Transcript Temperature Sensitve Micro-electro

A Novel System for HighTemperature Curvature
Measurements of T-MEMS
Amy Kumpel
Richard Lathrop
John Slanina
Haruna Tada
Introducing MACS
30 July 1999
Tufts University
TAMPL REU FINAL PRESENTATION
Overview
•
•
•
•
•
T-MEMS Background
The MACS system
Experimental Procedure
Theory
Imaging Results
– Curvature and Deflection
• Material Properties
– Analytical Model and Results
• Conclusion and Future Work
Background: Composition
• Tri-layered cantilever beams
• 1.03 m SiO2, 0.54 m poly-Si
• 0.19 m SiO2 (thin, protective coat)
0.54 m poly-Si
0.19 m SiO2
1.03 m SiO2
Si substrate
SiO2
poly-Si
Imaging System
reflection from curved beam
I.
Apparent Beam Length, lbeam
substrate
beam
well
II.
image of beam on camera
Experimental Setup
CCD camera
beam splitter
collimated
light source
quartz plate
Al reflector
thermocouple
Si wafer
W-halogen lamp
and housing
quartz rod
sample
Experimental Procedure
• Center sample to CCD camera
• Heat to ~850°C using tungsten-halogen lamp then
gradually cool to room temperature
– LabVIEW program records temperature vs. time
data
• Save grayscale images every 20 to 30 seconds
during the trial
– LabVIEW program determines lbeam from grayscale
values of each image
• Calculate beam curvature, K, at each temperature
Theory: Beam Curvature
C
Strategy
f
• Find room-temperature
R from initial h and Larc
R
qC
• Find qC from roomtemperature R and lbeam
h
2qC
A
qC
B
lbeam
• Solve for R at all other
temperatures from qC
and values of lbeam
Theory: Beam Curvature
f
= R ( 1 - cos f )
(1) h = R - R cos
C
f
R
(2)
qC
f =
Larc
R
(3) h = R ( 1 - cos
h
2qC
A
qC
B
lbeam
(4) lbeam = R sin
Larc
)
R
qC =
sin qC
K
Theory: The Angle b
qT
• Mismatched curvature data
– due to incident light angle, b
b
• Experimental Correction
– Perform two trials, using
different sample orientation
– Adjust numerical program to
compensate for b
– Find b so that curvature data
matches for the two trials
2qc
lbeam
qT
Imaging Results:
Beam Curvature (K) and Deflection (h) at High
Temperatures
1500
8
6
1000
500
2
0
0
-2
-500
-4
-1000
-6
-1500
-8
0
200
400
600
Temp (°C)
800
1000
h (m)
K (m-1)
4
Analytical Model
n

thermal 
e
E
t
j j j



n
=
t
j
1

E i g i i - e ithermal +

n

2
i =1
E
t
j j



=
j 1


K= n
p t t 2 
gi 1
2
2
2


+
p
g
+
(
)
E
t
t
3
t
t
i i 
i
i


2 12
i =1
 2 3 
(
n
neutral plane (p):
p
t
= 2-
ti
g
E
i i

2
i=1
n
 Ei t i
i=1
thermal strain: thermal
ei
Tf
=  a i(T) dT
T0
Townsend (1987)



)
Material Properties:
Determining a(T)
• K = f(
,
,
,
)
• Low temperature (50°C to 300°C)
– Find
through linear extrapolation
– Assume constant
, exhibiting glasslike behavior
• High temperature (300°C to 1000°C)
– Assume
– Find
through linear extrapolation
Material Properties:
Linear Approximation of a(T)
a
300
• Analyze different
ranges of data
• Average the a value
for each range
• Extrapolate through
temperature range
a
50
0
100
200
Temp (°C)
300
Material Properties:
a(T) Values from 50°C to 1000°C
6E-06
5.38E-06
Poly-Si
a (1/°C)
5E-06
6.13E-06
4E-06
3E-06
2.54E-06
2E-06
1.83E-06
SiO2
1E-06
5.00E-07
0E+00
0
300
600
Temp (°C)
900
1200
Conclusion and Future Work
•
•
•
•
Modified MACS for increased accuracy
Found values for a(T) of thin films
Created a website
Wrote and submitted paper to:
Measurement and Science Technology
• Modify MACS for nitride beam analysis
• Verify values of a(T) for SiO2 at high temperatures
• Obtain a(T) values for SiNx
Group T-MEMS
Thank You