Impurity Modes and Effect of Clustering in Diluted Semiconductor Alloys

Abstract

The variation of TO zone-center vibration spectra with concentration in mixed zincblende-type semiconductors can be understood within a paradigm of uni ed "one bond -two modes" approach, which has been recently outlined as a rather general concept, 1 and emerges from a number of previous experimental and theoretical studies. 2,3 The crucial issue is that the vibration frequency, associated with a certain cation-anion bond, depends on the length of the latter, and the bond length, in its turn, depends not only on the average alloy concentration, but on local variations of it. In an (A,B)C substitutional alloy, the A-C bond length differ in A-rich and A-poor regions, yielding a splitting of the A-C vibration frequency. Such splittings can be measured and reproduced in rst-principles calculations.An analysis of vibration spectra helps to get an insight into the structural short-range (clustering) and long-range (formation of extended chains of certain cation-anion pairs and other structural motives at the mesoscopic scale) tendencies. For this however, one needs rstprinciples benchmark calculations for representative model systems (see, e.g., Ref. 4 for the ZnSe-BeSe alloys). The simplest yet important result from rst-principles calculations is a prediction of how the impurity phonon mode evolves as isolated (distant) impurities get clustered.In the present contribution, we outline the results of rst-principles calculations of phonon frequencies and vibration patterns, in the dilution limits of several mixed semiconductor alloys, Be x Zn 1−x Se, Ga x In 1−x As and Ga x In 1−x P. The calculations have been done by the SIESTA method 5 for cubic 64-atom supercells, with one or two cation atoms substituted by impurity species, that corresponds to impurity contents of 3% and 6%, respectively. The initial unconstrained structure relaxation for each supercell chosen was followed by a calculation of phonons by nite displacement technique. Each of the atoms in the supercell were subject to 6 consecutive small cartesian displacements, and the forces induced on all atoms in the supercell resulted in corresponding force constants.The analysis of results is the simplest for Be x Zn 1−x Se, a system with large contrast in masses and elastic properties between its parent compounds, that leads to a big separation between Zn-related and Be-related phonon modes (see Ref. 4 for details). Fig. 1 shows the phonon Fig. 1. Phonon density of states of Be, after rst-principles calculations for Be n Zn 32−n Se 32 supercells, with 1,..4 Be cations neighbouring the same Se anion. The supercell for n=4 is shown in the inset.