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Holmi, Joonas; Bairamov, Bakhysh H.; Suihkonen, Sami; Lipsanen, HarriIdentifying threading dislocation types in ammonothermally grown bulk α-GaN by confocalRaman 3-D imaging of volumetric stress distribution

Published in:Journal of Crystal Growth

DOI:10.1016/j.jcrysgro.2018.07.024

Published: 25/07/2018

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Please cite the original version:Holmi, J., Bairamov, B. H., Suihkonen, S., & Lipsanen, H. (2018). Identifying threading dislocation types inammonothermally grown bulk -GaN by confocal Raman 3-D imaging of volumetric stress distribution. Journal ofCrystal Growth, 499, 47-54. https://doi.org/10.1016/j.jcrysgro.2018.07.024

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Journal of Crystal Growth

journal homepage: www.elsevier.com/locate/jcrysgro

Identifying threading dislocation types in ammonothermally grown bulkα-GaN by confocal Raman 3-D imaging of volumetric stress distribution

J.T. Holmia,⁎, B.H. Bairamovb, S. Suihkonena, H. Lipsanena

a Department of Electronics and Nanoengineering, Aalto University, P.O. Box 13500, FI-00076 Aalto, Espoo, Finlandb Ioffe Institute, St. Petersburg 194021, Russia

A R T I C L E I N F O

Communicated by Dr. Jaime Andrade Freitas

Keywords:A1. Confocal Raman spectroscopyA1. Three-dimensional (3-D) imagingA1. Stress distributionA1. Dislocation typesB1. Bulk hexagonal GaNA2. Ammonothermal crystal growth

2018 MSC:00-0199-00

A B S T R A C T

This study demonstrates all-optical Raman scattering study of dislocations in ammonothermally grown α-GaNcrystal and identifies an edge →a -type threading dislocation (TD) using a confocal Raman 3-D imaging technique.These findings make possible the characterization of volumetric stress field and low TD density distributionsover a large area on bulk α-GaN single crystal. The dislocation type effects on Raman shift are also discussed indetail (in order to identify the edge→a -type and mixed →

+→a c -type TDs, and theorize the invisibility of the screw

→c -type TDs). Authors are not aware of any previous reports using the confocal Raman 3-D imaging to identifythe edge →a -type and mixed →

+→a c -type TDs.

1. Introduction

The wide direct bandgap, piezo-electric, wurtzite-structure α-gal-lium-nitride (α-GaN) is a valuable material for the development ofoptical and optoelectronic applications, including highly efficient bluelight-emitting diodes [1,2] (with tunable colours by quantum dots [3])and laser diodes [4], high power devices for communications, radar andpower amplifiers, and detectors for blue and ultraviolet light [5,6]. Italso exhibits a low thermo-optic coefficient, high chemical stability andoptical damage threshold, and suits for high operating temperatures.Currently, a majority of α-GaN crystals are grown by hydride vaporphase epitaxy (HVPE), enabling up to 4-inch wafers with mid-105 cm−2

TD densities and controllable electron concentration down to 1015 cm−3

[7]. Unfortunately, the HVPE-grown crystals suffer from limitedthickness in the c-direction due to wafer bowing and crack formationinduced by parasitic growth and internal stresses [8,9]. At present, theammonothermal synthesis is one of the most promising commerciallyavailable methods, which enables industrial-scale, low-cost growth ofbulk single crystals of α-GaN at high crystalline quality. The latest ad-vances allow a very low reproducible 104 cm−2 TD densities [10,11],large arbitrarily-oriented substrates [12], and growth rates in the c-direction of about 350 μm/day [13], although slow compared to HVPE.Wafers sliced from the boule have excellent radius of curvature of about

600m [14] and have been successfully used in homoepitaxy for III-Ndevices (see Ref. [15] for a recent review).

Despite the apparent success in the crystalline quality of the as-grown ammonothermal α-GaN crystals, there still remains many furtherquestions about the mechanism of their crystallization and the nature ofthe intrinsic properties. For instance, the use of their key properties forvery promising device applications are hindered by the presence of ahigh background impurity concentration (in the range of 10 –1018 21

cm−3 [15]) and other defects, such as edge →a -type, screw →c -type, andmixed →

+→a c -type TDs. These dislocations in particular cause un-

desired local residual stresses in the grown lattice and they are still notwell understood nor easily identifiable in the α-GaN samples. Currently,there is no standardized method to characterize the dislocation densityand types in α-GaN, even though few good options already exist such asdefect selective etching (DSE) and synchrotron radiation X-ray topo-graphy (SR-XRT) [16]. However, these cannot conveniently and non-destructively be utilized to follow the dislocation propagation and in-teraction inside the grown crystal, although recently a successful multi-tool correlative study was done to construct three-dimensional (3-D)images of the dislocations [17]. For this reason, the viability of confocalRaman spectroscopy for identifying dislocations in α-GaN is explored inthis work. Raman spectroscopy is a non-destructive study of the uniquemolecular vibrational characteristics by the inelastic light scattering of

https://doi.org/10.1016/j.jcrysgro.2018.07.024

⁎ Corresponding author.E-mail address: jtholmi@gmail.com (J.T. Holmi).

Journal of Crystal Growth 499 (2018) 47–54

Available online 25 July 20180022-0248/ © 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/BY/4.0/).

T

light. Although residual stresses in the as-grown α-GaN single crystalsare already well studied by Raman spectroscopy via the peak shift of themain α-GaN Raman modes [18–22] (for at least two decades [23] andalso in 3-D [20,21]), only a recent Raman study by N. Kokubo et al.(2018) [24] has reported to have utilized Raman 2-D maps to in-tentionally estimate the TD densities and identify the edge →a -compo-nent directions in the material, but none has used the full potential ofthe confocal Raman microscopy, the diffraction-limited 3-D imagingcapability.

Hence, the authors demonstrate the capabilities of an all-opticalRaman study of ammonothermally grown α-GaN crystal by identifyingone edge →a -type TD using the confocal Raman 3-D imaging technique,revealing the stress distribution induced by the dislocation and thebackground impurities through the Raman shift of E H

2 . Surprisingly, theconfocal Raman 3-D imaging technique has only recently gained somepopularity [20,25–27], although it has been around for almost threedecades [28]. This is understandable after considering the main chal-lenges in using the technique, which lie in the handling of the variouspotential error sources that can interfere with the volumetric scanprocess in real-time [27,29,30], and in the post-processing and di-mensionality reduction of the hyperspectral (4-D) dataset (1-D spec-trum for each spatial 3-D pixel) [25]. Otherwise Raman is particularlyuseful because of its ability to simultaneously and non-destructivelycollect many material structural parameters, including doping andstress, into each of its spectrum. Main objectives of this study are thento (1) enable a successful confocal Raman 3-D imaging experience, (2)discuss the dislocation type effects on Raman shift in detail (in order toidentify the edge →a -type and mixed →

+→a c -type TDs, and theorize the

invisibility of the screw →c -type TD), (3) estimate the TD density (foredge →a -type and mixed →

+→a c -type TDs) over a large area by Raman

scattering, and (4) demonstrate the edge →a -type TD propagation intothe material by the 3-D imaging technique. In other words, this studyaims to present Raman scattering as a suitable supporting tool for thedislocation characterization of any low TD density α-GaN, in hopes toadvance the understanding of the α-GaN dislocation interaction andpropagation mechanisms. The novelties in this work are the first Ramanspectroscopic attempt to identify the edge →a -type TD from its volu-metric biaxial stress distribution below the Ga-polar surface while in-tentionally estimating the TD density with →a -content from a muchwider 2-D Raman shift map.

2. Experimental

2.1. Sample preparation

The studied × ×10 10 0.4 mm3 piece of c-oriented bulk α-GaN wasgrown by the ammonothermal method, using basic chemistry [31]. TheGa-side c-surface was polished to epi-ready quality. It has a high carrierconcentration as indicated later by the Raman measurements in Fig. 1.Oxygen is believed to be the dominant dopant as indicated by Sintonenet al. (2016) [32,33] and Suihkonen et al. (2017) [15].

2.2. Characterization: Confocal Raman spectroscopy

Commercial confocal Raman microscope, WITec alpha300 RA wasused for high spatial resolution Raman scattering imaging. It wasequipped with an ultra-high throughput spectrometer with 1800 g/mmgrating and a back-illuminated electron-multiplied CCD camera de-tector, Andor Newton DU970N-BV-353, thermoelectrically cooled to−60 °C. High confocality was achieved by high magnification and nu-merical aperture × 100/0.95 dry objective lens and 25 μm core diametermulti-mode detection fiber. The sample movement was controlled in afew nm precision with an XY(Z) piezo stage. For better stability, theRaman spectroscope is situated in the temperature, relative humidityand pressure differential controlled cleanroom at ambient conditions of

21.11(7) °C, 44.9(5) %rH and 30(3) dPa, respectively. Laser excitationwavelength of 488 nm was utilized in this work. For the most parts, 30mW power was used for the best signal, but 1.25 mW was used to de-termine the bulk hydrostatic stress state without the heating effect. Incase of high power, laser induced heating and stress effect on theRaman peak shift [34] was found to be +0.07(2) cm−1 or less. Ramanmeasurements in this study utilized point, area and volume scans.

2.3. Post-processing: Spectral nonlinearity calibration

One aim of this work was to determine the average hydrostaticstress in the α-GaN sample using precise knowledge of the Raman peakposition of EH

2 . The main obstacle is the requirement for the spectro-meter calibration, which determines the spectral axis and is easily un-intentionally affected by the current state of the environment. In case ofthe pixel array detection, the spectral axis can also become significantlynonlinear for various reasons, shifting both the laser wavelength andthe peak of interest in nonlinear way. Fortunately, the spectral axis canbe calibrated and linearized after measuring spectral atomic lines of acalibration lamp with well-known reference standards, available atAtomic Spectra Database by National Institute of Standards andTechnology (NIST ASD) [35]. If this is done right before or after theactual measurements, then the calibration remains valid and absoluteRaman spectroscopic features can be restored.

The spectral axis calibration of three widely-spaced 10-min-longpoint scans was done as a post-processing step in order to extract theneeded mean absolute hydrostatic stress in the bulk volume. It wascarefully checked from the CCD nonlinearities measured using 34spectral atomic lines of a neon lamp. The σ1 -noise was ∼0.1 cm−1 afterremoval of the dark current background and the cosmic ray spikes. TheRaman peak position, Pos(EH

2 ) was found to be upshifted by + 0.96(28)cm−1 instrumental shift, predicted by a photon noise weighted thirdorder polynomial spectral correction fit. The remaining σ1 -uncertaintyof instrumental shift (in parenthesis) leads to a significant uncertaintyin the reported absolute stress values. It is caused by the uncertainty inVoigt-fitting of the sparse and low intensity neon atomic lines near thepeaks of interest.

Fig. 1. Area-averaged Raman spectrum of the studied α-GaN over 50× 50 μm2.The incident light was polarized along the lattice m-axis and the scattered lightwas detected in unpolarized manner. Visible and highly up-shifted LPP− modeis a clear indicator of high free carrier concentration. While the E2 (low) and E2(high) modes were expected, E1 (TO), the forbidden mode in this backscatteringconfiguration, is still seen because the incident light is not strictly parallel to thec-axis. Inset: The linear relationship used in this work for converting the Ramanpeak positions, Pos(EH

2 ) into the biaxial component of stress, σB after removingthe hydrostatic stress, σH contribution to Pos(EH

2 ), as reported by Lu et al.(2011) [19].

J.T. Holmi et al. Journal of Crystal Growth 499 (2018) 47–54

48

2.4. Post-processing: Raman map scanline error correction

The 2-D biaxial stress distribution of the α-GaN Ga-polar surfacewas estimated from the peak position of EH

2 Raman mode, Pos(EH2 ),

obtained through the single Lorentzian lineshape fitting. All of the re-ported 2-D maps have been corrected from scanline errors, which arisedue to piezo-stage trace-retrace movement, microscope drifts and ar-bitrary fluctuations in the cleanroom environment, such as acoustic andmechanical noise. Median of line differences (an inverse log-trans-formed version of median of line ratios, aided by automatically gen-erated flatness mask) [36] was found as a robust and useful algorithmto correct all such scanline errors. Nevertheless, it was impossible tofully correct those more rarely occurring partial scanline errors, whichare seen in Fig. 2b background. Successful scanline and z-plane cor-rections were especially essential for the 3-D isosurface rendering of theedge →a -type TD shown in Fig. 4.

2.5. Post-processing: Depth axis rescaling

Diffraction-limited 3-D measurements in confocal Raman micro-scope require a tightly focused laser beam through an objective lensonto the sample, which is moved in atomic precision under the beamwith a piezo stage in three dimensions. Unfortunately, an abrupt changein the refractive index at the air/α-GaN-interface causes the laser spotto focus in different depth than predicted by the piezo z-sensor of themicroscope. Effects of numerical aperture and refractive index changewere accounted for by scaling factor of 3.7 [37] to estimate the real c-axis below the α-GaN Ga-polar surface, which was found at the firstorder derivative maximum of the intensity depth profile [38].

3. Results and discussion

3.1. Average Raman spectrum: The average free carrier concentration andhydrostatic stress in the bulk

The Raman measurements were performed in the +z xx xy z( )backscattering geometry, where z-axis corresponds to the Ga-polar di-rection, c+-axis or {0001}, x-axis to the m-axis or {1100}, and y-axis to

the a-axis or {1120}. The summation, +xx xy indicates the unpolarizedlight detection, whereas the first x means the incident light polarizationalong the m-axis. The Raman spectrum of the studied bulk α-GaNsample averaged over 50× 50 μm2 area is depicted in Fig. 1. The vi-brational excitations cause the Raman spectrum to exhibit the spectralresponse properties characteristic of the heavily doped n-type α-GaN.High free carrier concentration of = ×n 2.46(2) 1019 cm−3 was esti-mated from the visible and highly up-shifted lower longitudinal optical(LO) phonon-plasmon coupled (LPP−) mode centered at 499.14(29)cm−1 using the previously reported correlation with the free carrierconcentration by Kuball (2001) [39]. In the case of p-type doping, bothLPP− and LPP+ modes in Raman shift are considerably less sensitive tothe hole concentration and LPP+ should be visible near 736 cm−1 forthe realistic concentration values [40]. Impurity atom induced Ramanmode, P2 is believed to be at ∼420 cm−1 [41]. Theoretically forbiddentransverse optical (TO) mode, E1(TO) is also seen here because of theused high numerical aperture objective lens, since the incident laserbeam is not strictly parallel to the c-axis. This could be mitigated by theuse of low numerical aperture objective lens, what may also aid thelineshape fitting of EH

2 in the typically noisy 3-D imaging situations.Currently, there is no reliable and verified data for stress-free

α-GaN, as all reports are on material either heteroepitaxially grown onlattice-mismatched substrates, such as Si or sapphire, or contain highconcentration of defects and impurities, which affect the stress state ofthe crystal. In this work we used the linear dependence between theRaman peak position, Pos(EH

2 ) and the c-plane biaxial stress, σB, pre-sented by Lu et al. (2011) [19] (shown in inset of Fig. 1), from whichthe hydrostatic stress, σH contribution to the shift has already beensubtracted away. The relation is written as

= − −σ σPos(E ) 566.65 3.43· 4.205·HB H2 or = −

∼−ω K σPos(E ) ·H B

B2 0∼

= +∼

+ +∼K σ ω α σ σ β σ· ·( ) ·H

H xx yy zz0 , where ∼= −

∼+

∼K α β(2 )H and∼

= −∼K α2B . This assumes unstrained Pos(EH

2 ) frequency of =ω 566.650cm−1 through interpolation. Although the relation was obtained using514 nm laser excitation wavelength, the phonon deformation potentialsfor α-GaN are believed to be fairly wavelength insensitive.

The average Pos(EH2 ) in the bulk was obtained by averaging three

widely-spaced 10-min-long low power point scan measurements, 600

Fig. 2. 2-D maps over 50× 50 μm2 (200× 200 px2 in (b)): (a) High-pass filtered video image of the area, and (b) Raman peak position of EH2 , or biaxial component of

stress, σB distribution of the area. Pos(EH2 ) distribution in (b) reveals the TDs with →a -component of Burgers vector at the polished Ga-polar surface of α-GaN, while

optical image in (a) is clear apart from few unrelated dark spots on the surface. Simultaneously, map in (b) has a more direct and profound meaning through the use

of the Raman biaxial stress coefficient,∼

KB

for EH2 , which linearly transforms Pos(EH

2 ) into the biaxial stress, σB values, as shown on the left side of the colorbar inabsolute units with σ1 -uncertainty of 6.5MPa due to the standard deviation of ∼0.02 cm−1 after removing the hydrostatic stress contribution to the shift. The 3× 3μm2 area marked in blue contains one of the dislocations and will be analyzed further in the consecutive figures.

J.T. Holmi et al. Journal of Crystal Growth 499 (2018) 47–54

49

data point time series per point. After Voigt-fitting and meticulouscorrections (see details in Section 2.3) using neon atomic line referencesfrom NIST ASD [35], it was obtained that Pos(EH

2 ) in the Ga-side bulkα-GaN is 567.40(28) cm−1 with σ1 -confidence interval in the parenth-esis. This corresponds to absolute hydrostatic stress of −179(67) MPa,when assuming zero biaxial stress in the uniform areas of the bulk.Authors believe that ammonothermally grown low TD density α-GaN isdominated by the hydrostatic stress due to the high impurity con-centration, which are point defects and generate hydrostatic stress inthe lattice [42–47]. For instance, high concentrations of oxygen (si-licon) impurities are known to expand (shrink) the lattice almost uni-formly [47,45], causing tensile (compressive) hydrostatic stresses in thebulk material. Such impurities are thought to be introduced during theammonothermal growth conditions [15]. However, the implied com-pressive hydrostatic stress of −179 MPa is in contradiction with theexpected oxygen dominance [15,32,33], which causes tensile stresses[47]. One could reason that the discrepancy is caused by sufficientamount of other less dominant impurity atoms such as Si, whichmodulates the lattice constants in the opposite way three times strongerthan oxygen [47], but this is highly unlikely due to many contraryexamples of defect incorporation distributions such as by Sintonen et al.(2016) [33]. Second option is the fact that our Raman has significantCCD nonlinearity calibration σ1 -uncertainty, but this is still not enoughto down-shift Pos(EH

2 ) into the tensile stressed region required by theexpected oxygen dominance. The most probable explanation is an un-intentional instrumental shift in the interpolated stress free value, ω0due to lack of proper spectral nonlinearity calibration, which was notmentioned by Lu et al. [18,19]. This discrepancy will be a subject to beinvestigated in the future work.

3.2. 2-D Raman imaging: The spectral uniformity and the density of TDswith →a -content (in Burgers vector)

In order to see the biaxial stress field distribution on the Ga-polarsurface, optically video captured in Fig. 2a, a ×50 50 μm2 wide areawas confocally Raman 2-D imaged, what is illustrated in Fig. 2b. Atleast 20 defects are seen in this scan image Fig. 2b, excluding thosewhich either do not generate detectable Raman peak shift, such as purescrew →c -type TD (discussed later in this section), or are situated tooclose to each other to be detected separately [16]. None of them formslarge enough cluster to be seen in the optical image, Fig. 2a. This countis utilized to give a lower bound estimate for the density of TDs with→a -content in Burgers vector of an ideally uniform sample:> 8× 105

cm−2, which is rather low [15], but Sintonen et al. (2014) has de-monstrated even lower TD density for similar sample [16]. One of thedislocations, marked with blue square, was chosen to be investigatedfurther through the 3-D imaging technique.

The Raman peak shift of EH2 is in general sensitive to any linear

combination of uniaxial stresses (σ σ,xx yy and σzz) and experiences peaksplitting (or thus broadening) in presence of shear stresses (σ σ,xy xz andσyz, and their symmetric counterparts) [48–50]. However, the fact thatshear stresses do not produce any measurable shift in Pos(EH

2 ) (exceptsplitting or broadening), it was possible to completely neglect them inthis analysis of Pos(EH

2 ). This simplification is further supported by thein-depth analysis (later in this section) of the dislocation types and thedeformation they cause. It was also assumed that the intrinsic de-formation in the α-GaN lattice is a superposition of biaxial( = =σ σ σxx

ByyB

B with =σ 0zzB ) and hydrostatic ( = = =σ σ σ σxx

HyyH

zzH

H)components of stress, and cannot have lone uniaxial σxx

U or σyyU compo-

nents of stress without external forces. This is the route to the compactrelation for Pos(EH

2 ) by Lu et al. [19], expressed earlier in inset of Fig. 1.Authors believe that the deformation in the ammonothermally grownα-GaN is mainly caused by a constant hydrostatic component of stress,σH due to the uniform high impurity concentration within the scan re-gion. This simplification allows easy subtraction of the hydrostaticstress contribution to the Raman shift and direct estimation of the

absolute biaxial component of strain, σB in the non-uniform Pos(EH2 )

areas of Fig. 2b. For these reasons, both hydrostatic and biaxial stresses,σH and σB contribute to the Raman shift seen in Fig. 2b, but the hy-drostatic stress alone causes the background level.

There are three main types of dislocations in c-plane α-GaN: edge→a -type, screw →c -type and mixed →

+→a c -type TDs (a mixture of first

two), where the vectors (→a and →c ) represent the direction of the latticedistortion, also hereafter denoted as the Burgers vector components,either in one of the a- or c-axis directions. The edge →a -type TD causesbiaxial component of stress, σB and uniaxial stress, σzz

U [51–53] alongwith non-zero shear stress in c-plane, σxy [51,52], neglected in thisstudy. Importantly, low Poisson’s ratio, =ν 0.1830(3) for α-GaN [54]ensures that σB is significantly larger than σzz

U [51,52]. The screw→c -typeTDs behave differently and generate only two kinds of shear stress, σxzand σyz, but its shear stress in c-plane, σxy is still zero [51,52]. It isimportant to recognize that = = =σ σ σ 0xx yy zz (and =σ 0xy ) for thescrew character, all of which could have been detected when non-zeroby Raman peak shift (and split) [48–50]. This implies that the screw→c -type TDs are not detectable by means of Raman peak shift, at leasttheoretically, in case of the EH

2 phonon experimentally verified by arecent Raman study by N. Kokubo et al. (2018) [24]. To authors’ bestknowledge, phonon deformation potential, dE2

H for out-of-plane shearstresses has not yet been reported for α-GaN, even though it was foundzero for α-CdS [48]. This appears to convey that the screw charactermay not generate detectable Raman peak broadening at all, whichshould be put to test in the future. As a consequence, it may then bechallenging to distinguish the edge →a -type TD from the mixed→

+→a c -type TDs, which have both edge and screw character (ap-

proximately independent from each other [51]). Nevertheless, thetreatment in Fig. 2b is particularly useful, because deviation from theaverage Pos(EH

2 ) is mainly caused by σB, which dominates around theedge →a -type and mixed →

+→a c -type TDs [51–53,55]. But atomic-scale

studies have shown that the mixed →+

→a c -type TD (with larger Burgersvector) are fundamentally different from the edge →a -type TD[53,55–58]. For instance, it is calculated to have a stronger and morefar-reaching stress field [59], what could be utilized to distinguish itfrom the pure edge →a -type TD. As this is beyond the scope of this work,more experimental work is needed to test these theoretical implications.

3.3. 3-D Raman imaging: Z-stack representation of the biaxial stress fielddistribution around a dislocation

Confocal Raman microscopy at its best can be used to collect 1-Dspectra for each spatial 3-D pixel, generating a vast hyperspectral da-taset. Time-consuming post-processing, such as Lorentzian lineshapefitting like in this work, is often performed to reduce this 4-D datasetinto several more useful 3-D datasets for each property of the peaks ofinterest. This is the birth of the confocal Raman 3-D imaging technique,which has successfully been utilized in few recent studies [20,25–27].Optically transparent materials such as α-GaN (and its defects) areparticularly suitable for such diffraction-limited volumetric analysis.The main novelty of this work is the first attempt to volumetricallyidentify the edge →a -type TD from its biaxial stress distribution.

Volumetric z-stack of XY-images, depicted in Fig. 3, was collectedwithin 3× 3 μm2 area, previously marked by the blue square in Fig. 2aand b. Total number of 13500 Raman spectra, 250ms integration timeper spectra was gathered within total acquisition time of 1 h 15min. Forreasons described in previous Section 3.2, this area contains one eitheredge →a -type or mixed →

+→a c -type TD core and its biaxial stress field

distribution encoded as Pos(EH2 ) shifts. This long range visualization of

the biaxial stress distribution displays well the compressive (bright) andtensile (dark) stressed regions characteristic to the dislocations withedge character and appears to be similar to that of the recent atomic-scale study by Xiong et al. (2018) [55]. However, it is noted here thatthe true shape is smoothened out by oversampling (1 px =100 nm inthe lateral direction), because the Pos(EH

2 ) data is strongly convoluted

J.T. Holmi et al. Journal of Crystal Growth 499 (2018) 47–54

50

with the laser spot point spread function with waist radius of about200 nm. Furthermore, here the movement of the stress dipole centercould be interpreted as the movement of the dislocation core, but it israther believed to be an instrumental artefact due to both the piezo-stage error induced lateral drift and the off-center laser focus, to bediscussed in detail in next Section 3.4.

Due to a long total scan duration, Pos(EH2 ) scanlines were anom-

alously shifted in Fig. 3 by various instrumental and environmentalcauses, described in more detail in Section 2.4. This anomalous peakshift occurred both in scanline and depth cross-sections. Fortunately,the scanline errors were readily corrected by median of line differences,allowing evaluation of the underlying biaxial component of strain fielddistribution. Moreover, Raman peak shift z-drift was corrected bymedian z-plane offsets, where the z-plane with maximum signal wasused as the reference layer. Authors admit that the latter treatment willalso screen the true depth-dependent physical phenomena like thestress release mechanisms or the strong change in the carrier con-centration. But authors believe that such phenomena remain relativelyconstant for ammonothermally grown α-GaN within the short mea-surement depth of 25 μm. Additional benefit is compensation for thepossible laser induced heat and stress effect [34], although small due toa constantly moving laser beam spot. These two post-processing errorcorrections were necessary for proper 3-D isosurface rendering of thebiaxial component of stress caused by this dislocation. As a result, thisz-stack was finally 3-D isosurface rendered in Fig. 4.

3.4. Volume rendering of the compressive and tensile stress isosurfacesaround the dislocation

Previously represented volumetric z-stack of Pos(EH2 ) maps in Fig. 3

was post-processed further in order to merge the stack together into the3-D dataset. This was already shown to be a particularly challengingtask due to various potential error sources that can interfere with thevolumetric scan process, what is perhaps the main reason that confocalRaman 3-D imaging technique is still not widely utilized despite beingavailable for nearly three decades [28]. Here the piezo-stage error in-duced lateral drift was also compensated by performing the depth scanin the forward–backward manner, where half of the slices were for-ward-scanned and other half backward-scanned. This allowed followingthe dislocation core position via interpolation and correcting any de-viation from linear change in its location. Allowing linear movement ofthe dislocation core is based on the fact that, for instance, the mixed→

+→a c -type TD have been reported to have non-zero inclination angle

[58,60,61]. In addition, the z-axis was rescaled by 3.7 [37] below theGa-side interface (shown as a black plane in Fig. 4) to estimate the realc-axis, which was distorted due to an abrupt change in the refractiveindex. The resulting dataset lateral and depth dimensions per pixel are100 nm and 500 nm (∼1850 nm in α-GaN), respectively.

The obtained 3-D map for Pos(EH2 ) was found best rendered using 3-

Fig. 3. The depth scan stack subset of XY-maps over 3× 3 μm2 wide area,making a × ×30 30 15 dataset. The reported biaxial components of stress haveσ1 -uncertainty of 6.6MPa due to the standard deviation of ∼0.02 cm−1. The TDwith →a -component of Burgers vector is seen as this compressive (bright) /tensile (dark) feature, moving across the scan area when scanning deeper. Bluescalebar is 1 μm in length. The microscope z-sensor values here does not re-present the real c-axis but rather need rescaling below the top surface due toabrupt change in the refractive index [37]. When corrected, this depth scanspans over approximately 24.5 μm length. Total scan time was 1 h 15min. Thehistogram represents the biaxial stress distribution over the whole volume,which consists of 13500 elements. (For interpretation of the references tocolour in this figure legend, the reader is referred to the web version of thisarticle.)

Fig. 4. 3-D isosurface rendering of the 3× 3× 24.5 μm3 (30× 30× 15 px3)volume consisting a TD with →a -component of Burgers vector and its biaxialstress field distribution in three viewing angles: (a) °0 , (b) °45 , and (c) °90 . Twoisosurfaces or constant contours, denoted here as compressive and tensilebiaxial c-plane stresses (in addition to the bulk average hydrostatic stress), wereselected to best visualize the TD propagation down into the bulk material, butthey are not the stress maxima or minima, respectively. The colour variationdoes not represent the change in values but rather is caused by the lightshading. The dislocation core is invisible and can be thought to propagatesomewhere in between these two tubular stress features. Here the z-axis hasbeen rescaled by 3.7 [37] below the Ga-side interface (shown as a plane) toestimate the real c-axis, which was distorted due to abrupt change in the re-fractive index. Illustration of the six possible gradients between the minimumand maximum of the stress field (along with the Burgers vector →a -components)were adapted from study by Sintonen et al. (2014) [16], supported by a recentRaman study [24] and atomic-scale studies, such as ab initio calculation byXiong et al. (2018) [55]. This dislocation then has the Burgers vector →a -contentin direction of {1120} (down). (For interpretation of the references to colour inthis figure legend, the reader is referred to the web version of this article.)

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D isosurfaces, which represent constant value contours, in this casetensile and compressive biaxial stresses. They were chosen arbitrarily togive a good representation of the two stress contours near dislocationcore without being obscured by background noise level. The 3-D il-lustration in Fig. 4 immediately implies that the dislocation is incliningwith an angle of °5 in direction of a-axis. Determination of the dis-location inclination angle is important and can potentially be used todistinguish the mixed →

+→a c -type TD from the edge →a -type TD, be-

cause inclination angles of °12.2 ( °15.6 in theory) and °0 towards theBurgers vector edge a-component have been reported for the mixed→

+→a c -type and edge →a -type TDs, respectively [60], although this can

be perturbed by various imperfections during the growth process[58,60,61]. It is noteworthy that the mixed →

+→a c -type TDs have an

energy minimum in a fixed inclination angle towards the Burgers vectoredge →a -component, whereas the edge →a -type TDs are energy-mini-mized to a zero angle [60]. Authors believe that ammonothermallygrown α-GaN has sufficiently high crystalline quality in order to satisfythis condition. While there can be a minor c-plane miscut, sample bowand surface polish imperfections, they are unlikely to be in such a scale.Considering the smallness of °5 angle, authors believe it to be an in-strumental artefact due to a slightly off-center laser focusing. In otherwords, this particular dislocation would then appear to be the edge→a -type TD based on its nearly zero inclination angle.

Thinning (broadening) of the tensile (compressive) isosurface, seenin Fig. 4 when progressing deeper, is not a real feature but rather anunintentional artefact from the imperfect correction of the anomalousz-drift in Pos(EH

2 ). One limiting factor is believed to be the measure-ment σ1 -uncertainty of 0.01–0.02 cm−1 (or −3.4 6.9 MPa). This z-driftissue could be mitigated by modified CRS detection using real-timeneon calibration lamp via bifurcated detection fiber technique [29],which is planned to be utilized in the future. Simultaneously, thescanline errors could be removed and, at best, spectral axis nonlinearitycalibrated in real-time. Another misleading visual feature in Fig. 4 isthat the isosurfaces appear above the Ga-side interface in air, but this isunderstood as the laser point spread function convolution effect, whichmeans that the Raman scattering volume is still partially inside thesample. These should be taken in careful consideration when inter-preting the 3-D Raman data.

Study by Sintonen et al. (2014) [16] reports that the stress fielddipoles like in Figs. 3 and 4 can only be oriented in six different ways,experimentally verified by a recent Raman study by N. Kokubo et al.(2018) [24]. Ab initio calculations [53,55,57,62] and scanning trans-mission electron microscope studies [58,63] confirm the sixfold sym-metry for the stress field dipole orientation in the case of the edge→a -type and mixed →

+→a c -type TDs. These stress fields are bound to the

same symmetries as their host dislocations, in which the stresses aregenerated by the displaced atoms (and their bonds) in the dislocationcore, illustrated best in [55]. This 6-fold rotation symmetry in c-planefor the dislocation core orientation (and the corresponding stress fielddipole) is a direct consequence of the 3-fold rotation symmetry in c-plane for the α-GaN hexagonal lattice and the °180 changes in the c-plane symmetry by the consecutive c-plane atomic steps. For the samereason, the edge →a -type TD always has its Burgers vector along one ofthe six →a -directions. This information was used to determine that thedislocation shown in Figs. 3 and 4 has the edge→a -component of Burgersvector along {1120} (pointing down in Fig. 3). However, this study isnot sufficient to determine if this edge→a -type TD has the most commonand energetically favourable 5/7-atom ring core [57,58,63], due to thefundamental diffraction limitation of confocal Raman microscopy.

4. Conclusions

This study focused on the 1-D, 2-D and 3-D stress distributionanalysis of the Raman peak shift, Pos(EH

2 ) for the Ga-polar c-plane ofthe ammonothermally grown α-GaN with TDs. Three widely-spaced 10-min-long point scan measurements were analyzed after correcting them

for the spectral axis nonlinearities using a neon calibration lamp. Theaverage Pos(EH

2 ) was found to be 567.40(28) cm−1, where the value inparenthesis represents the σ1 -confidence interval due to the calibrationuncertainty. This shift from the interpolated stress free value of566.65 cm−1 [19] implied an absolute compressive hydrostatic stress of−179(67) MPa, supposedly caused by the impurity atoms, but was foundto be in conflict with the previously reported evidence of oxygendominance [15,32,33], which instead produces tensile stresses [47].For this reason, the used stress free value is put in doubt by the authorsin Section 3.1 and is expected to be unintentionally biased due to lackof spectral nonlinearity calibration, not mentioned by Lu et al. [18,19].Rather, strongly up-shifted LPP− mode indicated high free electronconcentration of = ×n 2.46(2) 1019 cm−3, believed to originate fromdominant oxygen impurities.

The 2-D distribution of Pos(EH2 ) was confocally imaged in large

50× 50 μm2 c-plane area in order to estimate TD density, analyze theresidual stresses and select one dislocation for a closer 3-D imagingstudy. Density of TDs with →a -component of Burgers vector was esti-mated low>8× 105 cm−2 by counting, typically even lower for am-monothermal α-GaN. Reported phonon deformation potentials andstress-free value [19] were used to separate Pos(EH

2 ) into the absolutehydrostatic and biaxial components of stress in the material, σH and σH ,respectively. The direct calculation of σB distribution was possible dueto uniform impurity concentration, which produces a constant σH

background in the material. This simplification was of high importance,because here σB is a dominating attribute of the edge →a -type and mixed→

+→a c -type TDs. It was also argued in Section 3.2 that the screw

→c -type TD cannot be seen as Raman peak shift because it only producesshear stresses, capable of generating Raman peak split (or broadening)instead. Consequently, Pos(EH

2 ) is sensitive only to the TDs with→a -content, conclusion experimentally supported by a recent Ramanstudy by N. Kokubo et al. (2018) [24].

Despite of being nearly three decades old technique [28], confocalRaman 3-D imaging has not yet been much used up-to-date, perhapsdue to the multitude of potential error sources that can make the vo-lumetric scan a particularly challenging task. Recent scientific andcomputational advances have mitigated these constraints and enabledcollection of 1-D spectrum for each spatial 3-D pixel, resulting in a largehyperspectral dataset for the transparent material of interest[20,25,27]. Such large 4-D datasets demand time-consuming post-pro-cessing steps, careful analysis and some kind of dimensionality reduc-tion, such as lineshape fitting, before they may be visualized. Onedislocation was selected for such 3-D analysis, for which several 2-Dmaps of Lorentzian-fitted Pos(EH

2 ) were collected as a function of in-creasing depth within smaller 3× 3 μm2 area. As described in Section3.3, various precautions were taken in order to correct the dataset frommany distortions and instrumental errors, such as anomalous scanlinedrift in Pos(EH

2 ). Still, it was found that the stress field dipole around thedislocation core appeared to move slightly, which was later in Section3.4 concluded to be caused by off-center laser focusing.

Finally, this 3-D stack of images was merged into a 3-D dataset,corrected for the distortion in c-axis below the Ga-polar surface due tothe abrupt change in refractive index as described in Section 2.5. Simpleisosurface 3-D rendering was chosen to visualize the tensile and com-pressive biaxial stresses around the edge →a -type TD in volume of3× 3× 24.5 μm3. The dangers of misinterpreting the 3-D rendered datawere emphasized in Section 3.4, few important factors being the laserpoint spread function convolution effect, the noise background and thepotential instrumental artefacts, all of which should taken in carefulconsideration. The studied dislocation was deduced to be of the edge→a -type based on its stress field dipole and near zero inclination angle.Important finding from literature was that there are only six possibleorientations in c-plane of stress field dipole around the TDs with edgecharacter, understood to originate from the sixfold c-plane symmetry inthe lattice. This was shown to have a strong support from variousatomic-scale calculations and experiments, even though not yet much

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52

exploited in the dislocation stress distribution studies and only directlysuggested by Sintonen et al. (2014) [16] and N. Kokubo et al. (2018)[24] to authors’ best knowledge. Based on the orientation of the stressfield dipole, the Burgers vector →a -content for the studied edge →a -typeTD was found to be in direction of {1120}. Due to the fundamentaldiffraction limitation of confocal Raman microscopy, it could not bedetermined if it has the most common and energetically favourable5/7-atom ring core, what should be indirectly attempted in the futurestudies.

The authors conclude that confocal Raman microscopy as non-de-structive and standalone tool is very suitable for the characterization ofTD types in the ammonothermally grown c-oriented bulk α-GaN. The 3-D imaging technique is highly recommended in order to distinguish theedge →a -type TD from the mixed →

+→a c -type TD by the inclination

angle and develop the understanding on their propagation and inter-action in the material. Further development of the Raman peak shift,Pos(EH

2 ) analysis is needed to expand this capability to heteroepitaxialα-GaN. Obviously, more work is also needed to verify if the screw→c -type TD can somehow be identified by, for instance, the broadeningof the Raman peak width, Fwhm(EH

2 ).

Declaration of interest

The authors declare that there is no conflict of interest.

Acknowledgments

J. T. Holmi wishes to express his great gratitude to Dr. NagarajanSubramaniyam for excellent discussions and coaching. This work wasfinancially supported primarily by the Academy of Finland (Grant297916) and secondarily by Graphene Flagship GrapheneCore1(696656). The research was performed at the OtaNano — MicronovaNanofabrication Centre of Aalto University.

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