This content has been downloaded from IOPscience. Please scroll down to see the full text.

Download details:

IP Address: 93.180.53.211

This content was downloaded on 18/12/2013 at 13:31

Please note that terms and conditions apply.

Surface striation, anisotropic in-plane strain, and degree of polarization in nonpolar m-plane

GaN grown on SiC

View the table of contents for this issue, or go to the journal homepage for more

2011 J. Phys. D: Appl. Phys. 44 375103

(http://iopscience.iop.org/0022-3727/44/37/375103)

Home Search Collections Journals About Contact us My IOPscience

IOP PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS

J. Phys. D: Appl. Phys. 44 (2011) 375103 (6pp) doi:10.1088/0022-3727/44/37/375103

Surface striation, anisotropic in-planestrain, and degree of polarization innonpolar m-plane GaN grown on SiCShih-Wei Feng1, Chih-Kai Yang1, Chih-Ming Lai2, Li-Wei Tu3, Qian Sun4

and Jung Han4

1 Department of Applied Physics, National University of Kaohsiung No.700, Kaohsiung UniversityRoad, Nan-Tzu Dist., 811. Kaohsiung, Taiwan, Republic of China2 Department of Electronic Engineering, Ming Chuan University, Taoyuan, Taiwan, Republic of China3 Department of Physics and Center for Nanoscience and Nanotechnology, National Sun Yat-SenUniversity, Kaohsiung, Taiwan, Republic of China4 Department of Electrical Engineering, Yale University, New Haven, CT, USA

E-mail: swfeng@nuk.edu.tw

Received 5 July 2011, in final form 8 August 2011Published 31 August 2011Online at stacks.iop.org/JPhysD/44/375103

AbstractWe report the roles of island coalescence rate and strain relaxation in the development ofanisotropic in-plane strains, striation feature, and subsequent degree of polarization inNH3-flow-rate-dependent m-plane GaN. In the high-NH3-flow-rate samples, the results ofcathodoluminescence, polarized Raman and in situ optical reflectance measurements revealthat a slower coalescence and unrelieved lattice misfit strain lead to larger anisotropic in-planestrains, striated surface and luminescence patterns, and a lower density of basal-plane stackingfault (BSF) and prismatic stacking fault (PSF). In contrast, a lower NH3 flow rate leads tomore rapid island coalescence and fully relaxed lattice misfit strain such that relaxed in-planestrains, a reduced striation surface, and a higher density of BSF and PSF are observed. It issuggested that the anisotropic in-plane strains, striation feature, and BSF and PSF density areconsequences of how rapidly coalescence occurs and the degree of relaxation of lattice misfitstrain. In addition, the simulation results of the k · p perturbation approach confirm a largeranisotropic strain results in a smaller degree of polarization. The research results provideimportant information for optimized growth of nonpolar III-nitrides.

(Some figures in this article are in colour only in the electronic version)

1. Introduction

III-nitride semiconductors have become the key technologicalmaterial for light-emitting diodes and laser diodes. Thesedevices are generally fabricated along the c-axis, wherepiezoelectric and spontaneous polarizations lead to quantum-confined Stark effect (QCSE) [1, 2]. Nonpolar devices grownalong the m- and a-axes have been demonstrated to bepolarization-free, so can be used to reduce the QCSE [3].The striation morphology, related to the island coalescence,has been commonly observed in nonpolar GaN [4–11].During the initial m-GaN growth on AlN buffer, nucleationislands develop (1 0 1 0), (1 0 1 1) and (0 0 0 1) facets withvarious densities, sizes and heights [4, 5]. As the growth

proceeds, coalescence islands along the c-axis go througha concave growth with a triangular gap. The filling upof the triangular gap leads to a striation feature along thea-axis. After the deposition of a thick m-GaN layer, thefully covered surface exhibits typical striation morphology.Also, other arguments have been proposed to explain thisfeature: incomplete nucleation coalescence during the initialgrowth [6], asymmetric growth rate along the in-plane axes [7],anisotropic in-plane strain between the substrate and epitaxiallayer [8, 9], and high basal-plane stacking fault (BSF) density[10, 11].

In addition, due to lattice mismatch and different thermalexpansion coefficients between the epilayer and substrate,the III-nitride epilayers usually show strain [12]. Because

0022-3727/11/375103+06$33.00 1 © 2011 IOP Publishing Ltd Printed in the UK & the USA

J. Phys. D: Appl. Phys. 44 (2011) 375103 S-W Feng et al

strain can modify the band structure and phonon mode,it is important to understand the strain distribution in thefilms. The six-fold symmetry of the hexagonal polar c-GaNepilayers dictates the isotropy in the basal plane, leading toisotropic basal-plane strain [12]. Stress evolution in c-GaNcan be monitored by in situ optical reflectance measurementat different growth stages: nucleation, grain growth, graincoalescence and film smoothing [13]. It has been reportedthat island coalescence during growth and the density of edgethreading dislocation can determine the development of stressin c-GaN epilayers [13]. On the other hand, the nonpolarGaN epilayers are under anisotropic bi-axial strain due to theanisotropic growth surface [3, 12]. Anisotropic in-plane strainsof nonpolar GaN cannot be determined separately by in situoptical reflectance measurement. Instead, ex situ polarizedRaman and x-ray diffraction measurements after growth canbe used to determine the in-plane strain distribution of nonpolarGaN. Distortion of GaN hexagonal unit cell with anisotropicin-plane strain was observed in a-plane GaN grown on r-planesapphire substrates [14, 15]. In contrast to polar c-GaN, theeffects of island coalescence rate and strain relaxation ofm-plane GaN on the striation feature and anisotropic in-planestrains were not well discussed.

Furthermore, m-plane GaN has been shown toexhibit polarized emission, absorption, reflectance andphotoreflectance [3, 16, 17]. The c-axis of the m-plane GaNlies in the growth plane, breaking the crystal symmetry andleading to anisotropic in-plane strains. Polarization anisotropyoccurs even without in-plane strains. Electronic band structure(EBS) of m-plane GaN under anisotropic in-plane strains hasbeen theoretically simulated by k · p perturbation approach[12]. The results show that transition energies from theconduction band (CB) to the highest (E1), second highest(E2) and third highest (E3) valence band (VB) transitions arepolarized in the x, z and y directions, respectively. However,the subsequent effect of the anisotropic in-plane strains on thedegree of polarization was not well discussed.

This study report that the anisotropic in-plane strains,striation feature, and BSF and prismatic stacking fault (PSF)density are consequences of how rapidly coalescence occursand the degree of relaxation of lattice misfit strain. In addition,the simulation results of the k ·p perturbation approach confirma larger anisotropic strain results in a smaller anisotropicpolarization.

2. Sample structures and experimental procedures

m-plane GaN films were grown in a metal-organic chemicalvapour deposition reactor. A 220 nm thick AlN bufferlayer on m-plane 6H-SiC was deposited at 1150 ◦C with aV/III ratio of 780. The growth condition for m-plane GaNincludes a pressure at 300 mbar and a temperature of 1070 ◦C.Trimethylgallium (TMG) and NH3 were used as the precursorsfor the Ga and N, respectively. Four samples with NH3 flowrates of 0.5, 1.0, 2.0 and 4.0 slm were prepared. The TMGflow rate was kept at 230 µmol min−1 for the four samples.The thickness of the GaN epilayer is approximately 1 µm forall samples. The details of growth procedure were described

Figure 1. SEM images of (a) 0.5, (b) 1.0, (c) 2.0 and (d) 4.0 slmsamples and the panchromatic CL images (e), (f ), (g) and (h) overthe same regions, respectively, with 10 kV excitation electronvoltage at RT.

in a previous study [5]. In addition, scanning electronmicroscope (SEM) and cathodoluminescence (CL) imageswere acquired with a Gatan monoCL3 spectrometer in a JEOLSEM system (model JSM 7000F) at room temperature (RT).Polarized Raman spectra were recorded in the backscatteringconfiguration using a Jobin Yvon-Horiba micro-Raman system(model T64000) with a 532 nm laser. PL measurements werecarried out with the 325 nm line of a 55 mW He–Cd laserfor excitation. The PL polarization was analysed using anultraviolet polarizer in front of the spectrometer. The sampleswere placed in a cryostat for low-temperature (10 K) PLmeasurement.

3. Results and discussions

3.1. SEM Image, CL Image, and CL Spectroscopy

Figures 1(a)–(d) show the SEM images. In the low-NH3-flow-rate samples (figures 1(a) and (b)), a relatively smoothand slightly striated surface was observed. As the NH3 flowrate increases, the striation microstructure and rougher surfacebecome apparent. This implies that the growth mode caninfluence the surface morphology and striation microstructure.It was reported that V/III ratio is one of the most importantgrowth parameters affecting island coalescence and striation

2

J. Phys. D: Appl. Phys. 44 (2011) 375103 S-W Feng et al

0

300

600

0

1000

0

1000

340 360 380 400 420 440 4600

1000

2000

3.6 3.4 3.2 3 2.8

20 kV 15 kV 10 kV 5 kV

Photon Energy (eV)

(a) 0.5 slm

Inte

nsity

(ar

b.un

it) (b) 1.0 slm

(c) 2.0 slm

Wavelength (nm)

(d) 4.0 slm

Figure 2. CL spectra of (a) 0.5, (b) 1.0, (c) 2.0 and (d) 4.0 slmsamples with the excitations of 5, 10, 15 and 20 kV electronvoltage at RT.

morphology of nonpolar m-GaN heteroepitaxy [5]. A highV/III ratio enhances coalescence islands’ preferential growthalong the striation direction (a-axis) while it slows the lateralgrowth along the c-axis, leading to striation morphology. Ithas been suggested that nucleation density and coalescenceislands influence the striation feature. In addition, figures 1(e)–(h) show the panchromatic CL images observed at thecorresponding SEM regions. The CL images reveal striatedlight spots along the striation direction. This is in contrastto the case of InGaN/GaN QWs in which In-rich InGaNclusters result in dotted light spots a few hundred nm in size[18, 19]. The 0.5 slm sample shows a low contrast and weakintensity image (figure 1(e)), while the high-NH3-flow-ratesamples show a higher contrast, a stronger intensity, and a moreapparent striated luminescence pattern. This result shows thatstriation microstructures can modify the surface morphologyand lead to the striated luminescence pattern.

Figure 2 shows the CL spectra taken over the sameSEM regions at RT. Except for the CL spectra of the 4.0 slmsample under higher electron voltages, all the spectra show amain peak around 375 nm (3.307 eV) together with a lower-energy shoulder around 385 nm (3.220 eV). The main peak isassociated with the partial dislocation (PD) terminating theBSF, while the lower-energy shoulder is correlated with thePSF and/or stair-rod dislocations at the intersection betweenthe BSF and PSF [20, 21]. The CL spectra provide the evidencethat the striated light pattern in the CL image originates fromthe PD-, BSF- and PSF-related emissions. During the initialgrowth of nonpolar GaN, atomic steps and/or impurities on therough surface of the AlN buffer layer trigger nucleation errorsand disorder basal-plane stacking sequences, leading to the

formation of BSF and PD [22]. Our previous transmissionelectron microscopy observations show that more BSF aregenerated at the m-GaN/AlN interface in the low-NH3-flow-rate samples [5]. The less striated surface of the 0.5 slmsample implies a higher defect density and a poorer samplequality. In addition, BSF and PSF are non-radiative traps innonpolar III-nitrides. The higher the SF density, the weaker theluminescence. In the 0.5 slm sample, the weak CL intensitiesfor the two emission bands reveal a high SF density and apoorer sample quality. This result is consistent with fewerstriated light spots in the CL image. As the NH3 flow rateincreases, the CL spectra show a stronger main peak and amore prominent lower-energy shoulder. This enhances thestriated light pattern in the CL image. In particular, for the4.0 slm sample, the lower-energy shoulder becomes a strongand broad emission under a high excitation electron voltage,which implies a better sample quality and less contribution ofnon-radiative processes. The SEM and CL results show thatthe striation microstructure and SF density were considerablyinfluenced by the growth mode.

3.2. Estimation of anisotropic in-plane strains by polarizedRaman measurement

The striated feature and nucleation islands are expected tocorrelate with the strain distribution of the epilayers. Toestimate the in-plane strain in the samples, polarized Ramanmeasurements were taken. Figures 3(a) and (b) showthe polarized Raman scattering spectra under y(xx)y andy(zz)y configurations, respectively. The y(xx)y spectraclearly display A1(TO) and E2-high modes for GaN whilethe y(zz)y spectra show A1(TO) mode. The A1(TO) mode(609 cm−1), originating from the buffer layer AlN, was alsoobserved in both configurations. The agreement of ourdata with the polarization selection rules shows the phasepurity of our samples [12, 23]. In addition, the two dottedlines (531.8 and 568.0 cm−1) show the phonon frequenciesω

A1(TO)0 and ω

E2(high)

0 , respectively, for strain-free GaN. As theNH3 flow rate increases, the decreasing phonon frequencyof the E2(high) mode implies a larger tensile strain alongthe a-direction [24]. Based on the deformation potentialapproximation, the frequency shifts �ω = (ω − ω0) can bedescribed as a function of in-plane strain �εxx and �εzz [25]

�ω(E2-high) = a[1 − C12/C11]�εxx + [b − (C13/C11)]

×�εzz = −533.8�εxx − 688.8�εzz (1)

�ω(A1(TO)) = −395.82�εxx − 1461�εzz (2)

where a = −850 and −920 cm−1 and b = −920 and−1290 cm−1 are the deformation potential constants for GaNE2(high) and A1(TO) modes, respectively [23]. C11 = 390,C12 = 145 and C13 = 106 GPa are the elastic stiffnessconstants [25]. To clearly identify the peak position, GaNE2(high) mode in the y(xx)y configuration and GaN A1(TO)mode in the y(zz)y configuration were chosen to estimate thein-plane strains by calculating equations (1) and (2).

As shown in figure 4, as NH3 flow rate increases, acompressive strain along the c-axis increases by two orders

3

J. Phys. D: Appl. Phys. 44 (2011) 375103 S-W Feng et al

Figure 3. Polarized Raman scattering spectra for the four samplesunder (a) y(xx)y and (b) y(zz)y configurations. The Cartesian axesx, y, and z correspond to the [1 1 2 0], [1 1 0 0] and [0 0 0 1]directions of GaN, respectively. Conventional Porto’s notation wasused to describe the scattering geometry: the letters outside theparentheses represent the direction of the incident and scatteredlight, while the letters inside the parentheses represent the incidentand scattered polarizations [13].

Figure 4. Estimated in-plane strains �εxx and �εzz determined byRaman measurement for the four samples. Inset shows the straindistribution.

of magnitude, while a tensile strain along the a-axis increasesonly about five fold. Anisotropic in-plane strain also existsin nonpolar ZnO and the mechanism for anisotropic in-planestrain relaxation was discussed [26, 27]. The estimated

0.00

0.05

0.10

0.15

360 370 380 390 4000.0

0.2

0.4

0.6

0.8

1.0

(a) 0.5 slm E // a-axis E // c-axis

Deg

ree

of P

olar

izat

ion

Int

ensi

ty (

arb.

unit)

Wavelength (nm)

0.5 slm 1.0 slm 2.0 slm 4.0 slm

(b)

Figure 5. (a) Polarized PL spectra with detected polarizations alongthe a- and c-axes for the 0.5 slm sample at 10 K. (b) The degree ofpolarization of the four samples.

in-plane strain observed at RT is the residual strain in thefilms, which consists of three components: (i) the intrinsicstrain (εintrinsic) due to lattice misfit between the film andthe substrate, (ii) the extrinsic strain (εextrinsic) due to thermalmisfit between the film and the substrate, and (iii) defect strain(εdefect) [26, 27]. For GaN, the thermal misfit (∼0.085%)strain and defect strain are relatively small and the latticemisfit strain is the dominant factor in determining the residualstrain [28]. Because of the same growth temperature, thethermal misfit strain is assumed to be the same for the foursamples. In addition, the estimated �εxx and �εzz seemto be correlated with the lattice misfit strain distribution(�a/aAlN = 2.5% and �c/cAlN = 4.1%) between theGaN and AlN buffer layer [29]. The smaller in-planestrains in the low-NH3-flow-rate samples imply that latticemisfit strain is fully relaxed during growth and only thermalmisfit and defect strains remain on cooling. Because BSFhave Burger’s vector of 1/6〈2 2 0 3〉 along the c-axis, strainrelaxation along the c-axis results in the formation of BSFand PD such that a higher density of BSF and PD and fewerstriation microstructures are observed [22, 30]. In contrast,for the high-NH3-flow-rate samples, the large anisotropicin-plane strains reveal an unrelieved lattice strain duringgrowth. Because the lattice strain is not effectively relaxed,the high-NH3-flow-rate samples exhibit a lower density ofBSF and PD and apparent striation microstructures. Thehigh compressive strain along the c-axis may induce a highertensile strain along the a-axis. This argument is consistentwith the large anisotropic in-strain observed in Ramanmeasurement.

The in situ optical reflectance measurement shows thatthe m-plane GaN coalescence occurs faster at lower NH3 flow

4

J. Phys. D: Appl. Phys. 44 (2011) 375103 S-W Feng et al

-0.50 -0.25 0.00 0.25 0.50-0.50

-0.25

0.00

0.25

0.50-0.50

-0.25

0.00

0.25

0.50

-0.50 -0.25 0.00 0.25 0.50

εzz(%)

(c) E3

ε xx(%

)

(b) E2

0.2 0.4 0.6 0.8

(a) E1

(d) E1+E

2+E

3

Figure 6. The degree of polarization for (a) E1, (b) E2, (c) E3 and (d) E1 + E2 + E3 transitions as a function of in-plane strains εxx and εzz.Arrow indicates an increasing anisotropic in-plane strains for εxx � 0 and εzz � 0.

rate than at higher NH3 flow rate [5]. This suggests thehigher nucleation density and more rapid island coalescenceof the low-NH3-flow-rate samples achieve strain relaxation,a reduced striation surface, and a higher density of BSF. Incontrast, a higher NH3 flow rate results in a lower nucleationdensity and slower coalescence such that unrelieved latticemisfit strain, apparent striation surface, and a lower density ofBSF are observed. Therefore, it is suggested that anisotropicin-plane strains, striation feature, and BSF and PSF densityare consequences of how rapidly coalescence occurs and thedegree of relaxation of lattice misfit strain.

3.3. Polarized PL measurement and degree of polarization

Anisotropic in-plane strain should have an impact on thepolarization anisotropy and degree of polarization. Figure 5(a)shows the polarized PL spectra with detected polarizationsalong the a- and c-axes for the 0.5 slm sample at 10 K. ThePL spectra show a large polarization anisotropy. A BSF-related emission around 365 nm (3.397 eV) and a PSF-relatedemission around 378 nm (3.280 eV) were observed [20, 21]. Inaddition, the PL spectra show a high polarization anisotropy.The degree of polarization, ρ, is defined as [17]

ρ = I⊥C − I‖CI⊥C + I‖C

(3)

where I⊥C and I‖C are the PL intensities polarizedperpendicular and parallel to the c-axis, respectively. As shownin figure 5(b), it was found that the larger the anisotropic in-plane strain, the lower the degree of polarization. This trendshould be related to the in-plane strain inside the epilayer.

4. EBS of m-plane GaN under anisotropic in-planestrain

4.1. Theoretical simulation: k · p perturbation approach

To understand the relation between in-plane strain and degreeof polarization, the k · p perturbation approach is used tosimulate the EBS of m-plane GaN under anisotropic in-planestrains to analyse our experimental results. The excitonictransition energies, Ej , are expressed as [12]

Ej = E∗ + Ec − Evj −Eb

ex (4)

where E∗ = Eg + �1 + �2 = 3.532 eV. Ec is the eigenvalueof the strain-dependent Hamiltonian for the CB. Ev

j are thethree maximum eigenvalues of strain-dependent Hamiltonianfor the VB. The exciton binding energy, Eb

ex, is assumed to be26 meV for all three transitions.

The components of the oscillator strengths for thetransitions are determined from momentum matrix elements|〈�CB|pl|�VB〉|2 with l = x, y, z [12]. px , py and pz are theorbital functions in the x-, y- and z-directions, respectively.〈�CB| and 〈�VB| are the orbital parts of the CB and VB basisfunctions, respectively. The details of the calculations weredescribed in [12]. Simulations were performed using in-housecode written for Matlab software.

4.2. Simulation result of degree of polarization as a functionof in-plane strains

Our simulation results of transition energies and oscillatorstrengths from the CB to the highest (E1), second highest(E2) and third highest (E3) VB in m-plane GaN stronglydepend on the in-plane strains εxx and εzz. The simulationresults of transition energy and oscillator strength in this study

5

J. Phys. D: Appl. Phys. 44 (2011) 375103 S-W Feng et al

are consistent with the reported results [12]. Except for theE3 transition, as the anisotropic in-plane strains increase forεxx � 0 and εzz � 0, the transition energies of E1 andE2 decrease. This implies larger anisotropic in-plane strainsdecrease the transition energies. In addition, the luminescenceintensity is shown to be proportional to the oscillator strength[31]. The degree of polarization ρ can be expressed as

ρ = I⊥ − I‖I⊥ + I‖

= [x-component Oscillator strength

−z-component Oscillator strength][x-component

Oscillator strength + z-component Oscillator strength]−1.

(5)

Figure 6 shows the simulation results of the degree ofpolarization for E1, E2, E3 and E1 + E2 + E3 transitionsas a function of in-plane strains. It can be seen that thedegree of polarization strongly depends on the in-plane strains.Except for E3 transitions, as the anisotropic in-plane strainsincrease for εxx � 0 and εzz � 0 (indicated by arrows), thedegree of polarization for E1, E2 and E1 + E2 + E3 transitionsdecreases. Although we do not have the necessary data toanalyse defect-related transitions in terms of polarization, thesimulation results of the degree of polarization for the E1, E2,and E1+E2+E3 transitions agree with the experimental results.

5. Conclusions

In summary, we have suggested that the anisotropic in-planestrains, striation feature, and SF density are consequences ofhow rapidly coalescence occurs and the degree of relaxationof lattice misfit strain. In addition, a larger anisotropic strainresults in a smaller degree of polarization. This trend isconsistent with the simulation results of the k · p perturbationapproach. The research results provide important informationfor optimized growth of nonpolar III-nitrides.

Acknowledgments

This research was supported by the National Science Council,Taiwan, Republic of China, under grants NSC 98-3114-E-110-001, NSC 99-2112-M-390-002-MY3 and NSC 99-2515-S-390-001.

References

[1] Bernardini F, Fiorentini V and Vanderbilt D 1997 Phys. Rev. B56 R10024

[2] Waltereit P, Brandt O, Trampert A, Grahn H T, Menniger J,Ramsteiner M, Reiche M and Ploog K H 2000 Nature406 865

[3] Paskova T 2008 Nitrides with Nonpolar Surfaces: Growth,Properties, and Devices (Weinheim: Wiley-Vch)

[4] Sun Q, Kwon S Y, Ren Z, Han J, Onuma T, Chichibu S F andWang S 2008 Appl. Phys. Lett. 92 51112

[5] Sun Q, Yerino C D, Zhang Y, Cho Y S, Kwon S Y,Kong B H, Cho H K, Lee I H and Han J 2009J. Cryst. Growth 311 3824

[6] Koblmuller G, Hirai A, Wu F, Gallinat C S, Metcalfe G D,Shen H, Wraback M and Speck J S 2008 Appl. Phys. Lett.93 171902

[7] Li D S, Chen H, Yu H B, Zheng X H, Huang Q and Zhou J M2004 J. Cryst. Growth 265 107

[8] Schaadt D M, Brandt O, Trampert A, Schonherr H P andPloog K H 2007 J. Cryst. Growth 300 127

[9] Founta S, Bougerol C, Mariette H, Daudin B and Vennegues P2007 J. Appl. Phys. 102 74304

[10] Hirai A, Haskell B A, McLaurin M B, Wu F, Schmidt M C,Kim K C, Baker T J, DenBaars S P, Nakamura S andSpeck J S 2007 Appl. Phys. Lett. 90 121119

[11] Haskell B A, Baker T J, McLaurin M B, Wu F, Fini P T,DenBaars S P, Speck J S and Nakamura S 2005 Appl. Phys.Lett. 86 111917

[12] Ghosh S, Waltereit P, Brandt O, Grahn H T and Ploog K H2002 Phys. Rev. B 65 075202

[13] Bottcher T, Einfeldt S, Figge S, Chierchia R, Heinke H,Hommel D and Speck J S 2001 Appl. Phys. Lett. 78 1976

[14] Paskovaa T, Darakchievaa V, Paskova P P, Bircha J,Valchevab E, Perssona P O A, Arnaudovb B,Tungasmittaa S and Monemara B 2005 J. Cryst. Growth281 55

[15] Darakchieva V, Paskova T, Schubert M, Arwin H, Paskov P P,Monemar B, Hommel D, Heuken M, Off J, Scholz F,Haskell B A, Fini P T, Speck J S and Nakamura S 2007Phys. Rev. B 75 195217

[16] Rau B, Waltereit P, Brandt O, Ramsteiner M, Ploog K H,Puls J and Henneberger F 2000 Appl. Phys. Lett. 77 3343

[17] Ghosh S, Waltereit P, Brandt O, Grahn H T and Ploog K H2002 Appl. Phys. Lett. 80 413

[18] Feng S W, Lin E C, Yang C C, Ma K J, Shen C H,Chen L C, Kim K H, Lin J Y and Jiang H X 2004J. Appl. Phys. 95 5388

[19] Feng S W, Tu L W, Chyi J I and Wang H C 2008 Thin SolidFilms 517 909

[20] Liu R, Bell A, Ponce F A, Chen C Q, Yang J W and Khan M A2005 Appl. Phys. Lett. 86 21908

[21] Mei J, Srinivasan S, Liu R, Ponce F A, Narukawa Y andMukai T 2006 Appl. Phys. Lett. 88 141912

[22] Sun Q, Kong B H, Yerino C D, Ko T S, Leung B, Cho H K andHan J 2009 J. Appl. Phys. 106 123519

[23] Davydov V Yu, Averkiev N S, Goncharuk I N, Nelson D K,Nikitina I P, Polkovnikov A S, Smirnov A N, Jacobson M Aand Semchinova O K 1997 J. Appl. Phys. 82 5097

[24] Wagner J M and Bechstedt F 2000 Appl. Phys. Lett.77 346

[25] Flissikowski T, Brandt O, Misra P and Grahn H T 2008Phys. Status Solidi b 245 913

[26] Saraf G, Lu Y and Siegrist T 2008 Appl. Phys. Lett.93 41903

[27] Pant P, Budai J D and Narayan J 2010 Acta Mater. 58 1097[28] Hond T, Fujita N, Maki K, Yamamoto Y and Kawanashi H

2000 Appl. Surf. Sci. 159 468[29] Founta S, Coraux J, Jalabert D, Bougerol C, Rol F, Mariette H,

Renevier H, Daudin B, Oliver R A, Humphreys C J,Noakes T C Q and Bailey P 2007 J. Appl. Phys. 101 63541

[30] Liu T Y, Trampert A, Sun Y J, Brandt O and Ploog K H 2004Phil. Mag. Lett. 84 435

[31] Chuang S L 1995 Physics of Optoelectronic Devices(Chichester: Wiley)

6