Effect of alloy disorder on the vibrational spectrum of silicon donors in ${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As

For substitutional defects in semiconductors, the lattice distortion and its effect on the vibrational behavior is examined in terms of a simple, but first-principles method. In the tight-binding framework and using a bond-orbital model (BOM), we have evaluated the total energy and the local distortions around ionized shallow donors in III-V compounds. The estimated distortions are found to be in good qualitative agreement with the extended x-ray-absorption fine structure measurements of Se-doped ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As and the photoionization data of lightly doped Si impurities in ${\mathrm{Al}}_{0.33}$ ${\mathrm{Ga}}_{0.67}$As. In the BOM, approximate central-force–constant changes are obtained for ${\mathrm{Si}}_{\mathrm{Al}}$ and ${\mathrm{Si}}_{\mathrm{As}}$ in AlAs. For ${\mathrm{Al}}_{\mathrm{Ga}}$, ${\mathrm{Si}}_{\mathrm{Ga}}$, and ${\mathrm{Si}}_{\mathrm{As}}$ in GaAs the accurate values of force constants are derived in the Green’s-function framework by fitting the existing optical data of impurity modes. With appropriate perturbation parameters for ${\mathrm{Si}}_{\mathrm{Ga}}$ and ${\mathrm{Al}}_{\mathrm{Ga}}$, our Green’s-function theory has predicted the splitting of a ${\mathrm{Si}}_{\mathrm{Ga}}$ impurity mode (∼384.0 ${\mathrm{cm}}^{\mathrm{-}1}$) into a triplet (∼386.1, 384.7, and 384.3 ${\mathrm{cm}}^{\mathrm{-}1}$), when an Al atom in ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As:Si (for x<0.04) occupies a next-nearest-neighbor Ga site relative to ${\mathrm{Si}}_{\mathrm{Ga}}$. This splitting can be observed by the high-resolution Fourier-transform infrared spectroscopy.