CHAPTER 6
T-MEMS AS TEMPERATURE SENSORS
6.1
Theoretical Performance
Original Specifications
The thermophysical properties of thin films, determined in Chapter 4, was used to
calculate the resolution and temperature ranges for T-MEMS. T-MEMS die used for this
analysis consists of beams between 100 and 50 m long (at 1 m increment). The width
ratios were varied between 0.85 (column 1) and 0.2 (column 14), at increment of 0.05.
This totaled in 51 × 14, or 714 beams on the die. Film structure of the beams were
identical to the actual beams: from top, 0.19 m SiO2, 0.54 m poly-Si, and 1.03 m
SiO2. The beams were assigned an initial deflection of zero, and the distance between
beam and Si substrate was 6 m. These specifications roughly correspond to the original
design specifications of the T-MEMS.
Figure 6.1 shows the progression of T-MEMS as temperature is increased, calculated
theoretically based on materials properties found earlier. The y-axis in the plot indicates
the number of beams within each column that have adhered to the substrate at any given
temperature. The figure shows that as temperature increases, fewer beams change states
per 100 °C change in temperature. This indicates a better temperature resolution at lower
temperature range for these T-MEMS. The original specifications of 14 columns, each
varying between 100 and 50 m long, results in a temperature range of 460 °C to over
2000 °C. Thermal processes in microelectronics industry rarely take place above 1200
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# of beams adhered
40
1100 °C
1000 °C
900 °C
800 °C
700 °C
600 °C
30
20
10
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
column
Figure 6.1 Temperature response of original design of T-MEMS
°C; therefore, much of the shorter beams in the original design do not offer any additional
information. Furthermore,
Modified Specifications
Based on these findings, a new T-MEMS die was designed with a narrower target
temperature range. The sensor is to be effective in 900 – 1100 °C temperature range, as
this is the most commonly used temperature range in RTP. The thermal expansion
coefficients found were used to determine the temperature response for beams with width
ratios ranging between 1.0 and 0.2, having lengths between 100 and 50 m. Of the 867
combinations (17 widths × 51 lengths), 97 beams were found to fall within the specified
temperature range. Width ratios of 0.65, 0.6, and 0.55 were omitted from the die due to
the similarity in temperature response to widths 0.7, 0.75, and 0.8, respectively. The
resulting combination of beam lengths, widths, and resulting temperatures are
summarized in Table 6.1. When the 97 beams are arranged on a die such that the fill
factors remain as described in Table 3.1, they will cover an area of approximately 1.3 mm
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× 1.3 mm. This configuration is optimal when T-MEMS are to be used on silicon wafer.
For use on other substrate materials, beam spacing may need to be altered to produce
more favorable temperature distribution over the wafer.
Table 6.1 Beam dimensions for T-MEMS die with
900 – 1100 °C target temperature
width ratio
1.0
0.95
0.9
0.85
0.8
0.75
0.7
0.5
0.45
0.4
0.35
0.3
0.25
0.2
beam lengths
(m, at 1 m increment)
62 – 68
62 – 68
62 – 68
62 – 68
62 – 68
62 – 68
62 – 68
62 – 68
62 – 68
63 – 69
63 – 69
64 – 70
65 – 71*
67 – 73
temperature range
(°C)
1099.7 – 923.1
1095.3 – 919.4
1091.4 – 916.1
1088.1 – 913.3
1085.5 – 910.9
1083.3 – 909.2
1082.1 – 908.1
1090.9 – 914.6
1098.7 – 920.6
1076.2 – 904.5
1092.6 – 917.6
1083.1 – 911.8
1085.4 – 915.5
1074.9 – 910.6
* - 70 m beam is omitted due to similar response to another beam
Figure 6.2 shows the temperature at which each of the 97 beams make contact the
substrate. The figure shows a non-uniform distribution in temperatures. In fact, the
temperature resolution within the 900 – 1100 °C temperature range varied from less than
1100
1080
1060
1040
1020
1000
980
960
940
920
900
0.1 °C to up to 9 °C. Improving the temperature resolution requires the design of beams
temperature (°C)
Figure 6.2 Temperature response of modified T-MEMS die
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that would adhere to the substrate at temperatures where current set of beam fails (for
example, at ~ 980 °C from Figure 6.2). Fabrication processes of T-MEMS beams require
that the film thicknesses of all beams on a die to be the same; therefore, this is not a
feasible method of customizing beam response. One possibility of adjusting beam
curvature is to vary the length of top and bottom layers. Thermally induced curvature
affects only the layered portion of the beams. However, if the bottom layer were made
substantially longer than the top layer, the extended bottom layer will continue the
downward deflection at a constant slope (matching the slope at the end of layered
portion). The total beam deflection can then be controlled simply by adjusting the length
of the bottom layer that extends out to the substrate. This concept is illustrated in Figure
6.3. This modification will not require any additional processing steps; furthermore, the
relation between deflection and curvature can be related by simple geometry for
modeling.
layered portion
straight
portion
Figure 6.3 Proposed method of improving
temperature resolution of T-MEMS
6.2
Repeatability
The beams were found to undergo permanent change at prolonged exposure to
temperatures above 800 °C. The change in curvature with time was studied for exposure
of up to 50 minutes, and the behavior is shown in Figure 6.4 along with corresponding
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0.002
-10
0.0015
-8
-6
0.001
-4
0.0005
deflection ( m)
curvature (m -1 )
-12
-2
0
0
0
15
30
45
time (min)
60
Figure 6.4 Change in T-MEMS tip deflection after
exposure to temperatures above 800 °C.
values of tip deflection. The sample used in this study had an initial deflection of zero
(flat). The beam deflections were measured after cooling to room temperature. Change
in curvature per minute of exposure was 3.94 × 10-5 m-1, corresponding to a change in
tip deflection of 0.2 m for a 100 m beam.
The cause of the change in beam curvature is not understood. Relaxation in residual
stress at high temperature will produce an opposite effect from what has been observed;
the larger thermal expansion coefficient of poly-Si layer will cause the beams to bend up
upon cooling to room temperature. A possible cause is oxidation of beam layers; the
experiment was conducted in ambient air which may lead to formation of thermal oxide
on the top layer of the beam. Since thermal oxides generally have compressive stress
[39], this may contribute to the negative curvature of the beam following exposure to
high temperature. Although geometric change at high temperature is not desirable for
application, an understanding and characterization of the mechanism may allow the TMEMS to be annealed prior to use to ensure a zero initial deflection. An initially-flat
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beam is beneficial since it will more closely follow the numerical models used to design
the beam dimensions.
6.3
Adhesion
In order for T-MEMS to function as proposed, the deflected beams must adhere to the Si
substrate when they come in contact. This has not been tested yet due to the large air gap
thickness of the present samples (~23 m). The maximum temperature reached by the
samples under experimental conditions is approximately 850 °C, and at this temperature,
the beams do not deflect enough to make contact with the substrate.
However,
preliminary study of adhesion was done using loose beams, scraped off the T-MEMS die,
on a clean Si wafer. Loose beams consisting of silicon nitride and SiO2, curved to a
radius of approximately 200 m, were placed on the Si wafer, which was heated by
conduction using a compact heater. The wafer reached a maximum temperature of
approximately 600 °C. After cooling to room temperature, the wafer surface was lightly
rubbed by a cotton swab, and was examined under the microscope. Several broken
beams were found on the wafer surface, indicating that some portion of the curved beams
had adhered to the wafer and the portion extending from the wafer surface was rubbed
off. This experiment showed that the beams adhere to the substrate with a force larger
than the fracture strength of the beams at room temperature.
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