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MECH 466Microelectromechanical Systems

University of VictoriaDept. of Mechanical Engineering

Lecture 8:Thermal Sensors & Actuators

© N. Dechev, University of Victoria

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Example of Heat Rise Time in a Polysilicon Beam

Thermal Expansion of Micro-devices

Thermal Bimorph Principle

Thermal Actuators

Thermal Resistors

Thermal Sensors and Actuators Overview

© N. Dechev, University of Victoria

3© N. Dechev, University of Victoria

Example of Heat Flow in a Polysilicon Beam:

Consider the doped polysilicon beam, as shown below:

PolysiliconBeam

Si Substrate

Lbh

gap bw

+V

GND

q’’

- Parameters Given:Applied voltage, V: 0.5 VElec. resistivity, ρ: 23 Ω umTemp of Air, T∞: 21˚CTemp of Substrate, T∞: 21˚C

Beam length, L: 100 um Beam width, bw: 4 umBeam height, bh: 4 umGap: 4 um

4© N. Dechev, University of Victoria

Example of Heat Flow in a Polysilicon Beam:

Questions:

(a) What is the thermal time constant, τ, for the beam?

(b) What is the final steady state temperature, T, of the beam?

(c) How long will it take to heat the beam to 95% of it’s S.S. temp?

5© N. Dechev, University of Victoria

Example of Heat Flow in a Polysilicon Beam:

Step 1: Find the heat input

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Step 2: Determine thermal capacitance, CTH:

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6© N. Dechev, University of Victoria

Example of Heat Flow in a Polysilicon Beam:

Step 3: Determine thermal resistance, RTH:

Consider the possible heat flows, q1, q2, etc... out of the beam:

Cross-Section

Si Substrate, Troom

Free AirTroom

Beam

q’’convection

q’’convectionq’’convection

‘Still’ Air q’’conduction

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Example of Heat Flow in a Polysilicon Beam:

Step 3 (continued): Model system as a ‘thermal circuit’:

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8© N. Dechev, University of Victoria

Example of Heat Flow in a Polysilicon Beam:

Step 4: Having defined the system parameters, such as: heat input, CTH and RTH answer the problem questions:

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Nearly all materials undergo a change in volume or dimensions as their temperature changes.

For solids such as semiconductors, metals and dielectric materials, their volume increases as the temperature increases, as follows:

where:

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Thermal Expansion of Micro-Devices

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Alternatively, we can define:

where:

Note the relation that exists between the two:

Note: Tables 5.2 and 5.3 in the textbook have common values listed for β, for a number of common MEMS materials.

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Thermal Expansion of Micro-Devices

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Liquids and gases typically have much greater thermal expansion, where:

note:

For gases, we can use the ideal gas law:

where:

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Thermal Expansion of Micro-Devices

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Two different materials, with different coefficients of thermal expansion, are joined together in such a way, that a temperature change will cause the entire structure to deform in a desired way.

Consider the following:

where we assume α1 > α2

© N. Dechev, University of Victoria

Thermal Bi-morph Principle

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δ-displacement

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The radius of curvature of the deformed structure can be expressed as (in terms of the variables of previous diagram):

To find a value for deflection, consider the arc-angle θ:

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Thermal Bi-morph Principle

rr

rsinθ

θ

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Example Displacement of Bimorph Actuator

See Class Notes:

15© N. Dechev, University of Victoria

Thermal Actuators

Operate based on Ohmic heating of different cross-sectional areas.

We will attempt to estimate the deflection of this device, based on the following assumptions:

-Cold arm remains straight-Hot arm will bend in an ‘arc’ shape-Connection of cold arm and hot arm considered as a point

Hot Arm

Flexture

Cold Arm

Anchor

PadsGap

δ-deflection

r

dor-radius of curvature

θ

‘Arc’ is length of hot arm

16© N. Dechev, University of Victoria

Thermal Actuators

Deflection Estimation:

Deflection Estimation:

Some useful circleformulas:

r

h

dor-radius of curvature

θ

‘Arc’ is length of hot arm

c-‘chord’ islength ofcold arm +flexture

17© N. Dechev, University of Victoria

Thermal Actuators

18© N. Dechev, University of Victoria

Thermal Actuators

For thermal actuators, we can assume:

Therefore, based on this information, we can determine both, r and θ.

Then, we can use r and θ to determine the tip deflection using:

19© N. Dechev, University of Victoria

Thermal Resistors

A thermal resistor is an electrical resistor with significant temperature sensitivity

The resistance of a thermal resistor is defined as:

where:

A Thermistor is a semiconductor thermal resistor.

20© N. Dechev, University of Victoria

Example of Thermistor

Consider the following doped polysilicon beam:

If the TCR of the doped material is 200 ppm/˚C, and the nominal (un-heated) resistance Ro is 1000 Ω, what is the resistance if the temperature increases by 300˚C?

A

B

w

t

L

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Thermal Resistors

Note: When measuring resistance, care must be taken so as not to create a significant current i, during measurement.

Otherwise, a large current could cause further ohmic heating, and invalidate the measurement.

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Case Study: Thermal Accelerometer (with no moving mass)

It is possible to create an accelerometer, with no moving structures at all, using thermal phenomena.

Figure 5.13. Thermal Accelerometer, [Chang Liu]

23© N. Dechev, University of Victoria

Case Study: Hot-Wire Anemometer

Hot-wire anemometry (HWA) is a thermal-sensor based method used for the measurement of fluid velocity.

Conventional HWAs are: (1) difficult to assemble and fabricate and (2) difficult to arrange in an array to measure an entire fluid flow field distribution.

Figure 5.14. Diagram of ‘Conventional’ HWA, [Chang Liu]

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Velocity of Fluid

24© N. Dechev, University of Victoria

Case Study: Hot-Wire Anemometer

MEMS technology is ideally suited to overcome both of these limitations.

Figure 5.15. MEMS based HWA, [Chang Liu]

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Case Study: Bimorph Artificial Cilia Actuator

Many micro-scale biological systems, can be mimicked using MEMS based devices.

This example shows how ‘cilia’ can be mimicked, and potentially used for handling and transporting micro-objects.

Figure 5.5. MEMS based Artificial Cilia for Micro-object Transport, [Chang Liu]

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Thermal Sensors and Actuators

For Homework:

Review Example 5.1.

Read Case Studies:

5.3 Lateral Thermal Actuators

5.8-Bimetallic Structure for Infrared Sensing