Linearized force constants method for lattice dynamics in mixed semiconductors

Abstract

A simple and accurate method of calculating phonon spectra in mixed semiconductors alloys, on the basis of preliminarily (from first principles) relaxed atomic structure, is proposed and tested for (Zn,Be)Se and (Ga,In)As solid solutions. The method uses an observation that the interatomic force constants, calculated ab initio for a number of microscopic configurations in the systems cited, show a clear linear variation of the main (diagonal) values of the interatomic force constants with the corresponding bond length. We formulate simple rules about how to recover the individual 3×3 subblocks of the force constants matrix in their local (bonds-related) coordinate systems and how to transform them into a global (crystal cell-related) coordinate system. Test calculations done for 64-atom supercells representing different concentrations of (Zn,Be)Se and (Ga,In)As show that the phonon frequencies and compositions of eigenvectors are faithfully reproduced in a linearized force constants calculation, as compared to true ab initio calculations.

Unification of the phonon mode behavior in semiconductor alloys: Theory andab initiocalculations

“…First, some of us checked the falling down of interatomic force constants in semiconductor alloys with distance, and found that the interactions beyond the second neighbors can be safely discarded, without noticeable differences in the phonon spectra. 32 In our supercell with an impurity pair, none of the second neighbors of an impurity is simultaneously a second neighbor to a spurious (translated) impurity. Second, even with the break of symmetry introduced by an impurity pair, the relaxed shape of the supercell remains remarkably cubic.…”

Bond-strength inversion in (In,Ga)As semiconductor alloys

“…Studies of vibrational properties therefore typically assume that the strength of the bonds and thus the frequency of the oscillations change proportionally to this change in bond lengths [21,22], a law commonly referred to as Grüneisen relation. Ab initio finitedisplacements calculations support the assumption of a linear relation between bond-stretching force constants and bond lengths for (In,Ga)As [23], but the proportionality factors differ substantially. Additionally, molecular dynamics simulations for (In,Ga)As [24] and first-principles calculations for (In,Ga)P [19] hint at a strong composition dependence of the force constants leading to a bond strength inversion.…”

“…Ab initio finite-displacements calculations in 64-atom (In,Ga)As supercells suggest that the influence of the matrix conserves the strict correlation between force constant k and bond length d [23]. The relation is linear with approximately the same slope for k Ga−As and k In−As , but it differs substantially from the empirical law for binary III-V materials [37].…”

“…III). A linear change between the binary values (black dashed line) is predicted by ab initio calculations[23] based on the element-specific Ga-As and In-As bond lengths d (open blue triangles and open red circles, respectively) measured with EXAFS[20]. The latter are shown on an inverted scale (right axis) since an increase of the bond lengths leads to a reduction of the force constants.…”

Unification Of The Phonon Mode Behavior In Semiconductor Alloys

“…First, some of us checked the falling down of interatomic force constants in semiconductor alloys with distance, and found that the interactions beyond the second neighbors can be safely discarded, without noticeable differences in the phonon spectra. 32 In our supercell with an impurity pair, none of the second neighbors of I: Comparison of the theoretical (ωimp, ∆) values of the leading AB1−xCx alloys in the MREI-VCA classification, as derived from the ab initio 'protocol', with the experimental ones. A more explicit notation for ωimp is AB:C (AC:B), that refers to an isolated B (C) atom in pure AC (AB).…”