A theory of regular associated solutions applied to the liquidus curves of the Zn-Te and Cd-Te systems
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A c o n s i d e r a b l e amount of work has been devoted to the study of the c o n g r u e n t l y m e l t i n g compound s e m i c o n d u c t o r s ZnTe and CdTe due to t h e i r potentially p r o m i s i n g e l e c t r i c a l and optical p r o p e r t i e s . ~-z The liquidus c u r v e s in the p a r e n t Z n - T e and C d - T e s y s t e m s a r e of p a r t i c u l a r i n t e r e s t to those c o n c e r n e d with the growth and perfection of these compounds and have r e c e n t l y been r e d e t e r m i n e d by s e v e r a l i n v e s t i g a t o r s .4-7 The p r i m a r y o b j e c t i v e s of this study a r e to c a l c u l a t e the equation of the liquidus b o u n d a r i e s in the Z n - T e and C d - T e s y s t e m s b a s e d on a model involving a s s o c i ation in the liquid phase and to e x a m i n e the t h e r m o d y n a m i c c o n s e q u e n c e s of the r e s u l t i n g theory. The liquidus c u r v e s of m a n y b i n a r y s y s t e m s i n v o l v ing e l e m e n t a l and compound s e m i c o n d u c t o r s have been found suitable for t h e r m o d y n a m i c a n a l y s i s in t e r m s of simple solution m o d e l s . In 1953, T h u r m o n d 8 d e m o n s t r a t e d that the r e p o r t e d s o l u b i l i t i e s of s i l i c o n and g e r m a n i u m in e l e m e n t s of Groups III, IV, and V of the periodic table could be d e s c r i b e d by a liquidus equation with a single t e m p e r a t u r e i n d e p e n d e n t constant, a, d e r i v e d from the theory of r e g u l a r s o l u t i o n s . In l a t e r work T h u r m o n d and Kowalchik 9 have shown, using t h e i r m o r e a c c u r a t e m e a s u r e m e n t s in the above s y s t e m s , that the data were b e s t r e p r e s e n t e d by a t w o - c o n s t a n t liquidus equation, a s s u m i n g the l i n e a r dependence of a on t e m p e r a t u r e . Vieland ~~has d e r i v e d an e x p r e s s i o n for the liquidus c u r v e of a b i n a r y s y s t e m with AB compound f o r m a tion. If the compound has a v e r y n a r r o w range of deviation from s t o i c h i o m e t r y and the heat capacity diff e r e n c e between liquid and solid AB is n e g l i g i b l e , then the equation of the phase b o u n d a r y takes the form
2-RT In a~(0.5)a2(0.5)a,a2 - AHf - TASf
- 89 RT In 4xlx2 - A H f + TASf c~ :
A. S. JORDAN is Member of the Technical Staff, Bell Telephone Laboratories, Murray Hill, N. J. Manuscript submitted April 7, 1969.
(xe - 0.5) 2
[2]
where the constant c~ is the i n t e r c h a n g e e n e r g y i n t r o duced by Guggenheim. ~2 T h u r m o n d ~3 has r e c e n t l y applied Eq. [2] to a study of the liquidus c u r v e s in the G a - A s and G a - P s y s t e m s and concluded that c~ i s a slow function of t e m p e r a t u r e , as in the case of m a n y s y s t e m s involving g e r m a n i u m and s i l i c o n . The l i q u i dus c u r v e s in these s y s t e m s s e e m to be p a r a b o l i c with a r e l a t i v e l y large r a d i u s of c u r v a t u r e n e a r the
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