lable at ScienceDirect

International Journal of Thermal Sciences 49 (2010) 1437e1445

Contents lists avai

International Journal of Thermal Sciences

journal homepage: www.elsevier .com/locate/ i j ts

Modelling of an infrared halogen lamp in a rapid thermal system

P.O. Logerais a,*, A. Bouteville b

aUniversité Paris-Est, Centre d’Études et de Recherche en Thermique Environnement et Systèmes (CERTES), IUT de Sénart, Avenue Pierre Point, 77127 Lieusaint, FrancebArts et Métiers ParisTech, LAMPA, 2 boulevard du Ronceray, BP 93525, 49035 Angers Cedex 01, France

a r t i c l e i n f o

Article history:Received 24 November 2009Received in revised form26 February 2010Accepted 8 March 2010Available online 10 April 2010

Keywords:Infrared halogen lampRapid Thermal Processing (RTP)ModellingNumerical simulationMonte-Carlo methodLamp temperature

* Corresponding author. Tel.: þ33 1 64 13 46 86; faE-mail address: pierre-olivier.logerais@u-pec.fr (P.

1290-0729/$ e see front matter � 2010 Elsevier Masdoi:10.1016/j.ijthermalsci.2010.03.003

a b s t r a c t

The heat flux distribution of an infrared halogen lamp in a Rapid Thermal Processing (RTP) equipment isstudied. An overview of lamp modelling in RTP systems is given and for the first time, the infrared lampbank is modelled by taking into consideration with accuracy a lamp portion in the bank environment.A three-dimensional (3D) lamp model, with a fine filament representation is largely presented. Themodel assumptions are in particular exposed with focusing on the thermal boundary conditions. Thelamp temperature is calculated by solving the radiative heat transfer equation by means of the Monte-Carlo method for ray tracing. Numerical calculations are performed with the finite volume method.A very good agreement is found with experimental data in steady state. The heat amount provided by thelamp is also determined. As a first development, transient calculations are performed with the validatedmodel and the dynamic behaviour of the lamp during heating process is determined with precision.Lastly, the model is discussed and further developments are proposed.

� 2010 Elsevier Masson SAS. All rights reserved.

1. Introduction

Rapid Thermal Processes (RTP) are essential in themanufacturing of semiconductor devices such as integrated circuits,memories or solar cells. They correspond to key stages in the waferproduction operations like annealing (RTA), oxidation (RTO) orChemical Vapour Deposition (RTCVD) [1e3]. As feature sizedecreases towards the nanometre scale and wafer diameterincreases, a deep knowledge of the phenomena involved in theprocesses is crucial. Indeed, there is a growing demand from rapidthermal equipment manufacturers and users to improve control,uniformity and repeatability of wafer processes. As wafer temper-ature requirement is especially moving to a drastic 1 K precision,wafer heating has to be mastered with high accuracy. Developmentof numerical tools has accompanied with success the evolution ofRTP over the last twodecades. Numerical tools have allowed a betterunderstanding of the various aspects of the processes such as waferheating, gas flow, thin film deposition, system control etc. Heat andmass transfer have been namely simulated by using the Computa-tional Fluid Dynamics (CFD) method in an efficacious way [4,5].

In RTP systems, a siliconwafer is heated up at a very high rate bythe radiative heat provided by halogen infrared lamps (Fig. 1a).Process times vary from a few seconds for implant annealing up to

x: þ33 1 64 13 45 01.O. Logerais).

son SAS. All rights reserved.

a few minutes for high-K annealing or curing [6]. The main tech-nological challenge is to obtain a well controlled uniform temper-ature at the wafer surface. So the perfect knowledge of radiativeheat emitted by the infrared lamps is necessary. The infrared lampsare usually arranged in banks in the furnace of RTP equipments(Fig. 1b). For information, in a cold wall reactor, the wafer is placedin a chamber and the wall is kept cooled by means of a water flow.A quartz window separates the chamber from the furnace. Theradiative heat is transported from the lamps to the wafer throughthe quartz window and by reflections on the chamber wall.A controller, commonly of Proportional Integral Derivate (PID) type,connected to a pyrometer fixes the input lamp power to respect thesetpoint wafer temperature.

Halogen infrared lamps consist of a tungsten filament ina middle of a quartz bulb (Fig. 1a). The latter is filled with nitrogenunder around 4 bar of over pressure to reduce the tungsten fila-ment evaporation. Halogen gases with Iodine (I), Bromine (Br),Chlorine (Cl) or Fluorine (F) are added. The created halogen cyclehelps tungsten redeposition on the filament. By this method, thelamp lifetime and lamp brightness are increased. Then, the tung-sten filament and the electrical power to apply can both remainstable. The lamp bases containing the connectors must be keptunder 600 K. Consequently, pulsed air is flowed on the lamp basesduring process.

The RTP systems were modelled in different ways. The realizedmodels tend to bemore andmore accurate to best follow the trendsof microelectronic manufacturing requirements.

Nomenclature

Ai area of the patch i surfaceAl spectral absorptivityAop absorptivity for an opaque surfaceAop,l spectral absorptivity for an opaque surfaceAst absorptivity for a semi-transparent parallel geometry

volumeAst,l spectral absorptivity for a semi-transparent parallel

geometry volumecp specific heat capacityd radiation travelled distancee distance between the centres of two neighbour lampsh0 specific total enthalpyi specific internal energy function of the temperature T

and the density r

I(r,U) radiation intensity function of both positionr and direction U

Ib(r) intensity of blackbody radiation at the temperature ofthe medium

k thermal conductivitykl spectral absorption indexL length of the lampM molar massMij radiation exchange matrix (fraction of radiation

emitted by patch i and absorbed by patch j)n! unit normal vector at the surface locationnl spectral refractive index~nl spectral complex refractive indexNs total number of patchesp static pressurep0 initial pressureP lamp applied powerPatm atmospheric pressureqi heat flux density for the patch iQi heat flux of the patch ir radial positionRop reflectivity for an opaque surfaceRop,l spectral reflectivity for an opaque surfaceRst reflectivity for a semi-transparent parallel geometry

volumeRst,l spectral reflectivity for a semi-transparent parallel

geometry volumeSh additional source term namely the one due to

radiative transferS!

M additional momentum source termt timeT temperature

Tfil filament temperatureTj average temperature of patch jTst transmissivity for a semi-transparent parallel

geometry volumeTst,l spectral transmissivity for a semi-transparent parallel

geometry volumeT0 initial temperatureu, v, w velocity components in the x, y and z directionsV!

velocity vectorx, y, z Cartesian coordinates

Greek symbolsal spectral absorption coefficiental,q spectral and directional absorptivitydij Kronecker deltaD4long longitudinal net exchanged heat flux between two

adjacent portionsD41e2 lateral net exchanged heat flux between lamp 1 and

lamp 2k absorption coefficient3 surface emissivity3j emissivity of the patch j3l spectral emissivity3l,q spectral and directional emissivityl radiation wavelengthn kinematic viscosityU propagation direction of the outgoing radiation beamU0 propagation direction of the incoming radiation

beam4bot average heat flux at the bottom of the furnace portion41/2 heat flux emitted by lamp 1 towards lamp 2F(U) phase function of the energy transfer from the

incoming direction to the outgoing direction U

r densityr surface reflectivitys scattering coefficients StefaneBoltzmann constant (5.669� 10�8 Wm�2 K�4)s transmissivitysij viscous stress tensorq radiation directionq1 angle of incidence with the surface normal in the

medium 1q2 angle of refraction with the surface normal in the

medium 2

Subscriptsi patch numberj patch number

P.O. Logerais, A. Bouteville / International Journal of Thermal Sciences 49 (2010) 1437e14451438

Plévert et al. represented the lamp banks of an RTP equipment asa continuous surface emitting infrared radiation [7]. This assump-tion led to an overestimation of the radiation emitted since only thelamp filaments radiate.

Balakrishnan and Edgar used two ways for modelling lamps inthe RTP equipment they considered [8]. Firstly, the relationshipbetween the lamp power and the wafer temperature is evaluatedfrom the heat balance of thewhole system. This relationship is validfor lamps in steady state because temperature variations are low.Secondly, the wafer temperature response and the lamp powerregulation system are identified as transfer functions. Thedynamics of the lamps are returned by a first order model. The timeconstant of the lamp depends on the filament temperature Tfil. It isproportional to Tfil

�3.

Kersch and Schafbauer modelled a rapid thermal system inwhich measured values for the lamp power are entered in thestudied RTP system model [9].

Habuka et al. studied an RTP systemwith circular lamps [10]. Thefilament lamp is modelled by source points. The DARTS method(Direct Approach using Ray Tracing Simulation) is used for raytracing. The lamp connectors are taken into consideration in themodel equations and their effect is found significant on the wafertemperature which is lower by a few percent just below them.

Chao et al. calculated view factors and approximated the radi-ative properties [11]. The representation of the lamps in the modelis a set of concentric rings. A uniform applied power is treated.Lamps are represented in the same way in other modelling workslike the one of Park and Jung [12].

Fig. 1. a) Infrared halogen lamp. b) Rapid Thermal Processing (RTP) system configuration.

P.O. Logerais, A. Bouteville / International Journal of Thermal Sciences 49 (2010) 1437e1445 1439

Chang and Hwang modelled linear infrared lamps by repre-senting the complete lamp geometry [13]. The boundary conditionsare applied to the quartz bulb and to the filament: their absorp-tivities, their transmissivities and the applied heat power areentered. Ray tracing and simulation of the absorption, reflection,refraction and diffusion of the light are performed by using theTracePro and ANSYS programs as well as the Monte-Carlo method.A 1 kW lamp power is supplied.

To continue all these efforts, in a previous work, we (Logeraiset al.) modelled an RTP equipment [14]. As the lamp filamentconsists of a large number of turns which are very close one to theother, its representation in three dimensions has been approxi-mated by a hollow cylinder with an imposed uniform temperaturein its outer surface. However, this representation involves a greatertungsten volume than the one of the real helix shaped filament. So,for a given supplied electrical power, the hollow cylinder repre-sentation should lead to an overestimated filament temperature.

In the present work, our aim is to determine the heat distribu-tion of an infrared halogen lamp in an RTP system according to thesupplied electrical power. In the model, a high accurate represen-tation of the filament is realized. The model is presented withemphasis on the equations and on the assumptions. Numericalcalculations are performed to achieve better knowledge of thethermal behaviour during thermal processes. In a last part, therealized lamp model and its results are discussed.

2. Lamp model

In this work, the infrared lamp used in the AS-One 150 equip-ment developed by the AnnealSys Company is modelled [15]. Thelamp shape and arrangement of this RTP system are common tomost of the RTP systems, thus the presented results can be trans-ferred to a lot of other systems.

2.1. Geometry

The model consists of a three-dimensional (3D) representationof one tenth of the lamp in a furnace portion (Figs. 2 and 3a).

The portion is in fact a slice of the furnace taken at mid-distancebetween a lamp and its direct neighbour lamps respectively to theright and to the left. Its width is therefore equal to the distancebetween the centres of two adjacent lamps. Its length is equal toone tenth of the lamp. Finally, its height is equal to the one of theupper part of the furnace. This representation can be first justifiedby the results obtained in Caratini’s work [16]. The latter indicatesthat the heat flux emitted by the filament remains almost uniformalong it. Even in the presence of support rings and also close to theedges of the lamp, the emitted flux decrease is low (maximum of5%). So considering one tenth of the lamp is representative. Theportion dimensions will be more justified in the below part 2.2 and2.5 with the mesh cell number and the boundary conditions.

2.2. Meshing

The realized meshing for the lamp is shown on Fig. 2. The lampfilament was achieved by generating helix curves with CFD’GEOMsoftware [17]. The number of whorls and the distance between twoconsecutive turns were specified after being measured witha calliper rule. A hybrid mesh was entered. The filament andnitrogen trapped in the bulb quartz is a tetragonal unstructuredmesh whereas the quartz bulb and the air in the portion are rep-resented by a structured mesh. The size of the cells was chosen tobe as most balanced as possible to facilitate the numerical solving.The domain is composed of around 150 000 cells. This huge cellnumber ensures a very accurate representation of the filament, sothe view factors are implicitly known perfectly. Furthermore, thismodel is less time consuming because a full filament lamp repre-sentation would involve an enormous number of cells and non-ending calculations.

2.3. Equations

The equations governing the conservation of mass, momentumand energy are solved [18]. Themass conservation equation and the

Fig. 2. Lamp model geometry with its mesh.

P.O. Logerais, A. Bouteville / International Journal of Thermal Sciences 49 (2010) 1437e14451440

momentum conservation equation are respectively given byexpressions (1) and (2).

vr

vtþ div

�rV!� ¼ 0 (1)

v�rV!�vt

þ rV!divV

! ¼ �grad��!

pþ mDV!þ S

!M (2)

The heat transfer is calculated by solving the energy conserva-tion equation (3):

vðrh0Þvt

þ divðrV!h0Þ ¼divðkgrad��!TÞ þ vp

vtþ�vðusxxÞ

vxþ v�usyx

�vy

þ vðuszxÞvz

�þ�v�vsxy

�vx

þ v�vsyy

�vy

þ v�vszy

�vz

�þ�vðwsxzÞ

vxþ v�wsyz

�vy

þ vðwszzÞvz

�þ Sh ð3Þ

in which h0 is the specific total enthalpy defined by the followingexpression (4):

h0 ¼ iþ prþ 12�u2 þ v2 þw2� (4)

One can remark that vp/vt, divðV!sijÞ and (1/2) (u2 þ v2 þw2) arenegligible in equations (3) and (4), and that the convective heattransfer can be overlooked with respect to the radiative heattransfer. So, afterwards, the flow field is not shown.

The radiative heat transfer equation for an emitting-absorbingand scattering medium can be presented as found below [18,19].

Ugrad��!ðIðr;UÞÞ ¼ �ðkþ sÞIðr;UÞ þ kIbðrÞ

þ s

4p

ZU0 ¼4p

Iðr;UÞF�U0/U�dU0 (5)

where,Ugrad��!ðIðr;UÞÞ is the gradient of the intensity in the specified

propagation direction U; �(k þ s)I(r,U) represents the changes inintensity due to absorption k and out-scattering s; kIb(r)

corresponds to the emission; ðs=4pÞ RU0 ¼4p

Iðr;UÞFðU0/UÞdU0 is the

gain due to in-scattering where F(U0/U) is the phase function ofthe energy transfer from the incoming U0 direction to the outgoingU direction; and the intensity at the surface is evaluated by:

Iðr;UÞ ¼ 3IbðrÞ þr

p

ZnU0

jnU0jI�r;U0�dU0 (6)

The radiative heat transfer equation (5) is solved by using theMonte-Carlo method. The used scheme is detailed in the work ofMazumder and Kersch [20]. In this scheme, the rays emitted by eachsurface of the system, called “patch”, are traced until they areabsorbed by the same surface or any other surface. Thus, theequation (5) solution corresponds to a radiation energy exchangebetween a given patch i and all the other patches j:

Qi ¼ qiAi ¼XNS

j¼1

�Mij � dij3j

�sT4j Aj (7)

where NS is the total number of patches and Mij is the radiationexchange matrix (fraction of radiation emitted by patch i andabsorbed by patch j).

A photon issued of a patch i, undergoes many events beforebeing absorbed by a surface. When radiation strikes a body, theprocesses of absorption, reflection (diffuse, specular or partiallyspecular) and transmission can occur [21]. Each of these events willdepend on the radiation wavelength, the radiation propagationdirection, the patch orientation and the patch optical properties.

The optical properties are described by the complex refractiveindex ~nl given by expression (8) which depends on the incidentradiationwavelength and also the patch temperature [22]. It allowsto determine the absorptivity, emissivity, reflectivity and trans-missivity of the different surfaces which can be semi-transparent oropaque.

~nl ¼ nl � ikl (8)

For semi-transparent parallel geometry like the quartz bulb,several assumptions presented in the book of Morokoff and Kerschare considered like a constant absorption coefficient al in thematerial volume [23]. The Snell law, the Fresnel formulas and

Fig. 3. Choice of the dimensions and boundary conditions.

P.O. Logerais, A. Bouteville / International Journal of Thermal Sciences 49 (2010) 1437e1445 1441

a matrix approach are used [24]. Absorptivity, reflectivity andtransmissivity for the semi-transparent parallel geometry are givenby the below expressions (9)e(11):

Ast ¼ ð1� rÞð1� sÞ1� rs

(9)

Rst ¼ r

"1þ ð1� rÞ2s2

1� r2s2

#(10)

Tst ¼ ð1� rÞ2s1� r2s2

(11)

where

r ¼ 12

tan2ðq1 � q2Þtan2ðq1 þ q2Þ

þ sin2ðq1 � q2Þsin2ðq1 þ q2Þ

!(12)

s ¼ e�dal (13)

al ¼ 4pkll

(14)

in which q1 is the angle of incidence with the surface normal in themedium 1, q2 is the angle of refraction with the surface normal inthe medium 2 and d is the radiation travelled distance.

For opaque surfaces, like the tungsten filament, obviouslytransmissivity is equal to zero. The reflectivity is calculatedknowing the absorptivity:

Rop ¼ 1� Aop (15)

In both the semi-transparent and opaque cases, the absorptivityis equal to the emissivity for a spectral and a directional conditionas stipulated by Kirchhoff’s law [25]:

al;q ¼ 3l;q (16)

Al ¼ 3l (17)

Most of all, the Monte-Carlo method is used to determine thewavelength, the direction and the trajectory of the photons fromtheir emission point to their absorption point. These characteristicsare obtained by inversing cumulated distribution functions [19].Representative bundles of photons are considered. Their trajecto-ries must be perfectly randomised to reproduce namely the diffuseemission phenomena. Hence, the choice of the Monte-Carlomethod is fully justified.

2.4. Volume properties and initial values

Each part of the lamp (the tungsten filament, the nitrogen gas inthe bulb, the quartz bulb and the air in the furnace) is considered asa volume. All the volume and initial data are reported in Table 1.They come from different sources [26e28]. Viscosities, specific heatcapacities and thermal conductivities all vary with temperature.The hypothesis of ideal gas law is supposed for the bulb nitrogenand the air. The halogen gases in the bulb, which are in minorquantities compared to nitrogen, are not introduced in the model.

2.5. Boundary conditions

The boundary condition descriptionwill allow us to explain fullythe choice of the lamp representation. The dimensions andboundary conditions of the portion are chosen to stay the closest tothe furnace conditions. The thermal conditions, in particular theradiative boundary conditions of the portion are depicted on theschematic diagrams of Fig. 3. The choice of the portion dimensionsis linked to the heat fluxes. The absorptivity, emissivity, reflectivityand transmissivity for all the surfaces are shown on Fig. 4. Theirvalues are calculated according to the material optical dataprovided by the book of Palik [22].

In Fig. 3b, a few lamps close one to the other in the furnace areconsidered. This diagram is practical to show the influence betweenlamps next to one another. In fact, in a lamp bank, the lamps aremutually heated. This mutual heating occurs mainly betweena lamp and its first neighbour lamp (lamp number 1 and 2). Ina section located midway between the two adjacent lamps 1 and 2,the heat flux emitted by the lamp 1 towards lamp 2 and the onereceived by lamp 1 from the nearby lamp 2, noted respectively41/2 and 42/1, are equal in absolute value and opposed regardingthe midway plan. The net exchanged flux D41e2 is therefore equalto zero in this plan. Hence, an adiabatic boundary condition ischosen for the lateral boundary condition of the portion.

Table 1Volume and initial properties.

Volume designation Volume property Value

Filament (tungsten) Density, r 19 300 kg m�3

Initial temperature, T0 300 KSpecific heat capacity, cp 0.0255T þ 124.35 J K�1 kg�1

Thermal conductivity, k 3.3 � 10�5T2 � 0.1144T þ 199.7 W m�1 K�1

Nitrogen in the bulb Molar mass, M 28 g mol�1

Initial pressure, p0 400 000 PaInitial temperature, T0 300 KKinematic viscosity, n 7 � 10�6 þ 4 � 10�8T � 6 � 10�12T2 m2 s�1

Specific heat capacity, cp 993.1 þ 0.161T J K�1 kg�1

Thermal conductivity, k 0.0068 þ 7 � 10�5T � 7 � 10�9T2 W m�1 K�1

Bulb (quartz) Density, r 2649 kg m�3

Initial temperature, T0 300 KSpecific heat capacity, cp 212.3 þ 4.75T � 6.26 � 10�3T2 þ 3.66 � 10�6T3 � 7.8 � 10�10T4 J K�1 kg�1

Thermal conductivity, k 0.96 þ 2.43 � 10�3T � 2.29 � 10�6T2 þ 7.94 � 10�10T3 W m�1 K�1

Air in the furnace Molar mass, M 29 g mol�1

Initial pressure, p0 100 000 PaInitial temperature, T0 300 KKinematic viscosity, n 8 � 10�6 þ 4 � 10�8T m2 s�1

Specific heat capacity, cp 951.71 þ 0.194T J K�1 kg�1

Thermal conductivity, k 0.0078 þ 6 � 10�8T W m�1 K�1

P.O. Logerais, A. Bouteville / International Journal of Thermal Sciences 49 (2010) 1437e14451442

An adiabatic boundary condition is also considered for the wallsin the longitudinal direction. When one moves along the axis of thelamp, the heat flux is uniform. By considering two portions put onebeside the other, in the section between the two portions, theemitted and received fluxes will cancel out (D4long ¼ 0). Hence, thechoice of an adiabatic condition is considered for the longitudinalboundary condition of the portion.

The “mirror” radiative property, that is to say a perfectlyreflective surface, is chosen for the lateral and longitudinal walls.Indeed, the rays emitted respectively by the nearby lamp and theportion beside are equivalent to those reflected by these perfectlyreflective walls.

The upper wall which is the furnace wall is made of stainlesssteel and its temperature is estimated at 573 K.

Finally, the convective and the radiative heat has to be evacu-ated, otherwise the temperature inside the portion is going toincrease indefinitely. The hot air evacuation outside the portiontowards the furnace is reproduced by applying an atmosphericpressure outlet condition at 300 K at the bottom portion. Thisboundary condition is called “hot air evacuation” on Fig. 3b and c.To take into account the radiation evacuation out of the portion tothe rest of the thermal system, the bottom portion optical propertyis considered like the one of a blackbody at 300 K with anabsorptivity equal to 1 (Fig. 4). This boundary condition ismentioned on Fig. 3b by the name “far”. In an RTP system, there areother radiations besides the ones emitted by the infrared lampscentred on 1 mm. These radiations are for example emitted by thesilicon wafer or by the quartz window. Consequently, a “farfield”condition is considered to take into account these incoming radi-ations with their various widespread wavelengths.

We can specify that themodel is valid for lamps near thewalls ofthe furnace as well. The distance between the lamp and the furnacewall is of the same order than the one between two adjacent lamps.As the wall is very reflective, the boundary condition with themirror radiative property is then a good approximation.

2.6. Numerical calculations

The numerical calculations are performed using the finitevolume method which consists in integrating the conservationequations (1)e(3) and (5) over each domain cell of the geometry

system [29,30]. A second order method is chosen for the spatialresolution. The ray tracing is performed for five millions rays inorder to ensure an accurate result. An at least four order magnitudedecrease of the residual sum is made sure during calculations tohave a satisfactory convergence. The numerical calculations arecarried out by using the CFD’Ace code on a PC type AMDAthlon 64,processor 32 with 1 Gb RAM. As an idea, the convergence is ach-ieved for steady-state calculations in about 3 h and in about 12 h forthe transient state ones.

In a previous work, the lamp filament temperature had beendetermined experimentally for five constant heating powers [14].The filament resistance had been deduced from measurements ofthe tungsten filament electrical voltage and intensity during heat-ing processes. As the filament resistivity is function of temperature,the filament temperature could be determined. Five percentageshad been studied: 10, 15, 20, 25 and 30% of the maximum lamppower had been applied. The obtained filament temperatures werewithin 1700 and 2300 K, which are commonly utilized values inRTP processes. The values of the measured electrical power densityare entered in the present model for the tungsten filament in orderto compare the lamp temperatures. Firstly, steady-state calcula-tions are performed and confronted to the above mentionedexperimental results. Secondly, transient simulations are per-formed with the unconditionally stable Euler first order method fortime solving.

3. Results and discussion

Fig. 5 shows the result of a steady-state calculation for a 25%applied power. We can see the incandescent tungsten filament andthe hot gases and bulb around it. For each applied power, the fila-ment temperature simulated varies by about 30 K around theaverage filament temperature which represents a deviation lessthan 2%. The lamp average temperature is then presented in all thiswork.

Since variation of the filament temperature is very rapid intransient state, the time response uncertainty is important. Thus,a steady-state comparison is more reliable. The steady-statecalculated filament temperatures are confronted to the experi-mental ones on Fig. 6 versus the five lamp power values [14]. Theexperimental uncertainty intervals are also indicated. A very good

Fig. 4. Surface radiative properties: a) Tungsten of the filament. b) Quartz of the bulb. c) Steel of the upper wall. d) Mirror. e) Far of the hot air evacuation.

P.O. Logerais, A. Bouteville / International Journal of Thermal Sciences 49 (2010) 1437e1445 1443

agreement can be noticed between experimental and calculatedfilament temperatures. All the calculated values are within theaccuracy interval and the differences found are less than 5%. So, thisvalidated model allows an accurate estimation of the heat fluxdensity flowing towards the bottom of the furnace and the reactionchamber. As this heat is evacuated out of the considered lampportion, its value is negative. This heat flux density is called 4bot. Itsabsolute average value, j4botj is reported on Fig. 7 versus the lampapplied power. The relation deduced from this figure will bepractical for the user to predict the heat flux received by thesubstrate according to the applied power to the infrared lamps.Moreover, this result is of great interest if we intend to study anentire RTP system in which the lamp bank is difficult to representdue to the numerous details. In fact, the upper part of the furnacewhich includes the lamp bank can be simplified by a wall with animposed heat flux with the determined values of Fig. 7. Thissimplification was realized in the work of Plévert et al. but the wallheat flux values were just estimated [7].

This validated model can also be simulated in transient state.Fig. 8 shows the simulated dynamics of the lamp for the fiveconsidered constant heating power. It allows to evaluate the lampresponse time.

Thereafter, a reflection is done on the possible developmentsthat can be put forward to the present precise lamp model.

As a first remark, the modelling method exposed in the presentwork is not limited to the AS-One 150 system. It can be applied tomodel cylindrical halogen infrared lamps of other RTP equipmentsby adapting the dimensions and the mesh. An application of thismethod to spherical bulbs is possible too with a preliminary studyon the mesh to realize. Besides, the present model is interesting tocomplete rapid thermal system models where the lamp tempera-ture was entered as a source term, like the ones we realized orthose in other achievements [10,14]. The source term values can bepreviously calculated with the lamp model before simulating thesystem. Moreover, different power applied instructions can beentered according to the processes [6,31]. The wafer temperature

Fig. 5. The heated infrared lamp filament (25% applied power).

Fig. 6. Comparison between the experimental filament temperatures and the calcu-lated ones versus the supplied power in steady state.

P.O. Logerais, A. Bouteville / International Journal of Thermal Sciences 49 (2010) 1437e14451444

evolution can be related to the one of the lamps in order to optimisethe thermal budget received by the wafer. Furthermore, modellingseveral nearby lamps would give even more precise results for thefilament temperature. A better knowledge of the mutual heatingwould be provided, namely if the amount of electrical power isdifferent from one lamp to another. In the present study, a uniformheating of all the lamps was taken into consideration. But, in many

Fig. 7. Absolute average heat flux density calculated at the bottom of the portion, j4botjversus the supplied power in steady state.

rapid thermal systems, the lamps can be piloted by groups in orderto get a uniform wafer temperature [32,33].

Developments of the present model to study the internalphenomena involved during RTP utilizations are also possible.Withincreasing computer capacities, it would be interesting to model atleast one quarter of the lamp with its base to see the temperaturedecrease towards the edge. Here, a uniform temperature wasconsidered and the portion is supposed to be taken more towardsthe mid part. We can mention that the Joule effect in the filamentcan be simulated by coupling the electrical current continuityequation to the heat conservation equation in themodel [18]. Goingfurther, by adding the rings in themodel, their thermal influence onboth the filament and thewafer could be appreciated. In spite of thehigh pressure and the halogen gases in the bulb, there is an inev-itable reduction of the tungsten filament volume by evaporationwith use and ageing. So, the introduction of a kinetic model for thetungsten evaporation would permit to find a relationship betweenthe lamp lifetime and the number of rapid thermal cycles.

As a final note, this model can be instrumental in controlling andregulating thewafer temperature in a tight way during lamp heatingprocess. For example, it can be integrated as a predictive model. Theaddition of a physical predictive model to the controller of RTPmachine permits an optimization of the thermal budget received bythe silicon wafer from the infrared lamps [8,34]. Specially, a wafertemperature very consistent with the required one can be obtainedwith a gradual rise before reaching the setpoint wafer temperature.

Fig. 8. Evolution of the simulated filament temperature for different lamp suppliedpower.

P.O. Logerais, A. Bouteville / International Journal of Thermal Sciences 49 (2010) 1437e1445 1445

Nevertheless, further developments are necessary for a wafer massproduction. The physical modelmust be as close as possible to realityto master the wafer process control, what we endeavoured to withthe realisation of an accurate lamp model.

4. Conclusion

The infrared halogen lamp model developed in the presentstudy gives a better knowledge of the provided heat amountaccording to the supplied power in the considered Rapid ThermalProcessing (RTP) system. In the present work, an overview ofinfrared lamp models in RTP systems is first given. A new three-dimensional deep model with a faithful representation of the lampfilament with its helix shape is afterwards largely developed. Themodel assumptions are indeed described with interest to thesurface radiative properties and the solving of the radiative heattransfer equation by means of the Monte-Carlo method. The modelis validated in steady state by a very good matching betweenexperimental and simulated infrared lamp filament temperature. Arelation is established allowing the user to predict the heat fluxreceived by the substrate according to the applied power of thelamps. This heat flux can be used to simplify forthcoming entire RTPsystem models. Moreover, the dynamics of the lamp is betterunderstood by the calculated temperature responses realized.Subsequently, they will allow to optimise the wafer thermalbudget. Many other developments are exposed in the last part inorder to go further in the mastering of lamp modelling accuracy, toimprove RTP system models and wafer control temperature.

Acknowledgments

The authors gratefully thank the French Ministry of Educationand Research and the AnnealSys Company, especially Mr. FranckLaporte for his help and fruitful discussions and Mr. Éric Dupuy fortechnical assistance.

References

[1] B. Liu, J. Gao, K.M. Wu, C. Liu, Solid State Communications 149 (17e18) (2009)715e717.

[2] R.A. Ismail, D.N. Raouf, D.F. Raouf, Journal of Optoelectronics and AdvancedMaterials 8 (4) (2006) 1443e1446.

[3] W.B. Dubbeldaya, K.L. Kavanagh, Journal of Crystal Growth 222 (1e2) (2001)20e28.

[4] J.D. Chung, Y.M. Cho, J.S. Lee, C.H. Jung, Y.J. Choi, K. Jung, IEEE InternationalSymposium on Industrial Electronics 2 (2001) 1208e1212.

[5] M.G. Giridharan, S. Lowry, A. Krishnan, American Society of MechanicalEngineers Paper (1995) 11.

[6] J. Niess, S. Paul, S. Buschbaum, P. Schmid, W. Lerch, Materials Science andEngineering B 114e115 (2004) 141e150.

[7] L. Plévert, S. Mottet, M. Bonnel, N. Duhamel, R. Gy, L. Haji, B. Loisel, JapaneseJournal of Applied Physics 34 (2A) (1995) 419e424.

[8] K.S. Balakrishnan, T.F. Edgar, Thin Solid Films 365 (2000) 322e333.[9] A. Kersch, T. Schafbauer, Thin Solid Films 365 (2) (2000) 307e321.

[10] H. Habuka, M. Shimada, K. Okuyama, Journal of the Electrochemical Society147 (12) (2000) 4660e4664.

[11] C.K. Chao, S.Y. Hung, C.C. Yu, Journal of Manufacturing Science and Engi-neering 125 (2003) 504e511.

[12] H.M. Park, W.S. Jung, International Journal of Heat and Mass Transfer 44(2001) 2053e2065.

[13] P.C. Chang, S.J. Hwang, International Journal of Heat and Mass Transfer 49(2006) 3846e3854.

[14] P.O. Logerais, D. Chapron, J. Garnier, A. Bouteville, Microelectronic Engineering85 (2008) 2282e2289.

[15] AS-One 150 is anAnnealSys product,Montpellier, France.www.annealsys.com.[16] Y. Caratini, Développement d’un four de recuit rapide, application à la crois-

sance et à la nitruration de couches minces d’oxydes sur silicium, Ph.D. thesis,Institut National Polytechnique, Grenoble, France, 1988.

[17] CFD Research Corporation, CFD’GEOM User Manual (2007) Huntsville: http://www.esi-group.com/.

[18] CFD Research Corporation, CFD’Ace (U) Module Manual (2007) Huntsville:http://www.esi-group.com/.

[19] M.F. Modest, Radiative Heat Transfer. McGraw-Hill International Editions,1993.

[20] S. Mazumder, A. Kersch, Numerical Heat Transfer, Part B: Fundamentals 37(2000) 185e199.

[21] R. Siegel, J.R. Howell, Thermal Radiation Heat Transfer. Taylor and Francis,Washington DC, 1992.

[22] E.D. Palik, Handbook of Optical Constants of Solids. Academic Press, New York,1998.

[23] A. Kersch, W.J. Morokoff, Transport Simulation in Microelectronics. Bir-khäuser, Basel, 1995.

[24] R.M.A. Azzam, N.M. Bashara, Ellipsometry and Polarized Light. North-Holland,Amsterdam, 1977.

[25] F. Incropera, D.P. Dewitt, Fundamentals of Heat and Mass Transfer. John Wileyand Sons, New York, 1996.

[26] Data available from CEA/NASA: http://cea.grc.nasa.gov/index.html.[27] Data available from NIST Webbook: http://webbook.nist.gov/chemistry/fluid/.[28] R.B. Sosman, The Properties of Silica: an Introduction to the Properties of

Substances in the Solid Non-conducting State. Chemical Catalog Co., NewYork, 1927.

[29] S.V. Patankar, Numerical Heat Transfer and Fluid Flow. Hemisphere PublishingCorporation, McGraw-Hill Book Company, New York, 1980.

[30] H.V. Versteeg, W. Malalasekera, An Introduction to Computational FluidDynamics, the Finite Volume Method. Longman, London, 1995.

[31] V.E. Borisenko, P.J. Hesketh, Rapid Thermal Processing of Semiconductors.Plenum Press, New York, 1997.

[32] N. Acharya, V. Kirtikar, S. Shooshtarian, H. Doan, P.J. Timans, K.S. Balakrishnan,K.L. Knutson, IEEE Transactions on Semiconductor Manufacturing 14 (3)(2001) 218e226.

[33] A.J. Silva Neto, M.J. Fordham, W.J. Kiether, F.Y. Sorrell, Revista Brasileira DeCiencias Mecanicas, Journal of the Brazilian Society of Mechanical Sciences 20(1998) 532e541.

[34] S.J. Kim, Y.M. Cho, Control Engineering Practice 10 (11) (2002) 1199e1210.