Raman-active modes of a -GeSe 2 and a -GeS 2 : A first-principles study Koblar Jackson, Arlin Briley, and Shau Grossman Department of Physics, Central Michigan University, Mt. Pleasant, Michigan 48859 Dirk V. Porezag and Mark R. Pederson Center for Materials Simulation, U.S. Naval Research Laboratory, Washington D.C. 20375 ~Received 26 August 1999! We have used a recently developed computational technique based on density-functional theory to study the Raman-active modes of amorphous GeSe 2 and GeS 2 . Vibrational modes and the associated Raman activities for three cluster building blocks of the glasses are calculated directly from first principles. The positions of the calculated symmetric-stretch modes in the cluster models are in excellent agreement with sharp features in the observed spectra. Moreover, simulated spectra based on the cluster results are in good agreement with experi- ment, accounting for all the observed features in the bond-stretch region of the spectra. The cluster results suggest a new interpretation for the 250 cm 21 mode appearing in the spectra of Ge-rich samples in the Ge x S 12x family. @S0163-1829~99!51846-8# Raman spectroscopy has been an important tool for inves- tigating the properties of chalcogenide glasses for over two decades. 1–4 Applications have ranged from early investiga- tions of short-range order in the glasses 3,5,6 to very recent probes of network rigidity. 7–9 The Raman spectra of glasses such as GeS 2 and GeSe 2 are interesting because they contain sharp, molecularlike features that can be associated with lo- cal structural elements of the materials. The molecular nature of the spectra has motivated calculations based on atomic clusters to interpret the spectral features. 1,2 These calcula- tions used empirical force fields to compute vibrational modes 10 and in some cases bond polarization models to com- pute Raman intensities. 11–13 Such calculations gave a useful qualitative understanding of the spectra but were limited by the empirical nature of the models in the amount of detail they could provide. Higher level calculations have been ap- plied to bulk a -GeSe 2 14,15 and to liquid GeSe 2 , 16 but these calculations were not aimed at interpreting the Raman spec- trum. In this paper we use a first-principles method based on the density-functional theory ~DFT! to study the Raman spectra of GeSe 2 and GeS 2 . We use standard DFT techniques to obtain the vibrational normal modes of cluster models and then a DFT-based method 17 to compute the associated Ra- man activities. We show that the main features of the ob- served spectra are reproduced in excellent agreement with experiment and that the overall spectra can be simulated very well using only the results of cluster calculations on three simple structures. Finally, we use the results of our calcula- tions to suggest a new interpretation for the 250 cm 21 mode observed in Ge-rich compositions of Ge x S 1 2x . 4 The calculations described here are based on the density- functional theory in the local-density approximation ~LDA!. 18–20 We use a Gaussian-orbital-based formulation of the theory, with a robust numerical integration scheme 21 that gives highly accurate total energies and atomic forces. 22 The cores of the heavy atoms are represented by norm-conserving pseudopotentials, 24 while the H atoms are included in an all-electron framework. 23 To study the Raman-active modes of GeS 2 and GeSe 2 , we use finite clusters of atoms containing structural units ex- pected to be important in the glasses. Dangling bonds on the cluster surfaces are terminated by H atoms, to better model the chemical environment of the glasses. The cluster geom- etries are optimized using a conjugate-gradient algorithm, and the vibrational normal-mode frequencies and eigenvec- RAPID COMMUNICATIONS PHYSICAL REVIEW B CONDENSED MATTER AND MATERIALS PHYSICS THIRD SERIES, VOLUME 60, NUMBER 22 1 DECEMBER 1999-II RAPID COMMUNICATIONS Rapid Communications are intended for the accelerated publication of important new results and are therefore given priority treat- ment both in the editorial office and in production. A Rapid Communication in Physical Review B may be no longer than four printed pages and must be accompanied by an abstract. Page proofs are sent to authors. PRB 60 0163-1829/99/60~22!/14985~5!/$15.00 R14 985 ©1999 The American Physical Society