Design & Fabrication of

MEMS GYROSCOPE

Abhishek Garg (10020) Guided by :Sanjeev Kumar (10645) Prof. N S Vyas Shobhit Yadav (10695) Dept. of Mechanical Engineering

IIT Kanpur

MEMS Devices Introduction

• MEMS are devices and systems integrated with mechanical elements,

sensors, actuators and electronic circuits on a common silicon substrate

through micro fabrication technology.

• Size of components vary between 1-1000 μm.

• MEMS emerged with development of IC fabrication.

• MEMS devices are manufactured by using batch fabrication techniques.

• Uses:- Navigation; Flight stabilization of aircrafts and rockets; military

application include use in missiles, barrage rounds and hypersonic

projectiles; automotive application.

Gyroscopes• Gyroscope is a device used for measuring and maintaining orientation and

works on the principle of angular momentum.

Working :- The device consists of a spinning wheel or a disc whose axle is free to

take any orientation and this orientation changes much less in response to a

given external torque. Since the external torque is minimized by mounting the

device in gimbals, its orientation remains nearly fixed, regardless of any motion

of the platform on which it is mounting. The traditional gyroscope derives its

precision from the large angular momentum that is proportional to the heavy

mass of the flywheel, its substantial size and its high rate of spin.

http://www.youtube.com/watch?v=cquvA_IpEsA

MEMS Gyroscope

• MEMS gyroscope is based on Coriolis force which is induced in it due to the

combination of vibration of a proof mass and an orthogonal angular rate input.

• The proof mass is generally suspended above the substrate by a suspension

system consisting of flexible beams and overall dynamic system can be realized

as a 2 degrees of freedom mass spring damper system.

• Prior works on MEMS gyroscope:- Tuning fork gyroscopes, torsional

gyroscopes, ring gyroscopes, piezoelectric vibrating gyroscopes and clover leaf

gyroscope.

• Application:- Spacecraft orientation, automotive sensors, image stabilization

systems on video and still cameras employ vibrating structure gyroscopes,

vibrating structure gyroscopes are used in radio controlled helicopters to help

keep the tail steady during take off.

Dynamics and design aspects of MEMS Gyroscope

• The most basic visualization of a MEMS gyroscope is a single proof mass suspended above a substrate. The proof mass is free to oscillate in two perpendicular direction the drive and sense direction.

• When gyroscope is subjected to an angular rotation a Coriolis force having

a frequency same as drive mode oscillation is generated in the sense

mode direction. This force excite the sense mode accelerometer causing

the proof mass to respond in the sense direction.

• Equations of motion can be expressed as :-

+ + = (1)

+ + = (2)

• The resonant frequency of the sense mode accelerometer is designed

closed to the frequency of the coriolis force. Then the coriolis force excites

the system into resonance in the sense direction.

Drive mode operation :- The drive mode oscillator is a 1 DOF resonator,

which can be modelled as a mass-spring-damper system consisting of the

drive proof-mass , drive mode suspension system providing the drive

stiffness and the drive damping consisting of viscous and thermal elastic

damping.

+ + (3)

(4)

by solving (3) and (4), we get

(5)

) where and At resonance = ꙍ Sense mode operation :- It is also 1 DOF resonator. (6)

where ,

If and • to achieve the maximum possible gain in sense mode it is generally

desirable to operate at or near the peak of sense mode response curve i.e. .

• Note:- the sense mode phase becomes -from the drive velocity

Phase relations

• The sense mode position phase depends on the drive and sense frequency

separation (∆ f ) and damping. The drive mode oscillator is usually operated at resonance and drive mode position phase is - relative to the applied drive signal.

from equation

,

• With the phase

where ∆f when drive and sense modes are matched, i.e. ∆f = 0, the sense mode phase becomes

Design Aspects

Linear suspension system :- The flexure system that suspends the proof mass above

the substrate consists of thin flexible beams. Common suspension structures include

crab-leg suspensions, serpentine suspensions, hair-pin suspensions, H-type

suspensions and U-beam suspensions.

• The same beams experience deflections in both modes, resulting in undesired

coupling between the drive and sense modes. A solution to this problem is to use a

decoupling frame.

• Linear flexure elements :- Suspension systems utilize narrow beams as the primary

flexure elements, aligning the narrow dimension of the beam normal to the motion

axis.

• Folded U-beam is two fixed guided beams connected in series. It eliminates the non

linearity and axial loading limitation of single fixed guided beams.

• A double folded beams is formed by connecting two U-beams in parallel.

Electrical design of MEMS gyroscope (Actuation and detection mechanisms):-

• In many MEMS applications, capacitive detection and electrostatic actuation is

mostly used because they provide good DC response, noise performance, high

sensitivity, low drift and low temperature sensitivity.

Electrostatic Actuation :- Actuation and sensing electrodes are modelled as a

combination of moving parallel-plate capacitors.

capacitance

0 electrostatic force

• The electrostatic force is expressed as the gradient of energy stored in capacitor.

Variable gap actuation :- Two plates of the parallel plate capacitor are movable in the normal direction.

• The electrostatic spring constant due to force non-linearity is - • The electrostatic spring constant of parallel-plates is a negative spring constant,

and always reduces the resonant frequency with increasing net DC bias across the electrodes.

Variable area actuation :- Two plates of the parallel plate capacitor are movable in the lateral direction.

• Since the force is independent of the initial overlap length, a good practice in comb-drive design is to keep the overlap length minimum, while greater than the expected actuation peak amplitude.

Balanced actuation-push-pull driving :- When a sinusoidal net actuation force is

desired the drive force can be linearized with respect to actuation voltages by

appropriate selection of voltages applied to opposite electrode sets. The net

electrostatic force generated by two opposing capacitors is

• A balanced actuation scheme is a common method to linearize the force with

respect to a constant biased voltage and time varying voltage

Comb drive actuator :- Since comb drive force in the x-direction is not a

function of displacement in the x-direction its partial derivative with respect to

x is zero which means that comb drive do not result in negative electrostatic

spring constant.

• Comb drive actuators make use of lateral electrostatic driving force to activate

the movable mass. Effect of normal force is eliminated by arranging stationary

electrodes symmetrically on both sides of each movable comb finger. Lateral

driving force from both side electrode which are same in direction and equal in

magnitude will not cancel out but the normal driving forces which are equal in

magnitude and opposite in direction cancel out each other. Movable fingers

are activated in horizontal direction only.

• For a comb drive structure with N fingers on each side, structural thickness t

and finger distance d

• For a parallel plate actuator structure with N plates on each side, thickness t,

overlap length l and plate gap d

Capacitive Sensing :- A change in gap distance d and overlap area S will cause

a change in capacitance and by measuring this change we know the value of

displacement in respective direction.

Variable gap capacitive sensing :- Displacement in the motion direction is y

and assuming y<< the capacitance change with an overlap length becomes

• They are used for detection of small displacement.

Variable area capacitive sensing :- They are used when the deflections are

larger than minimum gap or when variable gap capacitance become non-

linear.

where x is displacement

• Differential Sensing :- It is employed to linearize the capacitive change with deflection.

• The differential capacitance change is

Damping• Damping is the energy dissipation effect in an oscillatory system

Viscous damping :- is the viscous effects of the gas trapped between the proof

mass surfaces and the stationary surfaces.

• Slide-film Air damping :-occurs when two plates of an area A, separated by a

distance , slide parallel to each other.

• Squeeze-film Air damping :- occurs when two parallel plates move towards

each other and squeeze the fluid filled in between.

Structural damping :- It includes thermoelastic damping (TED), electronics

damping, damping due to anchor and material type and other damping

effects.

Proposed Design Design constraints :- Resonant frequencies should lie in the range 3-10 kHz, as

ambient noises and vibration lie in the range 1-3 kHz and sensitivity of

gyroscope is inversely proportional to the operating frequency.

• Coupling between drive and sense motion should be minimum, damping

should be low, device thickness should not increase 10 μm and no feature size

should be less than 3 μm and gap between any two feature should not be less

than 3 μm.

Proposed design :- The design comb driving plate differential capacitance

sensing vibratory gyroscope. The device can be fabricated through bulk micro-

machining process and DRIE (deep reactive ion etching) technique can be used

for comb finger etching. The device is based on glass-silicon compound

structure through silicon-glass anodic bonding technique.

Proposed structure: 1. Glass substrate 2. Anchors 3. Fixed driving fingers 4. Movable driving fingers 5. Folded driving beams 6. Folded sensing beams 7. Decoupling frame 8. Central movable mass 9. Bonding anchors

Features :-

• The folded beam structures in driving portion and sensing portion increases

the amplitude driving and sensing vibration which helps in increasing the

device sensitivity.

• Decoupling frame weakens the coupling between two bonds .

• Due to insulating substrate the parasitic capacitances are less which is helpful

for signal detection.

• Using single piece silicon crystal as structure helps to achieve high quality

factor for both driving and sensing modes, also there is no residual stresses.

• Variable area actuators are used for driving the structure and variable gap

sensing mechanism is used for sensing.

• The device uses differential capacitance sensing instead of sensing the single

capacitance change as it can further cancel the environment noise and improve

the device capacitance sensitivity.

Working principle :-

• AC driving voltage with same magnitude but phase difference are applied to

the left and right fixed driving fingers which introduces alternating electrostatic

forces on the movable driving fingers along x-direction.

• The frame along with central mass will vibrate along x-direction in a push-pull

mode, which is driving mode.

• The frequency of the driving voltage is chosen to match the resonant frequency

of the truss and central mass structure to achieve large vibration amplitude.

• Central mass experiences an alternating coriolis force along y-direction. The

central movable mass will be activated along y-direction (sensing mode).

• The sensing differential pair will change due to sensing vibration. By measuring

this differential capacitance change the value of angular velocity can be known.

Design Parameters :-

Device dimension including anchors = 1.42 mm * 1.12 mm

DESIGN PARAMETERS VALUES DESIGN PARAMETERS VALUES

Device thickness 10 μm Driving beam length 285 μm

Driving beam width 5 μm Sensing beam length 310 μm

Sensing beam width 5 μm Central mass length 400 μm

Central mass width 400 μm Comb finger length 40 μm

Comb finger width 4 μm Total number of finger pairs 35

Driving capacitance gap 3 μm Finger overlapping length 20 μm

Sensing capacitance gap 3 μm Sense electrode length 350 μm

Frame horizontal arms 900*60 μm Frame vertical arms 1000*30μm

Mathematical Model Analysis :-

Resonant frequency :-

• Total spring constant in driving direction (

• Total spring constant in sensing direction (

• Total driving mass (

• Total sense mass (

• Resonant frequency of drive mode (

• Resonant frequency of sense mode (

Electrostatic tuning :-

• for large sensing amplitude hence a DC biasing voltage is used to tune down

in differential capacitance sensing to precisely match . This technique is called

electrostatic tuning.

• We apply a DC biasing voltage between top and bottom frequency tuning electrodes.

,

• if ∆k the effective resonance frequency in sensing mode after electrostatic

tuning can be expressed as

,

• Biasing voltage can be calculated by using above equation and using the values

Damping Analysis :-

• Damping coefficient (

• Using the design parameters and viscosity coefficient

,

• Damping ratios

• The damping ratio for both the modes meet the requirement of light damping

(ζ < 0.7).

Dynamic Analysis :-

• Drive displacement :-

• The main design criterion is that we want approximately 2.5 micron drive

displacement.

• Using force equation for comb drive and design parameters

• For

for (atmospheric conditions)

for 000 (vacuum conditions)

• Sense displacement :-

• Using design parameters frequency values and drive displacement for ,

for (vacuum conditions)

for (atmospheric conditions)

Sensitivity Analysis :-

• Displacement sensitivity :- The gyroscope displacement sensitivity is defined

as sensing vibration amplitude of the central mass in response to unit angular

velocity

• When

nm/(°/sec) for = 126 (atmospheric conditions)

nm/(°/sec) for = 1000 (vacuum conditions)

• Capacitive Sensing :-

• The capacitance sensitivity of gyroscope can be expressed as

using design parameters

• Using these values

/(°/sec) for Q = 126 (atmospheric conditions) /(°/sec) for Q = 1000 (vacuum conditions)

Fabrication• MEMS process flows can be classified into two primary categories: bulk

micro-machining and surface micro-machining. Bulk micro machining means

that three dimensional features are etched into the bulk of the crystalline and

non-crystalline materials. In surface micro machining features are built up

layer by layer on the substrate.

• The MEMS vibratory gyroscope proposed here is a bulk micro machining

gyroscope.

• MEMS fabrication consists of following steps :-

Oxidation :- This process involves the deposition of Si layer on the top of a

silicon substrate. formed is used as a common insulating layer, as a mask and

as a sacrificial material. performs as a mask against diffusion of the common

dopants in silicon.

Doping :- The two means of doping silicon are diffusion and ion-implantation.

• Diffusion is a method of introducing impurities into the silicon wafer. The

dopants used are boron (p-type) and phosphorus (n-type). The rate of diffusion

is a function of temperature.

Photolithography :- It is a method of transferring patterns to the surface of

silicon wafers. Components involved are :-

• Mask :- It is a stencil used to generate a desired

pattern on photoresist coated wafers. It is a

optically flat glass (transparent to near UV) or

quartz plate(transparent to deep UV) with an

absorber pattern metal (opaque to UV light).

• Photoresist :- These are organic polymers

sensitive to UV radiation.

• When UV light falls on it their solubility gets altered. There are of two types

negative and positive.

Types of photoresist

Metallization :- In this process a layer of metal is deposited on the substrate

surface. The proposed design involves the deposition of Cr/Au layer on the

substrate by PVD (physical vapor deposition) process.

• PVD process is of two types :-

• Evaporation :- Metals are heated up to its vaporization temperature and then

evaporate to form a thin film on the surface of the target. To control the

composition of the deposited material evaporation is performed under vacuum

condition.

• Sputtering :- In this the target at a high negative potential is bombarded with

positive Ar ions created in plasma. The target (a disc of material to be deposited)

material is sputtered away mainly as neutral atoms by momentum transfer and

ejected surface atoms are deposited on the substrate placed at anode. Cr/Au

layer is used to make electric contact pads on the device and it provides good

adhesion properties.

Etching :- It is used to chemically remove layers form the surface of a wafer.

Wafer is protected from the etchant by a masking material which resists

etching. Etching process is classified as dry and wet etching :-

• In wet etching chemicals in liquid state are used while in dry etching ionized

gases are used. In the proposed design DRIE (Deep Reactive-Ion Etching) is

used.

Reactive-Ion Etching :- A radio frequency (RF) signal is applied to the anode

of the parallel plate reactor.

• After the base pressure is achieved gases are introduced into the chamber.

When the pressure is in the appropriate range RF power is applied to the anode

due which electrons are emitted from the anode. The negatively charged

particles collide with gas atoms and molecules creating free radicals and

stripping of electrons creating ions. These electrons combine with ions and

create photons to conserve energy. The substrate is placed on the cathode and

heated to an appropriate temperature for etching. The direction of the species

hitting the substrate surface is random. Hence ion flux changes as a function of

depth. As a result RIE is not suitable for high aspect ratio. The etching via RIE is

isotropic and rate is very fast.

Deep Reactive-Ion Etching - ICP Reactor :- This type of system is used for Deep-

RIE. Direction of the ion bombardment of the substrate is highly directional in

an ICP reactor which is very important for deep etching. After the base pressure

is achieved processed gases are turned on. Once the RF input power is applied

to the large coil that surrounds the vacuum chamber, plasma is created.

• In an ICP Reactor the AC current in the coil creates a magnetic field. The charge particles are accelerated by the magnetic force.

• The DRIE process is an alternation of short time isotropic etches in S plasma and short time polymer deposition using plasma. DRIE process is now called Bosch Process.

• Principle of Bosch Process :- A single short time etching step is applied to the

patterned silicon substrate in plasma and the exposed silicon is etched in an

almost isotropic manner.

• The process switches to a polymerization step and a polymer layer is

deposited on the exposed silicon surface as well as on mask.

• The polymer layer on the bottom of the structure is rapidly removed by ion

bombardment and the etchant continues to react with the exposed silicon.

The combination of etching and polymerization results in good anisotropy.

• High etching rate, high selectivity, ultra large etching depth, high aspect ratio

can be achieved.

Wafer Bonding:- Silicon can be bonded to the glass by anodic bonding

process.

Fabrication Flow• The MEMS gyroscope proposed is to be fabricated with the bulk micro

machining process. The fabrication flow is developed in IntelliFAB . The

fabrication process is done in 4 steps:-

• Step 1 :- Making anchors and wiring on glass substrate.

• Step 2 :- Gyro structures is formed on the silicon substrate

• Step 3 :- Both the formed structures are bonded anodically.

• Step 4 :- Undoped silicon is dissolved to release the device.

Mask Designing• The masks used in the process flow are designed for negative photoresists.

The fabrication step for this MEMS gyroscope are simple and only three

photolithography masks are needed. The masks are designed in IntelliMask.

Comparison with the Pre-fabricated Device

Specifications Values Values

Previous Design Proposed Design

Gyroscope size (mm²) 1 1.6

Structural layer thickness (μm) 10 10

Drive mode resonance frequency (Hz) 40,650 4,800

Sense mode resonance frequency (Hz) 41,250 4,900

Sense gap (μm) 1.5 3

Biasing voltage (V) 40 15

Sense capacitance (fF) 130 130

Drive-mode vibration amplitude (μm) 2 2.5

Quality factor (at atmosphere) 500 126

Advantage of proposed design over previous design :-

• Previous design cannot be operated for drive displacement more than 2 μm

whereas the proposed design can be operated for large drive displacements.

• The previous design utilizes variable area sensing elements which is not

suitable to measure small displacement change whereas the proposed design

utilizes the variable gap sensing element which is more suitable for smaller

displacement changes.

• The biasing voltage is low in the proposed design.

• Although the quality factor is greater in previous design the sense capacitance

is same.

Thanks