The of Computational Fluid Dynamics & its applications

The

PHOEKICS Joumal of Compuiaüooal Fluid Ojiomics and ils Applicaüons ISSN 0969-8248

CONTENTS L I S T

Volume 8 No 4

December 1995

J Heritage

pp 402 - 403

Foreword

Kleijn C R Kuijlaars K J

pp 404 - 420

The moddling of trampon phenomena in GVD reactors

KerschA

pp 421 - 438

Radiative heat innsfer roodcUing

Kuijlaars K J Kleijn C R van den Akker H E A

pp 439 - 454

Modelling of gas-phase and surface chemistiy in PHOENICSCVD

Brinkmann R P Werner Chr FuerstR

pp 455 - 464

The effective drift-diffusion plasma model and its implementation into PHOENICSCVD

Kuijlaars K J Kleijn C R van den Akker H E A

pp 465 - 490

Modelling of a cold wall tungsten C V D reaaor: validation of PHOENICS-CVD

Posclier S Schaefer M

pp 491 - 499

Simulaüon of a SijN^ hot wall batch reactor

Kersch A

pp 500 - 511

RTP reactor simulations

Brinkmann R P VoggG Werner Ch

pp 512 - 522

Plasma enhanced deposition of amorphous silicon

Huussen F

pp 523 - 537

Design of a high temperature batch furnace using computer simulation

Werner Chr Hierlemann M

pp 538 - 552

Application of PHOENICS-CVD to epitaxial Si/Ge, polysilicon and silicon deposition in a range of C V D reactors

Concentration Heat and Momentum Bakery House 40 High Street Wimbledon London SW19 5AU England

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t.rirVlVI

Telephone: (44) 181 947 7651 Facsimile: (44) 181 879 3497 e-mail: [email protected]

J o u r n a l

of Computational Fluid Dynamics & its applications. D e c e m b e r 1995 V o l u m e 8 No.4

^

Modeling of a Cold Wall Tungsten CVD Reactor: Validation of Phoenics-CVD K.J.Kuijlaars, C R . Kleijn and H.E.A. van den Akker KramcTS Laiomtorium voor Fysische Technologie Delft University of Technology Prins Bemhardlaan 6, 2628 BW Delft, The Netherlands

Abstract As a validation study for Phoenics-CVD, low pressure chemical vapor deposition of tungsten in a cold wall single wafer reactor was studied. Model predictions for gas temperatures and gas species concentrations, both in inert and in reacting gas mixtnres, were compared with in situ measurements and were fonnd to be in good agreement. The model was found to be capable of giving accurate predictions of the effects of thermal and multi-component diffusion. A modél for the surface chemistry, which considers adsorbed species and multiple reactions at the surface, was implemented in Phoenics-CVD. Good agreement js found between simulation results using this detailed chemistry model and recent experimental data.

1

Introduction

The Chemical Vapor Deposition (CVD) of tungsten is of interest for a number of applications i n modem integrated circuits (IC's). The good step coverage (high conformality) of the deposited film makes i t relatively easy too fill the small contact holes and via's present i n modem IC designs. Because of the high melting point of tungsten, narrow lines do not exhibit electromigration and stress migration effects. Further, ttmgsten is sometimes deposited on poly-5i as a shunt material to reduce the overall resistance. I n the past decade, tungsten CVD received a lot of attention because i t can be cairied out under conditions where deposition only takes place at substrate locations where either silicon or metallic surfaces are present. During this so-called selective process, no tungsten is deposited on oxide surfaces. This way, via's and contact holes can be filled i n a single s t ^ , which leads to a reduction in the number of process steps. Because of its importance and the availability of detailed experimented data on this process, the low pressure CVD (LPCVD) of tungsten in a cold wall single wafer reactor was chosen as a validation benchmark for Phoenics-CVD. The validation benchmark study was carried out along two simultaneous paths. A comparison was made of the performance

465

and results of Phoenics-CVD with the existing code CVDMODEL, which has been used extensively for the study of CVD processes in single wafer reactors and has been validated ag«nst experimental data [1, 2, 3]. Further, Phoenics-CVD results were validated with experimental results for blanket and selective tungsten LPCVD processes in a cold wall single wafer reactor, obtained at the Delft Institute of Microelectronics and Submicron Technology (DIMES) of T U Delft and at the University of Twente. This paper deals mainly with the second, experimental part of the validation study. The experimental data included measurements of growth rates and uniformities and gas temperature and gas species concentration measurements obtained from LRS (Laser Raman Spectroscopy). This way, a number of model features could be tested i n this benchmark exercise. Models for the transport properties of multicomponent gas mixtures and for both concentration-driven diffusion and thermally driven diffiision (Soret effect) could be validated by compeiring model predictions of temperature profiles and gas species concentrations i n the reactor with these in sitti measurements. Models for the chemistry of the hydrogen reduction of WFe could be validated with deposition rate measurements.

2

Gas inlet

D

cr

Heater Dome

It

Reactor geometry

Cooted reader walls

Gases to

Initially, most studies of tungsten LPCVD were done in conventional, hot-wall, tube-type batch reactors [4, 5, 6, 7, 8]. The advantage of these systems is the accurate temperature control and the large through-put. Later studies focussed on cold-wall single wafer reactors [9,10,11,12,13]. I n the present study, simulation results are validated with experimental results [2, 12, 14, 15, 16] obtained in an ASM single wafer low pressure cold-wall reactor statable for the processing of 100 mm Si wafers (Fig. 1). The iimer vacuum vessel contains the heating wires and thermocouples for temperature control o f t h e wafer, while the outer vessel contains the wafer and the process gasses. The wafer is placed on the quartz top plate of the inner vessel and is heated by the heating wires inside the inner vessel. A graphite chuck between the wires and the quartz plate improves the temperature uniformity of the wafer heater. In the reactor, the tungsten precursor WFe is mixed with oher reactive gases such as H2, which serve as reductor, and inert gases such as N2. The gases enter the reactor radially through a gas distribution ring at the top of the reactor and are ptimped out at the bottom. During experiments the flows of the gases are controlled by mass flow controllers. Experiments performed in this reactor at Delft University of Technology are described i n [14, 15, 16, 17]. An almost identical reactor, with small modifications in the heating of the susceptor and i n the susceptor size, was used for experiments at the University of Twente [2, 12, 18].

466

Figure 1: Cross section of ihe CVD reactor used for ihe experiments and the The inner diameter of the reactor is 0.4 m

3

simulations.

Chemical models for tungsten L P C V D

The two most common processes for tungsten LPCVD use WFe as tungsten precursor and Hi or SiH^ as reducing agents. In this benchmark we have studied the WFe — H2, or hydrogen reduction, process, because of its practical relevance i n metallization and the availability of detailed and reliable experimental data. I n contrast, experimental data for the WFe — SiH4 process appear to be highly inconsistent and unsuited for model validations. In general, two types of surface chemistry model can be used: Gn the one side simple, semi-empirical description of the overall deposition chemistry are used frequently in combination with multidimensional descriptions of the transport of heat, momentum aad species concentrations e.g. [19, 20, 21, 22) and can lead to improved reactor designs with respect to thickness uniformity, gas consumption, prevention of dead zones etc However, semi-empirical lumped chemistry models do not allow for the prediction of more detailed process characteristics such as selectivity, particle formation and dopant incorporation. In addition, they can only be applied at operating conditions for which empirical growth rate data are available. On the other side detailed ab initio chemistry models, involving large numbers of species and elementary reactions in the gas phase and at the surface, with reaction rate constants predicted from theoretical reaction kinetics, have been developed for various CVD processes, e.g. [23, 24, 25, 26]. They have been used mainly in combination with simple, one-dimensional models for the fluid flow i n idealized reactor

467

configurations, which causes this approach to be of limited value iu the design of actual reactors. However, predictive models for CVD that can be used successfully in reactor and process design, should combine the latter, detailed type of chemistry modeling with a multidimensional description of the transport of heat, momentum and species concentrations. Until recently, this modeling approach was prohibited by limitations i n computer capacity, by a lack of suitable computer codes and numerical techniques and by a lack of good detailed chemical models for relevant CVD processes. I n contrast, in this paper i t will be shown that such combined, comprehensive modeling can now be achieved successfully with the Phoenics-CVD code.

3.1

E m p i r i c a l models for the tungsten L P C V D c h e m i s t r y

where R^ff is the effective deposition rate, Rs is given by Eq. 3 zoid R^ff,wFc and Rdiffjr, are the maximum diffusive fluxes of the reactants towards the surface. This led to good agreement with experimental growth rates even at very low WFe concentrations [2]. Others proposed that the rate order is small but not zero, at least at low WFe concentrations. Van der Putte [28] assumed a change firom zero order to | order at low WFe concentrations, owing to changes in the reaction mechanism. Theoretical studies [9, 31] of the kinetics of the surface chemistry of the hydrogen reduction of WFe showed that an g order dependence in the WFe concentration can be expected i f the desorption of HF from the surface is the rate limiting step. Most experimental studies failed to give evidence for a non-zero order, but more recent measurements [13, 17] give clear evidence of the non-zero order dependence of the deposition rate on the WFe concentration. The experimental results in [17] lead to the following reaction rate expression for hydrogen reduction of WFe

For the common process conditions used for metallization i n micro-electronics (600 — 750 i r , 10^ - 1 0 * Pa), the LPCVD deposition rate of tungsten from and WFe appears to be fully determined by surface chemistry and the chemistry can be described by the overall deposition reaction WFe + 3H2 -y Wis) + 6HF

(1)

When deposited on a silicon wafer, this process is preceded by a self-limiting deposition step, i n which WFe is reduced by solid silicon [27]: 2WFe{g) -¥ ZSi{s)

2W(s) + ZSiF^lg)

(2)

Several authors have found [4, 5, 9, 28] that the deposition rate depends oa the hydrogen partial pressure and the temperature, and is virtually independent of WFe for a sufficiently high WFe concentrations, according to: i i . = CB[P,,,jrJ°[P^jV.exp(-^)

(3)

where PwFt PH, are the tungsten-hexafluoride and hydrogen partial pressures respectively. For the activation energy EA, values between 67 and 73kJ/mol have been reported. In Phoenics-CVD a value of 69 kJ mol~'^ was used for the activation energy and a value of 1.7 mol Pa-'^'^ m'^ was used for the rate constant ca [3]. Eq. 3 has been used successfully in tungsten CVD reactor design aad process optimization [2, 3, 29]. A disadvantage of the assumption of zero order kinetics i n WFe is that i t cannot be valid for very low WFe concentrations. This range is of interest for the description of the deposition inside contact holes and via's and for low stress deposition [30]. Therefore, it has been suggested [2, 29] that the overall growth mechanism is determined by the sequential processes of gas-phase diffusion of reactants to the stuface and a zero order heterogeneous reaction. 1

_ 1 ^

1

468

^ 3

R, = colPwF.mPH^f"

exp(-^)

(5)

Where co has a value of 0.37 ± 0.04 mol Pa''^'^ m'^ s"^ and EA has a value of 62 ± 2 kJ mol-^ K-^. Further, the assumption of zero order kinetics in WFe appears to lose its validity at large WFe'-H^ ratios. Creighton [32] showed that for these conditions the rate order i n WFe can become negative. This was qualitatively explained using a LangmuirHinshdwood reaction mechanism with competitive adsorption. Thus, there are ample questions regarding the validity and applicability of the lumped overall chemistry model formed by Eqs. 1, 3 and 4. A perhaps more important shortcoming of this model is that i t does not account for the formation i n the gas and at the surface of by-products and intermediates, such as tungsten-subfluorides (WF^, x = 3,4,5). These species are generally believed to play an important role in the mechanisms underlying phenomena such as selectivity loss [30].

3.2

A detailed model for the tungsten L P C V D c h e m i s t r y

The above illustrates the need for a more fundamental model of the elementary reactions in tungsten CVD, such as the model that was developed by Arora and Pollard [33]. Unlike empirical lumped rate expressions, such an ah initio detailed model should be able to predict the process behavior outside the range of process conditions for which experimental data are available. Moreover, i t should be able to predict the formation of by-products and intermediates and their influence on the process. Arora and Pollard applied this model i n one-dimensional simulations of an impinging jet reactor and concluded that i t satisfactorily predicts growth rates for a large range of process conditions. However, one-dimensional simulations are of limited value in actual reactor design. Therefore, the Arora chemistry model was combined with with multidimensional transport equations in Phoenics-CVD to gain insight in the influence of process conditions and

469

reactor geometry on deposition rates, uniformities and by-product formation. A description of this detailed model is given in appendices A and B . At the surface, the fractional coverages of the adsorbed species are calculated using aa ODE solver for the simultaneous calculation of stiff surface chemistry. The fluxes of reactants to the surface and of reaction products and intermediates from the surface are imposed as boundary conditions for the transport equations of the gas phase species. A description ofthe numerical technique is given in [34]. The gas phase reactions in Arora's model were found to be of minor importance to the model results [33]. Therefore, no gas phase chemistry is included in the present simulations. The kinetic and thermodynamic data for the calculation of thè reaction rates of the surface reactions were taken directly from [33]. However, lowering the factor Gj that determines the dependence of the adsorption equilibrium of Wspecies {x = 3,6) on the fractional coverage of vacancies at the surface (table 6) by -35 %, as suggested by [35], leads to a better agreement with recent experiments [17]. This factor was determined by fitting the model results to experimental data i n the original model as well. Thus, in the present study a "modified Arora model" was used, which nevertheless closely mimics the model behavior reported in [33]. As vfill be shown, the modified model predicts experimental growth rates in a large range of process conditions with reasonable accuracy. However, this change i n the model is not well supported, and obviously this ad hoc modification somewhat conflicts with the basic ideas underlying ah initio chemistry modeling.

4

Numerical simulations with. Phoenics-CVD

A two-dimenaonal cylinder-syirmietrical grid of 40 cells in the axial direction and 26 cells in radial direction was used to model the reactor (Fig. 1) in Phoenics-CVD. Uniform temperature boundary conditions were imposed on the cooled reactor walls. Adiabatic boundary conditions were used for the walls of the inner vessel.' Reactions took place on the wafer surface only, where an tmiform wafer temperature was prescribed. Some calculations were performed vdth. an ± 5 K non-uniformity in the wafer temperature. Although this had a large effect on the deposition uniformity, i t had little effect on the gas temperatures and reactant concentrations near the susceptor. The Soret effect (thermal diffusion) was included i n the Phoenics-CVD simulations and two different models for the thermal diffusion coefBdents were studied, based on a Leimard-Jones (6-12) and a rigid spheres intermolecular potential. Two different methods of modeling ordinary diffusion, the Stefaa-Maxwell equations and the simpler Pick equation, were studied and compared. Fig. 2 shows predictions of the gas temperatures aad the WFs mole fractions of a typical simulation. The high temperature gradient near the susceptor and the resulting thermal diffusion effect in the WFs concentration are clearly visible. Simulations required several hundreds of iterations, which took circa one hour on «in HP730 workstation. The simulations that used the detailed surface chemistry model

470

Figure 2: Contour plots of gas temperature and WFe mole fraction. A wafer temperature of 573 K, a total pressure of 133 Pa, and inlet flows of 100 scan WFe and 900 seem H2 were used. required considerably more calculation time, due to the time-consuming calculations of the chemistry at the wafer surface.

5

Results

The deposition of tungsten by CVD is mainly performed in single-wafer cold-wall reactors. The gas mixture in these reactors is subject to steep temperature gradients since the wafer is heated to a temperature of 500 — 800 K, while the reactor wall, at a distance of a few centimeters, is cooled down to room temperature. The cooling down of the reactor walls is necessary to prevent deposition of tungsten there, since this would lead to an increase in the depletion of the reactants aad the formation of particles and reaction products and intermediates, which influences the film properties negatively. These temperature gradients can have a large influence on the concentrations of reaction products, due to the thermal diffusion effect (the Soret effect). This effect causes the large and heavy molecules to concentrate i n the cold regions of the reactor and the small and light molecules to concentrate in the hot regions of the reactor. I n tungsten LPCVD, this will lead to a decrease of the concentration of the heavy WFe molecules near the heated susceptor, which can lead to a decrease in deposition rate and step coverage and reduced uniformity. To study this effect, aa experimental and modeling study was made of reactant concentrations near the wafer surface. Numerical results obtained with Phoenics-CVD were compared with in-situ, spatially resolved Laser Raman Spectroscopy (LRS) meastirements in a point in the reactor, 1.7 cm above the heated susceptor. This was done in four steps. Temperature predictions were validated with in-situ gas temperature measurements, concentration predictions were validated with in-situ measurements of gas spedes concentrations i n inert and i n reacting mixtures, and chemistry models were validated by comparing growth rate predictions with measurements.

471

5.1

V a l i d a t i o n of t e m p erature predictions w i t h in-situ measurements

T t e calculated temperatures in an inert (non-reacting) gas mixture at different radial positions above the wafer were compared with the experimentally observed temperature distribution. I n the absence of chemical reactions the gas composition is completely determined by thermal diffusion due to the temperature profile i n the reactor. Therefore a good validation of the temperature predictions is necessary before a proper comparison can be made between the experimentally obtained and the calculated partial pressures i n the reactor. I n Fig. 3 the temperature of pure inert N2 is shown as a function of the location i n the reactor, measured by means of Laser Raman Spectroscopy [14]. From the figure is is clear that the gas temperature decreases very rapidly towards the wafer edge. The axis of symmetry of the reactor is at 0 mm while the wafer extends from —50 to +50 mm. The laser beam, along which the probing volume is shifted, is located at 17 mm above the surface. The reactor was kept at a pressure of 533 Pa and a nitrogen flow of 500 seem was used. The temperature is determined from the reduction of the local nitrogen density compared to the density at room temperature. The measurements were taken from - 6 5 mm to -1-85 mm from the center of the wafer. Measurements at 293 isT, when the reactor is totally isothermal, were used to calibrate the LRS system. The measurements shown i n Fig. 3 were taken at wafer temperatures of 465,625 and 790 K. The solid lines i n Fig. 3 are the calculated values for the gas temperatures. Calculations were performed with Phoenics-CVD and with the academic code CVDMODEL, which gave almost identical results. To reach good agreement with the experimental data, a positive correction of less than 30 K in the uniform wafer temperattrres was made compared to the experimentally determined wafer temperatures. The necessity of this correction was attributed to inaccuracies in the wafer temperature measurements, a well known problem in low pressure, cold wall CVD experiments. Applying an experimentally determined non-uniformity of ± 5 K to the boundary conditions for the wafer temperature had negligible effect on the gas temperature profile. Fig. 3 shows that the calculations correctly predict the temperature profiles in an area that is most severely subject to temperature gradients. This provides sufficient confidence that the temperature is also correctly predicted in less critical parts of the reactor.

5.2

V a l i d a t i o n of concentration predictions w i t h in-situ s u r e m e n t s i n a n inert gas m i x t u r e s

mea-

As a validation of the modeling of thermal diffusion and its effect on the concentrations of reactants i n a cold-wall reactor, the behavior of a two-component gas system was studiedSince i n a reacting gas mixture the reactant concentrations are influenced not only by thermal diffusion, but by consumption due to the surface chemistry as well, an inert gas mixttire was used. I n figure 4 the partial pressures 17 mm above the wafer center are shown for a mixture

472

-100

-75

-50

-25

0 25 50 75 ICO Locatbn in reactor (mm)

Figure 3: The temperature 0} the nitrogen in the reactor as a function of the location in the reactor for various wafer temperatures. The wafer extends from —5 to 5 cm. The temperature profile is taken at 17 mm above the wafer surface along the laser beam. The solid lines are ihe calculated temperatures. of hydrogen and nitrogen at a flow rate of 300 ± 10 and 320 ± 10 seem respectively. The total pressure was 533 Pa and the wafer temperature was varied from 290 to 790 K. The probing volume was 17 mm above the center of the wafer. As the wafer temperature increases, the Soret effect causes a separation of the two gases. The concentration of the light hydrogen increases with increasing wafer temperature and the concentration of the heavier nitrogen decreases. A t the highest wafer temperature the nitrogen pressure has decreased 55 Pa with respect to the 275 Pa inlet pressure. Two models for thermal diffusion in Phoenics-CVD were tested. The sohd line represents the calculated values of the pcirtial pressures, assuming a Lennard-Jones (6-12) interaction between the molecules, while the dashed line represents the values calculated assuming a rigid-spheres interaction. Within the experimental error margins both the rigid-spheres and the Leimard-Jones approximation are in agreement with the measured values. The rigid-spheres approximation leads to a somewhat stronger separation due to the Soret effect, but the difference between the approximations is small. The fact that the rigid spheres model is in somewhat better agreement with experiments is in contrast with the general belief that the Lennard-Jones model describes molecular interaction more accurately, and is probably accidental. Therefore, in further simulations the Leimard-Jones model is used for the prediction of transport properties.

5.3

V a l i d a t i o n of concentration predictions w i t h in-situ s u r e m e n t s i n a reacting gas m i x t u r e s

mea-

Model simtilations for gas concentrations in a reacting gas mixture were compared to experimental data. I n Fig. 5 the results from a series of experiments with a mixture

473

223

2301 300

1 400

1 930

! 60O

' 700

1 SCO

Wafer temperature (K) XO

Figure 4: Results of an experiment performed with a hydrogen and nitrogen mixture. The measurements are taken in a point 17 mm ahove the center of the wafer. The partial pressures of both species are shown as a function of the wafer temperature. The solid lines were calculated using a Lennard-Jones (6-12) interaction potential function while the dashed lines were calculated using the rigid spheres interaction. of WFs and H2 are shown. The flows of II2 and WFs are 830 ± 50 and 60 ± 2.5 seem respectively, at a total pressure of 533 Pa. For wafer temperatures below 600 K the deposition rate is small and the changes i n the partial pressures of the reactants are caused by thermal diffusion. The partial pressure of WFs decreases near the heated susceptor, while the hydrogen pressure increases. At 600 K the partial pressure of WFs has decreased to 18 Pa, circa 55 % of its inlet value. At temperatures above 600 K the consumption of the reactants becomes important, leading to a decrease of the hydrogen partial pressure and a sharper decrease in the WFs partial pressure. A t 825 K the WFs partial pressure has decreased to 5 Pa, circa 14 % of its inlet partial pressure. The solid and the dashed line show the modeling results, which are in good agreement with the measurements. The empirical model Eqs. 1,3 and 4 were used for the description of the surface chemistry. In non-dilute gas mixtures the Stefan- Maxwell description of concentration driven multi-component diffusion should be used [36], rather than the more simple Fick diffusion models that are also present as an option in Phoenics-CVD. In Fig. 6 the influence of both diffusion models on the deposition rate predictions is shown. A t high WFs flows the difference between both models is small. A t lower flows, where the reactant concentrations near the wafer are low and the diffusive transport of the reactants is important, the Fick descriptions lead to an overprediction of the deposition rate.

400

500

600

700

803

900

Wafer temperature (K)

Figure 5: The partial pressures of WFe and hydrogen as a function of the wafer temperature. The WFe and H2 flows were 60 and 830 seem respectively. The total pressure is 533 Pa. Deposition takes place on a 0.1 m diameter wafer. The solid and dashed line are ihe calculated values for ihe partial pressures

10

100

1000

WFgflowCsocm)

Figure 6: The deposition rate as a function of the WFs flow, at a constant H2 flow of 830 seem. The total pressure is 533 Pa. A uniform wafer temperature of 772.5 K was used. The wafer diameter was 0.1 m . Experimental results (o) and model results using Stefan-Maxwell (—) and Fick (- - -).

474

475

Ql

0

1

1

1

1

1

20

40

60

80

100

WF partial pressure (Pa) Figure 7: Average deposition rate on a 3 at different wafer temperatures and total used to keep the total flow at 1200 scan. chemistry model (- - -) and experimental

5.4

in. wafer as function of the WF^ inlet pressure pressures. Qjj, = 1000 seem. An Ar flow was Detailed chemistry model (—), semi-empirical results fo, D).

V a l i d a t i o n of chemistry models by c o m p a r i n g growth rate predictions w i t h measurements

In Figure 7, 8 and 9 the predicted growth rates, obtained with the detailed chemistry model (appendix A and B) as well as with the lumped semi-empirical model (Eqs. 1, 3, 4), are compared to two different experimental datasets [2,17] and an important difference between the apparent kinetics of these two sets of experiments was observed. I n Figures 7 and 8 experimental results for the growth rate as a function of the WFs inlet concentration are shown. The experiments show a transition between two rate limiting processes. A t high WFs concentrations a small dependence of the deposition rate on the WFs concentration is found, whereas at low WFs concentrations this dependence is strong. This is often interpreted as a transition from kinetically limited growth to transport hmited growth. Indeed the semi-empirical model, which is based on this assumption, appears to predict the transition observed in Fig. 7 ([2]) with reasonable accuracy. I n contrast, i t can be seen that for the detailed chemistry model the agreement is less satisfactory. The detailed model predicts a slower transition between the two regimes and no zeroth order behavior in the WFs pressure is seen at higher WFs concentrations, apparently in disagreement with the experiments from [2]. However, a different picture is obtained when the same comparison is made for the data i n Fig. 8 ([17]). Here, a more detailed study is made of the deposition rate in the transition regime. For these data, the detailed model seems to be much more accurate than the semi-empirical model. The model results using Eq. 5, with rate parameters which

476

Figure 8: Average deposition rate on a 100 mm. wafer as function of the WFs flow at different wafer temperatures. Total pressure is 533 Pa, Qu, = 825 seem. Detailed chemistry model (—), empirical chemistry model with zero order dependence in WFs (—), empirical chemistry model with - order dependence in WFs (* " " j j experimental residts (o,A,0). were obtained by fitting this relation to the same experimental data, are also shown i n Fig. 8. This demonstrates that the detailed chemistry model shows a behavior that is dose to aa I order in WFe. When compztring the deposition uniformity predicted by the two models to the experimental data in Fig. 9 [2], the simple chemistry model appears again to perform slightly better than the detailed model. The latter predicts a better uniformity than the experimental data for low WFs concentrations and a worse uniformity for high WFs concentrations. This is an illustration of the more general difficulty of validating comprehensive CVD models i n the presence of often inconsistent experimental CVD data. I t is dear that this discrepancy between the two independent experimental data sets needs to be darified before definitive conclusions on the accuracy of the detailed chemistry model versus the lumped model can be made. In [2] (Fig. 7), as in most studies which observed a zeroorder WFg-dependence [4,5, 9,28,11], tungsten was deposited on silicon, which is known to react with WFe. In most cases, the hydrogen reduction reaction was preceded by a displacement reaction, Eq. 2. For kinetic measurements this is not very desirable, since i t cannot be exduded that this reaction will have an influence on the subsequent hydrogen reduction. I n [17] (Fig. 8), a sputtered tungsten film was used as a starting point for the deposition rate measurements, which comes closer to the perfect ttmgsten surface assumed i n the detailed chemistry model.

477

I

r

1

1

C

1

1

I

i _ i

I

1 1

I

ll|

1

1 1,1

I I

IU

1 I . 40 seem WFe

f O 2

I

0.5 1.3 seem WFs

O

0.01

0.02

0.03

0.04

radius (m)

Figure 9: Growth uniformity on a 3 in. wafer, for two different WFg flows. Total pressure is 133 Pa, Qjf^ = 1000 seem. An Ar flow was used to keep ihe total flow constant at 1200 seem. Detailed chemistry model (—), semi-empirical chemistry model (- - -) and experimental results (o, D).

5.5

G r o w t h rates at low H^iWFs

ratios

The overaU reaction rate expression (Eq. 3 ) was derived under conditions where hydrogen is present i n large excess, i.e. PH, : PWF^ > 5. At lower ratios the reaction order in WFe is found to becoine negative [32]. Figure 10 shows the predicted dependence of the deposition rate on the WFe partial pressure at low Pn^-.PwFi ratios. The empirical expression Eq. 3 leads to a very small negative-order dependence on the WFe concentration, caused by thermal diffusion effects. The detailed model predicts a transition to a negative order at decreasing PH,:PWFC ratios, in qualitative agreement with experimental observations.

6

Conclusions

A validation study has been made of numerical models for low pressure tungsten Chemical Vapor Deposition from WFe and H-i in a single wafer reactor. Good agreement between predicted and experimentally determined gas temperature profiles above the wafer was observed, which indicates that accurate predictions can be made of the gas temperatures elsewhere in the reactor. The influence of thermal diffusion (Soret effect) on the concentration of reactants i n the model has been validated by in-situ measurements. Model results using a empirical relation for the reaction rate have been validated by experimental results and by comparison with an academic code. A detailed description for the multiple reaction multi-spedes chemistry at the surface, based on the model developed by Arora and Pollard, has been implemented i n

478

0

• *' tul

1

1—1—IIT 1 m l

10

100

WFg parfial pressure (Pa)

Figure 10: Deposition rate as a function of WF$ partial pressure at a total pressure of 133 Pa and two different wafer temperatures. The hydrogen flow rate is 500 seem and an argon flow was used to keep the total flow at 1500 scan. Predictions, oltained hy using the Arora tungsten LPCVD model (—) and ihe empirical expression (- - -). Phoenics-CVD. I t has been shown that this detailed model for the tungsten CVD chemistry, induding a considerable number of surface processes aad spedes i n the gas-phase and at the surface, can be combined with a multi-dimensional transport model. This opens the door to the prediction of process characteristics outside the range of validity of empirical rate expressions. Growth rate predictions were \'alidated with two sets of experimental data, which show a different behavior in the transition between a regime where a high WFs concentration is present at the surface and a regime where the consumption of WFs leads to reactant starvation. I n a validation study with tungsten deposition experiments on silicon wafers, the empirical model, which assumes a zero reaction order in the WFs concentration, and which was based on these sets of experiments, performed better than the detailed chemistry model. However, this latter model showed better agreement with growth rate measurements on sputtered tungsten coated wafers. A n overall reaction rate expression, assuming a reaction order ia the WFs concentration of | , gave similar results, which indicates that the detailed model, which was derived without assuming rate-limiting steps, supports this reaction order under these process conditions. Indications have been found that the deposition mechanism for growth on tungsten wafers differs from that on silicon wafers.

479

Sl S2 S3 S4 S5 S6 S7 S8 S9 SlO SU S12 S13 S14 S15 S16

G l WFs + F ^ WFe G2 ^ G3 2 f G4 2WFs
(§)

k=i t"=i i=i !=l i=l where kj and h are the forward and backward reaction rates respectively. The activities of the gas phase species are partial pressures p; expressed in atmospheres; the activities

480

481

No.

of suiface species are statistical factors f j , multiplied by surface fractions Bj, which are defined as:

Sl S2 S3 S4 35 S6 S7 SS S9 SlO SU S12 S13 S14 S15 S16

where Cj is the concentration i n mol m ^ oi adsorbate j at the surface, CT is the concentration of t-ungsten atoms at the surface, which is 1.673 x 10~^ moZ m~^ for (100) tungsten and 77 is the number of dangling bonds available per W atom, which is 4 for (lOO)W. The (100) orientation is the most commonly obtained surface during polycrystalline growth [33]. The fractional coverage of vacancies 0^ is related to the fractional coverages of the adsorbates by:

ö» =

i -

E

vA-

(10)

where rjj is the number of sites to which an adsorbate forms bonds. The statistical factors for adsorbates and vacancies represent the likelihood that dangling bonds required for the surface processes to occur are oriented in the right position. The statistical factor for vacancies is ƒ„ = 0.625. For reaction S13 a different statistical factor of ƒ„ = 0.5 must be used. For singly bonded axisorbates a factor of ƒ„ = 0.25 is used. For adsorbates that form bonds with multiple sites, the activities are equated to the fractional surface coverages, i.e., f j is set to unity. The forward reaction rates are given by

A

0

4.72 X 10° 1.06 X 10" 1.26 X 10" 1.39 X 10" 1.63 X 10' 1.01 X 10^ 5.35 X 10* 7.93 X 10= 5.27 X 10= 1.47 X 10= 3.18 X 10= 1.73 X 10'' 7.30 X 10'' 2.22 X 10^ 2.12 X lO'^ 4.49 X 10'^

C/R

-0.96 0.68 0.05 0.01 0.89 0.9 1.11 -0.33 1.42 1.70 1.36 0.91 0.83 0.75 0.80 0.62

(X) xlO^ 2.0 26.9 26.9 26.9 8.3 2.0 26.7 2.0 13.2 5.5 12.5 12.5 2.0 14.2 18.5 8.5

D/R

(K)

xl(fi 0.0 -10.1 -10.1 -10.1 -5.9 0.0 -6.9 0.0 0.0 0.0 0.0 0.0 0.0 2.3 0.0 0.0

Table 3: Rate constants for the surface processes (table 2) involved in ihe deposition of tungsten by hydrogen reduction of WFe- The forward rate constants are given hy Eq. 11 in mol m~^ atm"" where n is unity for reactions Sl and S8 and zero otherwise. The standard enthalpy of formation of gas spedes i at temperature T is given by

AH^. = AJf^V, + £^ CidT fc... = ^ . T - e x p ( - ^ d : M ^ )

where At, 0k, Ck and Dt are rate constants ( table 3 ), i? is the gas constant and T, is the surface temperature. In this formulation, the activation energy of the surface reactions depends on the fraction of vac«uicies at the surface 6„. The reverse reaction rates i j , t can be calculated from the forward reaction rates and the equilibrium constants Kk • h . =

(16)

(H)

'^

(12)

and the entropy of gas spedes i at temperature T is given by S'r.i = Sl,,, + j^JfdT

(17)

Values for AH^ i and S^gs,,- and for the four-parameter fit for the heat capacity Cp that was used i n [33] (table 4 ) were converted into the shghtly different format of the Chemkin thermodynamic database, as shown in table 5. In table 4 the following fit was used for the heat capadties:

The equilibrium constants are calculated from C;,,. = a . + A r + 7 . r ' +