CRYSTAL GROWTH & DESIGN
Thermodynamic Calculations and Growth of ZnSe Single Crystals by Chemical Vapor Transport Technique
2002 VOL. 2, NO. 6 585-589
O. Senthil Kumar, S. Soundeswaran, and R. Dhanasekaran* Crystal Growth Centre, Anna University, Chennai-600 025, India Received April 1, 2002
ABSTRACT: A thermodynamic model has been proposed for the growth of ZnSe single crystals by the chemical vapor transport (CVT) method using iodine as the transporting agent. The optimum growth conditions for the growth of good quality ZnSe single crystals have been investigated theoretically using partial pressure values of I, I2, ZnI2, and Se2, which were calculated empirically at different growth temperatures and for different iodine concentrations, present inside the growth ampule. The diffusion-limited transport rates have also been calculated by taking into consideration the growth temperature, the ampule length, the total pressure present inside the ampule, and the partial pressures of ZnI2 at growth and source zones. The change in supersaturation ratio with respect to temperature and initial iodine concentration has also been calculated using this numerical model. The optimum growth temperature for the ZnSe-I2 system has been predicted from the theoretical results. Experiments were carried out for the growth of ZnSe crystals by the CVT technique using iodine as the transporting agent at different conditions. 1. Introduction Zinc selenide, a wide band gap semiconductor, is used to device blue light-emitting diodes. The lattice mismatch (0.26%) between ZnSe and GaAs is still a problem in heteroepitaxial growth of the ZnSe-GaAs system.1,2 Substrate quality single crystals of ZnSe were grown by the chemical vapor transport (CVT) technique for homoepitaxial applications. Iodine is widely used as a transporting agent in this technique. Only a few reports were available about the modeling of a CVT grown ZnSe-I2 system.3-5 The growth of a ZnSe single crystal is usually carried out in a horizontally placed closed ampule. Zinc selenide single crystals were successfully grown using the CVT technique by many researchers.6-8 In the present investigation, the growth parameters such as partial pressures of vapor components present inside the ampule during growth, the temperature difference between growth and source zones, initial iodine concentrations, and the length of the ampule are taken into consideration to optimize the growth conditions. Some other factors such as mechanism of vapor transport and angle at the conical tip of the ampule, etc., which can affect the growth of crystals from vapor, were discussed in detail.9,10 A simple thermodynamic model has been proposed for the ZnSe-I2 system by which partial pressures of the vapor components such as I, I2, ZnI2, and Se2 were calculated at different growth temperatures and for different iodine concentrations. The fluctuations in the diffusion-limited transportation rates with respect to the possible temperature fluctuations present at the growth interface have also been calculated using a numerical model from which the optimum growth conditions were predicted. The growth experiments were carried out at different conditions. The experimental results show that ZnSe crystals grown with growth parameters close to theoretically predicted * To whom correspondence should be addressed. Tel: +91-442352774. Fax: +91-44-2352870. E-mail address: rdhanasekaran@ hotmail.com or
[email protected].
optimum growth conditions are of better quality when compared to the other crystals grown under different conditions. 2. Estimation of Optimum Growth Parameters The vapor phase chemical transport of ZnSe with iodine is a triple reaction system, namely,
ZnSe + I2 S ZnI2 + 0.5Se2
(1)
ZnSe + I2 S Zn + 2I + 0.5Se2
(2)
ZnSe + 2I S ZnI2 + 0.5Se2
(3)
neglecting dissociation of ZnSe via
ZnSe S Zn + 0.5Se2
(4)
and dissociation of ZnI2 via
ZnI2 S Zn + I2
(5)
It is assumed that as the first approximation, the vapor phase contains only four components: I, I2, ZnI2, and Se2. Also, the law of mass conservation of iodine at equilibrium
I2 S 2I
(6)
and exact stoichiometry of ZnSe source material give the following equations.
pI2o ) pI2 + 0.5pI + pZnI2
(7)
pZnI2 ) 2pSe2
(8)
where pI2ο is the pressure corresponding to the iodine concentration initially taken and other p’s are the partial pressures of corresponding components. The
10.1021/cg020007n CCC: $22.00 © 2002 American Chemical Society Published on Web 10/11/2002
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equilibrium constants for the reactions 1 and 6 are
K1 ) (pZnI2pSe20.5)/pI2
(9)
K6 ) pI2/pI2
(10)
The values of K1 and K6 are given by ref 11
log K1 ) 7.64 - 5849 T-1 - 4154 T-2 - 0.83 log T - 1.5 × 10-4 T (11) log K6 ) 4.34 -7879 T-1 + 4264 T-2 + 0.33 log T + 2 × 10-5 T (12) The partial pressures of the components inside the ZnSe-I2 system were calculated for the range of temperatures from 500 to 1200 °C with various values of transporter concentrations ranging from 0.5 to 10 mg/ cm3 by using eqs 7-10. It has been assumed that iodine behaves as an ideal gas in these calculations. Using the partial pressure of ZnI2 with respect to that of initial iodine, the ratio R ) pZnI2/pI2o can be calculated. The transport rate of ZnI2 from the source zone to the deposition zone is proportional to the difference in the R values of source and deposition zones, i.e., ∆R. The difference between the source and the deposition zone temperatures was maintained at a constant (50 °C). It can be approximated to be equal to ∆pZnI2/pI2o, as there is not much difference between the values of pI2o in source and deposition zones. The number of moles of ZnSe transported in time t is given by ref 12.
nZnSe ∝ ∆R × t
Figure 1. Partial pressures pI, pI2, pSe2, and pZnI2 as a function of temperature for iodine concentration c ) 2 mg/cm3 in the ZnSe-I2 system.
(13)
However, diffusion-limited transport rates have been calculated following Faktor and Garret,13 Mandel,14 and Bottcher using the formula
JD ) (2DZnI2pT/RTL) ln {2pT - pZnI2(g)/2pT - pZnI2(s)} (14) where DZnI2 is the diffusion coefficient of the component ZnI2, pT is the total pressure at the temperature T, pZnI2(g) is the partial pressure of ZnI2 at the growth zone, pZnI2(s) is the partial pressure of ZnI2 at the source zone, R is the universal gas constant, and L is the length of the ampule used in the experiment. 3. Experimental Section About 3 gm of heat-treated and high purity zinc selenide polycrystalline powder was filled in a quartz ampule with a length of 15 cm and a diameter of 1 cm along with iodine. The ampule, cooled by ice, was evacuated to 2 × 10-6 Torr and sealed off. The ampule was placed into the double-zone horizontal furnace controlled by Eurotherm controllers of accuracy (0.1 °C. A reverse temperature profile was developed across the ampule over several hours to remove the sticking powder from the deposition zone of the ampule. The iodine concentration of 2 mg/cm3 was taken, and a temperature difference of 50 °C was maintained between source and deposition zones. The temperature of the growth zone was maintained at 700, 800, and 900 °C, respectively. Each growth
Figure 2. Variation of R with temperature for various concentrations of iodine. run was carried out for 15 days, and after that, the furnace was cooled to room temperature in 20 h.
4. Results and Discussions Figure 1 shows the change in partial pressure of I, I2, ZnI2, and Se2 with respect to temperature ranging from 500 to 1200 °C for the iodine concentration of 2 mg/cm3 taken initially. The partial pressure value of all of the components increases except that of the iodine molecule. The ratio between the partial pressure value of ZnI2 and the total pressure due to iodine components (pI + 0.5pI + pZnI2 ) has been calculated as R for the range of temperatures, as mentioned earlier. The variation of R with respect to temperature for the range of iodine concentrations from 0.5 to 10 mg/cm3 has been presented in Figure 2. The value of R was found to decrease with an increase in iodine concentrations at a given temperature. Even though iodine is added in large amounts, the formation of ZnI2 is limited with respect to the equilibrium conditions. It can be now concluded that an increase in iodine concentration has very little effect in the increase of pZnI2.
Calculations and Growth of ZnSe Single Crystals
Figure 3. Variation of ∆R with deposition temperature (T1) for various concentrations of iodine.
The transport rate of ZnI2 is proportional to the difference in the R values of source and deposition zones, i.e., ∆R. The variation of ∆R with respect to temperature for the range of iodine concentrations is shown in Figure 3. For a given iodine concentration, the value of ∆R is found to increase gradually, reach a maximum, and then decrease with the increase of temperature. As iodine concentration increases, the peak positions shift to higher temperatures and also the curves become more broadened. From the above figure, it was observed that for every iodine concentration, there is an optimum temperature region near the peak positions where the change in ∆R is minimum; hence, the fluctuations in transport rate should be minimum in that region. The change in transport rate is proportional to ∆pZnI2, i.e., the difference between the partial pressures of ZnI2 in source and deposition zones. So, it can be assumed that without considering the type of migration along the ampule, the growth rate is proportional to ∆R, which can be approximated to be equal to ∆pZnI2/pI2o. However, a slight drop in temperature at the deposition zone during the growth process causes the multiplicity of crystals, which leads to intergrowths and changes in the stoichiometry of the crystal.15 Because the flow of material is very much temperature-dependent and the control of temperature at the growth interface is always poorer than the accuracy shown by the temperature controllers in the furnace, the temperature variation up to (2 °C can normally be expected inside the quartz ampule during the growth process. The fluctuation in transport rates has been calculated using eq 14 for the temperature fluctuation up to (2 °C expected to be present inside the ampule during the growth process. The results are presented in Figure 4, from which it is observed that the fluctuation in transport rate was minimum at 800 °C, and better quality crystals can be grown at that temperature. Figure 5 shows the change in supersaturation ratio {∆pZnI2/pZnI2 (T1)} as a function of deposition zone temperature for the undercooling value of 50 °C and for various iodine concentrations. It has been observed from the figure that an increase in iodine concentration produces only a very small change in supersaturation at a given temperature. It can be now stated that iodine
Crystal Growth & Design, Vol. 2, No. 6, 2002 587
Figure 4. Fluctuations in transport rate for the fluctuations in temperature up to (2 °C in the ZnSe-I2 system for three different growth temperatures for ∆T ) 50 °C, I2 concentration c ) 2 mg/cm3, and ampule length ) 15 cm.
Figure 5. Change of relative supersaturation with deposition temperature (T1) for various concentrations of iodine.
concentration has very little influence on the supersaturation ratio at a given temperature and thus the growth of crystals. However, an iodine concentration of 2 mg/cc has been used in our experiment. From Figure 3, the optimum temperature range for the growth of ZnSe was found to be 750-900 °C where the change in ∆R is minimal for the iodine concentration of 2 mg/cm3. Figure 6a-c shows the ZnSe crystals grown at 700, 800, and 900 °C, respectively. The experimental results observed are in good agreement with the theoretical calculations. The following results have been obtained for the ZnSe crystals grown at three different temperatures with 2 mg/cm3 of iodine concentration and 50 °C difference in temperature between the source and the deposition zones. The crystals grown at 800 °C have complete faces. The quality of the crystals was found to be good. This can be due to the stability of the flow of materials, which are transported from the source zone to the growth zone,
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Figure 7. XRD spectra of ZnSe crystals grown at 700, 800, and 900 °C. Table 1. Comparison of Experimental Results with Previous Reports
Figure 6. (a) ZnSe single crystals grown at 700 °C. (b) ZnSe single crystals grown at 800 °C. (c) ZnSe single crystals grown at 900 °C.
and growth of crystals at predicted optimum growth conditions corresponding to the 2 mg/cm3 of iodine. The crystals that were grown at 700 °C, due to high partial supersaturation, have a larger number of smaller size crystals with irregular habits and poor quality. The crystals, which were grown at 900 °C, were found to have very poorly developed faces. This deficiency in quality can be due to the inconstancy of the transport
Sl. no.
Source temp (°C)
Deposition temp (°C)
∆T (°C)
Iodine concn (mg/cm3)
Ref
1 2 3 4 5
>850 850 850, 900 900 850
>750 843-825 843-830 850 800
5-200 7-25 7-20 50 50
0.3-8 5 5.4 1.8 2
3 16 10 17 present work
rate caused by small thermal fluctuations in temperature of the deposition zone where the slope of the ∆R curve is large. The results of our growth experiment were compared with earlier reports, and they are given in Table 1. Figure 7 shows the typical X-ray diffraction spectra obtained for the ZnSe crystals grown at 700, 800, and 900 °C. All three samples have common and main peaks of (111), (220), and (311). The crystal grown at 800 °C has an additional peak of (200), which also corresponds to ZnSe. Even when the XRD of all three samples was good, it was found to show the better crystalline nature of the samples, and the crystal grown at 700 °C shows additional peaks of Se and ZnI2. The crystal grown at 900 °C shows a peak for Zn, but there are no such peaks for the crystal grown at 800 °C. The ZnSe crystal grown
Calculations and Growth of ZnSe Single Crystals
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the ZnSe-I2 system. The ZnSe crystals were grown at three different temperature conditions (700, 800, and 900 °C). The good quality single crystals of ZnSe were grown under the theoretically predicted optimum growth conditions. Acknowledgment. We are thankful to the Council of Scientific and Industrial Research (CSIR), India, for the financial assistance to carry out this work. O.S. is also thankful to CSIR for the award of Junior Research Fellowship. References
Figure 8. (111) surface of the crystal etched with 30% NaOH.
at optimized temperature conditions was found to be free from precursors. The characteristic triangular etch pit patterns were observed on the (111) surface of the ZnSe single crystal, which was grown at 800 °C and etched by 30% NaOH, shown in Figure 8. The calculated etch pit density was 1.2 × 105 cm-2 in this case. The high value of etch pit density may be due to the temperature difference between the source and the deposition zone (50 °C in this case), which was high enough to produce more dislocations at the surface of the crystal. 5. Conclusions In the present investigation, the partial pressure of different components present inside the ZnSe-I2 system during CVT growth of ZnSe single crystals has been calculated assuming mass conservation of iodine. The optimum growth conditions for the growth of good quality ZnSe single crystals are predicted theoretically using the partial pressure of different components inside
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CG020007N
