Strain distribution and defect analysis in III-nitrides by dynamical AFM analysis

Strain distribution and defect analysis in III-nitrides by dynamical AFM analysis

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Nanotechnology 24 (2013) 145701 (7pp) doi:10.1088/0957-4484/24/14/145701

Strain distribution and defect analysis inIII-nitrides by dynamical AFM analysis

Albert Minj1, Daniela Cavalcoli1, Anna Cavallini1, Piero Gamarra2 andMarie-Antoinette di Forte Poisson2

1 Dipartimento di Fisica e Astronomia, Universita di Bologna, Viale Berti Pichat 6/2, 40127 Bologna,Italy2 Alcatel-Thales III-V Laboratory, Route de Nozay, 91461 Marcoussis, France

E-mail: [email protected]

Received 19 October 2012, in final form 8 February 2013Published 12 March 2013Online at stacks.iop.org/Nano/24/145701

AbstractHere, we report on significant material information provided by semi-contact phase-images ina wide range of hard III-nitride surfaces. We show that the phase contrast, which isfundamentally related to the energy dissipation during tip–surface interaction, is sensitive tothe crystalline nature of the material and thus could potentially be used to determine thecrystalline quality of thin nitride layers. Besides, we found that the structural defects,especially threading dislocations and cracks, act as selective sites where energy mainlydissipates. Consequently, in nitrides defects with very low dimensions can actually be imagedwith phase-contrast imaging.

(Some figures may appear in colour only in the online journal)

1. Introduction

Heterostructures based on III-nitrides such as InN, AlN andGaN are well known for their applications in the field of highspeed electronic devices and optoelectronic devices such asLEDs, LASERs, Bragg reflectors, etc with emission varyingin the range from IR to UV [1]. This is possible becauseof the presence of high polarization fields and the ease ofengineering high band offsets. Unfortunately, these devicessuffer from high leakage current, low efficiency and low lifetime because of the presence of various structural defectssuch as threading dislocations (TDs), cracks, etc [2, 3], wherecompositional inhomogeneity has been observed [4, 5]. InIII-N heterostructures, the origin of TDs is related to the latticemismatch and differences in thermal coefficients between theepitaxial layers such as GaN, AlN, InN, their alloys andtheir substrates. Cracks in the epitaxial layers, on the otherhand, occur when their thicknesses exceed a critical value [6,7]. These extended defects are also responsible for strainrelaxation in epitaxial layers. The structural and electronicproperties of TDs in III-nitrides are still under debate due tocontradicting theoretical and experimental results, and there isno general consensus on their nature [8–11]. For example, itis still not clear whether TDs act as radiative or non-radiative

recombination centers or whether they hold any charge state.This kind of study was carried out earlier [12] by finding arelation between the density of defects and the microscopicproperties of the sample. Due to the lack of general consensus,direct study of defects by micro-characterization techniquesis increasingly becoming important. Cathodoluminescence(CL), micro-photoluminescence, transmission electron mi-croscopy (TEM), current-AFM (C-AFM), Kelvin probe forcemicroscopy (KPFM), etc have contributed significantly to adeep understanding of these properties [13, 14]. Furthermore,TDs, which are also associated with high conductivity andloss of confinement especially in In containing alloys (InGaNand InAlN) [15–17], significantly affect the strain of the layerand current leakage in III-N based devices. Therefore, it isvery important to know their exact density and their structuralproperties in a vast area. However, detection of these defects isalso limited by their significantly small dimensions (0.3 nm inthe case of edge-type TDs) and the rough surfaces of nitrides.They almost go unnoticed in SEM and, consequently, cannotbe revealed by CL. This is also true to some extent in AFM.Thus, defect density estimation from the actual values by thesemethods could be affected by large errors. Although planarview TEM analysis can give a more accurate estimation ofthe counts, it suffers from a narrow view, sample destruction

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Table 1. Details of the samples used in this study.

Set Layers Thickness (nm) Alloy composition

A AlInN 15 13–14 In%AlN 0–7GaN 2100–3000

B AlGaN 20 20–30 Al%GaN 2100–3000

C InGaN 50 11–23 In%GaN 2100–3000

and high cost. Thus, it becomes increasingly important tohave a better way to image defects, study their electricalproperties and quantify their density. In this paper, AFMtopography and phase-contrast maps of samples containingextended defects such as threading dislocations (edge, screwand mixed), cracks and trenches will be presented anddiscussed. The phase-contrast values will be related to theenergy dissipated during the tip–surface interaction, anddiscussed in terms of the strain of the layers. We will showthat the phase-contrast images of tapping-mode AFM are notlimited by the tip-dimension, as in the case of topographyimages. Strain related features with size lower than the tipradius will be reported, demonstrating the capabilities ofphase-contrast AFM imaging in III-N compounds. Moreover,AFM topographical and phase contrast analysis of sampleswith very different crystal qualities and alloy compositionswill be shown and their comparison will allow us tounderstand the physical origin of the phase contrast.

2. Experimental section

The study was performed on three sets of samples:AlInN/AlN/GaN, AlGaN/AlN/GaN and InGaN/GaN het-erostructures grown by metal organic chemical vapordeposition (MOCVD) on c-plane sapphire substrates. Thedetails of the structures are reported in table 1. Thecompositions were determined by implementing Vegard’slaw on high-resolution x-ray diffraction (HRXRD) data. Thesurface morphology and surface properties were investigatedby AFM (NT MDT-Solver PRO 47). For the phase-contrastimages in constant-amplitude tapping mode, silicon-basedAFM tips (NSG10, NT-MDT) with triangular pyramidalshape (tip height from 14 to 16 µm, aspect ratio from3:1 to 5:1), mounted on rectangular cantilevers (length =95 µm, breadth = 3 µm,width = 2 µm, force constant kfrom 3 to 38 N m−1 and resonant frequency F0 from 140 to390 kHz), were used. The tip curvature radius was∼6 nm. Allthe features mentioned here are manufacturer specified. AllAFM measurements were performed in ambient conditions.

3. Results and discussion

3.1. Energy dissipation

In principle, the phase-lag (sinϕ) between the free oscillationand the damped one after the tip–sample interaction is related

to the energy dissipation that occurs during this interaction bythe following expression [18]:

sinϕ =ω

ω0

At(ω)

A0+

QEdis

πkA0At(ω), (1)

where A0 and At are the amplitudes, and ω0 and ω thefrequencies of the free and damped oscillations, respectively.k is the spring constant of the cantilever and Q is the qualityfactor.

As can be seen in this expression, if At is kept constant,sinϕ is directly proportional to the energy dissipation.

3.2. Extended defects

Due to the lattice mismatch between sapphire and GaN, theGaN layer at the initial stage of growth is compressivelystrained. The strain relaxation occurs during the growth viathe generation of threading dislocations along [0001]. Here,we will discuss the screw- (s-) and mixed-type (m-TD)threading dislocations present in AlInN and InGaN. s-TDsor m-TDs in nitrides terminate at the surface with invertedpyramidal structures (hence called V-shaped defects) in orderto reduce the surface energy [19]. Consequently, they appearsignificantly larger than their core when observed in AFM [20,21]. TEM observations, not shown here [22], confirmed thatthe V-shaped defects in AlInN originate from the threadingdislocations in GaN [4, 5]. The size of the V-shape canvary significantly, as the size of the V-shape is dependenton many factors such as the dislocation core energy, theformation energy of the facets of the V-shape and the strainenergy [19]. In compressively strained nitrides such as InGaN,strain relaxation could also occur to some extent via thegeneration of misfit dislocations (MDs) in the non-basalslip plane 〈1122〉{1123}. This has already been observed inInGaN [23]. For tensile strained nitrides, strain release canoccur via crack formation.

3.3. Energy dissipation at defects

Examples of phase contrast in the nitrides AlInN, AlGaN andInGaN (sets A, B and C, see table 1) are illustrated in figure 1,in order to show phase changes at relaxed nanostructures(defects) and in strained (defect free) regions. Since all thephase values reported are absolute (i.e. 90+ ϕ with respect tothe phase of the oscillation generator), darker contrast wouldindicate higher ϕ or higher energy dissipation. To show thestatistical fluctuation in the phase values measured over a1 × 1 µm2 area, phase-distribution profiles and full-widthat half maximum (FWHM) values for all the samples wereextracted. The phase-distribution for figure 1(a) is shown infigure 2. The FWHM values for various samples will bediscussed.

Figure 1(a) shows the topography of AlGaN with ahigh density of cracks. Cracks are known to occur inAlGaN layers grown on GaN substrate, as these layers arehighly tensile strained. The critical thickness for cracks tooccur is strictly dependent on the composition and growthconditions. Rudloff et al [24] demonstrated that cracks in

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Figure 1. (a) AFM topography map of AlGaN (set B) with cracks, (b) its corresponding phase-image and (c) topography and phase profilesacross the V defect; (d) AFM topography map of InGaN (set C) with misfit dislocations, (e) its phase-image and (f) topography and phaseprofiles; (g) AFM topography map of AlInN (set A), (h) its phase-image and (i) topography and phase profiles. All the profiles are takenacross the lines shown on the maps. The error bars sketched in figures (c), (f) and (i) refer to the FWHM of the phase-distribution in eachphase map. The operating conditions used are A/A0 = 0.6, scan frequency = 2.30 µm s−1 and fR = 300, 312 and 293 kHz for (a), (d) and(g), respectively.

Figure 2. Phase-distribution profile over the area shown infigure 1(b).

AlGaN are associated with highly relaxed local regions. Thecorresponding phase-image of the topography of figure 1(a) isshown in figure 1(b). It should be noted that in the vicinityof the crack, where the region is highly relaxed, there is astrong drop in phase. This drop is evaluated with respect tothe estimated mean phase over the whole phase map. Themean phase in figure 1(c) is the horizontal line with errorbars, where the error bars represent the full-width at halfmaximum (FWHM) of the phase-distribution in the samearea of figure 1(b). In (b), the mean phase value roughlycorresponds to the values in the region marked as R in (a),which we considered as the reference in the map. The drop inthe phase from the mean value is evident in the regions markedas M and N. Notably, in region M the phase values are alwaysbelow the reference and remain constant over a distance of50 nm. Within these regions, N and M, the phase profile doesnot show a one-to-one correspondence with the topographyprofile. However, outside these regions, there is a one-to-one

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relation between the rapid/abrupt increase in phase and thehollow regions of cracks/trenches (see the profiles in (c)). Thisis due to the tip–surface interaction that is instantaneouslychanged from a repulsive to an attractive regime at verynarrow pits.

Figures 1(d)–(f) are focused on the phase-change at MDsin InGaN. In the topography (figure 1(d)), MDs are visible,running along 〈1100〉, dividing the entire map into localMD-free and MD-occupied micro-regions. When comparedto the phase-contrast image (e), it is evident that the phasereduces where the misfit dislocation density is higher. Thiscan also be observed from the topography–phase profile (f)along the line marked in (d) and (e) running across threeregions: I (MD-free) followed by II (MD-occupied) and thenIII (MD-free). This clearly demonstrates that in this profile,the average phase in the MD-occupied region is lower thanthat in the MD-free region by 0.4◦. Other than MDs, V-defectscould also be seen, where a similar phase-drop appears. AFMmeasurements of V-defects in AlInN/GaN are presented in thefollowing.

In the AFM maps related to the AlInN samples(figures 1(g)–(i)), the phase-lag shows a similar phase-droparound the V-defects (marked as X,Y and Z) by ∼0.5◦. In theprofile across Y , the phase-drop can be seen in the markedregions. In all the cases above, the depths of the V-defects orcrack trenches measured with AFM are underestimated due tothe limitations in the AFM tip size.

The comparison between the topography and phasemaps and the corresponding profiles for InGaN, AlGaNand AlInN evidences that there is a phase-reduction inclose proximity to sites (cracks, MDs and V-defects) thatare known to be less strained. The phase-lag, in general,was asymmetrically distributed around these defects. Thisasymmetric distribution could be caused by compositionalinhomogeneity and/or non-uniform distribution of the strainfield around the defects [4, 5, 19], although the former assistsin the relaxation of the defects. Other than the phase-features,the magnitude of the phase-drop (with respect to the meanphase of the map) at all defects presented here is alsoworthy of note. A higher phase-drop is observed at cracksin AlGaN by ∼3◦ with respect to MDs in InGaN (∼0.4◦)and V-defects in AlInN (∼0.5◦). From the work of Rudloffet al and Rouviere et al [24, 25], where the stress almostreaches ∼0 GPa at cracks in AlGaN and the strain reducesat the core of dislocations by 60% in AlInN, respectively,it is comprehensible that the strain reduction is stronger atthe cracks. From here, it can be concluded that for all phasevalues below the reference, the phase map is directly relatedto the strain distribution and the magnitude of the phase-dropis related to the degree of relaxation.

It should be noted that this variation is significant becauseit is always larger than the statistical fluctuation in thephase value (which here is defined as the FWHM of thephase-distribution, as shown in figure 2). In the following, theimportance of statistical fluctuation in phase is discussed.

The C set (InGaN samples with different In content) wasanalyzed in order to study the effect of indium percentageon the phase contrast. For this analysis, AFM measurements

Figure 3. (a) Absolute phase (bottom) and the correspondingdissipation energy (top) plotted against indium percentage in the setC of InGaN samples with crystalline-like (shown by solid bluestars) and amorphous-like (shown by red open circles) quality. Thelines represent the linear fit of the absolute phase and energydissipation variation against In%. The error bars represent theFWHM of the phase map (or the corresponding energy dissipationdistribution). The mean phase was obtained from an area of1.5× 1.5 µm2 with the following operating conditions:A/A0 = 0.5, fR = 312 kHz, scan speed = 1.82 µm s−1.

were performed on all the samples with the same AFMtip in the repulsive regime. The phase-lag of the cantileverfree oscillation in air was carefully calibrated to 90◦ atits resonance frequency (fR). After each measurement, thephase-lag of free oscillation at its resonance frequency (90◦ isexpected) was checked in order to remove the possibilityof instability in the AFM system during scanning. Figure 3shows the absolute phase (average value) defined as 90 + ϕ,with ϕ as defined in equation (1) and the dissipated energyas obtained by equation (1), against the In(%) in InGaN. Theabsolute phase observed in all the samples falls in two distinctranges, 45◦–55◦ and 32◦–35◦.

In the set of samples relevant to the first range, theabsolute phase almost linearly correlates with the indiumpercentage, while in the set of samples relevant to the secondrange, the absolute phase does not show any significantdependence on the indium percentage. Interestingly, we foundthat the samples falling in the first range consisted only ofsamples with non-crystallographic structural defects such astrenches (figures 4(a) and (b)), where no XRD fringes wereseen. This is shown in figure 5(a) for In = 16% and17%. In other words, they likely contain a high fraction ofamorphous phase and may be referred to as ‘amorphous-like’.On the other hand, the second set consisted of sampleswhere only threading dislocations (from the GaN substrate) orcrystallographic structural defects (such as slip planes) couldbe observed (figures 4(c) and (d)). These samples consistentlyshowed XRD fringes (see figures 5(b) and (c)); this set couldbe referred to as ‘crystalline-like’.

From the average absolute phase values the dissipatedenergy was calculated by equation (1) and plotted in figure 3.The range of energy dissipated in the crystalline set of InGaN

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Figure 4. AFM topography maps of InGaN samples (set C) focusing on non-crystallographic defects such as (a) trenches and (b) highlydense cracks, and crystallographic defects such as (c) ∼108 cm−2 threading dislocations originating from the GaN substrate and (d) slipplane {1122}/misfit dislocations along 〈1100〉.

Figure 5. ω–2θ XRD curves of InGaN/GaN samples with different structural details. (a) Poor quality amorphous-like InGaN/GaN sampleswith 16% and 17% of indium. XRD fringes are not present. (b) High quality InGaN/GaN samples with varying indium percentage (13%,16.2%, 16.3%, 16.8% and 17%). These samples do not contain any misfit dislocations. (c) ω–2θ XRD curves of InGaN/GaN samples ofvarying indium percentage (18.8, 19.2 and 19.5%) containing misfit dislocations. XRD interference fringes are present but not clearlydistinguishable. The FWHM of the InGaN related peak is broader in (a) with respect to those in (b) and (c). The XRD peak related to GaNis situated here at 0.0◦.

samples was almost constant, ∼1240 eV, independent ofindium percentage; however, for the amorphous set of InGaNsamples the energy dissipated varied from 760 to 270 eVwith an almost linear relation with indium percentage (seefigure 3). From the above observations, we can emphasizethat the energy dissipated during the interaction propagateseasily in the crystalline material with respect to the amorphousone since the energy dissipated/lost in the crystalline materialshould occur in the form of lattice vibrations rather than

any physical deformation. These lattice vibrations should bemore prominent in ordered crystalline systems, resulting inhigh-energy dissipation.

Moreover, in amorphous-like materials the dissipatedenergy decreases with In%, as by increasing In% the alloyinduced disorder also increases, in turn also increasing theamorphous phase. This causes the FWHM of the phase map(represented in the form of an error bar in figure 3) to increasewith indium percentage. This also evidently explains why

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Figure 6. (a) AFM topography map of AlInN(15 nm)/GaN (set A) with an inset of scale of 100 nm and (b) its corresponding phase-image.The inset here clearly shows the presence of a TD in this region appearing as dark contrast, which does not appear in its topography image.

the FWHM is significantly smaller in crystalline-like samples(∼0.7◦) in comparison to amorphous-like samples (∼8◦).

However, in both crystalline and amorphous samples, theenergy dissipation increases in the vicinity of TDs, cracksand trenches, indicating that energy propagation is facilitatedalong these defects. This property of defects allows us tosurpass the limitations implemented on lateral resolutionby AFM probe dimensions. Since the phase-image ishighly sensitive to energy dissipation rather than topographyfeatures, defects smaller than the AFM probe dimensions canbe easily detected in phase-imaging mode. One example isshown in figure 6, where topography (a) and phase contrast(b) maps of the AlInN (set A) sample are shown. Here, athreading dislocation, almost invisible in the topographicalmap (6(a)), shows a well-resolved dark contrast in the phasemap (6(b)).

In addition, phase imaging allows us to obtain furtherinformation on material properties such as strain variations.In this respect, phase imaging by AFM is a useful method tomap local strain variations with very high spatial resolution.

4. Conclusions

In summary, from the careful study of tapping-modephase-images of a wide-range of III-nitride surfaces, we haveobserved that higher energy dissipation during tip–surfaceinteraction occurs in crystalline samples compared toamorphous ones, and at the defects, such as TDs, cracks andtrenches. This demonstrates that, if the interaction regimedoes not change from attractive to repulsive, the phase contrastcan be related more to strain variations than to topographicalfeatures. Therefore, by phase mapping very low dimensionalfeatures can be imaged even below the probe dimensions.

In addition, the results show that phase imaging canbe considered as a tool not only to obtain a highlyresolved topographical image, but also to map importantmaterial properties such as strain distribution with veryhigh spatial resolution. Moreover, the crystalline quality ofthe investigated samples can be obtained by phase-contrastmapping.

Acknowledgments

O Tuna, C Giesen and M Heuken of AIXTRON SE,Germany are gratefully acknowledged for sample growthand useful discussions. We are very grateful to DrArantxa Vilalta-Clemente for the TEM analysis of threadingdislocations. This work was supported by the EU underProject No. PITN-GA-2008-213238 (RAINBOW).

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