Optical Band Gap and Birefringence of ZnS Polytypes

Birefringence and optical band-gap measurements were performed at 20^∘{}C on structurally uniform regions of ZnS crystals. The regions were of one of the following polytype structures: $4L$, $6L$, $10L$, $14L$, $24L$, $26L$, $28L$, $40L$, $120L$; cubic ($3L$) and hexagonal ($2L$) regions were also investigated for reference. No stacking disorder was discovered in the regions studied. It was found that the absorption-edge positions (for polarization parallel and perpendicular to the optic axis) as well as the degree of birefringence Δn depend only on the value of a single structure parameter α. This parameter is defined as the percentage of (00.1) planes stacked in hexagonal order; its values were determined directly by x-ray structure analysis. The absorption edge positions were found to be linear functions of α. This linearity is explained on the basis of Birman's perturbation treatment for electron states with k vectors parallel to the c axis. It implies that in a polytype the perturbation potential caused by partially hexagonal stacking is proportional to α. The degree of birefringence was found to be proportional to α; an outline of a simple dispersion treatment is given for the explanation of this proportionality. The established linear relationships between absorption edges, birefringence, and α allow calculation of absorption-edge positions and α values from birefringence measurements. This may facilitate investigations of structure-sensitive properties (e.g., the anomalous photovoltaic effect) of ZnS samples which are composed of regions differing from each other in structure.