Progress in the field is rapid with evolution of new thin film actuation materials [12–14] and proliferation of increasingly complex micromechanical systems. Mechanical microactuators are part of Micro Electro Mechanical Systems (MEMS), a field which has grown to encompass a broad family of micromachined sensors, actuators, and systems that exploit coupled electrical, mechanical, radiant, thermal, magnetic, and selected chemical effects [15, 16]. The simulation of mechanical microactuators is the topic of this chapter.

Support electronics has become an essential part of the microtransducer providing necessary control and signal processing/conversion functions for improved accuracy, reliability, and functionality (see [1, 2]). Integration of these elements on a single chip constitutes the first step towards realization of microsystems [3, 4]. The efficient design of successful microsystems critically rests on accommodating the interaction of mixed electrical, thermal, mechanical, magnetic, radiant, and chemical signals. Most importantly, since the microtransducer is central to control and feedback operation, it cannot be isolated from circuitry in the design process. For example, in the design process for an integrated accelerometer microsystem (see Fig. 9.1a) one has to: evaluate the system response to transient electrical and mechanical signals; optimize operating bias and self-test procedures with respect to accelerometer reliability associated with electrostatic pull-in; minimize the influence of read-out operation on accelerometer performance; and evaluate the sensitivity of electrical and mechanical system performance to variations in accelerometer or circuit parameters. Thus, it is crucial that the simulation tool or environment accounts for the mixed-signal microtransducer-circuit interactions and yet provides reasonably accurate functional descriptions for both.