Bulk Modulus of A^I‐B^III‐C Chalcopyrite Compounds and Its Correlation with Pressure Induced Phase Transitions

Abstract

IntroductionThe ternary A'-B"'-C; ' chalcopyrite compounds (A' = Cu, Ag; BIT'= Al, Ga, In; and Cv'= S, Se, Te) have received considerable attention because of their academic interest and also their possible practical applications in solar cell and photodiode technologies [l]. These compounds show, at room temperature and ambient pressure, the ordered tetragonal chalcopyrite structure which may be seen as a superstructure of the zincblende phase with double primitive cell. As temperature and/or pressure rises they undergo a transition to a disordered zincblende-like structure, or to denser structures with high coordination number [2 to 161. Estimations of the isothermal bulk modulus B through semi-empirical models is of interest because of the continuity of the theory developed for other semiconductors. In this note we will use an extension of Cohen's semi-empirical model [17, 181 developed for semiconductors of groups IV, 111-V, and IILVI, and discuss the possible correlation with pressure induced phase transition values P,.

An Empirical Bulk Modulus Model of Ternary Chalcopyrite Structure Solids

“…In Table-1, the estimated values are listed along with the results of earlier researchers. 6,16,18,26,29,30,[36][37][38][39][40][41][42][43][44][45][46][47][48][49] It is observed that the calculated values are in better agreement with the experimentally reported values. The results also agree closely with the values reported for these compounds by earlier workers.…”

“…[36][37][38][39][40][41][42][43][44][45][46][47][48][49] The percentage deviation of equation (22) is calculated using the relation |experimental value-calculated value|/|experimental value|×100 and percentage deviation are given Table-1. Average percentage deviation of bulk modulus for ternary chalcopyrite's of I-III-VI2 and II-IV-V2 type has been found to be respectively7.5 and 0.02 for equation (22). For comparison, the average percentage deviation of B for each group of semiconductors is calculated with respect to the values reported by earlier workers.…”

“…The bulk modulus of ternary chalcopyrite structure solids is estimated using equation (22). In Table-1, the estimated values are listed along with the results of earlier researchers.…”

“…In this case, least square fitting method has been used. From the Fig.-1 it is found that bulk modulus ( B ) and the ratio of average principal quantum number of atoms constituting compounds and electronegativity of atoms are exponentially related, and the R 2 value is 0.86 and 1respectively.Therefore the effectiveness of least square fitting is reliable and the normal mathematical expression between bulk modulus ( B ) and the ratio of average principal quantum number of atoms constituting compounds and electronegativity of atoms is given in equation (22). For ternary chalcopyrite structure solids, the bulk modulus is assumed to be correlated to the contribution of three atoms A, B and C. Considering electronegativity value of two cations A, B and electronegativity value of two anions C the bulk modulus of ternary chalcopyrite semiconductors can be assumed as Ref.…”

“…In view of the above, a simple empirical relation has been proposed to evaluate the bulk modulus of ternary chalcopyrite's which are in excellent agreement with the previous estimation. [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] A fairly good agreement has been obtained between them.…”