Lattice Properties of Ge and GaAs Strained-Layers on Si
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ABSTRACT
A phenomenological lattice dynamics model has been developed that describes how strain affects phonon frequencies and elastic constants in Group IV and III-V semiconductor thin films and strained layers. Using this model, the phonon dispersion relations for strained-layer heterostructures of Ge and GaAs on Si have been obtained in the quasiharmonic approximation. This model uses available experimental data and can predict the effect of arbitrary strains on thin films. INTRODUCTION The symmetry of a crystal can be altered by the presence of strains. This strain can also lift phonon degeneracies, and induce upward or downward shifts of the frequencies that are linear in strain to first order. The strains can be either induced by external stresses, or due to growth conditions or modifications of the materials (built-in). Built-in strains in epilayers and superlattices are produced by lattice mismatch or by the different thermal expansion coefficients of the material layers involved. Considerable effort has been spent to understand the electronic and phonon properties of strained-layer superlattices, which depend critically on the effects of biaxial strain [1-3]. The folding of acoustic phonons and the confinement of optical phonons in superlattices can give rise to many k =0 zone center phonons that are IR and/or Raman active, depending on the superperiodicity. The measurement of strain-modified phonon frequencies can be used as a diagnostic tool to examine the structure of the thin film. Cerdeira el al. introduced the microscopic p, q, and r parameters to account for the strainshift and splitting of the zone center phonon frequencies [4]. They evaluated these parameters by using a Keating and valence force field model and assumed that the splitting between zone center TO and LO modes in heteropolar semiconductors is independent of strain. Later, Anastassakis et al. introduced effective charge deformation potentials to account for the different strain shift of these modes [5]. Talwar and Vandevyver used an 11 parameter rigid ion model to study the effects of pressure on the vibrational properties of Ga-In pnictides [2]. While their one phonon and two phonon densities of states, Debye temperatures, Gruneisen constants, and linear thermal expansion coefficients were all in reasonably good agreement with existing experimental data, this model showed the flatness of the lowest TA branches at ambient pressure but not at elevated pressures. This raised the question of whether the bending of the TA branch under compression was an artifact of the rigid ion model or was due to the peculiarity of compound semiconductors. Weinstein et al. suggested use of the bond charge model (BCM) to study the pressure dependence of phonon dispersion relations [1]. Mayer and Wehner tried to extend the BCM to account for the strain-dependent phonon properties of Si by including third order anharmonic
295 Mat. Res. Soc. Symp. Proc. Vol. 356 0 1995 Materials Research Society
potentials [6]. The mode Gruneisen parameters they obtained
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