ABSTRACT

An approach is made to calculate and analyze the combination of Lindemann’s role for melting and Debye temperature ( ) with that of lattice structure to examine ionicity and the structure factor for elements and compounds forming IV, III-V, II-VI, II-IV-V₂ and I-III-VI₂ tetrahedral group semiconductors. The results were found to have a direct relation of Lindemann’s ratio (ƒ) with the mean bond length d_mean of these materials in the form of ƒ=0.214d^-1_mean (1+ƒ_i) where _i is the group compound ionicity, which is zero, 0.19, 0.63, 0.28, and 0.57 for IV, III-V, II-VI, II-IV-V₂, and I-III-VI₂ respectively. Similar relations were found for the material dimensionless mass and material structure factor. The obtained relations had a systematic application for calculating values of both ƒ and  for all elements and compounds forming the above groups and those from ternary chalcopyrite compounds from II-IV-V₂ and I-III-V₂. Lindemann’s ratio of melting ƒ for the above groups was found to be in the range between 0.077 for Sn and 0.199 for CdS. Bond energies are used to explain both the dimensionless mass and Lindemann’s ratio of melting in group IV semiconductors. From the modification of above relations, the nanosize dependence for both Lindemann’s ratio and dimensionless mass with that of materials structure factor was calculated. The results are the decrease of Lindemann’s ratio and increase in the dimensionless mass with the size decreases, as given for Si, Ge, GaP, CdS, ZnSiP₂, CuAlS₂ as an example.