Author Proof
PROOF COPY [JSSP-15-3967] 0171603JSS
ECS Journal of Solid State Science and Technology, 5 (3) P1-P7 (2016) P1
2162-8769/2016/5(3)/P1/7/$33.00 © The Electrochemical Society
Thermal Shields for Heat Loss Reduction in Siemens-Type
CVD Reactors
1
2
A. Ramos,
z
J. Valdehita, J. C. Zamorano, and C. del Ca
˜
nizo3
Instituto de Energ
´
ıa Solar - Universidad Polit
´
ecnica de Madrid, ETSI Telecomunicaci
´
on, 28040 Madrid, Spain4
5
The use of thermal shields to reduce radiation heat loss in Siemens-type CVD reactors is analyzed, both theoretically and experi-
mentally. The potential savings from the use of the thermal shields is first explored using a radiation heat model that takes emissivity
variations with wavelength into account, which is important for materials that do not behave as gray bodies. The theoretical calcu-
lations confirm that materials with lower surface emissivity lead to higher radiation savings. Assuming that radiation heat loss is
responsible for around 50% of the total power consumption, a reduction of 32.9% and 15.5% is obtained if thermal shields with
constant emissivities of 0.3 and 0.7 are considered, respectively. Experiments considering different thermal shields are conducted
in a laboratory CVD reactor, confirming that the real materials do not behave as gray bodies, and proving that significant energy
savings in the polysilicon deposition process are obtained. Using silicon as a thermal shield leads to energy savings of between
26.5–28.5%. For wavelength-dependent emissivities, the model shows that there are significant differences in radiation heat loss, of
around 25%, when compared to that of constant emissivity. The results of the model highlight the importance of having reliable data
on the emissivities within the relevant range of wavelengths, and at deposition temperatures, which remains a pending issue.
6
7
8
9
10
11
12
13
14
15
16
© 2016 The Electrochemical Society. [DOI: 10.1149/2.0171603jss] All rights reserved.17
18
Manuscript submitted November 18, 2015; revised manuscript received December 18, 2015. Published 00 0, 2016.19
Scope20
90% of the polysilicon currently produced worldwide is demanded21
by the photovoltaic (PV) market, leaving the remaining amount for22
the microelectronics industry.
1,2
The chemical route -via chemical23
vapor deposition (CVD) of high purity trichlorosilane (TCS) on a24
hot filament, the so-called Siemens technology- currently dominates25
polysilicon production. High quality polysilicon is obtained, at the26
expense of high energy consumption.
3,4
27
In the case of polysilicon for PV (also known as solar grade silicon)28
the process accounts for between a quarter and a third of the total29
energy consumption.
5–7
Thus, lowering the energy consumption of30
the Siemens process is essential to achieving the two wider objectives31
for silicon-based PV technology: low production cost and low energy32
payback time.33
Furthermore, current price levels also press polysilicon produc-34
ers to reduce their production costs even more if they are seeking a35
sustainable business.
8
36
As radiation heat loss is the major contributor to energy37
consumption,
9
in this work the potential of thermal shields to re-38
duce radiation heat loss in an industrial Siemens reactor is studied.39
Thermal (radiation) shields have been implemented in a number of40
CVD reactors; e.g. for layer deposition in superconducting devices41
or for the epitaxial growth of silicon layers.
10,11
Several proposals42
have recently been made for polysilicon production,
12–14
but to our43
knowledge quantitative analysis supported by experimental data has44
not been provided in any of them.45
Radiation heat loss as regards thermal shields in a Siemens-type46
CVD reactor is studied first here using a theoretical model. Then, the47
theoretical results are compared with the experimental results in a48
laboratory Siemens reactor. Discussion of the latter will offer insights49
into the accuracy of theoretical calculations depending on the thermal50
shield materials’ optical properties, highlighting the relevance of the51
variation in optical properties with the wavelength for thermal shield52
materials.53
Potential to Reduce Radiation Heat Losses54
First, the radiative heat transfer phenomenon is briefly described55
and the radiation heat loss model is presented. Then, theoretical radia-56
tion heat loss calculations for different thermal shields in an industrial57
Siemens reactor are put forward.58
Radiative heat transfer.—Radiative heat transfer - also known as59
thermal radiation - describes the science of heat transfer caused by60
z
E-mail: alba.ramos@ies-def.upm.es
electromagnetic waves. These electromagnetic waves have the prop- 61
erty of traveling through a vacuum or matter-containing media. The 62
temperature of the radiant body governs the thermal radiation emis- 63
sion, and it occurs in the 0.1 to 100 μm wavelength range.
15,16
It is not 64
the aim of this section to explain the thermal radiation phenomenon 65
in detail, but to describe a number of concepts and properties of the 66
radiation heat transfer mechanism that will support the arguments we 67
develop in this document. 68
As regards the radiation properties, four dimensionless magnitudes 69
are defined: absorptance (α), reflectance (ρ), transmittance (τ) and 70
emissivity (ε). Absorptance, reflectance and transmittance are defined 71
as the ratio of the total amount of radiation absorbed, reflected or 72
transmitted by a surface to the total amount of radiation incident on 73
the surface, respectively. The emissivity
a
Emissivity is defined as the 74
ratio of the power per unit area radiated by a surface to the power 75
per unit area radiated by a black body at the same temperature. These 76
properties for real surfaces are dependent on temperature, direction 77
and wavelength. The relationship indicated in Equation 1 is obtained 78
by applying the energy balance to any real surface. 79
α + ρ + τ = 1 [1]
In addition, according to Kirchhoff’s law, all opaque surfaces (τ =
80
0) reach ε
λ
(λ, T ) = α
λ
(λ, T ).
15,16
81
A black body is defined as any body that emits and absorbs the 82
maximum possible radiation in all wavelengths, that is: α = 1, ρ = 83
τ = 0. Plack’s law defines the spectral radiated power of a black body. 84
In addition, according to Stefan-Boltzmann’s law the expression for 85
the total radiation emitted per unit area of a black body is indicated in 86
Equation 2; where T is the temperature and σ the Boltzmann constant. 87
E
b
(T ) = σT
4
[2]
However, the majority of the surfaces do not behave as black bod-
88
ies; thus, the gray body concept arises. A gray body is any opaque 89
body (τ = 0, α + ρ = 1) whose reflectance, absorptance and emis- 90
sivity properties are non dependent on the wavelength. The behavior 91
of many real surfaces can be approximated to that of a gray body; in 92
Equation 3 the expression of the total radiation emitted per unit area 93
of a gray body is presented. 94
E
g
(T ) = ε
g
σT
4
[3]
The parameter ε
g
corresponds to the emissivity of a gray body. 95
But, being more rigorous, real surfaces do not necessary behave 96
as gray bodies, and their properties vary with the wavelength for a 97
a
Some authors refer to this parameter as ‘emittance’. In this work emissivity and emittance
are the same concept; however, there is a subtle difference between the two.
16
Author Proof
P2 ECS Journal of Solid State Science and Technology, 5 (3) P1-P7 (2016)
given temperature. These surfaces radiate a different fraction ε
λ
at98
each wavelength; thus, the expression of the total radiation emitted99
per unit area of a real surface is indicated in Equation 4. Note that the100
parameter ε
r
in Equation 4 is calculated by means of Equation 5; that101
is, integrating ε
λ
along all the radiation spectrum.102
E
real
(T )
∼
=
ε
r
σT
4
[4]
103
ε
r
=
∞
0
ε
λ
E
bλ
dλ
∞
0
E
bλ
dλ
[5]
Real material properties.—As said previously, the radiative prop-
104
erties of real materials are not necessarily those of gray bodies. The105
difficulty is how to characterize the radiative properties of a selected106
material under working conditions. The reflectance (ρ
λ
) and transmit-107
tance (τ
λ
) of real surfaces can be determined by means of the Fourier108
transform infrared spectroscopy (FTIR);
17
thus, from Equation 1 ab-109
sorptivity (α
λ
) can be obtained. But these measurements are typically110
performed at room temperature; there are no overall techniques for111
the measurement of radiative properties at high temperatures. It is true112
that for certain materials, in particular for some metals, it is accept-113
able to consider that their radiative properties remain constant with114
temperature, although this cannot be easily generalized.
16,18,19
115
Radiation heat loss model.—A radiation heat loss model for heat116
loss calculations in a Siemens-type reactor was presented and de-117
scribed in detail in Ref. 20, and validated in Ref. 21. It is further118
developed within the framework of this research to broaden its appli-119
cability and account for materials that do not behave as gray bodies.120
One parameter needs to be defined for radiation heat loss calcu-121
lations: radiosity ( J ), the rate of outgoing radiant heat per unit area122
from a surface. It is the sum of the directly emitted heat flux (E) and123
the reflected incoming radiant heat flux from the surface (G). The124
fraction of heat flux from one surface to another is determined by the125
so-called configuration factor, or geometrical factor. The calculation126
of the configuration factors (F
i− j
) is made using a geometric Hottel’s127
crossed-string method.
22
In the present case note that the rods and the128
reactor wall have a cylindrical geometry.129
If the material properties, the geometrical arrangement, the surface130
temperatures and the incoming and directly emitted radiant heat flux131
are known, the net heat flux exchanged (Q) in Watts from any surface132
(S
i
), is obtained from the difference between the radiosity and the133
incoming radiant heat flux. Then, the net radiation heat flux exchanged134
for a certain surface i can be expressed as shown in Equation 6.135
Q
i
= S
i
· (J
i
− G
i
) = S
i
· J
i
−
n
j=1
S
j
· F
j−i
· J
j
[6]
For a Siemens reactor of n-1 rods, a n-equations system needs to
136
be solved, as the reactor wall is considered as an additional surface.137
The radiosities of each surface (Ji) are the unknowns of the system.138
The temperature of the rod surfaces and the reactor wall is known, as139
is the corresponding surface emissivities. Once the J
i
is obtained for140
the n surfaces, the incoming radiant heat flux per unit area (G
i
) is also141
known. Thus, the net radiation heat exchanged by each surface (Q
i
)142
is obtained by substituting J
i
and G
i
in Equation 6.143
To account for emissivity variations with the wavelength, radiation144
heat loss is obtained by means of Equations 7, 8, 9 and 10, which are145
solved independently for each wavelength146
S
i
·
1
1 − ε
i
(λ)
· J
i
(λ) −
n
j=1
S
i
· F
i− j
· J
j
(λ) = S
i
·
ε
i
(λ)
1 − ε
i
(λ)
· σ · T
4
i
[7]
147
E
i
(λ) = ε
i
(λ) · σ · T
4
i
[8]
148
G
i
(λ) =
1
1 − ε
i
(λ)
· (J
i
(λ) − E
i
(λ)) [9]
149
Q
i
(λ) = S
i
· (J
i
(λ) − G
i
(λ)) [10]
where i = 1, ..., n. 150
The net heat flux exchanged (Q
i
) in Watts by any surface (S
i
), 151
is obtained by integrating Q
i
(λ) along all the radiation spectrum. In 152
Equation 11 the net heat flux exchanged by a surface is presented; 153
E
b
(λ) is the total radiation emitted per unit area of a black body 154
indicated in Equation 2. 155
Q
i
=
∞
0
Q
i
(λ)E
b
(λ) dλ
∞
0
E
b
(λ) dλ
[11]
This radiative model allows extra surfaces in the Siemens reactor 156
to be considered and their positive or negative effect on heat savings 157
studied. This can be the case of a thermal shield. A thermal shield 158
is a cylinder surrounding the polysilicon rods and placed between 159
them and the reactor wall. The presence of this shield may block 160
a significant part of the radiated heat that otherwise would be lost 161
through the reactor wall. 162
Now, the net heat flux exchanged (Q
i
) in Watts by any surface 163
(S
i
), is again obtained by integrating Q
i
(λ) along all the radiation 164
spectrum; but by replacing Equation 7 with Equations 12–15 (where 165
i = 1, ..., m − 1, and m is the number of thermal shields considered). 166
167
S
i
·
1
1 − ε
i
(λ)
· J
i
(λ) −
m
j=1
S
i
· F
i− j
· J
j
(λ) = S
i
·
ε
i
(λ)
1 − ε
i
(λ)
· σ · T
4
i
[12]
168
S
m
·
1
1 − ε
m
(λ)
·J
m
(λ) −
m
j=1
S
m
·F
m− j
·J
j
(λ) = S
m
·
ε
m
(λ)
1 − ε
m
(λ)
· σ · T
4
m
[13]
169
S
m
·
ε
s
(λ)
1 − ε
s
(λ)
+
1
γ(λ)
· σT
4
m
− S
m
·
ε
s
(λ)
1 − ε
s
(λ)
· J
m
(λ) =
σT
4
n
γ(λ)
[14]
170
γ(λ) =
1
S
m
· ε
s
(λ)
+
1
S
n
·
1
ε
n
(λ)
− 1
+ (
2
ε
s
(λ)
− 1) ·
n−1
i=m+1
1
S
i
[15]
Note that even if the emissivity values now considered may be
171
wavelength dependent, materials still are considered opaque (τ = 0). 172
Theoretical calculations.—The potential of different thermal 173
shields for radiation heat savings in an industrial Siemens reactor is 174
studied here. The equations presented above are applied to a 36-rod, 175
state-of-the-art Siemens reactor, and as a first approach, the emissivity 176
of the materials is considered constant and wavelength independent. 177
The initial and final diameter of the polysilicon rods is 0.7 and 13 cm, 178
respectively, and their length is 2 m. 179
In Figure 1 the heat loss due to radiation in Watts (W) throughout 180
a polysilicon deposition process for a constant surface temperature of 181
1150
◦
C is shown; the curves correspond to the case with no thermal 182
shield and four cases with thermal shields. The emissivities of the 183
thermal shields are 0.3, 0.45, 0.55 and 0.7. In Table I the theoretical 184
radiation heat loss savings for the aforementioned thermal shields are 185
presented. The radiation heat loss savings, compared to the heat loss 186
if no thermal shield is considered, are 65.8, 52.6, 44.3 and 30.5% for 187
thermal shield emissivities (ε) of 0.3, 0.45, 0.55 and 0.7, respectively. 188
This means, assuming that the radiation heat loss is responsible for 189
around 50% of the total power consumption, that with a thermal shield 190
with ε = 0.3 a reduction in power consumption of 32.9% is obtained, 191
while for ε = 0.7 the reduction would be of 15.5%. 192
The temperature reached by the different thermal shields depend- 193
ing on their emissivity is presented in Figure 2. In all cases, and from 194
the beginning of the process, these temperatures are above 850
◦
C, 195
which will result in polysilicon deposition on these surfaces. Thus, 196
Author Proof
ECS Journal of Solid State Science and Technology, 5 (3) P1-P7 (2016) P3
Table I. Theoretical radiation heat loss savings for different
thermal shields.
Thermal shield Radiation heat loss
ε [-] savings [%]
0.3 65.8
0.45 52.6
0.55 44.3
0.7 30.5
Figure 1. Radiation heat loss for a 36-rod Siemens reactor considering dif-
ferent thermal shields. No thermal shield (blue), ε = 0.7 (purple), ε = 0.55
(cyan), ε = 0.45 (red), ε = 0.3 (green).
after a few minutes into the deposition process the thermal shield’s197
surface emissivity will be 0.7, that of silicon at high temperatures.
23
198
Furthermore, contamination issues can arise unless the shields are of199
a highly pure material. One way to overcome these drawbacks would200
be to use a thermal shield made of purified silicon.
12
Not only will it201
avoid contamination, but one can also collect the silicon deposited on202
the shields, adding it to the silicon produced in a batch.203
The potential of thermal shields can be compared to the use of a204
polished or a reflective-coated inner wall of a reactor, which will lower205
the wall emissivity. For a given growth rate, and knowing the power206
consumption throughout a deposition process, and the initial and the207
final diameters of the polysilicon rods, the energy consumption in208
kWh/kg can be calculated. In Figure 3 the kWh/kg ratio for the case209
of a reflective-coated wall is compared to those considering a silicon210
thermal shield, no thermal shield and a thermal shield of ε = 0.3. For211
the calculations in Figure 3 the emissivity of the wall and the thermal212
Figure 2. The temperature of thermal shields depending on their emissivity (ε)
throughout a deposition process. Thermal shield emissivities: ε = 0.7 (purple),
ε = 0.55 (red), ε = 0.45 (blue), ε = 0.3 (green).
Figure 3. Total power consumption of a 36-rod Siemens reactor for different
growth rates considering: no thermal shield -ε
wall
= 0.5- (green), silicon
thermal shield -ε = 0.7- (purple), thermal shield with ε = 0.3 (cyan) and no
thermal shield and polished reactor wall -ε
wall
= 0.3- (blue).
shields is considered constant throughout a deposition process; and the 213
radiation heat loss is 50% of the total power consumption. The lowest 214
kWh/kg ratio is obtained for a low emissivity thermal shield, and the 215
kWh/kg ratio for that with a silicon thermal shield and a polished 216
inner wall are quite close. However, note that the low emissivity 217
thermal shield and the polished walls will not maintain their initial 218
emissivities for more than a short period of time, as silicon or a silane- 219
based compound will deposit. After a few minutes into the deposition 220
process the blue curve will start to move slowly upwards until it 221
reaches the green curve; and the cyan curve will quickly move to 222
behave like the purple curve. Thus, the effect of a thermal shield is 223
more efficient in terms of energy savings than considering a polished 224
reactor wall; this statement is true even when considering a high initial 225
emissivity value for the thermal shield (e.g., ε = 0.7). 226
Laboratory Scale Experiments 227
A number of experiments considering thermal shields are con- 228
ducted in a laboratory Siemens reactor,
24
and the effect on radiation 229
heat savings obtained is put forward. 230
Since the temperature of the thermal shield in the laboratory reac- 231
tor will be lower than in the industrial case, the laboratory prototype 232
allows us to test the effect of thermal shields with different emissivi- 233
ties. The key parameter for the selection of the thermal shield material 234
is the emissivity (ε); but also, the material selected must be easily 235
machinable, and available with the geometries and thickness required 236
for its assembly inside the reactor chamber, so its mechanical strength 237
must be assured. The following materials are evaluated: molybdenum, 238
boron nitride, stainless steel, aluminum oxide (alumina), zirconium, 239
graphite foil and silicon. Some of the relevant properties of these 240
materials are presented in Table II; the values shown are considered 241
wavelength independent since this dependence is unknown. 242
Table II. Properties of different materials considered for the
thermal shields.
25,26
ε [-] ε [-] Ease of
Material (T = 25
◦
C) (T ∼ 600
◦
C) machining
Molybdenum - 0.8-0.9 Medium
Stainless steel 0.6-0.8 0.7-0.9 Low
Alumina - 0.3-0.4 Medium
Boron nitride 0.9-0.95 - Medium
Zirconium - 0.1-0.3 High
Graphite foil 0.7-0.9 0.4-0.6 Low
Silicon - 0.7 Medium
Author Proof
P4 ECS Journal of Solid State Science and Technology, 5 (3) P1-P7 (2016)
Figure 4. Radiation heat loss in the laboratory Siemens reactor for a 7-rod
configuration considering a silicon thermal shield (blue), a low emissivity
thermal shield -ε = 0.3- (red) and without thermal shield (orange).
Figure 5. Laboratory Siemens reactor power consumption (P) predicted in
theory for different thermal shield emissivities and for the case of no thermal
shield considering a 7-rod configuration.
First, the radiation heat loss equations with thermal shields are243
applied to the laboratory Siemens reactor. The radiation heat loss244
for a 7-rod configuration with a low emissivity shield, with a silicon245
thermal shield and without thermal shield is presented in Figure 4; it246
can be seen how the lowest radiation heat losses are obtained for a low247
emissivity thermal shield. The temperatures reached by the thermal248
shields are in the range of 600-750
◦
C.249
The power consumption predicted by the model for different ther-250
mal shield emissivities and for that of no thermal shield, are presented251
in Figure 5. For these calculations a constant deposition temperature252
of 1100
◦
C, the same growth rate and the same duration of the depo-253
sition processes, is considered, thus averaging the measured data. It254
can be seen that the lower emissivity of the thermal shield, the higher255
radiation heat savings.256
Experiments with thermal shields.—A 7-rod configuration is cho-257
sen as a compromise solution between a dense compactness - a large258
number of rods - and the size of the reactor chamber. The length of259
the rods is 10 cm and their initial diameter is around 0.7 cm.260
From the thermal shield materials listed in Table II, the following261
have been selected for testing: silicon, alumina and stainless steel.262
Different thickness of the selected materials are considered, and in263
some cases the outer surface of the thermal shields is silver coated
b
.264
b
The silver coatings deposited are a few hundred nanometers thick.
Table III. Experiments conducted with 7-rod configuration in the
laboratory Siemens reactor.
Experiment name Description
No shield (No) Without any thermal shield
Silicon shield (Si1) Multi-crystalline silicon thermal
shield (290 μm/layer; 3 layers)
Silicon shield (Si2) Mono + Multi-crystalline silicon thermal
shield (400 + 290 μm; 1 + 1 layers)
Silicon shield (Si3) Mono + Multi-crystalline silicon thermal
shield (400 + 290 × 4 μm; 1 + 4 layers)
Alumina shield (Alu1) Alumina shield
(1 mm thick)
Alumina shield (Alu2) Alumina shield silver coated
(1 mm thick)
Steel shield (Ste) Stainless steel shield
(1 mm thick)
Table IV. Experimental data obtained for the 7-rod configuration
experiments: ‘silicon shields’.
Experiment (No) (Si1) (Si2) (Si3)
T
deposi t i on
[
◦
C] 1106 1101 1108 1108
Si deposited [gr] 50.7 61.9 59.3 59.8
Power
aver age
2343 1979 2042 2122
Time [min] 392 406 385 375
T
wall
[
◦
C] 280 233 184 181
T
shi eld
[
◦
C] - 678 641 616
Growth rate [μm/min] 2.9 3.5 3.6 3.6
Consumption [kWh/kg] 311 216 221 222
Energy savings [%] - 28.4 26.8 26.5
The emissivity of silver is very low (ε ∼ 0.02-0.05), so if this coating 265
withstands the process temperatures, it will act as a mirror making a 266
non-opaque body behave almost as if it were. 267
The relevant data related to these experiments is presented in the 268
following tables. First, the different thermal shields are described and 269
related to their corresponding label in Table III. Then, the experimental 270
results are grouped together in ‘silicon shields’ and ‘alumina and 271
stainless steel shields’; Tables IV and V, respectively. 272
From the data presented in Table IV, the energy savings obtained 273
with the different silicon thermal shields are similar. The reduction 274
in the kWh/kg ratio obtained considering thermal shields related to 275
experiment (No) are between 26.5 and 28.4%. All these experiments 276
were conducted under similar conditions and their duration is similar. 277
Despite the fact that the deposition surface temperature is in all cases 278
around 1100
◦
C, there is a difference in the growth rate obtained in 279
experiment (No). This is so because the presence of a thermal shield 280
changes the distribution of the gas temperature, and higher tempera- 281
tures are achieved in the gas surrounding the silicon rods. 282
From the data presented in Table V, the energy savings in kWh/kg, 283
compared with experiment (No), vary between 15.1 and 30.7%. The 284
Table V. Experimental data obtained for the 7-rod configuration
experiments: ‘alumina and stainless steel shields’.
Experiment (No) (Alu1) (Alu2) (Ste)
T
deposi t i on
[
◦
C] 1106 1107 1108 1098
Si deposited [gr] 50.7 65.3 53.7 49.3
Power
aver age
2343 2333 1669 1915
Time [min] 392 430 404 388
T
wall
[
◦
C] 280 142 175 152
T
shi eld
[
◦
C] - 736 705 570
Growth rate [μm/min] 2.9 3.6 3.2 3.0
Consumption [kWh/kg] 311 256 205 251
Energy savings [%] - 15.1 30.7 16.8
Author Proof
ECS Journal of Solid State Science and Technology, 5 (3) P1-P7 (2016) P5
kWh/kg values in the laboratory scale reactor are several times higher
285
than those found in industrial processes, mainly since the process pres-286
sure is 6-7 times lower. Comparing experiments (Alu1) and (Alu2),287
the silver coating seems to be effective; however its behavior differs288
from that expected from its theoretical ε (further explanations will be289
presented in Discussion on energy savings section).290
Lastly, in experiments conducted with silicon thermal shields etch-291
ing is detected on the surface of the shields. This is attributed to the292
presence of SiCl
4
as a by-product of the reduction reaction. The oc-293
currence of this phenomenon versus polysilicon deposition depends294
on the mol fraction of SiCl
4
, which will depend on the deposition sur-295
face temperature.
27,28
High SiCl
4
concentrations and low temperatures296
favor the etching. However, as already explained, under industrial de-297
position conditions the temperature of the thermal shields will be298
such that polysilicon will be deposited on the thermal shields, and no299
etching is expected.300
Discussion on energy savings.—From the above, energy savings301
have been confirmed for the 7-rod configuration experiments consid-302
ering different thermal shields.303
If the experimental data from Tables IV and V (average power304
consumption and energy savings) is compared with the theoretical cal-305
culations for different thermal shields (Figure 5), a good agreement306
for the case of no thermal shields is obtained; differences between307
both values are under 3.8%. Note that our calculations consider con-308
stant deposition conditions, while the experimental conditions of the309
deposition process vary slightly from one experiment to another.310
For the experiments conducted with thermal shields, the averaged311
power consumption and energy savings obtained vary between 1667-312
2333 W and 15.1–30.7%, respectively. According to data presented in313
Figure 5, the previous values correspond to thermal shield emissivities314
above 0.6. In the case of the silicon thermal shields, the energy savings315
obtained correspond to ε = 0.7–0.8, for the alumina shields to ε >316
0.9, for the silver coated alumina shield to ε = 0.6–0.7; and for the317
stainless steel shield to ε > 0.9. These ε values do not correspond318
to those found in the bibliography assuming the gray body approach,319
which is no surprise since the gray body approach simplifies much of320
the radiative behavior of real bodies.321
Reflectance, transmittance and emissivity measurements.—With322
the aim of clarifying the real emissivity of the thermal shield materials323
tested in the laboratory Siemens reactor, reflectance (ρ) and transmit-324
tance (τ) measurements for different λ are taken. Both, ρ(λ) and325
τ(λ), can be measured directionally or integrated; in the present case326
integrated measurements are suitable since the materials considered327
do not have specular surfaces. These measurements are conducted at328
room temperature.329
In Figure 6 the integrated transmittance measurements, within the330
wavelength range λ ∈ (2.5–20) μm, for different thermal shields are331
presented. In all cases, noticeably for the silicon shield, the integrated332
transmittance is τ ?= 0. Measurements for a silicon, alumina and333
stainless steel thermal shields are presented in Figure 6. The integrated334
transmittance measured is on average 41.3, 8.1 and 0.5% for the335
Figure 6. Integrated transmittance (τ) of: 290 μm multi-crystalline silicon
(red), 1 mm alumina (green) and 1 mm stainless steel (cyan).
Figure 7. Integrated reflectance (ρ) of: 290 μm multi-crystalline silicon (red),
1 mm alumina (green) and 1 mm stainless steel (cyan).
290 μm multi-crystalline, 1 mm alumina and 1 mm stainless steel 336
samples, respectively. 337
Integrated reflectance measurements are also conducted; ρ(λ) for 338
λ ∈ (2.5–20) μm for silicon, alumina and stainless steel are presented 339
in Figure 7. From Figure 7, the averaged reflectance of the silicon 340
sample is 40%, while the respective values for that of alumina and the 341
stainless steel samples are 48.1 and 92.8%, respectively. 342
From the average values of the aforementioned transmittance and 343
reflectance integrated measurements, only the stainless steel sample 344
presents a very low transmittance. Materials experimentally tested in 345
the laboratory Siemens reactor at room temperature definitely do not 346
behave as gray bodies, and similar behavior can be expected at higher 347
temperatures.
18,19
The latter explains the differences between the pre- 348
dicted energy savings and the empirically obtained ones. The next 349
section discusses the effect that the wavelength-dependent emissivi- 350
ties can have on the radiation heat losses. 351
Discussion on the Contribution to the Radiation Heat Loss Model 352
The model for radiation heat loss is applied here for the radi- 353
ation heat loss calculations of a 36-rod industrial Siemens reactor, 354
considering thermal shields that do not behave as gray bodies. Two 355
hypothetical thermal shields with an averaged ε(λ) = 0.7 are con- 356
sidered, with an emissivity variation presented in Figure 8. It can be 357
seen that ε(λ) of material 1 is approximately constant, while ε(λ) of 358
material 2 is heavily dependent on the wavelength. 359
The radiation heat loss for λ ∈ (0.1, 20) μm, calculated for a 36-rod 360
industrial Siemens reactor, is presented in Figure 9. The two scenarios 361
presented; hereinafter scenarios 1 and 2, correspond to material 1 and 362
material 2 thermal shields, respectively. In both cases, the radiation 363
Figure 8. Emissivity ε(λ) for two different thermal shield materials: material
1 (cyan) and material 2 (blue). In both cases, the averaged ε(λ) = 0.7.
