Anisotropic vibrations in crystalline and amorphous InP

Abstract

The temperature-dependent evolution of atomic vibrations in crystalline and amorphous InP has been studied using extended x-ray absorption fine-structure (EXAFS) spectroscopy. Measurements were performed at the In K edge for temperatures in the range of 20-295 K. In crystalline InP, the first nearest-neighbor (NN) EXAFS Debye-Waller factor, representative of the correlated mean-square relative displacement (MSRD) parallel to the bond direction, is considerably smaller than the uncorrelated mean-square displacement (MSD) determined from x-ray diffraction measurements. In contrast, the MSRD perpendicular to the bond direction agrees well with the MSD. This clearly demonstrates that vibrations of two neighboring atoms relative to each other are strongly reduced along the bond direction but are unhindered perpendicular to it, consistent with the well-known behavior of III-V semiconductors where bond bending is energetically favored over bond stretching. With increasing interatomic distance, the correlation of atomic motion quickly vanishes as manifested by increased EXAFS Debye-Waller factors. For the third NN shell the value closely approaches the MSD demonstrating the nearly uncorrelated motion of atoms only three shells apart. In the amorphous phase, only information about the first NN shell is accessible although the latter is now comprised of both P and In atoms. The EXAFS Debye-Waller factors are significantly higher than in the crystalline phase but exhibit a very similar temperature dependence. This results from strongly increased structural disorder in the amorphous phase whereas the thermally induced disorder is very similar to that in crystalline InP. A correlated Einstein model was fitted to the Debye-Waller factors yielding Einstein temperatures that vary as functions of the vibrational phase difference and reduced mass of the atomic pair, and represent a measure of the strength and thermal evolution of the corresponding relative vibrations.