Effect of anisotropic strain on phonons in a-plane and c-plane GaN layers

Abstract

We have studied phonons in two types of anisotropically strained GaN films: c-plane GaN films grown on a-plane sapphire and a-plane GaN films grown on r-plane sapphire. The anisotropic strain in the films is determined by high-resolution X-ray diffraction (HRXRD) in different measuring geometries and the phonon parameters have been assessed by generalized infrared spectroscopic ellipsometry (GIRSE). The effect of strain anisotropy on GaN phonon frequencies is presented and the phonon deformation potentials $a_{A_1(\mathrm{TO})}$, $b_{A_1(\mathrm{TO})}$, $c_{E_1(\mathrm{TO})}$ and $c_{E_1(\mathrm{LO})}$ are determined.

Introduction

During the last three decades group-III nitrides have continuously attracted strong research interest due to their unique properties and application in optoelectronics, high-power and high-frequency electronics. Despite the remarkable progress in the field, growth of group-III nitrides still suffers from the lack of native substrate and nitride-based technology vastly relies on heteroepitaxy. The growth on foreign substrates typically leads to the presence of built-in strain in heteroepitaxial nitride layers due to the difference in lattice parameters and thermal expansion coefficients between layers and substrates. Sapphire and SiC are among the most often used substrates and typically growth is realized on the basal (0 0 0 1) c-plane of sapphire and SiC. In such instances nitride films grow along the [0 0 0 1] direction and experience isotropic strain. Whenever growth is realized on non-c-plane sapphire and SiC the nitride films will be under anisotropic strain (independent of the film orientation) as a consequence of the anisotropy of the hexagonal (nitrides, SiC) and rhombohedral (sapphire) crystal structures.

Strain has a significant impact on fundamental properties and device-relevant characteristics of materials. The effect of anisotropic strain on the optical response and electronic band structure has been experimentally studied for c-plane GaN [1], [2], a-plane GaN [3], [4] and m-plane GaN films [5], [6]. The impact of anisotropic strain on lattice parameters of c-plane GaN films grown on a-plane sapphire [7] and on the structural properties of a-plane GaN [8], [9] has been also reported. In contrast, the vibrational properties of anisotropically strained GaN are poorly studied and no effect of anisotropic strain on phonons has been reported. Theory predicts that some of the group-III nitride phonons split under anisotropic strain [10], since the GaN [1 1 $\overline{2}$ 0] and [1 $\overline{1}$ 0 0] directions are no longer equivalent in terms of strain as it is in the isotropic case. However, no experimental evidence has been given. Furthermore, no information on the c phonon deformation potentials, related to the strain anisotropy in the basal hexagonal plane exists. In addition, non-c-axis oriented GaN allows an access to the complete set of polar phonons by infrared spectroscopic ellipsometry (IRSE), which provides an alternative or complementary tool to Raman spectroscopy when studying vibrational properties. In this respect it is worth mentioning that there is a lack of agreement between some phonon deformation potentials of GaN and AlN as determined by theory [10] and by employing Raman scattering spectroscopy (RS) [11], [12], which makes further clarification of these issues by independent techniques highly desirable.

The goal of this work is to study the effect of anisotropic strain on the phonon modes of GaN films exhibiting different strain patterns and to determine the phonon deformation potentials. The phonon parameters have been assessed by generalized IRSE (GIRSE), and the anisotropic strain in the films is determined by high-resolution X-ray diffraction (HRXRD) in different measuring geometries.