Optical polarization anisotrop in nonpolar GaN thin films due to crystal symmetry and anisotropic strain

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In this work, we focus on the optical response of GaN thin films grown along various orientations. The optical properties of strained M- and A- and unstrained C-plane GaN thin films are investigated, and the results are explained with help of band-structure calculations. Unstrained C-plane films do not show any in-plane polarization anisotropy due to the underlying crystal symmetry. However, the surface normal of M- or A-plane films is perpendicular to the unique c axis of the wurtzite crystal structure of GaN, and the optical properties of such films are therefore expected to be strongly dependent on the in-plane polarization of a normally incident light beam. This anisotropy has two contributions: — the reduced crystal symmetry of the M and A plane of GaN. — the electronic band structure (EBS) modification due to the biaxial, anisotropic in-plane strain in the layer. We calculate the strain-induced band-structure modification using the k·p perturbation approach. The valence-band (VB) states are modified affecting both the transition energies as well as the oscillator strengths. We observe that C-plane GaN does not show any in-plane polarization anisotropy, when an isotropic in-plane strain is applied. However, one expects to see an anisotropy in the optical response with the application of an anisotropic in-plane strain. For the case of M-plane and A-plane GaN, one expects to see an in-plane polarization anisotropy even for the unstrained case. Additionally, the inplane strain significantly changes the band structure and the symmetry of the VB states. The dependence of the transition energies and the values of oscillator strength on the in-plane strain, for A-plane GaN is similar to M-plane GaN except for the exchange of x and y axis. The three transitions, involving electrons in the conduction band (CB) and holes in the top three VBs, will exhibit a very different polarization characteristic than the ones for C-plane GaN. These transitions are labelled as T1, T2, and T3 and are predominantly x, z, and y polarized, respectively, for a certain range of in-plane strain values, present in our samples. We measure the energies for these transitions using various optical methods and compare these values with the one derived from the theoretical calculations. For M-plane GaN thin films, two fundamental transitions can be identified, which occur when the electric field vector E is ? and ? c. These transitions give rise to a transmittance spectrum separated by 50 meV at room temperature with respect to each other. The M-plane GaN film also exhibits different dielectric constants for E ? c and E ? c giving rise to linear dichroism in addition to linear birefringence. This results in a polarization filtering of an incident, linearly polarized light beam after transmission, because the component of the electric field vector ? c is more strongly absorbed than the one ? c. This filtering manifests itself, for quasi monochromatic light, as a rotation of the polarization vector toward the c axis and can be as large as 40? for an initial angle of 60?, for our samples. We compare the measured polarization rotation with calculated values taking into account the birefringence of the GaN film. In the energy range where the filtering is most effective, the birefringence almost disappears and can therefore be neglected for the determination of the rotation angle. Finally, the rotation, which is determined by the transmittance for the two orthogonal polarization directions, can be very well approximated by the product of the film thickness and the difference of the absorption coefficients for the two polarization directions. The in-plane polarization anisotropy is also studied in emission for both the M- and the A-plane GaN thin films by measuring the photoluminescence (PL) spectra at low and elevated temperatures. The degree of polarization (?) is calculated to quantify the in-plane polarization anisotropy. At low temperatures, only the top most VB state is occupied giving rise to a large value of ?. As the occupation of the second highest VB state increases with increasing temperature, the degree of polarization decreases.