Analysis of the bending T-MEMS
The bending structures are heated using the “rapid radiant heater” setup, which consists of a
tunsgsten-halogen heat source, sample holder, reflector plates, CCD camera, and fiber optic
illuminator (see figure). The W-halogen lamp radiatively heats the sample to up to 1000°C. The
reflector plates minimize the radiative heat loss from the sample, as well as supress the
convective current above the sample which may distort the image seen by the CCD camera. The
sample is illuminated by a collimated light source from fiber optics, and is monitored by the
CCD camera as they bend. During the heating, temperature is monitored by a type-K
thermocouple bonded to a small piece of Si wafer.
CCD camera
telescopic lens
fiber optics
collimator
beam splitter
Al reflector plates
type-K
thermocouple
Si wafer
quartz rod
T-MEMS die
small Si wafer
W-Halogen Lamp
The consequence of using collimated light source to view curved structure is that only a portion
of the beam appear bright as seen by the CCD camera. This is due to the numerical aperture of
the CCD (the extent of the “cone” of light entering the camera). The curvature of the beams can
be found by geometrically relating the angle of the beam with respect to the collimated light, and
the numerical aperture of the camera.
Microscale Radiative Effects
Microscale radiative effects are most prominent when the wavelength of radiation in question is
on the same order of magnitude as the thickness of thin-films involved in the process. The TMEMS use sub-micron thick films, and are subject to microscale effects when heated radiatively.
The effect of thin film interference and the resulting change in radiative properties on the
temperature distribution on the wafer was analyzed for the bending T-MEMS [1].
Thin-film interference in the bending structures result in a highly non-linear spectral radiative
properties. The figure below shows the spectral reflectivity for two cases of bending beams: etch
depth of 1m () and 2m (). The figure also shows the normalized blackbody emissive
power for a lamp temperature of 700K. The large fluctuations in reflectivity is due to the thin
film interference between the two layers of the beam, as well as the cavity underneath the beam.
The total reflectivity is found by integrating the product of the blackbody emissive power and the
spectral reflectivity. Therefore, one can see that if a large peak in the spectral reflectivity
coincides with high blackbody emission, then the result is a high total reflectivity. Similarly, a
low spectral reflectivity in the high blackbody emission region of the spectrum will result in a
low total refletivity. Because the peaks and valleys of the spectral property fluctuates with
minor changes in thin film structure, the total radiative properties changes dramatically as well.
Note, for opaque materials, absorptivity = 1 – reflectivity (evaluated using blackbody emissive
power at lamp temperature), and emissivity = 1 – reflectivity (evaluated using blackbody
emissive power at wafer temperature).
0.7
1.00
0.6
0.75
0.5
 0.4
0.50
Eb
(Eb,)max
0.3
0.25
0.2
0.1
0.00
1
2
3
4
5
6
7
wavelength (m)
8
9
10
The total radiative properties found by the above method was used to find the steady-state
temperature distibution of a wafer. The results are shown in detail in [1] and [2]. This analysis
for T-MEMS is important for two reasons. First, the T-MEMS are designed to be a mechanically
non-intrusive sensor. However, they can be indirectly intrusive by affecting the local
temperature on the wafer, thereby causing unnecessary thermal stress. The degree of this effect
must be evaluated and analyzed. Second, in order to be used effectively as temperature sensors,
T-MEMS must accurately measure the wafer temperature. If the presence of T-MEMS affect the
local temperature distribution, then the temperature indicated by the T-MEMS may not
accurately represent the temperature of the wafer. A general rule can be assessed from the
results from [2]: a) temperature distribution on the wafer approaches that of a uniform wafer
when the dies are small and far-spaced, and b) temperature uniformity improves when the dies
are large and closely packed; however, in this case, the temperature approaches that of a wafer
having the property of the die.
References
1. H. Tada, I. N. Miaoulis, and P. Y. Wong, "Numerical Simulation of Radiant Thermal
Processing of Bilayer Microcantilevers," American Society of Mechanical Engineers
Conference Proceedings, DSC-Vol.66, pp.37-44, 1998.
2. H. Tada, A. R. Abramson, I. N. Miaoulis, and P. Y. Wong, "Effect of Surface Patterning in
Thin Film Structures on the Thermal Radiative Properties During Rapid Thermal Processing,"
American Society of Mechanical Engineers Conference Proceedings, HTD-Vol. 361-2, pp.9398, 1998.