Micro Electro-Mechanical Systems

2016 Micro Electro-Mechanical Systems

Nadia Paderno

Politecnico di Milano

22/07/2016

Sommario

• Introduction ....................................................................................................................2
• Fabrication process .........................................................................................................2
• Basic notion of kinematics ................................................................................................3
• Basic notions of dynamics .................................................................................................4
• One degree freedom oscillator ........................................................................................4
• Basic notions of electrostatics ............................................................................................5
• Parallel plate capacitors ................................................................................................6
• Interdigitated “comb-finger” capacitors .............................................................................6
• Coupled electro-mechanical problem ......................................................................................6
• Parallel plate connected with an elastic spring .......................................................................6
• Comb-finger connected with an elastic spring ........................................................................7
• Capacitive accelerometers ...................................................................................................7
• Capacitive gyroscopes ........................................................................................................9
• Piezoelectricity ................................................................................................................9
• Energy harvester .......................................................................................................... 10
• Resonant accelerometers .................................................................................................. 10
• A-Resonant accelerometer .............................................................................................. 10
• B-Resonant accelerometer .............................................................................................. 11
• Electrostatic stiffness variation ..................................................................................... 11
• Momentum of inertia variation ...................................................................................... 11
• Geometrical stiffness variation ...................................................................................... 11
• Torsional resonator ....................................................................................................... 12
• Thermo-mechanical problem .............................................................................................. 12
• Electro-thermo mechanical actuators ................................................................................... 13
• Fracture and fatigue ........................................................................................................ 13
• Weibull approach ......................................................................................................... 14
• Fatigue ...................................................................................................................... 15
• Residual stresses ............................................................................................................. 15

Introduction

MEMS are made up of components between 1 to 100 µm (as the human hair diameter) in size. They usually consist of a central unit that processes data, the microprocessor, and several components that interact with the outside such as microsensors or microactuators to exercise a control action.

Fabrication process

On a silicon wafer substrate, generally monocrystalline thanks to the Czochralski method, an oxide sacrificial layer is deposited (with the desired pattern), followed by a mechanical/structural layer. Both of them are generally in silicon, respectively thin polysilicon and thick epitaxial polysilicon. The structural layer is patterned by photolithography and etching. The end of the process consists in sacrificial oxide removal and contact metallization deposition. Many processes start with the thermal oxidation of the substrate to protect and electrically insulate the substrate from the upper device.

Contact printing occurs when the mask is directly posed on the photoresist, giving the possibility of contamination. On the other hand, proximity printing can cause diffraction; actually, projection printing is the most used technique to avoid both problems and even thanks to reduced costs (bigger masks can be produced). The etching process consists of three steps: mass transport of reactants to the surface; reaction between reactants and the films to be etched at the surface; mass transport of reaction products. The advantage is the high selectivity, because it is based on a chemical process; the disadvantage is related to poor process control. Plasma etching has largely replaced wet etching because of the possibility to have directionality (thanks to ionic components). Reactive Ion Etching is also used to obtain nearly vertical sidewalls.

The complexity of the structure depends on the number of repeated steps and generally is defined by the number of used masks. Raw polycristalline silicon is produced starting from selected sands and by reduction and refining in a reaction furnace. A pure silicon seed crystal is placed into the molten bath, pulled out slowly as it is rotated (homogeneous nucleation). The product is a monocrystalline silicon ingot, which is cut, lapped, polished, and cleaned. Through dry or wet oxidation process, at 800 – 1200 °C. Through CVD (epitaxy, electrodeposition) or PVD (evaporation, sputtering) processes.

A micromachined silicon wafer cap protects the mechanical element and ensures the right damping to the MEMS. Wafers are aligned to each other and bonded by direct fusion (1000 °C), anodic bonding (Pyrex glass, 500 °C, positive voltage application), glue layer (glass frit or gold, thermo-compression process). Packaging is applied to a unique box made of MEMS dies and ASIC (Application Specific Integrated Circuit). It is possible to use: plastic, low cost, access for light, but possibility to break due to encapsulation process; ceramic materials, durable, well-sealed, higher costs; metals, solution for harsh environments, can be well sealed. Hermeticity is very important.

Basic notion of kinematics

One reference frame in motion with respect to another, considering P fixed: the components c and n change in time. The velocity of the point P as seen from O’ is given by where the c derivative is the velocity of O with respect to O’. So we obtain. We can also compute the relative acceleration. One reference frame in motion with respect to another, considering P in motion: motion composition. Inertial reference frame: all inertial frames are in a state of constant, rectilinear motion with respect to one another, they’re not accelerating.

Basic notions of dynamics

So “apparent forces” can be defined. Note that these equations are referred to a material point, not to a rigid body. However, they can be interpreted as governing the motion of the centroid of the body.

One degree freedom oscillator

The material point is in dynamic equilibrium under the action of: linear elastic, viscous damping, external and inertial forces. The equation of motion is. The general solution is given by the sum of a general integral of the homogeneous equation plus a particular solution of the whole equation. Forced oscillations, considering an external sinusoidal force with amplitude A. Looking for a particular solution we find. It is like a “filter”.