Anisotropic strain and phonon deformation potentials in GaN

V. Darakchieva, T. Paskova, M. Schubert, H. Arwin, P. P. Paskov, B. Monemar, D. Hommel, M. Heuken, J. Off, F. Scholz, B. A. Haskell, P. T. Fini, J. S. Speck, and S. Nakamura

Phys. Rev. B 75, 195217 – Published 29 May 2007

Abstract

We report optical phonon frequency studies in anisotropically strained $c$ -plane- and $a$ -plane-oriented GaN films by generalized infrared spectroscopic ellipsometry and Raman scattering spectroscopy. The anisotropic strain in the films is obtained from high-resolution x-ray diffraction measurements. Experimental evidence for splitting of the GaN $E_{1} (TO)$ , $E_{1} (LO)$ , and $E_{2}$ phonons under anisotropic strain in the basal plane is presented, and their phonon deformation potentials $c_{E_{1} (TO)}$ , $c_{E_{1} (LO)}$ , and $c_{E_{2}}$ are determined. A distinct correlation between anisotropic strain and the $A_{1} (TO)$ and $E_{1} (LO)$ frequencies of $a$ -plane GaN films reveals the $a_{A_{1} (TO)}$ , $b_{A_{1} (TO)}$ , $a_{E_{1} (LO)}$ , and $b_{E_{1} (LO)}$ phonon deformation potentials. The $a_{A_{1} (TO)}$ and $b_{A_{1} (TO)}$ are found to be in very good agreement with previous results from Raman experiments [V. Yu. Davydov et al., J. Appl. Phys. 82, 5097 (1997)]. Our $a_{A_{1} (TO)}$ and $a_{E_{1} (LO)}$ phonon deformation potentials agree well with recently reported theoretical estimations [J.-M. Wagner and F. Bechstedt, Phys. Rev. B 66, 115202 (2002)], while $b_{A_{1} (TO)}$ and $b_{E_{1} (LO)}$ are found to be significantly larger than the theoretical values. A discussion of the observed differences is presented.

Received 27 December 2006

DOI:https://doi.org/10.1103/PhysRevB.75.195217

Authors & Affiliations

V. Darakchieva^1,*, T. Paskova², M. Schubert³, H. Arwin¹, P. P. Paskov¹, B. Monemar¹, D. Hommel², M. Heuken⁴, J. Off^5,†, F. Scholz^5,‡, B. A. Haskell⁶, P. T. Fini⁶, J. S. Speck⁶, and S. Nakamura⁶

¹IFM, Linköping University, SE-581 83 Linköping, Sweden
²Institute of Solid State Physics, University of Bremen, 28359 Bremen, Germany
³Department of Electrical Engeneering, University of Nebraska, Lincoln, Nebraska 68588, USA
⁴Aixtron AG, D-52072 Aachen, Germany
⁵4th Physical Institute, University of Stuttgart, 70569 Stuttgart, Germany
⁶Materials Department, University of California, Santa Barbara, California 93106, USA

^*Corresponding author. FAX: +46 13 142337. Electronic address: vanya@ifm.liu.se
^†Now with Osram Opto Semiconductors, Germany.
^‡Now at Ulm University, Germany.

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Vol. 75, Iss. 19 — 15 May 2007

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Images

Figure 1
(Color online) Schematic drawings of the relative arrangement of the unit cells and the orientations of the crystallographic axes of the (a) $c$ -plane GaN on $a$ -plane sapphire (hatched area) and (b) $a$ -plane GaN on $r$ -plane sapphire (hatched area). Distortions of the GaN basal plane under anisotropic strain: (c) $c$ -plane GaN on $a$ -plane sapphire and (d) $a$ -plane GaN on $r$ -plane sapphire. The undistorted basal planes are indicated by dashed lines in (c) and (d).Reuse & Permissions
Figure 2
(Color online) Experimental (dots) and calculated (lines) GIRSE spectra of one representative $c$ -plane GaN film on $a$ -plane sapphire for different angles $φ$ between the plane of incidence and the GaN $[11 \bar{2} 0]$ direction: (a) $Ψ_{p p}$ , (b) $Ψ_{p s}$ , and (c) $Ψ_{s p}$ . The strain-free frequencies of the GaN phonon modes of $A_{1}$ and $E_{1}$ symmetry are indicated by dashed lines. For the sake of clarity the phonon frequencies are given only for polarization along the $[11 \bar{2} 0]$ direction. The $A_{2 u}$ and $E_{u}$ phonon modes of sapphire are indicated in brackets.Reuse & Permissions
Figure 3
(Color online) Real and imaginary parts of the dielectric function $ε$ and imaginary part of the dielectric loss functions $- 1 ∕ ε$ for in- $(x)$ and out-of-plane $(z)$ directions of one representative $c$ -plane GaN film grown on $a$ -plane sapphire surface. For clarity, the functions for directions $y$ are given through the differences between those for directions $(x)$ parallel to the GaN $[11 \bar{2} 0]$ and $(y)$ parallel to the GaN $[1 \bar{1} 00]$ directions.Reuse & Permissions
Figure 4
(Color online) Raman spectra in parallel $(x x)$ and cross-polarized $(y x)$ scattering geometries from one representative $c$ -plane GaN film on $a$ -plane sapphire in the vicinity of the GaN $E_{2}$ mode.Reuse & Permissions
Figure 5
(Color online) Experimental (dots) and calculated (lines) GIRSE spectra of one representative $a$ -plane GaN on $r$ -plane sapphire for different angles $φ$ between the plane of incidence and the GaN [0001] direction: (a) $Ψ_{p p}$ , (b) $Ψ_{p s}$ , and (c) $Ψ_{s p}$ . The frequencies of the GaN phonon modes of $A_{1}$ and $E_{1}$ symmetry are indicated. For the sake of clarity the phonon frequencies are given only for polarization along the $[11 \bar{2} 0]$ direction.Reuse & Permissions
Figure 6
(Color online) Contour plot of $A_{1} (TO)$ frequency versus the strain components $ϵ_{x x}$ and $ϵ_{z z}$ according to Eq. (16) and using our results on the phonon deformation potentials $(a = - 664 {cm}^{- 1}$ and $b = - 1182 {cm}^{- 1}$ ) and strain-free frequency $(ω_{0} = 531.2 {cm}^{- 1})$ . The squares show the calculated frequencies using our measured $ϵ_{x x}$ and $ϵ_{z z}$ , and the respective labels give the frequency values as determined by GIRSE analysis.Reuse & Permissions

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