The kinetics of silicon contamination of liquid gallium in silica boats

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1 Journal of Physics D: Applied Physics The kinetics of silicon contamination of liquid gallium in silica boats To cite this article: P D Greene 1973 J. Phys. D: Appl. Phys Related content - Radiative Properties of Semiconductors: Gallium arsenide N M Ravindra, S R Marthi and A Bañobre - Epitaxy G B Stringfellow - Carbon, oxygen and silicon impurities in gallium arsenide M R Brozel, R C Newman and J B Clegg View the article online for updates and enhancements. This content was downloaded from IP address on 23/08/2018 at 07:09

2 J. Phys D: Appl. Phys., Vol. 6, Printed in Great Britain The kinetics of silicon Contamination of liquid gallium in silica boats PD Greene Standard Telecommunication Laboratories Limited, London Road, Harlow, Essex, CM17 9NA Received 24 April 1973 Abstract. The rate of silicon contamination of a gallium melt in contact with silica is controlled by the water content and flow rate of the hydrogen atmosphere. Calculated contamination rates are in good agreement with the work of Weiner. 1. Introduction Growth of layers of gallium arsenide by solution epitaxy is widely employed in the production of a variety of electronic devices. For those devices which use high-purity gallium arsenide, it is important to have an understanding of the factors which control the contamination of the system. In an earlier paper by Hicks and Greene (1970), a simple thermodynamic method was used to calculate the equilibrium concentration of silicon in a gallium melt in a silica vessel in a stream of hydrogen. It was shown that, by controlling the water content of the hydrogen stream and avoiding high growth temperatures, the equilibrium silicon concentration could be reduced to a level acceptable for the growth of high-purity gallium arsenide. More recently, Weiner (1972) has calculated rates of silicon contamination for a number of systems used in epitaxial growth of gallium arsenide. Weiner s case B refers to the system with a gallium melt in a silica vessel and is based on the consideration of several reactions. The purpose of the present paper is to show that the approach used by Hicks and Greene can be extended to calculate the rate at which the silicon concentration in the melt changes, as well as the ultimate equilibrium concentration. The analysis of both the kinetic and the thermodynamic aspects of the system is greatly simplified by considering the reaction Si02 (vitreous) +2Hz(g)+Si(l) +2HzO(g) as the only significant one. From the thermodynamic point of view this can be justified by application of the phase rule. With three phases (gas, gallium melt and silica vessel) and four components (H, Si, Ga and 0) there are three degrees of freedom. If the pressure and temperature are chosen, only one other variable needs to be fixed to define the system. The most convenient variable to control is the partial pressure of water in the gas stream. The justification when the kinetic aspects are considered is provided by 1550

3 Kinetics of silicon contamination of liquid gallium in silica boats 1551 the data of Cochran and Foster (1962). The equilibrium constant for the reaction 2Ga(l) + HzO(g)+GazO(g) + Hz(g) is less than one in the temperature range of interest (up to 1000 "C). This means that HzO rather than GazO is the predominant species involved in the removal of oxygen from the vicinity of the boat. 2. Thermodynamics The Gibbs free energy of reaction (1) can be obtained from the free energies of the following reactions : Si02 (vitreous)+si(c) + Oz(g) (2) 2H&) + Oz(g)+2HzO(g) Si(c)+Si(l in Ga). If one assumes that the free energy difference between vitreous silica and quartz is small enough to be neglected, the standard Gibbs free energy change for reaction (2) is given by AGz0=9O3-173*5T/1O3 kj mol-1 (all thermodynamic data are from Kubaschewski et a1 1967). The standard Gibbs free energy change for reaction (3) is given by AG30= ?"/lo3 kj mol-1. For reaction (4) the standard Gibbs free energy change can be derived from the melting point and heat of fusion of silicon if the correction arising from the difference in heat capacity between solid and liquid silicon is assumed to be negligible: AGdO = TI103 kj mol-1. Reaction (1) is the sum of reactions (2), (3) and (4), so that AGlo=AGzO+ AG30+AGgO= T/lO3 kj mol-i. If KR is defined as the equilibrium constant of reaction (l), it is related to the activities of the species involved in the reaction by asi ahzo2 KR = a~~~ asio2' Since the hydrogen and silica are virtually in their standard states, and ahz=asioz= 1 KR=asi ah202. According to the van? Hoff isotherm, AGIO= - RT In KR, so that Ig KR= x 1O3/T If it is assumed that the activity coefficient for water vapour has the value one and that the activity coefficient y for silicon in gallium is given by Thurmond and Kowalchik (3) (4)

4 1552 P D Greene (1960)-lg y = 711/T it follows that lg KR* = x lo3/t where KR* = [Si] [H20]2, the terms in square brackets referring to concentrations. 3. Kinetics It was pointed out in the introduction that the rate at which reduction can occur and silicon enters the gallium melt is determined by the rate at which water can be removed by the hydrogen stream. A gas flow Fin litres (measured at 1 atm pressure at temperature Tnl) per unit time corresponds to a flow of F/RTm moles per unit time. The rate of water removal is dependent on the total flow rate and the difference between the water concentrations upstream [HzO in] and downstream [HzO out] of the boat. Hence the rate dnsi/dt at which silicon enters the melt is given (in moles per unit time) by dnsi -([HzO out] -[HzO in]) F dt 2RTm/ In the temperature range of interest it can be assumed that the melt consists almost entirely of gallium so that dnsi NGa d [Si] dt dt where NG~ is the number of moles of gallium. Hence d [Si] - ([HzO out] - [HzO in]) F dt 2RTmNca On the assumption that the water concentration downstream is the equilibrium value appropriate for the solution in the boat at the time in question, d [Si] {(K~*/[Si])ll~- [HzO in]}f - dt 2RTmNca This is the important differential equation describing the rate at which the silicon concentration varies. When the rate of change of silicon concentration is zero, the equation reduces to the simple equilibrium expression. Alternatively, when the silicon concentration is very small, the term [HzO in] is negligible compared with the term (K~*/[Si])ll~ so that the above expression reduces to d [Si] - K~*/[Si])l/z F dt 2RTmNca With the additional condition that [Si]=O when t=o, differential equation is [Si] =KR*'~~ (~F/~RT~NG~)'/~ t213. the solution of the simplified The striking feature of this solution is that, in these initial stages, the temperature dependence (arising only from the variation of KR* with temperature) of the silicon concentration is much less than the temperature dependence of the final (equilibrium)

5 Kinetics of silicon contamination of liquid gallium in silica boats 1553 value, which depends on KR" to the power of one. It is because it takes longer to reach equilibrium at higher temperatures that results such as those presented in figure 3 of Hicks and Greene's paper are obtained. From the same condition of [Si]=O when t=o, the full differential equation has been evaluated numerically for the temperatures of 800 "C and 1000 "C, and various input water concentrations. A fixed hydrogen flow of 1 litre min-1 measured at room temperature and a 25 g gallium melt were assumed in the calculation: the results are shown in figure 1. The data for other flow rates and melt sizes can be obtained simply by changing.. _. I lo-4p _. _. _. _ !;.. / Ih I month ' c Y T m ' I,,,,,,, I IO Time ( h 1 Figure 1. Silicon contamination of liquid gallium in silica boat at (U) 800 "C and (b) 1000 'C. It is assumed that contamination is zero at zero time, that the melt consists of 25 g gallium, and that the hydrogen flow rate is 1 litre min-l measured at 25 "C. Concentrations of silicon in the liquid and of water in the gas stream are expressed as a mole fraction. the horizontal time scale in the appropriate proportion. The figure shows that high levels of silicon contamination arising from the use of high temperatures and low water concentrations in the gas stream require extremely long times (of the order of days) to approach the equilibrium values, but that when the conditions are chosen to limit the silicon contamination of the melt to less than 1 part in 107, the equilibrium concentration is attained with sufficient rapidity. 4. Discussion When due allowance is made for differences in experimental conditions, in particular in gas flow rate, it can be seen that the curves presented in figure l(a) and (b) are virtually identical to the Weiner case B results at the corresponding temperatures, The essential difference between the approaches is that in the present paper the mathematical analysis has been greatly simplified by identifying the important chemical reaction, whereas Weiner's analysis is more exhaustive and more complex. Although Weiner states that direct contact between liquid gallium and quartz should be avoided in a system where the surface of the gallium is exposed to the flowing gas, it must be emphasized that extremely-high-purity gallium arsenide can be grown from solution under such conditions when the gas composition and the growth temperature are suitable. In this laboratory, layers with free electron concentrations below 1013 cm-3 and with electron mobilities up to 2.0 x lo5 cm2 V-1 s-1 at 77 K have been grown in open Spectrosil boats (Hicks and Manley 1969; P D Greene, unpublished). 139

6 1554 P D Greene Acknowledgments This paper incorporates work carried out under a CVD contract and is published by permission of the Ministry of Defence. The author is indebted to Mr I G Davies for his interest and assistance. References Cochran C N and Foster L M 1962 J. Electrochem. Soc Hicks HGB and Greene PD 1971 Proc. 3rd Int. Symp. on Gallium Arsenide and Related Compounds. Aachen 1970: Inst. Phys. Phys. Soc. Con5 Ser. No. 9 pp 92-9 Hicks H G B and Manley D F 1969 Solid St. Commun Kubaschewski 0, Evans E L1 and Alcock C B 1967 Metallurgical Thermochemistry 4th edn (Oxford: Pergamon) Thurmond CD and Kowalchik M 1960 BelZSyst. tech. J Weiner ME 1972 J. Electrochem. Soc

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