Novel Microelectromechanical Systems (MEMS) for the
Study of Thin Film Properties and
Measurement of Temperatures During Thermal Processing
A Master’s Thesis
submitted by
Haruna Tada
In partial fulfillment of the requirements
for the degree of
Master of Sciences
in
Mechanical Engineering
TUFTS UNIVERSITY
September, 1999
Advisors: Peter Y. Wong and Ioannis N. Miaoulis
Novel Microelectromechanical Systems (MEMS) for the Study of Thin Film
Properties and Measurement of Temperatures During Thermal Processing
Haruna Tada
Thermal Analysis of Materials Processing Laboratory
Mechanical Engineering Department
Tufts University
Medford, MA 02155
ABSTRACT
Rapid thermal processing (RTP) has become an important processing technique in the
microelectronics industry. In RTP, wafers are heated individually by radiative heat
sources to a temperature of over 1000 °C at heating rates of up to 100 °C/sec. RTP
requires precise control of temperature to ensure successful processing; however,
currently available techniques for measuring temperatures lack accuracy or are highly
intrusive in nature. A novel temperature sensor based on microelectromechanical systems
(MEMS) was developed as a non-intrusive, inexpensive alternative for RTP temperature
measurements.
The sensor, called T-MEMS, consist of an array of multilayered
microcantilever beams. At high temperatures, the beams bend down due to difference in
thermal expansion coefficients of the layers. At some temperature, the beams come in
contact with the substrate material, at which point they adhere to the substrate. An ex situ
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examination of the T-MEMS allows the determination of maximum temperature reached
during processing.
Designing and modeling of T-MEMS require accurate values for thin film properties:
Young’s moduli (E) and thermal expansion coefficients () of polycrystalline silicon and
silicon dioxide, both as functions of temperature. However, such data are lacking in
literature, and the need for accurate determination of E and  at high temperatures is one
of the large concerns among the quickly growing MEMS industry.
An innovative
technique was developed to use the T-MEMS as testing structures for the determination
of Si and SiO2 at high temperatures. An experimental apparatus was developed to
optically measure T-MEMS curvature as they are heated by tungsten-halogen lamp. The
curvature was related to a numerical model of thermally-induced multilayer curvature in
order to extract the material properties for temperatures up to 1000 °C. Properties found
above were used calculate the theoretical resolution and temperature range for T-MEMS
design, and a modified design was developed to better address the temperature range of
interest, and to improve the resolution of the sensors.
The effect of T-MEMS on surrounding wafer temperature was determined using a steadystate heat transfer model. Local variation in radiative properties of wafer was found by
applying coherent and incoherent radiative effects. Results indicate that T-MEMS cause
negligible effect to the temperature distribution when fabricated on a plain Si wafer,
thereby satisfying the condition for being a non-intrusive temperature sensor.
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ACKNOWLEDGEMENTS
The past few years have unquestionably been the most rewarding years of my life so far,
and I have many people to thank for making it so. I would like to express my greatest
gratitude to my advisors for the past 5 years, Professor Peter Wong and Dean Ioannis
Miaoulis, for introducing me to research early in my undergraduate study, encouraging
me to stay involved, and convincing me to continue on for graduate degree.
I’d like to thank my lab partner, Seth Mann, for constant help, support, and all the laughs
– we’ve come a long way since BASH. I am also grateful for the contributions from
Alexis Abramson, without whom much of the numerical work would not have been
possible. Thanks also extend to all the undergraduate researchers who have contributed
so much time and mind to this project: Emilie Nelson, Melissa Bargman, Amy Kumpel,
Richard Lathrop, and John Slanina. Patricia Nieva and Professor Paul Zavracky of
Northeastern University have been a source of many ideas, and I am especially grateful
for all the work that has gone into fabrication of the samples. I also thank the National
Science Foundation for funding this project under grant number DMI-9612068.
Finally, a huge thanks to my friends and family for the constant encouragement.
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TABLE OF CONTENTS
Abstract................................................................................................................................ ii
Acknowledgements............................................................................................................ iv
Table of Contents................................................................................................................. v
Nomenclature..................................................................................................................... vii
List of Figures..................................................................................................................... iv
List of Tables..................................................................................................................... xii
Chapter 1: Introduction.................................................................................................... 2
1.1 Temperature Measurement in Microelectronics Industry.................................... 2
1.2 Thermophysical Properties of Thin Films............................................................5
Chapter 2: Experimental Study..................................................................................... 11
2.1 T-MEMS Fabrication........................................................................................ 11
2.2 Curvature Measurements................................................................................... 14
2.3 Radiative Property Measurements..................................................................... 18
Chapter 3: Numerical Models........................................................................................ 22
3.1 Thermally Induced Curvature............................................................................ 22
3.2 Radiative Properties........................................................................................... 26
3.3 Temperature Distribution on a Wafer................................................................ 34
Chapter 4: Thermophysical Properties......................................................................... 37
4.1 T-MEMS Curvature Measurements................................................................... 37
4.2 Determination of Thermophysical Properties.................................................... 38
Chapter 5: Radiative Properties.................................................................................... 42
5.1 Verification of Numerical Model.......................................................................42
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5.2 Radiative Properties of T-MEMS...................................................................... 51
5.3 Steady-State Temperature Distribution During RTP......................................... 53
Chapter 6: T-MEMS as Temperature Sensors............................................................ 58
6.1 Theoretical Performance.................................................................................... 58
6.2 Repeatability...................................................................................................... 61
6.3 Adhesion............................................................................................................ 63
Chapter 7: Conclusions................................................................................................... 64
Chapter 8: Future Work................................................................................................. 68
Appendix A.........................................................................................................................??
Appendix B.........................................................................................................................??
References.......................................................................................................................... 69
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NOMENCLATURE
A
area
a
absorption coefficient
Cv
specific heat
d
wafer thickness
E
Young’s Modulus
F
area fill factors
h
tip deflection of beam
K
curvature
k
thermal conductivity
Lbeam
actual beam length
lbeam
apparent beam length as seen by CCD camera
q
heat transfer
rc
radius of curvature
T
temperature
t
beam thickness
V
voltage
w
beam width


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Greek

absorptivity

thermal expansion coefficient

nodal distance in heat transfer model

emissivity

strain

arc angle formed by the entire length of beam

wavelength

angle between the beam and horizontal

reflectivity

transmissivity
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LIST OF FIGURES
Figure 2.1
T-MEMS fabrication process........................................................................ 12
Figure 2.2
Layout of beams on T-MEMS die................................................................ 13
Figure 2.3
SEM micrograph of bending T-MEMS........................................................ 14
Figure 2.4
Schematic of experimental setup for measurement of
thermally induced curvatures of T-MEMS................................................... 15
Figure 2.5
Geometry of beam.........................................................................................16
Figure 2.6
Schematic of experimental setup for spectral reflectivity measurements..... 19
Figure 2.7
High temperature sample holder for the integrating sphere......................... 21
Figure 3.1
Discretization of thin film layers.................................................................. 22
Figure 3.2
Linear approximation of low-temperature thermal expansion
coefficient of poly-Si.................................................................................... 25
Figure 3.3
Radiative effects through a wafer................................................................. 27
Figure 3.4
Partial transparency effects........................................................................... 28
Figure 3.5
Blackbody emissive power function for various temperatures..................... 31
Figure 3.6
a) Top-view of T-MEMS under optical microscope;
b) T-MEMS regions..................................................................................... 33
Figure 3.7
Control volume for heat transfer model....................................................... 35
Figure 4.1
Beam curvature and deflection at high temperatures................................... 37
Figure 4.2
Thermal expansion coefficient of poly-Si at low temperatures.................... 39
Figure 4.3
Thermal expansion coefficient of silicon at high temperatures.................... 40
Figure 4.4
Thermal expansion coefficient of SiO2 thin films........................................ 40
Figure 4.5
Thermally induced curvature in T-MEMS beam.......................................... 41
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Figure 5.1
Spectral reflectivity of double-sided silicon wafer....................................... 43
Figure 5.2
Total normal absorptivity and emissivity of double-sided silicon wafer...... 44
Figure 5.3
Spectral reflectivity of single-sided silicon wafer and
0.25 m SiO2 film at room temperature....................................................... 45
Figure 5.4
Spectral reflectivity of 0.25 m SiO2 film at high temperatures.................. 46
Figure 5.5
Total normal absorptivity and emissivity of single sided silicon and
0.25 m SiO2 film........................................................................................ 46
Figure 5.6
Effect of film thickness on total normal absorptivity and
emissivity of SiO2 films on Si wafers at 800 °C........................................... 47
Figure 5.7
Spectral reflectivity of 3-layered film structure at room temperature.......... 48
Figure 5.8
Total normal absorptivity and emissivity of 3-layered film
structure on single-sided Si wafer................................................................. 48
Figure 5.9
SiO2 grating patterns on Si wafer..................................................................49
Figure 5.10 Spectral reflectivity of SiO2 gratings at room temperature........................... 50
Figure 5.11 Spectral reflectivity of SiO2 gratings at ~ 500 °C ........................................ 50
Figure 5.12 Spectral reflectivity of T-MEMS regions......................................................51
Figure 5.13 Total normal absorptivity and emissivity of T-MEMS regions.................... 52
Figure 5.14 Temperature distribution on a uniform Si and 3-film wafers....................... 54
Figure 5.15 Temperature profile of wafers with T-MEMS dies...................................... 55
Figure 5.16 Temperature distribution over uniform wafers for
Si and T-MEMS wafer................................................................................. 56
Figure 5.17 Temperature distribution of 3-film wafer with T-MEMS dies;
die spacing of 10 mm.................................................................................... 56
x
Figure 5.18 Temperature distribution over 3-film wafer with
modified T-MEMS dies................................................................................ 57
Figure 6.1
Temperature response of original design of T-MEMS................................. 59
Figure 6.2
Temperature response of modified T-MEMS die......................................... 60
Figure 6.3
Proposed method of improving temperature resolution of T-MEMS.......... 61
Figure 6.4
Change in T-MEMS tip deflection after exposure to
temperatures above 800 °C........................................................................... 62
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LIST OF TABLES
Table 1.1
Survey of existing literature on Young’s modulus of
polycrystalline silicon films............................................................................ 7
Table 3.1
Fill factors for T-MEMS regions.................................................................. 34
Table 4.1
Input parameters to numerical model........................................................... 38
Table 4.2
Average Si for low temperature ranges....................................................... 39
Table 5.1
Grating pattern sizes..................................................................................... 49
Table 5.2
Total radiative properties of wafer regions................................................... 53
Table 5.3
Wafer layouts used for simulation................................................................ 53
Table 5.4
Fill factors of modified die........................................................................... 57
Table 6.1
Beam dimensions for T-MEMS die with 900 – 1100 °C
target temperature......................................................................................... 60
xii