Lattice Dynamics of Semiconductors from Density-Functional Perturbation Theory

In this thesis we present the modern methods for calculating the vibrational properties of extended systems and we apply them to pure bulk semiconductors. Furthermore, we develop an approach to describe more complex systems such as superlattices and alloys. To this end, we first give a detailed theoretical description of the DFPT and of the computational techniques necessary to implement it. We then demonstrate the predictive power of these methods in the case of semiconducting pure crystals, where a wealth of well established experimental results exists. We present the first ab-initio calculation of full phonon dispersions of three group IV elements, C, Si and Ge, and four compound semiconductors, GaAs, AlAs, GaSb, and AlSb. In the case of AlAs-whose vibrational properties are poorly known because of the lack of neutron-scattering data-the accuracy of our predictions is confirmed by the excellent agreement between the phonon dispersions calculated for the closely related compound AlSb, and recent neutronscattering data. [s] A complete description of harmonic lattice dynamics requires the knowledge of both eigenvalues and eigenvectors of the dynamical matrix. To this purpose we also calculate the eigendisplacements along some high-symmetry lines in diamond and some elemental (Si, Ge) and compound (GaAs, AlAs) semiconductors. The peculiar behaviour of the eigenvectors in the case of diamond is analyzed and discussed in terms of the competition between angular (bond-bending) and radial (bond-stretching) force constants. As a byproduct we calculate the internal strain parameter for these materials. As a further application, thermal expansion of semiconductors can be calculated within the so-called Quasi Harmonic Approximation. While most of the materials expand upon heating, many tetrahedral semiconductors (e.g. Si, Ge, GaAs) exhibit negative thermal expansions at low temperatures. [9 ,lO] For long time these features have been investigated theoretically only within semi-empirical models. Only recently, the first attempts of realistic calculations have been carried out on silicon [u,i2 ,l 3] and diamond. [l 3] We improve the previous ab-initio calculation [12l of the thermal expansion coefficient of Si, and extend the application to some other semiconductors (Ge, GaAs, AlAs). Finally, we focus our interest on mixed semiconductors ( superlattices and alloys), particularly on the possibility of using for these systems the informations gained from calculations on pure materials. To this aim, we examine to which extent the interatomic force constants of pure bulk semiconductors are similar to each other, in view of using them to study the vibrational properties of mixed systems, such as alloys, superlattices (both ordered and partially disordered), or other quantum structures. In the case of III-V compounds, we find that the force constants of materials which differ by their cations are rather similar to each other, while this is less so when the materials differ by their anions. The situation is intermediate in the case of elemental semiconductors. Phonon frequencies of thin (AlAs)n(GaAs)n (001) superlattices (SL's) are evaluated using the force constants of the corresponding virtual crystal. The values obtained in such an approximation compare very well with those of full ab-initio calculations of the same systems. The detailed features of the Raman spectra in these systems are still far from being completely understood. A simple approximation has been recently proposed for the Raman intensity in AlAs/GaAs systems, [H] in which the differences of the atomic polarizabilities between the two cationic species are neglected. Though adequate for many qualitative purposes, this approximation fails to reproduce the observed relative intensity of the various peaks. In order to improve the quantitative understanding of Raman spectra in AlAs/GaAs systems, we present a model based on a perturbative expansion of the dielectric susceptibility of the crystal upon composition. In this model the Raman tensor is expressed in terms of a restrict number of parameters which are obtained by a fitting procedure applied to the results of ab-initio calculations of Raman intensities of some short-period SL's. The method which we have developed can then be used to obtain Raman spectra of any AlAs/GaAs mixed structure.