CHAPTER 5
RADIATIVE PROPERTIES
5.1
Verification of Numerical Model
In order to assess the effects of T-MEMS on surrounding wafer temperature during
radiative heating, the average radiative property over the die must be calculated as a
function of temperature. The radiative properties, specifically the total emissivity and
absorptivity, over the T-MEMS is found by a combination of numerical models
developed in Chapter 3.
Each component of the model was first verified against
experimental results from simple cases.
Properties of Silicon
Silicon wafer is used as the substrate material for T-MEMS; therefore, the properties of
Si play a strong role in determining the average property of the dies. As described in
Chapter 3, the radiative properties of silicon are governed by the three absorption
mechanisms of silicon. Figure 5.1 shows the spectral reflectivity of a double-polished
silicon wafer from 400 to 2000 nm at temperatures up to 1000 °C. Also shown are the
experimental results at room temperature, ~320 °C, and ~500 °C. The wafer is doublepolished; therefore, the backside reflectivity is equal to the frontside reflectivity. At
room temperature, the spectral reflectivity shows a rapid increase at ~ 1100 nm. This
increase is located at the absorption edge of silicon, where bandgap absorption ceases.
Free carrier absorption is weak at low temperatures; therefore, at wavelengths past
bandgap absorption edge, partial transparency effect enhances silicon reflectivity. At
42
0.6
0.55
C
0.45
500 °C
300 °

25 °
C
0.5
0.4
600 °C
0.35
1000 °C
800 °C
0.3
400
600
800
1000
1200
1400
1600
1800
2000
wavelength (nm)
Figure 5.1 Spectral reflectivity of double-sided silicon wafer.
() experimental at room temperature, (×) experimental at ~330 °C,
() experimental at ~500 °C, (—) numerical.
higher temperatures, the absorption edge shifts to higher wavelengths, and free carrier
absorption increases. These effects are shown clearly in the numerical and experimental
results. The numerical model shows that at temperatures above ~800 °C, the wafer
becomes completely opaque as free carrier absorption increases.
The total normal absorptivity and emissivity of silicon wafer are shown in Figure 5.2 as
functions of temperature.
Lamp temperature of 2200 °C was used for absorptivity
calculations. The increase in free carrier absorption at ~ 500 °C is indicated by the
increase in both absorptivity and emissivity at the temperature. At temperatures above
800 °C, the properties remain nearly constant as the wafer becomes completely opaque.
43
, 
0.8
0.7

0.6

0.5
0.4
0.3
0.2
0.1
0
0
200
400
600
800
1000
wafer temperature (°C)
Figure 5.2 Total normal absorptivity and emissivity of double-sided silicon wafer
Properties of Thin Films
The effects of a single SiO2 film on radiative properties was studied using a 0.25 m
oxide film deposited on a single sided Si wafer. The backside reflectivity for the wafer is
approximated to be 0.25 for all wavelengths.
Figure 5.3 shows the numerical and
experimental spectral reflectivity of the wafer at room temperature, along with the
reflectivity of silicon substrate. Thin film interference from the oxide layer causes a large
fluctuation in the spectral reflectivity; however, the values always fall below the
reflectivity of silicon.
The net effect of a single layer of film is a reduced total
reflectivity, and consequently an enhanced total emissivity and absorptivity. The partial
transparency of silicon substrate still has a strong effect on the wafer reflectivity, which
shows the characteristic rise in reflectivity at the absorption edge.
44
0.55
0.5
Si
0.45
0.4

0.35
0.25 m film
0.3
0.25
0.2
0.15
0.1
400
600
800
1000
1200
1400
1600
1800
2000
wavelength (nm)
Figure 5.3 Spectral reflectivity of single-sided silicon wafer and 0.25 m SiO2
film at room temperature. (×) experimental for Si wafer,
() experimental for SiO2 film, (—) numerical
The spectral reflectivity of the thin film wafer at high temperatures are shown in Figure
5.4. The plot includes numerical results for temperatures up to 1000 °C, as well as
experimental result measured at ~ 500 °C. The change in spectral reflectivity at high
temperature follows the changes of the silicon substrate; the shift in bandgap absorption
edge and the decrease in partial transparency effect is shown in this case as well. The
general shape of the total normal emissivity and absorptivity of the single-film wafer,
shown in Figure 5.5, also mimic that of silicon. The presence of the film, however,
results in an increase in both absorptivity and emissivity.
The deviation from the
properties of silicon depends non-linearly on film thickness, as shown in Figure 5.6. For
very thin films, the properties approach that of silicon. The properties approach constants
for films with thicknesses above ~ 1.2 m. In all cases, the properties are higher than that
for plain silicon.
45
0.6
0.5
0.4
25°C
 0.3
0.2
500°C
0.1
1000°C
0
400
600
800
1000
1200
1400
1600
1800
2000
wavelength (nm)
Figure 5.4 Spectral reflectivity of 0.25 m SiO2 at high temperatures.
() experimental at ~500 °C, (—) numerical.

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.9
0.8
0.7
0.6
0.5

0.4
0.3
0.2
0.1
0
film
Si
0
200
400
600
800 1000
film
Si
0
temperature (°C)
200
400
600
800 1000
temperature (°C)
(a)
(b)
Figure 5.5 a) Total normal absorptivity and b) total normal emissivity of
single-sided silicon and 0.25 m SiO2 film, determined numerically.
46
0.85

0.8
 film
 film
 silicon
 silicon
0.75
0.7
0.65
0
0.5
1
1.5
2
SiO2 film thickness (m)
Figure 5.6 Effect of film thickness on total normal absorptivity and emissivity
of SiO2 films on Si wafers, calculated numerically at 800 °C.
Multilayered films on wafers produce a more dramatic change to spectral reflectivity of
the wafer. The three-layer film structure used in T-MEMS was used for the analysis.
The layers consist of (from top): 0.19 m SiO2, 0.54 m poly-Si, and 1.03 m SiO2 on
single-sided Si wafer. The spectral reflectivity of the structure at room temperature is
shown in Figure 5.7. Although the locations of peaks for numerical and experimental
results show good agreement, the amplitudes of peaks do not coincide in some cases.
This is attributed to slight variations in film thickness of the structure. Unlike the singlefilm case, the effect of partial transparency is less obvious in this case, and the wafer
reflectivity is dominated by the thin film interference effects from the three layers. For
three-layered film, the spectral reflectivity does not always fall below that of silicon, and
the net effect on the total properties is less predictable. The variation in total normal
absorptivity and emissivity with temperature for the multilayered structure is shown in
Figure 5.8. For the layers studied here, the total absorptivity and emissivity are both
reduced by as much as 7% below the values for plain Si wafer.
47
0.8
0.7
0.6
0.5

0.4
0.3
0.2
0.1
0
400
800
1200
1600
2000
wavelength (nm)
Figure 5.7 Spectral reflectivity of 3-layered film structure at room temperature.
() experimental, (—) numerical.
0.7

0.7
0.6
3-films
0.6
3-films
0.5
Si
0.5
Si
0.4

0.3
0.4
0.3
0.2
0.2
0.1
0.1
0
0
0
200
400
600
800 1000
0
temperature (°C)
200
400
600
800 1000
temperature (°C)
(a)
(b)
Figure 5.8 a) Total normal absorptivity and b) total normal emissivity of
3-layered film structure on single-sided Si wafer, calculated numerically.
48
Properties of Surface Patterns
0.25 m SiO2 film
Two grating patterns with feature on
the order of microns were used to
study the effect of micron-scale
Si substrate
w
patterns on the radiative property.
The gratings are as illustrated in
s
Figure 5.9 SiO2 grating patterns on Si wafer
Figure 5.9, and the sizes are listed in
Table 5.1 Both of the patterns had a
Table 5.1 Grating pattern sizes
fill factor of 37% (the ratio between
w
2.2 m
6.7 m
grating 1
grating 2
grating width and oxide width). The
patterns
were
fabricated
F
0.37
0.37
by
photolithographically etching the 0.25 m oxide layer studied earlier.
The spectral
reflectivity of the pattern measured experimentally at room temperature is compared to
results from numerical model based on the average area technique (Figure 5.10). Also
shown on in the figure is the empirical result, calculated by applying the average area
technique to the experimental results from plain silicon wafer and the 0.25 m oxide
film.
All three curves show excellent agreement, indicating that the average area
technique can be validly used for the length scales studied. The experimental, numerical,
and empirical results at ~500 °C are shown in Figure 5.11. The numerical and empirical
results show good agreement; however, the reflectivities of the two patterns diverge in
the partially transparent region. This is likely due to slight change in temperature during
the experiment; the reflectivity in the transparent region falls rapidly between 400 and
600 °C, leading to a large error in reflectivity with small change in temperature.
49
0.55
0.5
0.45
0.4
 0.35
0.3
0.25
0.2
400
800
1200
1600
2000
wavelength (nm)
Figure 5.10 Spectral reflectivity of SiO2 gratings at room temperature (F=0.37).
() grating 1 experimental, (×) grating 2 experimental,
(—) numerical averaging, (+) experimental averaging.
0.6
0.55
0.5
0.45

0.4
0.35
0.3
0.25
0.2
400
800
1200
1600
2000
wavelength (nm)
Figure 5.11 Spectral reflectivity of SiO2 gratings at ~500 °C (F=0.37).
() grating 1 experimental, (×) grating 2 experimental,
(—) numerical averaging, (+) experimental averaging.
50
5.2
Radiative Properties of T-MEMS
A T-MEMS die consist of five distinct regions: 1) Si substrate, 2) three-layered film, 3)
single layered film, 4) three-layered beam suspended over Si, and 5) single layered beam
suspended over Si. The fill factors for each area on the die is listed in Table 3.1. The
spectral reflectivity of each region was calculated numerically, and are shown in Figure
5.12 for all regions excluding the three-film region, which was calculated earlier in
Figure 5.7. Region 3, with the single SiO2 layer, exhibits the same characteristic as was
seen in Figure 5.3; however, because the film here is thicker than the 0.25 m film
studied earlier, the peaks occur more frequently. For regions 4 and 5, the airgap between
T-MEMS beams and the Si substrate is approximately 23 m thick, and must be treated
by analysis of incoherent effects. The spectral reflectivity of these regions are both
higher than that of silicon, and results in net increase in the properties for these regions.
0.8
0.7
0.6

0.5
0.4
0.3
0.2
0.1
0
400
800
1200
1600
2000
wavelength (nm)
Figure 5.12 Spectral reflectivity of T-MEMS regions. (×) region 1: single-sided Si
wafer, () region 3: SiO2 film on Si, () region 4: 3-layered film
suspended over Si, () region 5: SiO2 film suspended over Si.
51
The total radiative properties of each region were found by applying the average area
techniques to the properties of individual regions. The results are shown in Figures 5.13
as functions of temperature. Again, the single oxide region has higher total properties
than silicon due to reduction in spectral reflectivity, while all other regions experience a
decrease in total properties.
The beams are arranged on the die with large spacing between each beam; therefore, the
three-layer film region covers over 50% of the die. Consequently, T-MEMS properties
are relatively close to that of the three-layer film region. However, the high absorptivity
and emissivity of the silicon and one-film regions, which collectively covers over 30% of
the die, raises the T-MEMS properties by as much as 6% over the three-layered region.
This difference is large enough to cause a considerable difference in wafer temperature
distribution during radiant heating, as will be shown in the following section.
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
 0.4
 0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0
200
400
600
800
1000
temperature (°C)
0
200
400
600
800
1000
temperature (°C)
(a)
(b)
Figure 5.13 a) Total normal absorptivity and b) total normal emissivity of T-MEMS regions.
(×) region 1: Si wafer, (+) region 2: 3-layered film, () region 3: SiO2 film on Si,
() region 4: 3-layered film suspended over Si, () region 5: SiO2 film suspended over Si.
52
5.3
Steady-State Temperature Distribution During RTP
Total normal absorptivity and emissivity for T-MEMS found above were used to
determine the effects of T-MEMS on the wafer temperature during radiant heating. Since
the properties remain relatively unchanged at high temperatures, values at wafer
temperature of 800 °C were used in the model. Properties used are summarized in Table
5.2 for T-MEMS die, silicon, and three-film region. Lamp filament was estimated to have
a temperature of 2200 °C with a constant emissivity of 0.3. Constant shape factor of 0.1
was used for the entire wafer. Dies (4 mm square) were patterned within the inner 34
mm radius of a wafer having 38 mm radius and 0.35 mm thickness. All wafers were
modeled as rough backside, with constant backside emissivity of 0.75. Types of wafers
considered in this study are listed in Table 5.3.
Table 5.2 Total radiative properties of wafer regions


T-MEMS die
0.623
0.580
Si
0.664
0.669
multilayered film
0.603
0.525
Table 5.3 Wafer layouts used for simulation
case
1
2
3
4
5
6
wafer type
Si wafer
3-layered film
Si wafer
3-layered film
3-layered film
3-layered film
die type
----T-MEMS, original configuration
T-MEMS, original configuration
T-MEMS, original configuration
T-MEMS, packed configuration
die separation
----1 mm
1 mm
10 mm
1 mm
Two types of wafer surfaces were considered: plain Si wafer and a wafer with threelayered film with the same film structure as T-MEMS three-film region (Cases 1 and 2).
53
Temperature distributions for uniform wafers having these surfaces are plotted in Figure
5.14.
The silicon wafer reaches a center temperature of ~ 852.2 °C, with lower
temperatures toward the wafer edge due to emission from wafer edge. The multilayered
wafer has a lower total absorptivity than silicon; however, it reaches a higher steady state
temperature due to low emissivity. Furthermore, the low emissivity results in less edge
cooling, and a slightly improved temperature gradient at the wafer edge.
temperature (°C)
854
3-films
852
850
Si
848
846
844
0
5
10
15
20
25
30
35
40
position (mm)
Figure 5.14 Temperature distribution on uniform Si and 3-film wafers.
The temperature distribution on the two wafers with T-MEMS dies were calculated for
die spacing of 1 mm. The results are plotted, along with uniform wafer cases, in Figure
5.15. With three-layered films surrounding the T-MEMS (Case 4), the temperature
distribution of the wafer is affected greatly by the structures, and the overall temperature
of the wafer decreases by ~ 1.5 °C below the uniform wafer case. However, when the TMEMS are surrounded by plain Si wafer (Case 3), the temperature distribution remains
very close to that of uniform Si wafer. Although the radiative properties of T-MEMS are
considerably lower than those of silicon, the low emission counterbalances the low
absorption in such way that the devices reach the same steady-state temperature as a plain
54
temperature (°C)
854
853
852
851
850
849
848
847
846
845
0
5
10
15
20
25
30
35
40
position (mm)
Figure 5.15 Temperature profile of wafers with T-MEMS dies. () uniform 3-film
wafer, () T-MEMS on 3-film wafer, (×) uniform Si wafer, () T-MEMS on Si wafer.
silicon wafer. This is further confirmed by simulating the steady state temperature
distribution over a wafer having the properties of T-MEMS die, as shown in Figure 5.16.
The temperature near the center of the wafer is nearly identical to the temperature
reached by silicon. The effect of low emissivity is seen near the edge, where the TMEMS wafer suffer slightly less edge cooling effect then the silicon wafer. These results
indicate that T-MEMS can be used effectively on plain Si wafers as passive temperatures
sensors. However, when the wafer is surrounded by other surfaces such as thin films,
their presence may affect the temperature of the wafer globally and locally, resulting in
greater non-uniformity and overall altered temperature.
The impact of the T-MEMS on overall wafer temperature for the three film case is
improved dramatically by introducing large spacing between the dies.
The wafer
temperature resulting from a 10 mm die separation (Case 5) is shown in Figure 5.17
along with the results for 1 mm separation. When the dies are spread sparsely on the
wafer, the overall wafer temperature is only reduced by less than 0.3 °C. Within the dies,
55
temperature (°C)
852
851
850
849
848
847
846
845
0
5
10
15 20 25
position (mm)
30
35
40
Figure 5.16 Temperature distribution over uniform wafers.
(×) Si wafer, () uniform wafer having average T-MEMS properties.
temperature (°C)
854
uniform wafer
853
T-MEMS wafer
852
851
850
849
848
0
5
10
15 20 25 30 35 40
position (mm)
Figure 5.17 Temperature distribution of 3-film wafer with
T-MEMS dies; die spacing of 10 mm.
local temperatures are reduced further by approximately 0.1 °C.
This level of
temperature change and local gradients may be acceptable in some thermal processing
applications.
Finally, a different type of T-MEMS die was simulated, where the beams are more tightly
packed within the die (Case 6). The fill factors resulting from the new configuration is
listed in Table 5.4. In this configuration, the individual T-MEMS beams were separated
56
by approximately 10 m, as opposed to
Table 5.4 Fill factors of modified die
up to 100 m for the original layout.
region
1
2
3
4
5
The temperature distribution resulting
from the new dies on three-film wafer is
F
0.338
0.281
0.197
0.079
0.050
shown in Figure 5.18. The temperature
is reduced by as much as 4 °C from that of the plain multilayered wafer. However, the
temperature uniformity across the dies is excellent, with outer dies reaching nearly the
same steady state temperature as the center dies. This is due to the enhanced heating of
outer dies from the three-film region immediately surrounding them. This type of TMEMS wafer may find application in characterization of RTP systems. Since there are
very little radial temperature gradient due to the radiative properties, these wafers may be
aid in identifying shape factor non-uniformities within an RTP chamber, which will result
in a temperature non-uniformity indicated by T-MEMS.
temperature (°C)
854
uniform wafer
853
852
851
850
T-MEMS wafer
849
848
847
0
5
10
15 20 25
position (mm)
30
35
40
Figure 5.18 Temperature distribution over 3-film wafer with modified T-MEMS dies
57