TECHNICAL REPORT

Modeling & Simulations of The Lamp Heating-type
Rapid Thermal Processor
M. HATTORIThe RTP (Rapid Thermal Processor) is a single-wafer thermal processing apparatus used in the semiconductor
field featuring high temperature ramp rates and fast processing. In recent years, the use of materials and processes
in research and development applications under processing conditions not originally anticipated is expanding. To
meet these needs, we worked on modeling, simulation and experimental analysis of heating phenomena by halogen
lamps, optical properties of materials and thermal balance inside the furnace. Through these efforts, we clarified
the points for carrying out highly accurate thermal processing performance under a broader range of conditions. In
this paper, we describe the modeling and simulation of RTP, and the verification of the actual device.
Key Words: RTP, lamp annealing, silicon wafer, heat treatment

1. Introduction
Thermal processors for semiconductors can be roughlyclassified into two groups of furnaces and RTP (Rapid
1)
Thermal Processor) . Furnaces are used to perform
uniform thermal processing for extended periods oftime in a stable environment and for batch production.
RTPs, also known as lamp annealing devices, are used
for single wafers and offer high ramp rate heating andfast processing. In semiconductor manufacturing, to date,
RTPs have been used for formation of an extremely thinthermal oxide film as well as annealing and metal silicide1)
contact formation, etc. following ion implantation ,however RTPs are also often used for materials otherthan silicon and for process R&D. Particularly in recent
years, there has been an increase in cases of using RTPs
in applications other than those originally anticipated,namely, to keep several stages of temperatures for fixed
periods of time such as the multi-stage heating method
used for solar cell electrode firing, or to keep a hightemperature for an extended period of time. As such, there
is a greater need for RTPs tailored specifically to R&D
applications which can be used with ease for a broad
range of applications. As such, from the perspective ofpractical modeling useful for RTP device development,
we performed verification and identification of physicalconstants, as well as analysis of heating mechanisms andradiation thermometer measurement characteristics, etc.
and leveraged the obtained results in the development of
2)“DTL-6” , a desktop RTP with a lamp output of 24kW
and heating area of 150mm squares. This article will78

focus on the silicon wafer, which is typical target of RTP
heating, to discuss the RTP modeling and simulation
conducted for this development, as well as an actual
verification using DTL-6.

2. RTP Basic Structure
Figure 1 shows the basic structure of an RTP. Nearinfrared light emitted by a halogen lamp (lamp) is usedas the heat source. As the target of the heating, the siliconwafer is positioned inside a quartz process tube, and thelight source and quartz tube are enclosed in aluminum
housing which features water-cooling means. Wafer
temperature is measured using a radiation thermometer
through an optical filter positioned on the aperture of thequartz tube. Moreover, nitrogen gas is used inside thehousing to cool the lamp surface and housing itself.

Al housing

cooling N2
cooling water

wafer

halogen lamp
optical filter

radiation
thermometer

process
gases

quartz process tube

Fig. 1 RTP basic structure

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−Modeling & Simulations of The Lamp Heating-type Rapid Thermal Processor−

3. Essential Summary of the Lamp
Heating Process
3. 1 Fundamental Equation for Silicon Wafer
Heating
Figure 2 shows the heat balance during siliconwafer heating. It is thought that a silicon wafer withthe temperature T w emits a thermal energy of ewrT w4
and absorbs energy multiplied by its own emissivity tothermal energy radiated by the surrounding space. For
heat balance, radiation is the domination therefore, here,
first we must ignore convection and thermal conduction,and in order to generalize, we shall discuss using physicalquantity per unit area.
rewTw4u

3. 2 Optical Absorption/Radiation Temperatureand Wavelength Dependency of a Silicon
Wafer

ewre0Tw4

Fig. 2 Heat balance on a silicon wafer

Equation ⑴ shows the fundamental equation relating
to wafer heating.

Cw

dT w
4
4
＝ u − r（ e wT w − e w e 0 T 0 ）dt⑴

Where,

u : Effective irradiation energy density contributing to2wafer heating [W/cm ]C w: Heat capacity per unit area of wafer [J/K]
T w: Silicon wafer’s temperature [K],T 0: Ambient temperature [K]ew: Silicon wafer’s emissivity,
e0: Ambient emissivity−122
r: Stefan-Boltzmann constant [= 5.68 × 10 W/cm ]Here, if we consider the point where the lamp
illuminates in a thermal equilibrium state at room
temperature (T w4 = e0T 04), then Equation ⑴ becomesu ＝ CwdT w
dt⑵

and if the desired ramp rate is applied, it is possible to findthe lamp energy density required for heating. If this value
is made u m then it is possible to obtain an approximate of
the wafer’s maximum attainable temperature, T wm [K],from u m.
In other words, if we establish dT w/dt = 0 in Equation ⑴1/4um
Twm ＝ e r ＋ e 0 T 04
w

From Equations ⑵ and ⑷, for example, in order toheat a u150 SEMI spec silicon wafer (t = 0.675mm, C w
2= 0.114 J/Kcm , e = 0.67) at 100℃/second, u m = 11.4 W/
2cm would be necessary and, at this time, T wm ~ 1 315 K(= 1 042℃).
If a wafer for crystal silicon solar cells (t = 0.2mm,
C w = 0.034 J/Kcm2, e = 0.9) is heated with this energy,
the ramp rate would be 335℃/second and the attainabletemperature would be T wm ~ 1 222 K (= 949℃).
A c t u a l l y, t h e r e i s t h e c o m p o n e n t o f a m b i e n ttemperature T 04, therefore the maximum attainabletemperature would be higher than the value shown above.
In this way, the ramp rate and the maximum
temperature which are basic specifications of device
cannot be determined independently.

It is well-known that the spectral emissivity of silicon3)
wafers is highly dependent on temperature . Figure 3
shows the spectral emissivity of a silicon wafer. Siliconemissivity has high temperature dependency up to 600℃ in a wavelength region with an optical absorption
edge of 1.1 μm or more. Emissivity is a parameterto be specified at temperature measurement using aradiation thermometer however, due to the fact that, forphysical optical absorption, emissivity = absorptance,
this temperature dependence must be consideredwhen discussing the heating process of silicon wafers.
Normally, this emissivity change would be foundby calculating the area surrounded in curved lines
corresponding to each temperature in Fig. 3, howeveras this temperature dependence is thought to be caused
by electronic transition, we assumed it would adhere to
Fermi-Dirac’s distribution function and expressed it as
Equation ⑸.
e（ T ）＝ e 1 ＋

e2 − e1T 2 −T
1 ＋ exp
B⑸

Where,
e1: Initial emissivity at low temperature
e2: Final emissivity
T 2: Temperature where emissivity becomes e2
B : Parameter which adjusts the emissivity change
temperature range⑶

and if we ignore T 04 in relation to T w4,
1/4

Twm 〜（ u m / e w r ） ［ K ］⑷

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0.8

T q, T h: quartz tube, housing temperature [K]C q, C h: quartz tube, heat capacity per housing unit area

873K

0.6
Emissivity

Where,

1 073K
793K

743K

0.4

693K
623K

0.2

543K
0.5

1

10

20

Wavelength, µm

Fig. 3 Spectral emissivity of a silicon wafer

4. RTP Heat System Modeling4. 1 Interaction of Heat within an RTP
Inside the RTP, the lamp heats not only the siliconwafer, but also the quartz tube and housing. Moreover,there is interaction between the heat of the wafer andquartz tube, and the quartz tube and housing, respectively.
Figure 4 shows the heat radiation of each part.
e0rT04nhu e rTq4q

Al housing

ehrTh4

lamp

nqu

u

quartz process tube

eqrTq4ewrTw4wafer

ffewrTw4
optical filter

efrTq4

Fig. 4 Interaction of heat radiation within the RTP

If this is established as a state equation, it would
express as Equation ⑹.
ew
Cw
eq ew
Cq

d Tw
T ＝r
dt T q
h

0

＋

80

ew eq
0
Cw
eq eq eh
−
Cq
Cq
eh eq
eh
−
Ch
Ch

1
Cw
0
0
1
nq
u ＋ e h r e 0 T 04
Cq
Ch
1
nh
Ch

4. 2 Temperature Detected by a Radiation
Thermometer
By converting the temperature into radiation energy,
add and subtract calculations become possible. Because
the thermal radiation ray from the housing does notincident as a direct ray on the radiation thermometer, itis the radiation ray from the wafer and the radiation ray
from the observation window on the quartz tube that aredetected by the radiation thermometer. Therefore, as theoutput of Equation ⑹, the radiation energy E rad detectedby the radiation thermometer is expressed by Equation⑺, and observation temperature T rad is given by Equation ⑻.
Where, we have made filter temperature = quartz tube
temperature.

T w4
E rad ＝ r［ ff e w g rad（T w ） e f g rad（T q ） 0 ］ T q4
T h4

radiation
thermometer

−

[J/K]
eq, eh: quartz tube, housing emissivity
nq, nh: Effective irradiation energy ratio toward quartz
tube/housing in relation to wafer effective
irradiation energy
The silicon wafer, quartz tube and housing each havedifferent spectroscopic absorption properties therefore,technically speaking, there is a need to find the energy
contributing to the heating of each from the lamp’s
emitting state, and we simplified a model expressing
this as the ratios nq and nh in relation to the input to thesilicon wafer, u .

Where,
ff: optical filter’s transmission,
ef: optical filter’s emissivity
grad (T ): the radiation energy ratio of the wavelength
region detected by the radiation thermometerat temperature T

E rad
T rad ＝ e
w

T w4
T q4
T h4

⑺

1/4

⑻

4. 3 Temperature Dependence of the Physical
Constant⑹

In modeling to date, we have treated physicalquantities like a constant, however in reality, temperaturedependence must be considered, therefore we expressed
them by polynomial approximation to make them easy
to use for calculations. For the specific heat of quartz,
4)
we scanned a graph used in technical documentation
prepared by the manufacturer and carried out quartic
approximation (this is not the C q of Equation ⑹ which

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−Modeling & Simulations of The Lamp Heating-type Rapid Thermal Processor−

Table 1 Polynomial approximation coefficient of temperature dependent parameterc（T̃ ）− 8.45 × 10

（T̃ ）
grad

2.46

a3

a2

a1

a0

3.53

− 5.594.18− 7.52 × 10 − 2

2.23 × 10− 1.95 × 10

7.32

− 5.90−1− 1.20 × 10

establishes c q (T ) [J/gK] but rather the specific heat ofquartz as a material).
grad is Planck’s radiation law

L（ k ，T ）＝

2 p hc 2
k5

exp

1
hc
−1
k kT

⑼

Where, we usedk : Boltzmann constant [1.381 × 10−23J/K],
h : Planck constant [6.626 × 10−34J s],c : Light speed [2.998 × 108 m/s]
and performed polynomial approximation by calculating
the wavelength region k1 k k2 radiation energy and allradiation energy ratio when the temperature is T [K].

ʃ kk L（ k ，T ）d k
ʃ ∞0 L（ k ，T ）d k
2

g rad（T ）＝1⑽

Table 1 shows the polynomial approximatedcoefficients of c q (T̃ ) and grad (T̃ ). Where, T̃ = T/1 000
and a i are coefficients of T̃ i when the polynomialnexpression is expressed as R i=0aiT̃ i, therefore nq andn h . Are quantities introduced as the references toexpress heating energy on the silicon wafer, which is anobservable quantity regarding the extent to which theenergy emitted by the lamp is supplied to the quartz tube
and housing. This parameter value was found based on
experiments and analysis of halogen lamp which were
executed separately.

Temperature, ℃

1 000
Temperature (measured)Temperature (simulation)
Ramp rate (measured)
Ramp rate (simulation)

800
600

1 000

120
90

200

5

10

15

20

Figure 5 shows the result of using the DTL-6 toapply full power to the lamp (24kW) and heat, as wellas the result of a simulation considering the fluctuationin emissivity in accordance with Equation ⑷. ⑴ is a
u150SEMI spec silicon wafer and ⑵ is a polycrystalline
silicone bare wafer for solar cells (it must be noted that

150

60

0

5. 1 Silicon Wafer Temperature Increase Process

1 200

400

0

5. Model Verification

180

Ramp rate, ℃/s

1 200

For nh, the optical absorption region is biased toward
the short wavelength side of the spectrum emitted
by the lamp therefore, we estimated 0.05 to 0.1 withconsideration to the emissivity of the aluminum semigloss surface at a wavelength of 1 μm. Housing has aheat capacity 20 times greater than the other portions,
good thermal conduction and is water-cooled, therefore ispractically not affected at all if nh changes.
Quartz will transmit rays with a cut-off wavelengthof 4.5 μm or less and absorb rays with wavelengths over5)
this . A halogen lamp is of a structure whereby a tungsten
filament is enclosed in a quartz tube (bulb), and rays
equivalent to or greater than the cut-off wavelength are6)
not emitted but the bulb surface absorbs filament rays
until it increases in temperature between 250 and 800℃ then the heat radiation from the bulb (secondary ray)heats the quartz tube. The nq exceeds 0.4 at the minimal
output of u , however decreases to 0.05 at maximum
lamp output, therefore we performed linear interpolation
between these two.

180
150
Temperature (measured)Temperature (simulation)
Ramp rate (measured)
Ramp rate (simulation)

800
600

120
90

400

60

30

200

30

0

0

Time, s(1) Simulation conditions of a u150SEMI
spec silicon wafer ( t = 0.675mm)
e1＝0.44, e2＝0.71, T 2 ＝750, B ＝50

0

5

10

15

20

Ramp rate, ℃/s

a4

Temperature, ℃

a5
q

0

Time, s(2) Simulation conditions of a polycrystalline
silicon bare wafer for solar cells ( t = 0.2mm)
e1＝0.84, e2＝0.90, T 2 ＝700，B ＝25

Fig. 5 Comparison of measured and simulated wafer temperature-increase profile and ramp rate

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−Modeling & Simulations of The Lamp Heating-type Rapid Thermal Processor−

5. 2 Effect of Disturbance
When temperature control is performed to keep ahigh temperature for a set period of time using radiation
thermometer, a phenomenon occurs in which the actual
temperature of the wafer decreases although the control
temperature is constant. This state is shown in Fig. 6 ⑴.
The control temp. shown in the figure is the instruction
value of the radiation thermometer used in feedback
control, the wafer temp. is the instruction value of the TC
wafer and the MV (manupirate value) is the lamp’s power
control value. This kind of phenomenon was raised asa problem when RTPs began being used for processing
requiring high temperature to be kept for a certain
period of time. For this phenomenon, we carried out thesimulation of temperature control with T rad feedback
using the models of Equation ⑹ though ⑻. Figure 6⑵ shows the results of this simulation. T rad is a valueof Equation (8), and equates to the measured control
1 200

As described above, we performed modeling to verify
factors such as the optical absorption of a silicon wafer,the interaction of heat inside an RTP, radiation ray
input into a radiation thermometer and the temperaturedependencies of materials and physical quantity. We also
performed simulations applying the RTP to a “wider
usage scope and more rigorous thermal processing.”
We performed some extremely rough simplifications
and approximations for portions, however these canbe said to have reproduced the actual phenomena withgood accuracy. These analysis results clarified thenecessary and sufficient conditions for realizing physicalspecifications in the development of the desktop RTP,
DTL-6, and directly led to the achievement of a device
with higher efficiency, reduced size and lower cost. As
for the non-physical aspect, these analysis results were
utilized for the implementation of various functions
compensating process experimentation, such as theemissivity interpolation functionality preventing thephenomenon described in Section 5.
This article only introduced the application of RTP in
silicon wafer processing, however RTPs can be used formany materials and we intend to offer the knowledge
and know-how obtained here for our customers in theirdevelopment of new materials and processes.

control temp.

80

MV

600

60

60

80

100

600

60

MV

20

200

20

0

0

200

40

80

800

40

40

20

100

Tw

400

400

0

Temperature, ℃

800

T rad

1 000

100

wafer temp.

120

1 200

MV, %

Temperature, ℃

6. Conclusion

120

1 000

0

temp. T w is the measured wafer temp. of component 1,
Equation ⑺.
Conventionally, in order to deal with this phenomenon,
processing would be once performed using a TC wafer,and the processing recipe (processing pattern given to thedevice as a command value) was corrected by measuring
the temperature decrease. With such simulation, it waspossible to predict the compensation value.

0

20

40

60

Time, sTime, s(1) Actual measurements(2) Simulation

80

100

MV, %

the time axis and ramp rate scales differ for both).
The thermocouple generates heat due to the lamp
7)
light and a large measurement error occurs therefore ,temperature measurement was performed using
measurement wafer which was embedded thermocouple
tip and fixed with ceramic bond (TC wafer). The
ramp rate was calculated from the temperature profile.
Furthermore, for the simulation, we used the open source
numerical calculation software, Scilab.
The ramp rate of a SEMI wafer stagnates at around
100 to 400℃, and due to the fact that this phenomenon
was reproduced in a simulation also, depending on thetemperature dependence of emissivity, if one wished toperform more accurate processing in this temperature
range, it is clear that caution is needed. Meanwhile, inthe case of solar cell wafers, which have an anti-reflective
layer on the surface in order to absorb as much light as
possible, emissivity change is minimal, therefore theimpact of the abovementioned phenomenon is slight.

0

Fig. 6 Wafer actual temperature error caused by temperature control using radiation thermometer feedback

82

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−Modeling & Simulations of The Lamp Heating-type Rapid Thermal Processor−

7. Acknowledgment
The modeling and simulations featured in this article
were accomplished in a course called Fundamental
8)
PIER Program (Pioneering Integrated Engineering
Research Program), which is being implemented at the
Department of Adaptive Machine Systems Graduate
School of Engineering, Osaka University, where theauthor serves as a visiting lecturer. Fundamental PIER
Program is an industry-academia partnerships course
for practicing actual R&D whereby a corporate coach
introduces a development issue for students to solve
over a period of one year. I would like to extend thanks
to the students who participated in the Koyo Thermo
Systems team from FY2013 to FY2016 and undertook
the tasks of investigating literature and various data, as
well as conducting experiments and analyses. I wish
these students great success moving forward. Moreover,I would like to prepare another article to announce themodeling and simulations of the halogen lamp, as well as
the measurement characteristics of the wavelength region
detected by the radiation thermometer; all of which wasomitted in this article.

References
1)

2)
3)

4)

5)

6)
7)

8)

K. MAEDA: Hajimete no handoutai-seizousouchi,
Kogyo Chosakai Publishing Co., Ltd(1999)118-127 (inJapanese).
http://www.koyo-thermos.co.jp/products/handou/
handou_dtl6.html
N. M. RAVINDRA, B. SOPORI, O. H. GOKCE, S. X.
CHENG, A. SHENOY, L. JIN, S. ABEDRABBO, W.
CHEN, and Y. ZHANG: ｢Emissivity Measurement andModeling of Silicon-Related Materials: An Overview｣,
International Journal of Thermophysics, Vol. 22, No. 5,
September 2001(2001).
｢Sekieigarasu gijutugaido1-sekieigarasu no kagakuteki,buturiteki tokusei｣, Shin-Etsu Quartz Product Co., Ltd(2010)9 (in Japanese).
｢Sekieigarasu gijutugaido2-sekieigarasu no kougakuteki
tokusei｣, Shin-Etsu Quartz Product Co., Ltd (2010)3 (inJapanese).
｢Halogen lamp no kiso｣, Light Edge, No. 22 USHIO
INC., (2001) (in Japanese).
M. HATTORI: ｢Lamp kanetu-souti niyoru Si-wafer nonetusyori｣, Jisedai no taiyou-dennchi · taiyoukouhatsuden- sono hatudennkouritsu koujou, youto to sijou no
kanousei, TECHNICAL INFORMATION INSTITUTE
CO., LTD(2018)423-428 (in Japanese).
http://www.ams.eng.osaka-u.ac.jp/fpp-j.html

M. HATTORI**JTEKT ENGINEERING JOURNAL English Edition No. 1016E (2019)

Product Development Dept., Koyo Thermo Systems Co.,Ltd.

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