(SEM VI) THEORY EXAMINATION 2024-25 INTRODUCTION TO MEMS

BOE063 – INTRODUCTION TO MEMS

Section-Wise Solved Answers (2024–25)

SECTION A

Attempt all questions in brief (2 × 7 = 14 marks)

(a) Define MEMS and list two applications.

MEMS (Micro-Electro-Mechanical Systems) are miniature devices that integrate mechanical elements, sensors, actuators, and electronics on a single silicon chip using microfabrication techniques. These systems sense, control, and actuate on the micro-scale.
Common applications include accelerometers in smartphones and pressure sensors in automotive systems.

(b) What is the piezoresistive effect?

The piezoresistive effect refers to the change in electrical resistance of a material when mechanical stress is applied to it. In MEMS, this effect is widely used in sensors where mechanical deformation of beams or diaphragms produces a measurable change in resistance, enabling sensing of pressure, force, or acceleration.

(c) State Hooke’s Law in the context of beam structures.

Hooke’s Law states that within the elastic limit, stress is directly proportional to strain. For beam structures in MEMS, this means that the deformation of a beam is proportional to the applied force, provided the material remains within elastic limits.

(d) Explain the term “moment of inertia” for a beam.

The moment of inertia of a beam is a geometrical property that represents the resistance of the beam to bending. It depends on the beam’s cross-sectional shape and dimensions. A larger moment of inertia results in lower deflection under applied load.

(e) What is viscous flow in the context of air damping?

Viscous flow refers to air motion where viscous forces dominate over inertial forces. In MEMS devices, viscous flow causes energy loss due to friction between moving microstructures and surrounding air, leading to air damping that affects dynamic response.

(f) Differentiate between squeeze-film and slide-film air damping.

In squeeze-film damping, air is trapped between two closely spaced surfaces and resists motion when the gap changes.
In slide-film damping, air resists motion when surfaces slide parallel to each other. Squeeze-film damping is generally stronger and more dominant in MEMS.

(g) What is the role of fringe effects in electrostatic actuation?

Fringe effects arise due to non-uniform electric fields at the edges of electrodes. In electrostatic actuation, fringe fields increase the effective capacitance and electrostatic force, influencing actuator performance, especially at small dimensions.

 SECTION B

Attempt any three (7 × 3 = 21 marks)

(a) Explain the technique of PVD for MEMS device fabrication and list its advantages.

Physical Vapour Deposition (PVD) is a thin-film deposition technique where material is vaporized in a vacuum and deposited onto a substrate. Methods include sputtering and evaporation.
Advantages of PVD include good film purity, precise thickness control, low contamination, and compatibility with MEMS microfabrication processes.

(b) Derive the expression for displacement of a cantilever beam under its own weight.

For a cantilever beam of length L, uniformly distributed load w per unit length, Young’s modulus E, and moment of inertia I, the maximum deflection at the free end is:

δmax=wL48EI\delta_{max} = \frac{w L^4}{8 E I}δmax​=8EIwL4​

This expression is widely used in MEMS to estimate deflection of micro-beams under self-weight or uniform loading.

(c) Explain Reynolds’ equation for squeeze-film air damping and its significance.

Reynolds’ equation describes pressure distribution in thin fluid films. In MEMS squeeze-film damping, it explains how trapped air resists motion between closely spaced surfaces. It is significant because it helps predict damping forces, resonant frequency, and quality factor of MEMS devices.

(d) Describe the working principle of a parallel-plate actuator focusing on capacitive sensing.

A parallel-plate actuator consists of two electrodes separated by a small gap. When voltage is applied, electrostatic force pulls the plates together. The change in gap alters capacitance, which is measured for sensing displacement. This principle is widely used in MEMS sensors and actuators.

(e) Discuss design considerations for a MEMS resonator including one-port modeling.

Design considerations include resonant frequency, quality factor, material properties, geometry, damping effects, and fabrication limits.
In one-port modeling, the resonator is represented by an equivalent electrical circuit that simplifies 
analysis of resonance behavior and energy loss.

SECTION C

Attempt any one (7 × 1 = 7 marks)

(a) Explain the processes for micromachining in MEMS fabrication, highlighting materials and substrates.

Micromachining involves creating micro-structures on silicon substrates. It includes bulk micromachining (etching into the substrate) and surface micromachining (building structures layer by layer). Materials such as silicon, polysilicon, silicon dioxide, and metals are commonly used due to their mechanical and electrical properties.

(b) Describe the piezoresistive sensor and its applications in MEMS.

A piezoresistive sensor converts mechanical stress into resistance change. In MEMS, these sensors are fabricated on beams or diaphragms and are used in pressure sensors, accelerometers, and force sensors due to high sensitivity and easy integration.