- Email: [email protected]
An experimental and modeling analysis of vapor transport deposition of cadmium telluride
ARTICLE IN PRESS
Solar Energy Materials & Solar Cells 83 (2004) 55–65
An experimental and modeling analysis of vapor transport deposition of cadmium telluride James M. Kestnera, Sarah McElvaina, Stephen Kellyb, Timothy R. Ohnob, Lawrence M. Woodsc, Colin A. Woldena,* a
Chemical Engineering Department, Colorado School of Mines, Golden, CO 80401, USA b Physics Department, Colorado School of Mines, Golden, CO 80401, USA c ITN Energy Systems, 8130 Shaffer Parkway, Littleton, CO 80127-4107, USA
Abstract Vapor transport deposition (VTD) was employed for high-rate deposition of CdTe thin film solar absorbers. A detailed model was developed for CdTe deposition that included the role of source conditions, convective mass transport, and deposition chemistry. A Langmuir formulation that was consistent with experimental observations of resublimation was used to describe the surface reaction probability. Comparisons of experiment and model showed very good agreement over a range of operating conditions. The model predicts an optimum operating pressure for VTD, arising from a competition between surface kinetics and dilution of the precursor species. For VTD deposition of CdTe the optimum pressure is in the range of 2–5 Torr. These modeling concepts may be easily extended to VTD of other materials as well. r 2004 Elsevier B.V. All rights reserved. Keywords: Vapor transport deposition (VTD); Cadmium telluride (CdTe); Modeling; Pressure
1. Introduction Cadmium telluride is a leading thin film photovoltaic that has been employed to fabricate record cells with 16% efficiency [1, 2]. The record cells have been grown by close space sublimation (CSS), a batch process that works well in laboratoryscale studies but has inherent limitations for large-scale manufacturing. Alternative deposition technologies that are more amenable to high-throughput processing are therefore of interest. Vapor transport deposition (VTD) has the *Corresponding author. Tel.: +1-303-273-3544; fax: +1-303-273-3730. E-mail address: [email protected] (C.A. Wolden). 0927-0248/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.solmat.2004.02.013
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attractive feature of decoupling the source and substrate environments. The manufacturability of this process has been demonstrated by First Solar using moving substrates with high throughput [3]. Despite its promise, there are relatively few reports of experimental or modeling treatments of VTD compared to CSS. In this paper, we describe an experimental VTD deposition system and develop a detailed model that predicts deposition rates as a function of operating conditions. Although the specific conditions simulated are germane to our experimental conditions, the model components are generic and can be extended to other VTD systems.
2. Experimental Fig. 1 shows a schematic diagram of the system studied in this work. CdTe source material was packed into a 1 in diameter quartz tube that was heated by nichrome ribbon wrapped around its exterior. One end of the packed-bed source was terminated by a porous quartz frit, while helium carrier gas was introduced at the other. Saturated vapor exited the quartz frit and impinged on a heated substrate located a distance L away in the stagnation flow configuration. The helium flowrate (QHe) was varied from 100–500 sccm using an electronic mass flow controller. The stagnation flow configuration produced films with radial symmetry, and it is easily amenable to modeling. The temperature of both source and substrate were measured with type K thermocouples and maintained at desired values using resistive heating and feedback control. The source and substrate pressure were monitored using convection gauges.
Fig. 1. Schematic of VTD system used to deposit CdTe thin films.
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The quartz frit played two important roles. First, it decoupled the two process environs allowing the source conditions (T1, P1) to be controlled independently from the substrate conditions (T2, P2). Second, it prevented CdTe particles from falling onto the substrate. Differential heating was employed so that the frit was maintained at a slightly higher temperature than the source, preventing premature condensation within the frit. Glass substrates coated with conducting tin oxide (1 mm thick) and chemical bath deposited CdS (300 nm thick) were placed on a resistively heated susceptor located at L ¼ 2 cm below the frit. The entire deposition setup was housed in a standard six-way cross and evacuated by a mechanical pump to a base pressure of B10 mTorr. A shutter could be positioned between the source and substrate so that the deposition time was precisely controlled. The film thickness was measured by profilometry and scanning electron microscopy (SEM) was used to characterize the morphology.
3. Modeling considerations A numerical model was developed to describe the thin film growth of CdTe using VTD. The purpose of developing a numerical description of the deposition process was to provide a useful tool for scale-up of this manufacturing technology. The model is based on scaling relationships developed for the stagnation flow geometry. The three basic components of the model include the characterization of the source, convective mass transport from source to substrate, and surface chemistry occurring at the substrate. The first step was to accurately describe the composition of the vapor exiting the source as a function of operating conditions. Experimentally, the operating pressures were set by the pump speed, the carrier gas flowrate, and the resistance across the frit. The substrate chamber pressure P2 could be independently controlled by the use of a throttle valve between the pump and the deposition chamber. Experimentally, it was found that the relationship between source (P1) and substrate (P2) pressures obeyed the following relationship: P1 ¼ P2 þ 0:22Qtot ;
ð1Þ
where both pressures are expressed in (Torr), and Qtot is the total flowrate (sccm) through the frit. The scaling value of 0.22 reflects the pressure drop across the frit and was determined experimentally by measuring source and substrate pressures at known gas flowrates. It is well known that cadmium telluride congruently sublimes to form cadmium vapor and tellurium molecules as described by 2CdTeðsÞ 22CdðgÞ þTe2ðgÞ :
ð2Þ
The thermodynamics and temperature dependence of this reaction have been well characterized [4]. The length of the packed bed was sufficient such that the gas exiting the source was saturated with vapor in equilibrium at the source
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temperature. The mole fraction of tellurium molecules exiting the source is then simply given by xo ¼
P1;Te2 ; P1
ð3Þ
where P1;Te2 is the equilibrium partial pressure of Te2 over CdTe at the source temperature and P1 is the total pressure in the source [4]. The vaporization of CdTe increases the total molar flowrate exiting the frit in accordance with the stoichiometry provided in Eq. (2): Qtot ¼
QHe : 1 3xo
ð4Þ
Eqs. (1), (3), and (4) are coupled and were solved iteratively by successive substitution until converged values of Qtot, P1, and xo were obtained as a function of the control parameters QHe, P2, and T1. The next step was to characterize the convective mass transport of Te2 molecules from the source to the substrate. The mass transfer coefficient, hm (cm/s), may be estimated using the following correlation that was developed for the stagnation flow geometry [5]: hm L 1=2 ShL ¼ ¼ 0:78ReL Sc1=3 ; ð5Þ DAB where ShL is the dimensionless Sherwood number, L is the nozzle to substrate spacing (cm), DAB is the diffusivity of Te2 in He (cm2/s), and Re and Sc are the Reynolds and Schmidt numbers for the systems, respectively. Strictly speaking, this correlation is valid for isothermal operation, dilute solutions, and for Re > 10: Temperature-dependent physical properties were used, which were evaluated at the midpoint temperature, ðT1 þ T2 Þ=2: More accurate results could be obtained by solving the fully coupled stagnation flow equations [6]. However, the error introduced by using the above correlation is at most 20%, which is sufficient for this work as we observe trends that vary by orders of magnitude. With knowledge of the inlet mole fraction and mass transfer coefficient the deposition rate can be calculated from the following [5]: ks Cs;tot xo Vs Deposition rate ¼ ; ð6Þ 1 þ ks =hm where ks is the first-order surface reaction velocity (cm/s), Cs,tot is the total gas-phase concentration at the substrate surface (mol/cm3), Vs is the specific volume of the deposited material (cm3/mol), and xo is the inlet mole fraction exiting the nozzle. All the parameters in Eq. (6) are known with the exception of the surface reaction velocity, ks, which may be estimated using kinetic gas theory and a reaction probability, g [7] g RT2 1=2 ks ¼ ; ð7Þ 1 þ g=2 2pW
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where R is the universal gas constant, T2 is the substrate temperature, and W is the molecular weight of the reactive species. In our work, it was assumed that transport of Te2 was the rate-limiting step, since its diffusivity is somewhat lower than atomic cadmium. The remaining unknown parameter in the above equations is the reaction probability or sticking coefficient, g, which is constrained between 0 and 1. Inspection of film morphology showed that re-sublimation can dramatically impact the growth rate. Fig. 2 shows SEM images of films deposited as a function of
Fig. 2. Cross-section SEM images of VTD CdTe as a function of substrate temperature. (a) 300 C; (b) 400 C; (c) 500 C.
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1.0 T2 = 673
γ,, Reaction Probability
0.9
T2 = 773
0.8
T2 = 873
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 10-6 10-5 10-4 10-3 10-2 10-1
100
101
102
103
Chamber Pressure (P2) [Torr] Fig. 3. Plot of the reaction probability, g, as a function of chamber pressure (P2) for three substrate temperatures. Calculations reflect typical deposition conditions (QHe ¼ 150 sccm and T1 ¼ 1100 K) and the Langmuir constant was set at C ¼ 104 :
substrate temperature. At the lowest temperature the grains have a distinct columnar morphology. As the substrate temperature was increased to 400 C and 500 C the columnar morphology gives way to a dense morphology, which was attributed to sublimation/condensation. In order to reflect the observed behavior, the following relationship based on the classic Langmuir isotherm [8] was proposed for the reaction probability: g¼
Kxo P2 ; ð1 þ Kxo P2 Þ
K¼
C ; PTe2 -sub
ð8Þ
where is K is an adsorption constant (Torr1). To capture the re-sublimation behavior the adsorption constant K was defined using PTe2 -sub ; the partial pressure of Te2 over CdTe in equilibrium at the substrate temperature [4], and an empirical constant C. Fig. 3 plots the reaction probability as a function of chamber pressure for three different substrate temperatures. Note that the sticking coefficient approaches unity at high pressures, where re-sublimation is suppressed. Conversely, it approaches the limit of zero at low pressures. As the substrate temperature increases the curves shift to the right, reflecting the increased tendency for re-sublimation.
4. Results and discussions A number of films were grown as function of substrate and source temperature, with the helium flowrate and chamber pressure fixed at QHe ¼ 150 sccm and
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P2 ¼ 0:5 Torr, respectively. The experimental data were compared with predictions in order to validate the model. Fig. 4 is an Arrhenius plot of the deposition rate as function of substrate temperature. At low substrate temperature the reaction probability approached unity and the deposition rate was insensitive to temperature. As the substrate temperature increased above 700 K the rate decreased exponentially, as the rate became limited by the surface kinetics. The model does an excellent job of capturing the experimental results. Fig. 4 also shows the sensitivity of the model to C, the empirical constant in the Langmuir formulation. The best fit was achieved for C ¼ 104 ; which was used in all subsequent plots. Adjusting this value an order of magnitude simply shifts the falloff temperature by B50 . This reflects the uncertainty in the experimental conditions. Although the relative substrate temperature was well controlled and reproducible, an uncertainty in the absolute temperature of 750 C remained due to complications related to thermocouple placement and radiative heating from the source. At low substrate temperature surface kinetics are not the rate-limiting step and the model in insensitive to the value of C. Fig. 5 is an Arrhenius plot of the deposition rate as function of source temperature. These films were all deposited at a substrate temperature T2 ¼ 673 K, where the deposition rate was insensitive to surface kinetics. As expected the growth rate increased exponentially with source temperature, in accordance with the CdTe vapor pressure. The model again does an excellent job of capturing this behavior. Maximum deposition rates achieved were in excess of 20 mm/min. The primary limitation to the rate of the VTD process is simply the amount of Te2 in the source,
3
ln deposition rate
2.5 2 1.5 1 0.5 0
Data C =10-3 C =10-4 C =10-5
-0.5 -1 -1.5 -2 1.0
1.2
1.4
1.6
1.8
2.0
2.2 2
2.4
-1
1000/ T2 [K ] Fig. 4. Arrhenius plot comparing measured and modeled deposition rate as function of substrate temperature (QHe ¼ 150 sccm, P2 ¼ 0:5 Torr, T1 ¼ 1037 K).
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Model
3
ln Deposition Rate
Data 2
1
0
-1
-2 0.8
0.9
1
1.1
1.2
-1
1000/ T1 [K ] Fig. 5. Arrhenius plot comparing measured and modeled deposition rate as function of source temperature (QHe ¼ 150 sccm, P2 ¼ 0:5 Torr, T2 ¼ 673 K).
while substrate kinetics can limit the rate at combinations of high substrate temperature and low deposition pressure. The carrier gas flowrate was found to have a minimal impact on experimental deposition rates. This was also consistent with the model. Increasing QHe enhances the mass transfer coefficient, however it also contributes to dilution of the source as described by Eqs. (1) and (3). Over the relatively narrow range of flowrates examined these two factors cancelled each other out. Having validated this model, we now use it to explore the influence of operating conditions on deposition rate. With regard to film quality, the best devices (B10% efficient) were fabricated from those films deposited at high substrate temperature [9]. When using glass substrates the maximum allowable temperature is typically 600 C, so the value of T2 will be fixed at this value for this analysis. Fig. 6 plots the predicted VTD deposition rates as a function of deposition pressure for different values of source temperature. A number of important concepts may be inferred from this graph. First, regardless of the source temperature there is a optimum operating pressure with respect to deposition rates. At low pressure the rate is limited by the surface kinetics as described in Eq. (8). At high pressure the rate is limited by dilution of the source, as expressed in Eq. (3). The maximum deposition rate occurs in the relatively broad plateau bounded by these limiting regimes. The model predicts that the optimum pressure also increases slightly with source temperature, shifting from 2 to 5 Torr as the source temperature is increased from 650 C to 1050 C. The deposition rate increases with source temperature, however the gains diminish with increasing temperature. The source temperature primarily influences the growth rate through control of the mole fraction of tellurium molecules exiting the source, xo. Beginning at a source temperature 650 C the tellurium vapor is quite dilute
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63
1050 ºC 950 ºC
Rate [micron/min]
10 850 ºC
This Work
750 ºC
1
0.1
650 ºC
APVTD
0.01
0.001 0.001
0.01
0.1
1
10
100
1000
Chamber Pressure [Torr]
Fig. 6. Predicted VTD deposition rates as a function of chamber pressure for various source temperatures (T2 ¼ 600 C, QHe ¼ 150 sccm). The experimental regime explored in this work and experiments done at atmospheric pressure [10] are highlighted as well.
(xo o103 ), and the rate increases exponentially with source temperature. However, at higher source temperatures the fraction of Te2 vapor begins to approach the ultimate constraint of xo ¼ 13 in the case of pure Te2 and Cd. So although the vapor pressure of tellurium continues to increase exponentially with source temperature, these gains are not fully realized in terms of the mole fraction. The operating conditions explored in this work are highlighted in Fig. 6. The maximum deposition rate of 75 mm/min is predicted for a pressure of 5 Torr and a source temperature of 1050 C. Unfortunately this regime could not be explored experimentally due to equipment limitations. The model presented was validated using parameters reflecting our experimental setup, however its components are general and may be easily adapted to other materials and VTD systems. For example, this model could be adapted for VTD deposition of cadmium sulfide or vapor-phase cadmium chloride treatment. The only change that would be required is replacing the CdTe vapor pressure dependence with that of the material of interest. The primary experimental feature that is unique to our system is the pressure drop caused by the quartz frit, as described in Eq. (1). In other systems may operate with a different pressure drop, or perhaps in a configuration where there is no significant pressure drop between source and substrate. In either case Eq. (1) would need to be modified to reflect the performance of the individual setup, however the rest of the model would remain unchanged. Previously we deposited CdTe in a VTD system that operated at atmospheric pressure in a configuration that was very similar to the design shown in Fig. 1 [10].
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The primary difference between the two reactors was that the CdTe source was farther upstream and no frit was present, so the source and substrate pressures were equal. Otherwise the rest of the analysis was applied as described in Eqs. (3)–(8). The predicted rates are also shown by the cross in Fig. 6, which is in very good agreement with the experimental findings of B0.1 mm/min achieved at a source temperature of 725 C [10]. Clearly atmospheric pressure is far from the ideal operating pressure for VTD. Although growth rates could be improved by heating the source, experimentally it was found that source temperatures greater than 725 C resulted in excessive dust formation due to gas-phase nucleation. Homogeneous nucleation is always possible when saturated vapor is transported to a relatively colder substrate, particularly at combinations of high temperature and pressure. This phenomenon was not included in the current model; however we note that in our experience operating VTD at B1 Torr no particle formation has ever been observed.
5. Conclusions A VTD system was employed for the high-rate deposition of CdTe thin films. A complementary model was developed to predict deposition rates as a function of operating conditions. A Langmuir formulation was found to accurately capture the resublimation aspects in deposition observed at high substrate temperatures. The model was validated using experimental measurements of deposition rate as a function of both source and substrate temperature. For this system, the model predicts an optimum operating pressure that is between 2 and 5 Torr. Deposition rates initially increase exponentially with source temperature, with the improvements becoming mitigated above 1000 C. The model may be generally applied to VTD systems, and was found to accurately predict experiments performed at atmospheric pressure as well.
Acknowledgements This work is partially supported by NREL Contract Nos. ZAK-8-17619-03 and ADJ-2-30630-05. We thank Ms. Rosine Ribelin of ITN Energy Systems for providing CdS-coated substrates.
References [1] C. Ferekides, J. Britt, Appl. Phys. Lett. 62 (1993) 2851. [2] H. Ohyama, T. Aramoto, S. Kumanzawa, H. Higuchi, T. Arita, S. Shibutani, T. Nishio, J. Nakajima, M. Tsuji, A. Hanafusa, T. Hibino, K. Omura, M. Morozono, Proceedings of the 26th IEEE Photovoltaic Specialists Conference, 1997, pp. 343–346. [3] D. Rose, R. Powell, U. Jayamaha, M. Maltby, D. Giolando, A. McMaster, K. Kormanyos, G. Faykosh, J. Klopping, G. Dorer, Proceedings of the 28th IEEE Photovoltaic Specialists Conference, 2000, pp. 428–431.
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R.F. Brebrick, A.J. Strauss, J. Phys. Chem. Solids 25 (1964) 1441. J. Zhou, C.A. Wolden, J. Electrochem. Soc. 147 (2000) 4142. M.E. Coltrin, R.J. Kee, J.A. Miller, J. Electrochem. Soc. 131 (1984) 425. H. Motz, H. Wise, J. Chem. Phys. 32 (1960) 1893. S. Dushman, in: J.M. Lafferty (Ed.), Scientific Foundations of Vacuum Technique, 2nd Edition, Wiley, New York, 1985, p. 806. [9] J.M. Kestner, S. McElvain, C.A. Wolden, S. Kelly, T.R. Ohno, L.M. Woods, R. Ribelin, Mater. Res. Soc. Symp. Proc. 763 (2003) B5.22.1. [10] J.M. Kestner, C.A. Wolden, P.V. Meyers, L.L. Raja, R.J. Kee, in: Proceedings of the 28th IEEE Photovoltaic Specialists Conference, 2000, pp. 595–598.
Solar Energy Materials & Solar Cells 83 (2004) 55–65
An experimental and modeling analysis of vapor transport deposition of cadmium telluride James M. Kestnera, Sarah McElvaina, Stephen Kellyb, Timothy R. Ohnob, Lawrence M. Woodsc, Colin A. Woldena,* a
Chemical Engineering Department, Colorado School of Mines, Golden, CO 80401, USA b Physics Department, Colorado School of Mines, Golden, CO 80401, USA c ITN Energy Systems, 8130 Shaffer Parkway, Littleton, CO 80127-4107, USA
Abstract Vapor transport deposition (VTD) was employed for high-rate deposition of CdTe thin film solar absorbers. A detailed model was developed for CdTe deposition that included the role of source conditions, convective mass transport, and deposition chemistry. A Langmuir formulation that was consistent with experimental observations of resublimation was used to describe the surface reaction probability. Comparisons of experiment and model showed very good agreement over a range of operating conditions. The model predicts an optimum operating pressure for VTD, arising from a competition between surface kinetics and dilution of the precursor species. For VTD deposition of CdTe the optimum pressure is in the range of 2–5 Torr. These modeling concepts may be easily extended to VTD of other materials as well. r 2004 Elsevier B.V. All rights reserved. Keywords: Vapor transport deposition (VTD); Cadmium telluride (CdTe); Modeling; Pressure
1. Introduction Cadmium telluride is a leading thin film photovoltaic that has been employed to fabricate record cells with 16% efficiency [1, 2]. The record cells have been grown by close space sublimation (CSS), a batch process that works well in laboratoryscale studies but has inherent limitations for large-scale manufacturing. Alternative deposition technologies that are more amenable to high-throughput processing are therefore of interest. Vapor transport deposition (VTD) has the *Corresponding author. Tel.: +1-303-273-3544; fax: +1-303-273-3730. E-mail address: [email protected] (C.A. Wolden). 0927-0248/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.solmat.2004.02.013
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attractive feature of decoupling the source and substrate environments. The manufacturability of this process has been demonstrated by First Solar using moving substrates with high throughput [3]. Despite its promise, there are relatively few reports of experimental or modeling treatments of VTD compared to CSS. In this paper, we describe an experimental VTD deposition system and develop a detailed model that predicts deposition rates as a function of operating conditions. Although the specific conditions simulated are germane to our experimental conditions, the model components are generic and can be extended to other VTD systems.
2. Experimental Fig. 1 shows a schematic diagram of the system studied in this work. CdTe source material was packed into a 1 in diameter quartz tube that was heated by nichrome ribbon wrapped around its exterior. One end of the packed-bed source was terminated by a porous quartz frit, while helium carrier gas was introduced at the other. Saturated vapor exited the quartz frit and impinged on a heated substrate located a distance L away in the stagnation flow configuration. The helium flowrate (QHe) was varied from 100–500 sccm using an electronic mass flow controller. The stagnation flow configuration produced films with radial symmetry, and it is easily amenable to modeling. The temperature of both source and substrate were measured with type K thermocouples and maintained at desired values using resistive heating and feedback control. The source and substrate pressure were monitored using convection gauges.
Fig. 1. Schematic of VTD system used to deposit CdTe thin films.
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The quartz frit played two important roles. First, it decoupled the two process environs allowing the source conditions (T1, P1) to be controlled independently from the substrate conditions (T2, P2). Second, it prevented CdTe particles from falling onto the substrate. Differential heating was employed so that the frit was maintained at a slightly higher temperature than the source, preventing premature condensation within the frit. Glass substrates coated with conducting tin oxide (1 mm thick) and chemical bath deposited CdS (300 nm thick) were placed on a resistively heated susceptor located at L ¼ 2 cm below the frit. The entire deposition setup was housed in a standard six-way cross and evacuated by a mechanical pump to a base pressure of B10 mTorr. A shutter could be positioned between the source and substrate so that the deposition time was precisely controlled. The film thickness was measured by profilometry and scanning electron microscopy (SEM) was used to characterize the morphology.
3. Modeling considerations A numerical model was developed to describe the thin film growth of CdTe using VTD. The purpose of developing a numerical description of the deposition process was to provide a useful tool for scale-up of this manufacturing technology. The model is based on scaling relationships developed for the stagnation flow geometry. The three basic components of the model include the characterization of the source, convective mass transport from source to substrate, and surface chemistry occurring at the substrate. The first step was to accurately describe the composition of the vapor exiting the source as a function of operating conditions. Experimentally, the operating pressures were set by the pump speed, the carrier gas flowrate, and the resistance across the frit. The substrate chamber pressure P2 could be independently controlled by the use of a throttle valve between the pump and the deposition chamber. Experimentally, it was found that the relationship between source (P1) and substrate (P2) pressures obeyed the following relationship: P1 ¼ P2 þ 0:22Qtot ;
ð1Þ
where both pressures are expressed in (Torr), and Qtot is the total flowrate (sccm) through the frit. The scaling value of 0.22 reflects the pressure drop across the frit and was determined experimentally by measuring source and substrate pressures at known gas flowrates. It is well known that cadmium telluride congruently sublimes to form cadmium vapor and tellurium molecules as described by 2CdTeðsÞ 22CdðgÞ þTe2ðgÞ :
ð2Þ
The thermodynamics and temperature dependence of this reaction have been well characterized [4]. The length of the packed bed was sufficient such that the gas exiting the source was saturated with vapor in equilibrium at the source
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temperature. The mole fraction of tellurium molecules exiting the source is then simply given by xo ¼
P1;Te2 ; P1
ð3Þ
where P1;Te2 is the equilibrium partial pressure of Te2 over CdTe at the source temperature and P1 is the total pressure in the source [4]. The vaporization of CdTe increases the total molar flowrate exiting the frit in accordance with the stoichiometry provided in Eq. (2): Qtot ¼
QHe : 1 3xo
ð4Þ
Eqs. (1), (3), and (4) are coupled and were solved iteratively by successive substitution until converged values of Qtot, P1, and xo were obtained as a function of the control parameters QHe, P2, and T1. The next step was to characterize the convective mass transport of Te2 molecules from the source to the substrate. The mass transfer coefficient, hm (cm/s), may be estimated using the following correlation that was developed for the stagnation flow geometry [5]: hm L 1=2 ShL ¼ ¼ 0:78ReL Sc1=3 ; ð5Þ DAB where ShL is the dimensionless Sherwood number, L is the nozzle to substrate spacing (cm), DAB is the diffusivity of Te2 in He (cm2/s), and Re and Sc are the Reynolds and Schmidt numbers for the systems, respectively. Strictly speaking, this correlation is valid for isothermal operation, dilute solutions, and for Re > 10: Temperature-dependent physical properties were used, which were evaluated at the midpoint temperature, ðT1 þ T2 Þ=2: More accurate results could be obtained by solving the fully coupled stagnation flow equations [6]. However, the error introduced by using the above correlation is at most 20%, which is sufficient for this work as we observe trends that vary by orders of magnitude. With knowledge of the inlet mole fraction and mass transfer coefficient the deposition rate can be calculated from the following [5]: ks Cs;tot xo Vs Deposition rate ¼ ; ð6Þ 1 þ ks =hm where ks is the first-order surface reaction velocity (cm/s), Cs,tot is the total gas-phase concentration at the substrate surface (mol/cm3), Vs is the specific volume of the deposited material (cm3/mol), and xo is the inlet mole fraction exiting the nozzle. All the parameters in Eq. (6) are known with the exception of the surface reaction velocity, ks, which may be estimated using kinetic gas theory and a reaction probability, g [7] g RT2 1=2 ks ¼ ; ð7Þ 1 þ g=2 2pW
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where R is the universal gas constant, T2 is the substrate temperature, and W is the molecular weight of the reactive species. In our work, it was assumed that transport of Te2 was the rate-limiting step, since its diffusivity is somewhat lower than atomic cadmium. The remaining unknown parameter in the above equations is the reaction probability or sticking coefficient, g, which is constrained between 0 and 1. Inspection of film morphology showed that re-sublimation can dramatically impact the growth rate. Fig. 2 shows SEM images of films deposited as a function of
Fig. 2. Cross-section SEM images of VTD CdTe as a function of substrate temperature. (a) 300 C; (b) 400 C; (c) 500 C.
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1.0 T2 = 673
γ,, Reaction Probability
0.9
T2 = 773
0.8
T2 = 873
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 10-6 10-5 10-4 10-3 10-2 10-1
100
101
102
103
Chamber Pressure (P2) [Torr] Fig. 3. Plot of the reaction probability, g, as a function of chamber pressure (P2) for three substrate temperatures. Calculations reflect typical deposition conditions (QHe ¼ 150 sccm and T1 ¼ 1100 K) and the Langmuir constant was set at C ¼ 104 :
substrate temperature. At the lowest temperature the grains have a distinct columnar morphology. As the substrate temperature was increased to 400 C and 500 C the columnar morphology gives way to a dense morphology, which was attributed to sublimation/condensation. In order to reflect the observed behavior, the following relationship based on the classic Langmuir isotherm [8] was proposed for the reaction probability: g¼
Kxo P2 ; ð1 þ Kxo P2 Þ
K¼
C ; PTe2 -sub
ð8Þ
where is K is an adsorption constant (Torr1). To capture the re-sublimation behavior the adsorption constant K was defined using PTe2 -sub ; the partial pressure of Te2 over CdTe in equilibrium at the substrate temperature [4], and an empirical constant C. Fig. 3 plots the reaction probability as a function of chamber pressure for three different substrate temperatures. Note that the sticking coefficient approaches unity at high pressures, where re-sublimation is suppressed. Conversely, it approaches the limit of zero at low pressures. As the substrate temperature increases the curves shift to the right, reflecting the increased tendency for re-sublimation.
4. Results and discussions A number of films were grown as function of substrate and source temperature, with the helium flowrate and chamber pressure fixed at QHe ¼ 150 sccm and
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P2 ¼ 0:5 Torr, respectively. The experimental data were compared with predictions in order to validate the model. Fig. 4 is an Arrhenius plot of the deposition rate as function of substrate temperature. At low substrate temperature the reaction probability approached unity and the deposition rate was insensitive to temperature. As the substrate temperature increased above 700 K the rate decreased exponentially, as the rate became limited by the surface kinetics. The model does an excellent job of capturing the experimental results. Fig. 4 also shows the sensitivity of the model to C, the empirical constant in the Langmuir formulation. The best fit was achieved for C ¼ 104 ; which was used in all subsequent plots. Adjusting this value an order of magnitude simply shifts the falloff temperature by B50 . This reflects the uncertainty in the experimental conditions. Although the relative substrate temperature was well controlled and reproducible, an uncertainty in the absolute temperature of 750 C remained due to complications related to thermocouple placement and radiative heating from the source. At low substrate temperature surface kinetics are not the rate-limiting step and the model in insensitive to the value of C. Fig. 5 is an Arrhenius plot of the deposition rate as function of source temperature. These films were all deposited at a substrate temperature T2 ¼ 673 K, where the deposition rate was insensitive to surface kinetics. As expected the growth rate increased exponentially with source temperature, in accordance with the CdTe vapor pressure. The model again does an excellent job of capturing this behavior. Maximum deposition rates achieved were in excess of 20 mm/min. The primary limitation to the rate of the VTD process is simply the amount of Te2 in the source,
3
ln deposition rate
2.5 2 1.5 1 0.5 0
Data C =10-3 C =10-4 C =10-5
-0.5 -1 -1.5 -2 1.0
1.2
1.4
1.6
1.8
2.0
2.2 2
2.4
-1
1000/ T2 [K ] Fig. 4. Arrhenius plot comparing measured and modeled deposition rate as function of substrate temperature (QHe ¼ 150 sccm, P2 ¼ 0:5 Torr, T1 ¼ 1037 K).
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Model
3
ln Deposition Rate
Data 2
1
0
-1
-2 0.8
0.9
1
1.1
1.2
-1
1000/ T1 [K ] Fig. 5. Arrhenius plot comparing measured and modeled deposition rate as function of source temperature (QHe ¼ 150 sccm, P2 ¼ 0:5 Torr, T2 ¼ 673 K).
while substrate kinetics can limit the rate at combinations of high substrate temperature and low deposition pressure. The carrier gas flowrate was found to have a minimal impact on experimental deposition rates. This was also consistent with the model. Increasing QHe enhances the mass transfer coefficient, however it also contributes to dilution of the source as described by Eqs. (1) and (3). Over the relatively narrow range of flowrates examined these two factors cancelled each other out. Having validated this model, we now use it to explore the influence of operating conditions on deposition rate. With regard to film quality, the best devices (B10% efficient) were fabricated from those films deposited at high substrate temperature [9]. When using glass substrates the maximum allowable temperature is typically 600 C, so the value of T2 will be fixed at this value for this analysis. Fig. 6 plots the predicted VTD deposition rates as a function of deposition pressure for different values of source temperature. A number of important concepts may be inferred from this graph. First, regardless of the source temperature there is a optimum operating pressure with respect to deposition rates. At low pressure the rate is limited by the surface kinetics as described in Eq. (8). At high pressure the rate is limited by dilution of the source, as expressed in Eq. (3). The maximum deposition rate occurs in the relatively broad plateau bounded by these limiting regimes. The model predicts that the optimum pressure also increases slightly with source temperature, shifting from 2 to 5 Torr as the source temperature is increased from 650 C to 1050 C. The deposition rate increases with source temperature, however the gains diminish with increasing temperature. The source temperature primarily influences the growth rate through control of the mole fraction of tellurium molecules exiting the source, xo. Beginning at a source temperature 650 C the tellurium vapor is quite dilute
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1050 ºC 950 ºC
Rate [micron/min]
10 850 ºC
This Work
750 ºC
1
0.1
650 ºC
APVTD
0.01
0.001 0.001
0.01
0.1
1
10
100
1000
Chamber Pressure [Torr]
Fig. 6. Predicted VTD deposition rates as a function of chamber pressure for various source temperatures (T2 ¼ 600 C, QHe ¼ 150 sccm). The experimental regime explored in this work and experiments done at atmospheric pressure [10] are highlighted as well.
(xo o103 ), and the rate increases exponentially with source temperature. However, at higher source temperatures the fraction of Te2 vapor begins to approach the ultimate constraint of xo ¼ 13 in the case of pure Te2 and Cd. So although the vapor pressure of tellurium continues to increase exponentially with source temperature, these gains are not fully realized in terms of the mole fraction. The operating conditions explored in this work are highlighted in Fig. 6. The maximum deposition rate of 75 mm/min is predicted for a pressure of 5 Torr and a source temperature of 1050 C. Unfortunately this regime could not be explored experimentally due to equipment limitations. The model presented was validated using parameters reflecting our experimental setup, however its components are general and may be easily adapted to other materials and VTD systems. For example, this model could be adapted for VTD deposition of cadmium sulfide or vapor-phase cadmium chloride treatment. The only change that would be required is replacing the CdTe vapor pressure dependence with that of the material of interest. The primary experimental feature that is unique to our system is the pressure drop caused by the quartz frit, as described in Eq. (1). In other systems may operate with a different pressure drop, or perhaps in a configuration where there is no significant pressure drop between source and substrate. In either case Eq. (1) would need to be modified to reflect the performance of the individual setup, however the rest of the model would remain unchanged. Previously we deposited CdTe in a VTD system that operated at atmospheric pressure in a configuration that was very similar to the design shown in Fig. 1 [10].
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The primary difference between the two reactors was that the CdTe source was farther upstream and no frit was present, so the source and substrate pressures were equal. Otherwise the rest of the analysis was applied as described in Eqs. (3)–(8). The predicted rates are also shown by the cross in Fig. 6, which is in very good agreement with the experimental findings of B0.1 mm/min achieved at a source temperature of 725 C [10]. Clearly atmospheric pressure is far from the ideal operating pressure for VTD. Although growth rates could be improved by heating the source, experimentally it was found that source temperatures greater than 725 C resulted in excessive dust formation due to gas-phase nucleation. Homogeneous nucleation is always possible when saturated vapor is transported to a relatively colder substrate, particularly at combinations of high temperature and pressure. This phenomenon was not included in the current model; however we note that in our experience operating VTD at B1 Torr no particle formation has ever been observed.
5. Conclusions A VTD system was employed for the high-rate deposition of CdTe thin films. A complementary model was developed to predict deposition rates as a function of operating conditions. A Langmuir formulation was found to accurately capture the resublimation aspects in deposition observed at high substrate temperatures. The model was validated using experimental measurements of deposition rate as a function of both source and substrate temperature. For this system, the model predicts an optimum operating pressure that is between 2 and 5 Torr. Deposition rates initially increase exponentially with source temperature, with the improvements becoming mitigated above 1000 C. The model may be generally applied to VTD systems, and was found to accurately predict experiments performed at atmospheric pressure as well.
Acknowledgements This work is partially supported by NREL Contract Nos. ZAK-8-17619-03 and ADJ-2-30630-05. We thank Ms. Rosine Ribelin of ITN Energy Systems for providing CdS-coated substrates.
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