We develop a theory for the diamagnetic susceptibility (χ) of amorphous Si and Ge by analyzing χ of a tetrahedrally bonded model amorphous semiconductor. We adopt a linear combination of hybrids method, recently developed by us, and derive an expression for χ of tetrahedral semiconductors in terms of matrix elements between hybrids of the same site and hybrids of the same bond. We introduce distortions in the bond angles and construct an orthonormal set for each site for the disordered network to obtain an expression for χ(Δ) in terms of the bond-angle distortion parameter Δ. Our expression for χ(Δ) contains three terms: (i) a core diamagnetic term, ${\mathrm{\chi }}_{\mathit{c}}$; (ii) a Langevin-like diamagnetic term due to valence electrons, ${\mathrm{\chi }}_{\mathit{v}}$(Δ); and (iii) a Van Vleck–like paramagnetic term, ${\mathrm{\chi }}_{\mathit{p}}$(Δ). We calculate χ(Δ), using various Δ parameters, and compare our results with the corresponding crystalline values. ${\mathrm{\chi }}_{\mathit{c}}$ is found to be independent of Δ and there is also almost no change in ${\mathrm{\chi }}_{\mathit{v}}$(Δ) with a change in Δ. However, we find that ${\mathrm{\chi }}_{\mathit{p}}$ is proportional to ${\mathit{S}}^2$/(1-${\mathit{S}}^2$), where S is the overlap integral between two hybrids forming a bond. Since S decreases with increasing disorder, ${\mathrm{\chi }}_{\mathit{p}}$(Δ) is appreciably reduced with increasing Δ. Since ${\mathrm{\chi }}_{\mathit{v}}$(o) and ${\mathrm{\chi }}_{\mathit{p}}$(o) are individually large and nearly cancel each other for covalent semiconductors such as Si and Ge, this reduction of ${\mathrm{\chi }}_{\mathit{p}}$(Δ) in the amorphous phase gives rise to a large diamagnetic enhancement. We expect our results to improve with further inclusion of effects of dihedral-angle disorder and bond-length disorder in our formulation.

• Received 3 February 1992

DOI:https://doi.org/10.1103/PhysRevB.45.13336