CoherentPotential Approximation for the Lattice Vibrations of Mixed III–V Crystals

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A mean-field approach is applied to the lattice dynamics of quaternary alloys. Specific results are obtained for the quaternaries A1,Gal --zAsl -yP, and Ga,Inl -,PI --2/A~y. Calculations are restricted to a mass-disordered linear chain model. For the end-member components the approach reproduces the results of the coherent-potential approximation (CPA). The cluster density of states of eight atoms embedded in the mean-field effective medium is compared with the numerical spectrum obtained for a 20000-atom random chain by using the negative eigenvalue theorem. The predictions of the calculated mean-field dielectric susceptibility agree a t least qualitatively with experimental results. With some qualifications the approach can explain the change of mode behaviour within the composition range, as it is expected to occur in some 111-V quaternary alloys.Eine Nliherung des mittleren Feldes wird auf die Gitterdynamik quaternarer Mischkristalle angewandt. Spezielle Resultate werden fur die Systeme A1,Gal -sAsl und Ga,Inl-,PI --2/Asy erhalten. Die Berechnungen beschranken sich auf ein lineares Kettenmodell mit Massenunordnung. Fur die Endkomponenten werden die Resultate der Naherung des kohiirenten Potentials (CPA) reproduziert. Die Cluster-Zustandsdichte von acht Atomen, die in ein effektives Medium des mittleren Feldes eingebettet sind, wird mit dem numerischen Spektrum einer aus 20000 zufallig verteilten Atomen bestehenden Kette verglichen, das mit Benutzung des negativen Eigenwert-Theorems erhalten wurde. Mit einigen Einschrankungen kann dieser Zugang die h d e r u n g des Modenverhaltens mit der Konzentration erklaren, wie das fur einige quaternare III-V-Mischkristalle erwartet wird.

Self‐Consistent Field Approximation for the Vibrational Spectra of Quaternary Alloys

Kleinert¹

1985

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A Theoretical Study of the Vibrational Properties of In_xGa_1‐xAs_1‐ySb_y Quaternary Alloys

Kleinert¹

1985

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First theoretical investigations of the lattice dynamics of In,Gal -%As1 -,Sb, quaternary semiconducting alloys are presented. All corresponding pseudobinary end member components are known to exhibit mixed-mode behaviour. Within a mean-field approximation a Hethe lattice is self-consistently constructed in such a way that for all mixed ternary end member compounds the results of the coherent-potential approximation (CPA) are reproduced. Special results are obtained for the dielectric susceptibility spectra, which display only one dominant band for mixed quaternaries mainly containing GaAs but two bands for systems which contain mainly InSb. With respect to an interchange between x and y the lineshape of the spectra is nearly unchanged.Die ersten theoretischen Untersuchungen des halbleitenden quaternaren Mischsystems In,Gal --2. .As1 -,Sb, werden vorgestellt. Alle entsprechenden pseudobinaren Endkomponenten zeigen ein Mischmoden-Verhalten. Im Rahmen einer Effelctivfeld-Naherung wird ein Bethe-Gitter so in seibstkonsistenter Weise konstruiert, daB sich fur alle ternairen Mischverbindungen die Resultate der Naherung des koharenten Potentials (CP.4) ergeben. Einzelne Ergebnisse werden fiir die Spektren der dielelrtrischen Suszeptibilitat erhalten, in denen nur eine Bande auftritt, fur Systeme, die hauptsachlich GaAs enthalten, jedoch zwei Eanden fiir quaternare Mischsysteme, in denen hauptsachlich InSb eingeht. Die Linienform der Spektren iindert sich kaum, wenn z und y vertauscht nerden.

Mixed Mode Behavior of Ga_1‐xIn_xAs

Sinai

1985

In another work we identified and discussed three interacting factors which determine the success o r failure of any theoretical approach to the study of mixed crystals /l/. They are the treatment of the underlying lattice structure, the treatment of local disorder, and the treatment of the interactions.Here-to-fore the most commonly used approach has been the single-site coherent potential approximation o r C PA /2/. Early calculations using that approach met with differing degrees of success in predicting the one-mode/twomode behavior of some mixed crystals but generally failed i n predicting mixed mode behavior /3/. However, recently Kleinert was able t o predict mode switching for Gal-,InxAs and Gal -xInxSb using two different approaches /3, 4/. One was based on a cluster Bethe lattice treatment using only nearest neighbor interactions and the other on a single site CPA treatment of disorder and included second neighbors in the determination of the mean field.In our previous work /1/ we compared the Bethe lattice calculation with an approach we developed. We showed that the Bethe lattice approach is successful in predicting one-mode/two-mode behavior because i t maintains the coordination number and in the nearest neighbor approximation that factor plus the m a s s e s and the force constant parameter are what determine the band placements and the band widths and hence the mode behavior. The other two factors. the underlying lattice structure and the interactions beyond nearest neighbors do not appreciably affect the spectrum in that regard and consequently one cannot draw any conclusions regarding the effect of those factors.