Chiang Mai J. Sci. 2008; 35(3) 495

Chiang Mai J. Sci. 2008; 35(3) : 495-520www.science.cmu.ac.th/journal-science/josci.htmlReview Article

ABSTRACTAtomic-resolution high-angle annular dark-field (HAADF) scanning transmission

electron microscopy (STEM) has been used to the structural and compositional analysis ofmaterials. The first part of this paper is a review of our recent HAADF-STEM investigations,which comprise physics to understand its imaging, and illustration of artifacts in images andimaging process. Next, we present our investigations of the multiple InGaN/GaN quantumwells and the strained AlGaN/GaN superlattice cladding in InGaN-based light emitting diodesor laser diodes, which have been performed by HAADF-STEM, high-resolution field-emissionscanning electron microscopy, and high-resolution transmission electron microscopy. Theobservation of ultra-high density InGaN quantum dots is also shown.

Keywords: high-angle annular dark field scanning transmission electron microscopy,field-emission scanning electron microscopy, high-resolution transmission electron microscopy,InGaN-based light emitting diodes, laser diodes, multiple quantum wells, strain-layer superlatticecladding, quantum dots.

1. INTRODUCTIONOn January 14 and 15, 2008, I presented

lectures at the Department of IndustrialChemistry, Faculty of Science in Chiang MaiUniversity. The lectures reviewed our electronmicroscopy investigations, which have beenperformed since 1961 on the structure andgrowth of various metallic, semiconducting,ceramic, other inorganic or organic materialsand devices, using different types of electronmicroscopes and microscopy techniques. Theelectron microscopy is theory and techniquefor macro- and nano-structural analysis and

characterization. Therefore, the lectures aimedat providing each of the audience withknowledge to find appropriate electronmicroscopy for her or his investigation, byshowing many electron microscopy investi-gations. This paper is a part of my lecturesand a review of our recent investigations onhigh-angle annular dark-field (HAADF)scanning transmission electron microscopy(STEM) and on InGaN-based light emittingdiodes (LEDs) and laser diodes (LDs).

HAADF-STEM is a quite new technique

Imaging of High-Angle Annular Dark Field ScanningTransmission Electron Microscopy and MicroscopyStudies of GaN-based Light Emitting Diodes andLaser DiodesMakoto ShiojiriProfessor Emeritus of Kyoto Institute of Technology, 1-297 Wakiyama, Enmyoji, Kyoto 618-0091, Japan.e-mail: shiojiri@pc4.so-net.ne.jp

Received: April 3, 2008Accepted: May 13, 2008

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developed in 1990’s [1], more than 50 yearsafter the invention of a transmission electronmicroscopy (TEM) instrument by Ruska in1931 and the idea of scanning electronmicroscopy (SEM) by Ardenne in 1937.Howie [2] proposed to use a detector to high-angle range, so-called Howie detector, in orderto exclude elastic coherent scattering andeliminate the phase problem. HAADF-STEMis used to characterize the structure of grainboundaries and precipitates as well as perfectcrystals [1]. It has become a quite populartechnique since Kawasaki first installed aHAADF detector in a commercial STEMinstrument with Schottky field emission gunin 1997, which was reported by James et al. in1998 [3]. He succeeded in taking atomicresolution HAADF-STEM images [3-6]. Theelectron beams run in reverse between STEMand conventional transmission electronmicroscopes (CTEM) (Figure 1). The bright

Figure 1. Ray diagram of scanningtransmission electron microscope(STEM) and conventional transmis-sion electron microscope (CTEM).The ray runs downward in STEMand upwards in CTEM.

field (BF) STEM imaging is exactly the samewith the CTEM imaging according to thereciprocity rule [7], but HAADF-STEM iscompletely different from CTEM. We havebeen engaged in HAADF-STEM investiga-tions since 1998 [4-6, 8-37]. The first part ofthis paper is a review from our investigationson HAADF-STEM imaging.

GaN-base light emitting diodes (LEDs)and laser diodes (LDs) [38] have been widelyused as light sources over a range of visibleand ultraviolet wavelength. This is due toexceptionally high photoemission efficiencyfrom InxGa1-xN quantum wells (QWs) despitenot a few of defects involved. Next, wepresent our recent investigations of GaN-based LEDs and LDs, which were per-formed using HAADF-STEM as well as fieldemission (FE) SEM, cathodoluminescenceSEM and high-resolution (HR) TEM [26-37,39,40].

Figure 2. Coherency, incoherency, and partial time- orspatial-coherency of classic particles. (a, b) Coherency.Two ballistic missiles 1 are coherent with each othersince they are launched with the same velocity (energy)from the same pad and run in the same orbit. (c)Spatial incoherency. Missile 2 that is launched from adifferent pad with the same energy is incoherent withmissile 1. Missile 3 hitting a given target area is in partialspatial-coherency with missile 1. (d) Time incoherency.Missile 2 that is launched with different energy fromthe same pad is incoherent with missile 1 (because timeof arrival is different). Missile 3 hitting the target areais in partial time-coherency with missile 1.

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2. HIGH-ANGLE ANNULAR DARK FIELD (HAADF)SCANNING TRANSMISSION ELECTRONMICROSCOPY (STEM)2.1 Physics of HAADF-STEM Imaging

First of all, we explain the terms of‘coherency’ and ‘incoherency’ [32]. It is afundamental concept of quantum physics thata quantum particle also behaves as wave. Aswell known, the light waves passed throughdifferent holes interfere with each other toshow Young’s fringes. The interference alsooccurs between the electron waves scatteredby different atoms (exactly, electrostaticpotential around atoms). It is caused onlybetween elastically scattered waves or betweeninelastically scattered waves with the samewavelength. The former gives Braggreflections and the latter Kikuchi pattern. Here,we call the scattering that causes Braggreflections ‘Bragg scattering’. The ‘elasticscattering’ is no energy-loss scattering.According to quantum mechanism, theinterference never occurs between waves ofdifferent electrons [41]. Thus, the interferenceoccurs only between the waves of the samewavelength incorporated with ‘a singleelectron’. The electron is observed in termsof the intensity I, which gives a probabilityof the appearance. The observed electrondoes not indicate the position r where it alwayslocates, but indicates only a place where it isaccidentally captured. For the visualization ofthe probable position of an electron, we needto detect many electrons that are captured ata region assigned with the same interferencecondition. These electrons are ‘coherent’ witheach other. They show a physically valuableintensity distribution (such as interferencefringes or diffraction spots) as a result of thecooperation. Thus, ‘interference’ is a term forthe intra-electron relation of waves, while theterm of ‘coherency’ or ‘incoherency’ is forthe inter-electron relation between the wavesthat belong to different electrons. In other

words, the interference is described asΦj=Σi φij, where φij is the wave of electron jscattered by atom i, while the coherency andincoherency are described as I=Σ j Ij =Σj|Φj|

2, where Ij=|Φj|2 is the interference

intensity for the electron j. The coherency is inthe case of that all Φj are the same, that is,I=n|Φ |2 where n is the number of electrons.Coherent electrons must have the same birth-place (the source or the resource for thescattered electrons) and the same energy. Afield-emission gun can supply a coherentelectron beam because it provides the samesource at the top of the tip and gives the sameenergy to the emitting electrons. The spatialor time incoherency and partial coherency canbe simply understood by schemata in Figure2 which are shown for the classic particles byanalogy with ballistic missiles. For the quantumparticles such as electrons, we use the termof ‘partial coherency’ when the source posi-tions or energies are different within apermissible limit given by the Rayleighcriterion.

All atoms in the specimen vibratethermally around their equilibrium positions.The electrons whose waves are elasticallyscattered from the atoms at their thermalequilibrium positions keep both timecoherency and spatial coherency with eachother. They give rise to Bragg reflections.Actually each atom is differently displaced fromthe equilibrium position at different momentsand does elastically scatter electrons. Thus, thewaves of different electrons scattered by thisatom are partially incoherent with each other.The frequency of the thermal lattice vibration~ 1013 Hz is the fifth power of 10 times assmall as a frequency of incident electron wave~1018 Hz, so that the displacements areobservable using the electron beam. Thescattering from the displaced atoms, thus,gives diffuse intensity distribution, which isthermal diffuse scattering (TDS). We use the

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Einstein model which assumes atoms movingindependently with each other and the meansquared displacement of them. This leads tothe Debye-Waller factor [42,43]. The latticevibration may be quantized as phonon. Theincident electrons interact with the phonons,losing or gaining energy ΔE, during thecollision. The energy of phonons is in theorder of 10-1 eV or less (~infrared radiation)and that of the incident electrons is 105 eV sothat ΔE is negligibly small. In any case, theBragg scattering is elastic, coherent scattering,while TDS is treated as elastic, incoherentscattering. Then, their intensities are given bythe formulae shown in Figure 3.

In atomically resolved HAADF-STEM,the contrast of an atom column (along theincident electron beam probe) may be simply

obtained as the integrated intensity for a timeexposed to the probe, since the atoms in thecolumn vibrate thermally and scatter electronsincoherently as TDS. This is one of the reasonswhy HAADF-STEM imaging is incoherent,and the contrast may be called ‘longitudinallyincoherent’. Another reason of the incoherentimaging is ascribed to scanning of theconvergent beam. The electrons scatteredfrom an atomic column might be differentwith those scattered from different atomiccolumns because of time difference.Therefore columns separated laterally areimaged incoherently, that is, STEM image isalso transversally incoherent.

The above-argument about ‘coherency’is based on quantum physics and very strict[32]. However, according to classic wave

Figure 3. Intensities of Bragg scattering (BS) and thermal diffuse scattering (TDS), anddifferential cross section of TDS. (a) Ewald construction for convergent electron beams withsemiangle α=6 and 12 mrad. (b) Intensities of BS and TDS for a single N, Ga and In atoms.(c) Differential cross sections or intensities detected in a range of 30-190 mrad (shown in (b))of BS and TDS for a single N, Ga and In atoms.

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optics the waves that can interfere with eachother used to be defined as being coherent.When different objects (for example, atoms)are illuminated with a plane wave, the scatteredwaves from the objects, which are consideredto be resources, are coherent because theyhave a definite phase relationships. A perfectincoherent image results from a self-luminousobject. Therefore, the incoherent imaging canbe obtained when the convergent beamilluminates only a single object, because it emitsthe scattered wave as a self-luminous resource.In case of atomic-resolved electron micro-scopy, whether it is coherent or incoherentimaging depends on whether the Airydiscs of neighboring atomic columns havepermanent and definite phase relationships ornot, applying the concept of Lord Rayleigh[1]. This is another and prevailing answerfor why (HAADF) STEM is incoherentimaging. This definition is correlated with thetransversally incoherent imaging due to thebeam scanning mentioned above.

The incident electrons are scattered byatoms in the specimen as Bragg scattering andTDS. As seen in Figure 3a, reciprocal pointsin the zero-order Laue zone (ZOLZ) crosswith one of Ewald spheres within a scatteringangle of 2α , where α is a semiangle of theprobe, and strong Bragg reflections (as theconvergent beam electron diffraction)are caused, accordingly [17]. At higher angles(>> 2α), reciprocal points in ZOLZ and lowhigher-order Laue zone are not on any Ewaldsphere, which means that no strong Braggreflections occur. Furthermore, the intensityof the Bragg scattering reduces greatly withincreasing scattering angle as shown in Figure3b, comparing with TDS intensity. The incidentelectron probe shown in Figure 1 scans overthe surface of the specimen in STEM mode.The HAADF-STEM image is the focalsignal, as a function of the probe position, byelectrons scattered in a high-angle range andcaptured on the annular detector. Thedifferential cross section s or the intensity of

Figure 4. Formalism of HAADF-STEM imaging. Ro: the center of the beam probe. k||:transverse component of each plane wave having a wave length λ within the incident electronbeam. Aj(Ri-Ro, z): the wave function at a depth of z in i-column, due to the probe located atthe surface (Ro, 0). t: specimen thickness.

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TDS recorded with the detector is givenby an equation shown in Figure 3. As shownin Figure 3c, the TDS cross section is ap-proximately proportional to the square of theatomic number Z, which comes from theRutherford scattering for the electron. TDSis an origin of unfavorable background,particularly in a high angle range, in electrondiffraction and X-ray diffraction, but it isactively used in HAADF-STEM imaging.Bragg reflections scarcely influence HAADF-STEM imaging. We have confirmed this bysimulation of the high-angle DF and middle-angle DF images, which explained theobserved images of Si crystals [12].

Based on this principle, one can writeSTEM image simulation programs. Wedeveloped a program for HAADF-STEMsimulations based on the Bethe method.[8, 9]. The probe function and the imageintensity can be given by the equations shownin Figure 4. Then, we proposed an algorithmfor first calculations of Bragg scatteringimages and TDS images [12], which is basedon the Bethe method using two kinds ofoptical potentials [43] and available to aroutine work. The important optical para-meters in HAADF-STEM imaging are thesemiangle of the electron probe α, thedefocus of the probe forming lens Δf andthe angle range of the annular detector D aswell as the spherical aberration coefficientof the lens Cs and accelerating voltage V ofthe electron microscope used. These effectswere examined and discussed in detail in ourprevious papers [8-20]. A typical example ofthe effects is artifacts in HAADF-STEMimages, which are dealt with in the nextsection.

2.2 Artifacts in HAADF-STEM ImagesIt was believed that HAADF-STEM

images exhibit strong atomic number (Z)contrast and can be directly inverted to the

object without the need for image simulation,because the phase problem is eliminated [1].However, we found experimentally andtheoretically that bright spots appear onchannels between the atomic columns in [110]Si images [11,12] and extraordinary intensityof spot contrasts occurs on light columns in[001] SrTiO3 images [13], when the incidentprobe is focused to have strong subsidiarytails around a sharp central peak. Figure 5reproduces some of simulated images of [110]Si crystals [19]. ‘Total’ means STEM imagesto be observed at given imaging conditionsshown by parameters; detection range D,defocus value Δf and thickness t. The imagescalculated for D=60~160 mrad are ofHAADF-STEM and the images forD=18~48 mrad are of middle angle (MA)ADF-STEM. The Si-dumbbells arecompletely resolved but the artificial spotsappear in the HAADF-STEM images atΔf = –70 nm. It was explained from wavefield calculations that this is caused by the sharpprobe but having strong subsidiary maximum,which is shown in Figure 6a [12,19]. Thereason is that when the incident beam islocated on channels between the atomiccolumns, the subsidiary tail forms strong wavefields along the neighboring columns to emitTDS. These artifacts might mislead thestructure analysis unless one finds them fromimage simulation or predicts them fromcalculation of the probe function. The probeat Δf = –30 nm is so wide (having noappreciable subpeaks) that cannot distinctlyresolve Si-dumbbells.

The shape of probe depends on Cs, Δfand α, as seen from formulae in Figure 4.An optimum imaging condition, whichmakes the effect of diffraction aberrationand spherical aberration minimum, isαopt=21/2(λ Cs)

1/4 and Δfopt = –(λ Cs)1/2., and

provides the most quality HAADF-STEMimage. Probe functions and simulated images

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Figure 5. Simulated high-angle ADF images (a) and middle-angle ADF images (b) of [110]Si crystals 20 nm and 60 nm thick, focused at Δf= –30, –50 and –70 nm using a semiangle ofα=12 mrad with a probe forming lens of Cs=1.0 mm at 200 keV. A defocus ofΔf= –50 nm corresponds to the optimum focus of this lens. Images due to Bragg scattering(BS) and TDS were calculated separately, and then the total image which means an image to beobserved was evaluated. CPU time for any one BS image is about 5 min on a PC (CPU ofIntel Pentium 4 (2001) 2 GHz/400 MHz System Bus, 256 KB Cache). The CPU time for anyone TDS image is twice as long as that for the BS image because it is necessary to calculate theintensities using two kinds of optical potentials. Additional calculation of an image at differentthickness or focus takes about 11 s. Then, these HAADF and MAADF image simulationswere done within 20 min [(5 min + 11 s 5) + (10 min + 11 s 5)].

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* Private communication from Prof. H. Kurata, Institute for Chemical Research, Kyoto University.

around the optimum conditions are shownin Figure 6b and Figure 7[19], respectively. Asfar as the lens of Cs as large as 1.0 mm isemployed, the appearance of the artificialspots is inevitable.

Cs-correctors have now been developed[44,45]. (A recent STEM instrument installedat Institute for Chemical Research, KyotoUniversity, has achieved a corrected value ofCs of -0.025 mm and a resolution power Rof ~0.09 nm for α=23 mrad, for the lenswith Cs=0.5 nm and R=~0.14 nm for α=11mrad *). In a previous paper, we discussedthe resolution of the ideal lens in terms ofthe contrast transfer function [17]. The Sidumbbells are completely resolved in an imagecalculated for the lens of Cs=0.1 mm, asshown in Figure 7b. However, a smalldeviation from the optimum focus, particularlyto over-focus side, forms very low contrastimage, whose Michelson visibility, defined asC= (Imax–Imin)/(Imax+Imin), is as small as 0.133for the [110] Si 60 nm thick, while C=0.566at the optimum focus. This occurs with theillumination of larger area, which is causedby focusing the probe with the large semiangleabove or below the surface of the crystal (seeFigure 6b). The Cs correctors allow large αfor high resolution, but may cause unfavorableBragg scattering in HAADF-STEM images.Certainly, the Bragg scattering for the 0.1-mmCs lens influences the resultant images morethan that for the 1.0-mm Cs lens does in thesame detection range of D=25~45 mm, asseen in Figure 7. However, HAADF-STEMgenerally uses the detector in high-angle range,and the strong incident probe due to use ofthe large semiangle allows us to make thedetection range much higher, which wouldeliminate the coherent scattering influence.

Concerning the dependence of D, weshowed experimentally and theoretically that

the contribution of the Bragg scattering is sosmall that can be neglected in HAADF-STEMimage, but that it cannot be neglected inMAADF STEM image [11]. In Figure 5, thesimulations of Bragg scattering images andTDS images are shown, separately, togetherwith the total images, for D=60~160 mradand 18~48 mrad (and also in Fig 7, thesimulations for D=25~45 mrad). Themultiplicity of intensity indicated in figuresshows that the Bragg scattering, which formsvery complicated image contrast dependingon focus and thickness, contributes moregreatly to the total images as D is settled insmaller angle range.

Each atom ejects TDS electrons,depending on the dynamical wave field ofthe incident electrons in the crystal. Thedynamical wave field is represented by theequation Aj in Figure 4. It oscillates andattenuates in the crystal. Since the contrast ofthe HAADF-STEM image is given by a simplesum of intensities of TDS electrons collectedon the detector, it monotonously increaseswith increasing thickness t [11], as seen inFigures 5 and 7. The influence of defocusingconditions and thickness on the experimentalHAADF-STEM image was also illustratedusing ceramic materials [16].

The lattice distortion around precipitatesor substitutes influences the induced wavefield in the crystal and causes unexpectedimage intensity from the simple Z-contrast,accordingly. The effect of the lattice distortionon the HAADF-STEM images was examinedusing SrTiO3. It should be taken into accountfor the image simulation of quantitativecomposition analysis [10,13] (see Figure 12).It was also found that a small tilt of the crystalzone axis with respect to the coma-axis ofthe probe-forming lens causes asymmetricdumbbells in the [110] Si image [14].

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Therefore, special care to the beam alignmentor the image simulation is needed forquantitative HAADF-STEM applications suchas the determination of crystallographicpolarity or the compositional analysis.

Thus, HAADF-STEM image contrastdoes not always depend on the number oratomic number of atoms in columns, or doesnot always show Z-contrast. The imagesimulation allows correct interpretation andquantification of atomic-scale HAADF-STEM images.

2.3 HAADF-STEM Image ProcessingAn experimental raw HAADF-STEM

image can be processed by noise filtering

through filtering and reconstructing of itsdiffractogram, which is a way generally usedfor HRTEM investigation. The processedimage is served to compare with the calculatedimage. Recently, Re nik et al. [46] havedeveloped a new method for processingdistorted HR-STEM images which is basedon finding the displaced vertices in theexperimental image and warping togeometrically correct reference grid of theobject. We applied this method to analysis ofthe ZnO:Sb structure [20, 22].

HAADF-STEM image intensity I(R)may be given by convolution between theprobe function P(R) and object function(projected atom structure) O(R), that is,

Figure 6. Various probes. (a) Calculated probe functions of α=12 mrad focused atΔf = –70, –50 and –30 nm with the lens of Cs=1.0 mm at 200 keV. (b) Calculated probefunctions of α=10 mrad focused at Δf= –50, –40 and –60 nm with a lens of Cs=1.0 mm at200 keV (left) and of α=18 mrad focused at Δf= –16, –6 and –26 nm with a lens of Cs=0.1 mm(right). The one sides of the probes are presented. The optimum condition is αopt=10 mradand Δfopt= –50 mm for Cs=1.0 mm, and αopt=18 mrad and Δfopt= –16 mm for Cs=0.1 mm.Calculations were made using a formula indicated in Figure 4.

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Figure 7. Simulated middle-angle ADF images of [110] Si crystals 20 nm and 60 nm thick,focused at Δf= –40, –50 and –60 nm using α=10 mrad with the lens of Cs=1.0 mm at 200keV (a) and at Δf= –6, –16 and –26 nm using α=18 mrad with the lens of Cs=0.1 mm (b).The CPU time for the simulation of images in (a) is almost the same as the simulation of theimages shown in Figure 5. Since the semiangle is large, it takes a long time for the simulation in(b). The CPU time for a BS image is about 2 h and that for a TDS image is about 4 h.Additional calculation of an image at different thickness or focus takes about 11 s. Then, allthese calculations were done in about 6 h [(2 h +11 s 5) + (4 h + 11 s 5) ].

I(R)H”P(R)*O(R), under an approximationof nondispersive Bloch waves. Then, anexperimental HAADF-STEM image that isdeformed by the incident probe can bededuced to the object function by the decon-

volution, O(R)= -1{ [I(R)]/ [Pe(R)]},where and -1 represent Fourier and inverseFourier transformation, respectively (Figure 8).We have developed a deconvolution proces-sing technique, where the defocus value

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assigning the effective probe function Pe(R)is determined using the maximum entropymethod [15]. Images having unresolved Sidumbbells or the artificial bright spots areretrieved to the projected atomic structure(Figure 9). Thus, the deconvolution processingis completely different from any conventionalimage processing method such as noisefiltering through Fourier transform,smoothing or averaging of images, whichcannot eliminate the influence of the probe,for instance, the artificial spots.

HAADF-STEM images recorded withfield-emission electron microscopes wereoften deformed by instrumental andenvironmental instability. The deconvolutionprocessing was applied to retrieve asystematically distorted image by referring aHRTEM image [18]. Figure 10 shows adeconvolution processing which successfullyderived the Z-contrast image of a Zn2Sb-monolayer inversion twin-boundary from adistorted HAADF-STEM image of Sb2O3-doped ZnO.

2.4 Quantitative Composition Analysis byHigh-resolution HAADF-STEM

Sections 2.2 and 2.3 imply that we havetwo approaches to the structural and chemicalanalysis by HAADF-STEM; the imagesimulation and the retrieval image processing.These two approaches have been discussed,illustrating images of Sb-rich inversionboundaries in ZnO ceramics [20]. It wasshown that the artifacts may mislead thestructural analysis unless one finds them fromimage simulation or eliminates them by anappropriate image processing. Paradoxicallyspeaking, the simulation of HAADF-STEMimages provides the structural and composi-tional information of every atomic column

along the incident beam. In fact, we havereported HAADF-STEM concentrationanalyses of As atoms along every [110] columnin As-doped Si wafers (Figure 11) [8], and Biatoms along every [001] column in theboundary layer in SrTiO3 ceramic condensers(Figure 12) [9,10], with the aid of the imagesimulation.

3. ELECTRON MICROSCOPY INVESTIGATIONSOF GAN-BASED LIGHT EMITTING DIODES ANDLASER DIODES

The lifetime of LDs with multipleInGaN/GaN quantum wells has attained tomore than 15,000 h [38, 47]. This was achievedthanks to the epitaxial lateral overgrowth(ELOG) method for a GaN:Si layer on thesapphire substrate, which reduces dislocationdensity in the GaN:Si layer [48,49], and to thedevelopment of strained-layer superlattices(SLSs) of AlGaN/GaN for cladding [38].The nanostructures of MQW InGaN/GaNactive layer and SLS cladding layers greatlyinfluence the final laser properties. However,there have been very few structuralinvestigations of the InGaN/GaN layers andAlGaN/GaN layers. Figure 13 illustrates oneof the LD devices we used for electronmicroscopy observations [50]. Figure 14reproduces a HAADF-STEM image of aprototype ultra-violet LED wafer [35].Al0.005In0.02Ga0.975N QWs (bright) andAl0.12In0.005Ga0.875N:Si barriers (dark) aredefinitely resolved in the MQW active layer,and n-type and p-type cladding layers ofAl0.15Ga0.85N/GaN SLSs can be seen. It maybe noted that the results shown in section 3would not be obtained by any conventionalmicroanalysis technique such as HRTEM alone,but were successfully achieved by usingHAADF-STEM.

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Figure 8. Formalism of deconvolutionprocess. and -1 represent Fourier and inverseFourier trans-formation, respectively.

Figure 9. Deconvolution processing of HAADF-STEM images. HAADF-STEM imagecan be regarded as a convolution of the object function (projected atom structure) and theeffective probe function, which is schematically shown for two typical probes. The effectiveprobe function is not the real one. Observed images in (a) were retirieved to Z-contrastimages in (c) by the deconvolution. The effective probe functions used for the deconvolutionwere obtained from Δ f corresponding to the maximum entropy values shown in (b). (Theimages were taken with JEM 2010F-TEM/STEM (Cs=1.0 mm), at V=200 keV, α=6 mrad,and D=50~110 mrad.)

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Figure 10. Deconvolution processing of a [01 0] HAADF-STEM image of an Sb-rich basalplane inversion boundary in Sb2O3-doped ZnO ceramics. Left: ZnO in the matrix. Right:Inversion boundary. HAADF-STEM images (a) were additionally processed using the Savitzky-Golay smoothing. The process includes correction of the diffractograms of HAADF-STEMimages (c) by referring to the diffractograms of HRTEM images (d), as a pre-treatment ofthe deconvolution. The corrected diffractogarms (e) were used as [I(R)] for the deconvolution.The reconstructed images (f) were obtained by inverse Fourier transformation of (e), and arethe representatives of the experimental images, noise-filtered but including the effect of theprobe. The most probable defocus for the images was determined to be Δf= -36 nm fromthe entropy calculation for the matrix image. Retrieved HAADF-STEM images (g) wereobtained by deconvolution using a probe at Δf= -36 nm, and exhibit Z-contrast, indicating Zncolumns (bright spots) and Sb columns (brighter spots). FT: Fourier transformation. IFT:inverse Fourier transformation. (The images were taken with JEM-2010F TEM/STEM(Cs=0.48 mm), at V=200 keV, α=10 mrad, and D=100~220 mrad.)

Figure 11. Two-dimensional distribution of As atoms doped in aSi crystal. (a) Experimental (noise-filtered) [110] HAADF-STEMimage of a pure region in the Si wafer. Si dumbbells are notcompletely resolved under this imaging condition. (b) Experimental(noise-filtered) [110] HAADF-STEM image of a region implantedwith 1.9 at. % As. Insets are evaluated number of As atoms substitutedfor Si atoms on the 65 atom sites along each [110] atomic column inthe crystal 25 nm thick. (c) The most fitted simulated intensity profileswith experimental profiles, along rows 1-8 in (a and b). Experimentalintensity profiles are not shown in this figure (See ref. 8). Si dumbbellsin (a) are symmetric (see fine curves), which means the atom sites areoccupied only by Si. Si dumbbells in (b) are asymmetric due to thesubstitution of As atoms (see thick curves). The thickness and thenumbers of As atoms in (b) were determined from the simulationof the intensity profiles. (The images were taken with JEM 2010F-TEM/STEM (Cs=1.0 mm), at V=200 keV, Δf = -50 nm, α=6mrad, and D=50~110 mrad.)

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Figure 12. Atomic-scale quantitative elemental analysis of boundary-layer semiconductingSrTiO3 ceramic condenser. (a) TEM image of a grainboundary having Bi diffusion layers ofinsulators. (b) Atomic resolved (001) HAADF-STEM image near the grain edge. (c) Enlargedimage of a part of (b). (d,e) Bi concentration in Sr and Ti(O) columns near the edge, andobserved and calculated HAADF image intensity of Sr, O, and Ti(O) columns. The intensityprofiles are along X-Y on the (100) Sr-O-Sr layer and X’-Y’ on the (100) O-Ti(O)-O layer in(c). The observed profiles were averaged along (010) layer over the area in (c). The calculatedprofiles from a preliminary simulation which took no account of the lattice distortion are alsoshown together with the Bi concentration used in this preliminary simulation (in bracket).(The image was taken under the same condition as that shown in Figure 11 with JEM 2010F-TEM/STEM (Cs=1.0 mm)).

Figure 13. (a) Schematic structure of a violetLD with In0.25Ga0.75N (2.5 nm)/GaN (8nm)MQWs and Al0.14Ga0.86N/GaN SLS claddinglayers, prepared by production-scalemetalorganic vapor phase epitaxy. (b) Roomtemperature emission spectra of the 10μm× 10 μm ridge-waveguide InGaN LDmeasured under pulsed operation. At theinjection pulsed current above a thresholdcurrent of 0.87 A, a strong stimulated emissionappears at around 415.5 nm with a FWHMof 0.2 nm, as well as two small emission peaksbetween 416 and 417 nm. (Ref. 50).

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3.1 V-defects in InGaN MQWs and LightEmission Mechanism of GaN-basedDevices

Even low magnification HAADF-STEMimages gave certain information about thestructure and composition of the ultrathinInGaN layer, as seen in Figure 14. The imagesshown hereafter are from prototypes of theLED or LD devices where some parts ofthe heterostructures were not deposited.Figure 15a shows a low magnified image ofcapped MQW In0.25Ga0.75N (2.5 nm) andGaN (13.9 nm) layers deposited on underlyingGaN:Si layer. Bright bands are In49Ga31N7

layers and dark ones are Ga31N7 layers, aspredicted from Figure 3c. This was confirmedby energy dispersive X-ray spectroscopy(EDX) [26]. High-resolution HAADF-STEMimage, processed by the deconvolutionmethod [15], clearly defined the interfacebetween InGaN and GaN layers at the atomicscale [26], as seen in Figure 16a.

Threading dislocations (TDs), whichwere formed by the big lattice misfit betweenthe GaN and sapphire, are seen with brightcontrast due to large distortion around thedefects (Figure 15a). HAADF-STEM alsorevealed V-defects or inverted hexagonalpyramid defects (IHPs). The names comefrom the empty V-pit in hexahedron conesharp, with six sidewalls on {101 } planes,which nucleates at a TD extending along the[0001]-axis growth direction, in the InGaNlayers [51-53]. We demonstrated that the V-defects grow in the form of a thin six-walledstructure with InGaN/GaN {101 } layers(Figures 15b and c) [28]. This structure hadbeen predicted by Wu et al. [52]. Sharma et al.[54] had reported the InGaN MQWs endingabruptly at the V-defect interfaces withoutthese thin InGaN/GaN layers. Therefore, wewere the first to establish the structure of V-defects having thin sidewalls of InGaN/GaNQWs, which are different from the main c-

plane QWs. Then, we succeeded indistinguishing the MQW In0.25Ga0.75N (2.5 nm)and GaN (13.9 nm) layers in a secondaryelectron image and a backscattered electronimage in an HR-FESEM, and confirmed thethin six-walled structure of the V-defect [40].We also found that the V-defects start even atIn-rich dots, as seen at B in Figure 15b [28].On the basis of these observations, we haveproposed a formation mechanism of the V-defects, taking into account the growth kineticsof the GaN crystal and the masking effect ofIn atoms on the analogy of ELOG [33, 36].The In-rich area at B in Figure 15b may beregarded as an example of the masks.

A green LD having thick QWs andbarrier layers of In0.18Ga0.82N (4 nm)/GaN(40 nm) has been observed [36]. Figures 15dand e are a CTEM image and a HAADF-STEM image of a V-defect in the QWs ofthe green LD, respectively. The HAADF-STEM image provided undoubted evidenceof the thin InGaN/GaN {10 1} MQWwalled structure of the V-defect. A bright spotin Figure 15d or strong contrast spot in Figure15e that appears at the apex of the V-defectindicates an In-rich region. Indium atoms weretrapped and segregated in the strained field(Cottrell atmosphere) around the core of theincorporated TD and then formed a smallmask for the growth of V-defect. The curvedcorners of the thin MQW walls with the mainMQWs seen in Figures 15d and e wereexplained on our formation mechanism ofV-defects [36].

A HAADF-STEM image (Figure 16a),processed by two-dimensional smoothing anddeconvolution, provides precise positions ofthe atomic columns (Figure 16b) and clearatomic number dependent contrast, therebyallowing us to map both the strain field (Figure16c) and In atom distributions (Figure 16d)[27]. The lattice expanded largely along the caxis as seen in Figure 16c but hardly in the c

510 Chiang Mai J. Sci. 2008; 35(3)

plane in the In0.25Ga0.75N QWs. The maps,thus, directly led to that there is a localfluctuation of In atoms in the InGaN layers,and that the In-rich regions, considered tobe quantum dots (QDs), correspond withlattice expansion along the c axis. This was thefirst direct evidence of local phase separationor QDs.

The QDs are observed as diffractioncontrast caused by the strain field (Figure 15d).Several reports, including the paper by Y.Narukawa et al. [55] who first proposed theQDs for explanation of the high lightemission efficiency, had assumed indirectly theIn concentration from the lattice strain onlyusing the Vegard law approximation. Theyexplained the high emission efficiency of

Figure 14. HAADF-STEM image of a wafer of ultra violet LED. GaN:Mg (20 nm) contactlayer, p-AlGaN/GaN (0.1 μm) SLS cladding layer, AlGaN:Mg (50 nm) electron blockingand capping layer, AlInGaN (2.5 nm)/AlInGaN:Si (7.5 nm) MQW layer, AlGaN:Si (50 nm)carrier blocking layer, the n-AlGaN/GaN (0.1 μm) SLS cladding layer, and a part of theGaN:Si (4μm) contact layer are clearly distinguished. The Al0.005In0.02Ga0.975N QW layers andAl0.12In0.005Ga0.875N:Si barrier layers in the MQW are definitely resolved, appearing as brightbands and dark bands, respectively. The indicated value is a nominal thickness of each layer.(The image was taken with Tecnai 30 (Cs=1.2 mm), at V=300 keV, α=15 mrad, and D=36~181mrad.)

InGaN-based LED to be mostly due to thelarge localization of excitons because thepathways of nonradiative recombination arehindered once the excitons are captured in asmall volume. However, the mechanism ofthe high emission of InGaN-based LEDs andLDs has not been fully established, at thepresent becoming more and more confusedby some reports doubting the In-rich quantumdots and their effect [56, 57]. In any case, theside-walled InGaN/GaN layers mightstrongly correlate with unfavorable weak long-wavelength emissions like the 416-nm and417-nm emissions seen in Figure 13b [33, 36,52]. The detection and control of these V-defects are, therefore, very important forfabrication of these LEDs and LDs.

Chiang Mai J. Sci. 2008; 35(3) 511

3.2 Observations of Strained-layer AlGaN/GaN Superlattice Cladding Layers

The claddings of AlGaN/GaN strained-layer superlattices (SLSs) have been used forthe following two reasons. Thick AlGaNcladding layers need for optical confinement,

but cracks and dislocations induced by thelattice mismatch between GaN and AlGaNmake the formation of the thick claddinglayers impossible. It is the first reason todepress the formation of these defects bystrain relief of the AlGaN/GaN SLSs [38].

Figure 15. V-defects in MQWs. (a) Low magnified HAADF-STEM image of In0.25Ga0.75N(2.5 nm) / GaN (13.9 nm) MQWs. Ten bright stripes parallel to the basal plane are InGaNlayers. V-defects nucleate at the threading dislocations in the MQWs layer. (b) EnlargedHAADF-STEM image in the same specimen. V-defect A is the first image that was revealedto have the thin six-walled structure of InGaN/GaN {101 } layers (Ref [28]). V-defect Bnucleated at a large bright spot, which shows the In rich region. (c) Schematic representationof the structure of V-defect. (d) CTEM image of V-defect in In0.18Ga0.82N (4 nm)/GaN (40nm) MQWs. Arrowheads indicate the curved corners of thin MQWs with main MQWs.Local lattice-strained spots, which are In-rich spots or quantum dots, can been seen in thediffraction contrast along the main QWs. (e) HAADF-STEM image of the same area. TheIn-rich spots are confirmed as bright spots in the main QWs. A bright spot in (d) and strongcontrast spot in (e) appearing at the apex of the V-defect are regarded as the In-rich mask forthe formation of the V-defect. (The images were taken with Tecnai F30 (Cs=1.2 mm) operatedat V=300 keV. For HAADF-STEM, α=26 mrad and D= 36 ~190 mrad.)

512 Chiang Mai J. Sci. 2008; 35(3)

Figure 16. (a) Experimental deconvolution-processed high-resolution HAADF-STEMimage of an InGaN QW in the In0.25Ga0.75N (2.5 nm)/GaN (13.9 nm) layer. The defocus ofthe probe-forming lens was evaluated to be Δf = -44 nm in deconvolution process. (b)Projected atomic column positions derived from (a). The distortion hardly occurred along the[1 00] direction. (c) Strain field maps along the [0001] direction. Arrowheads show the interfacesbetween GaN and InGaN layers. (d) Two-dimensional In atom distribution. There is localfluctuation of In atoms in the InGaN layers, and the In-rich regions enclosed, considered asquantum dots, cause large expansion along the [0001] direction. (The image was taken underthe same condition as that shown in Figure 15 in Tecnai F30 (Cs=1.2 mm)).

There are very few reports on thestructural analysis of AlGaN/GaN SLSs. Itwas confirmed by image simulation thatHRTEM images exhibit no difference incontrast between Al0.14Ga0.86N and GaN inthe cladding (Figure 17a) [31,34]. The TEMdiffraction contrast due to small strain fieldappears along their interfaces but TEM imagesnever provide the real widths of AlGaN orGaN layers. We have observed the SLSs(Figure 17b) which are 200 coupled layers ofn-Al0.14Ga0.86N (3 nm) and n-GaN (3 nm) onthe n-GaN:Si grown directly on a (0001)sapphire substrate, and distinguished theAl13Ga31N7 and Ga31N7 layers as dark andbright fringes, respectively, in a [10 0]HAADF-STEM image (Figures 17c) [34].

From a HAADF-STEM image shownin Figure 17e, the averaged thicknesses of theAlGaN and GaN layers were determined,with the aid of image processing, to be2.24 0.09 nm and 2.34 0.15 nm, respectively,which corresponds to nine atom layers in thec direction [34]. The AlGaN lattice shrunk for~4 % along the c direction while no changewas measured in the basal plane, as comparedwith the GaN lattice. This is a direct illustrationof the strained lattice in the superstructurecladding layer. Namely, a good lattice matchingin the basal plane between the AlGaN andthe GaN suppresses the generation of misfitdislocations on the Al0.14Ga0.86N/GaNinterfaces in the SLS as well as on the interfacebetween the Al0.14Ga0.86N and GaN:Si layers.

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Figure 17. N-type strain Al0.14Ga0.86N (3 nm)/n-GaN (3 nm) superlattice cladding layer thatwas grown on the n-GaN:Si deposited on a (0001) sapphire substrate. (a) HRTEM imagesof AlGaN and GaN layers. The AlGaN and GaN layers cannot be distinguished in the HRTEMimages. (b) CTEM image of the whole specimen. (c) HAADF-STEM image of the wholeSLS cladding layer. 200 pairs of AlGaN (dark bands) and GaN layers (bright bands) areclearly resolved. The AlGaN layers are numbered. (d) BF-STEM image of the same area.Dislocations are visible in strong diffraction contrast. (e) HAADF-STEM image, distinguishingbetween the AlGaN (dark stripes) and GaN layers (bright stripes). (f) HAADF-STEM imageof the area I in (b). Dislocations are seen, exhibiting bright contrast due to lattice distortion.Note a dislocation turning its course from running along the c axis to lying in the basal plane.It apparently cannot reach the MQW. As a result the number of defects in MQW is reduced.Semi-quantitative energy dispersive X-ray spectroscopy (EDX) nanoanalysis was performedalong A, B, C, and D. (Observations were performed in JEM-2010F TEM/STEM (Cs=0.48mm). V=200 keV. Δf = the optimum condition. For HAADF-STEM, α=10 mrad andD=100~220 mrad.)

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Semi-quantitative EDX nanoanalysis forthe areas B and D in Figure 17f confirmedthe chemical composition of the Al0.14Ga0.86N[34]. Dislocations run either parallel orperpendicular to the c axis. They appear asbright contours in HAADF-STEM images asa result of random static atom displacementaround the dislocations, while they appear asdark contours due to diffraction contrast inBF-STEM images (Figure 17d). EDXnanoanalysis also revealed that the area Aalong a TD and the area C along a dislocationin the basal plane were Al-rich, suggesting theprecipitation of Al along the dislocations.Figure 17f shows TDs reverted from runningalong the c direction to running in the basalplane. The converted dislocations would notreach the upper MQW layer. This evidentlyshows an important role of the SLS insuppressing the defect propagation, whichresults in the overall reduction of structuraldefects in the active MQW layer.

The same SLS sample was examined inthe FE-SEM [39]. The fringes due to SLSswere observed in the secondary electronimages taken at voltages of 10~25 keV, butthey could not be detected in the backscatteredelectron images. This is obvious because themass difference between Al0.14Ga0.86N andGaN is so small that the image contrast dueto the back scattered electrons or Rutherfordscattered electrons is undetectable. Thesecondary emission yield is greatly dependingon the surface state of materials so that wemight resolve the Al0.14Ga0.86N and GaNlayers in the secondary electron images. Wealso observed the p-Al0.14Ga0.86N(3.0 nm) /p-GaN(3.0 nm) structure at the same imagingconditions. Any fringe was detected neither inthe secondary electron image nor in thebackscattered one. Difference in the secondaryemission yield between p-Al0.14Ga0.86N and p-GaN seems to be very small. Then, we trieda HAADF-STEM observation of an SLS

cladding including thirty four pairs ofp-Al0.1Ga0.9N and p-GaN:Mg layers [35].The Al0.1Ga0.9N layers and the GaN layerswere distinguished as dark and brightbands, respectively. The average thickness ofthe pair was roughly estimated to be ~12 nm,which corresponds to 48 atom layers in the cdirection.

3.3 Ultra-high Density InGaN QuantumDots

The performance of LDs has beenexpected to greatly improve if the density ofQDs can be made to far exceed that ofdislocations. Therefore, structures of the activelayer with QDs, instead of QWs, have beenpursued. One approach for fabricating the 3DInGaN QDs is the deposition of siliconanti-surfactant or SiNx nano-masks, whichaltered the morphology of the InGaN filmsfrom that of step flow to that of a three-dimensional island. We have observed a deviceof ultra-high density InGaN QDs [37] thatwas prepared by Tu et al. [60]. It exhibitedstrong PL emission at room temperature.Figure 18a shows its structure together withgrowth condition. Masks with a rough SiNxlayer were formed on the GaN:Si underlyinglayer, at flow rates of 5 slm for NH3 and 50sccm for diluted Si2H6. The deposition of apair of the SiNx and InxGa1-xN was repeatedusing a spacer of the GaN:Si barrier layerdeposited at 1000oC, and finally the lastInxGa1-xN layer was capped with an un-doped GaN layer. All the layer thicknessesshown in Figure 18a are nominal values.Figure 18c shows a low magnified HAADF-STEM image of the specimen, in which theareas for EDX analysis are indicated. Figure18d shows EDX spectrum in the area P, whichcomprises emissions from In, Ga, N, and Si.Figures 18e and f (or Figures 18g and h) arethe line profiles of HAADF-STEM imageintensity and In-Lβ emission intensity along

Chiang Mai J. Sci. 2008; 35(3) 515

A-B (or C-D), respectively. The bright areaalong C-D in Figure 18c might be a layercontaining InGaN QDs (QDs layer). FromFigure 18f the width of this layer is estimated

to be ~15 nm. Figure 18h indicates that veryroughly estimated width of the QDs is 10nm on the C-D.

Figure 18b shows a HAADF-STEM

Figure 18. Ultra-high density InGaN quantum dots. (a) Structure and growth condition ofthe InGaN quantum dot device. (b) HAADF-STEM image near the top of the specimen.The layer of SiNx masks appears as a dark line. The area between two dotted lines is a QDlayer which comprises the InGaN QDs and is capped with GaN. (c) HAADF-STEM imagein which the areas for EDX analysis are indicated. (d) EDX spectrum in the area P (a probesize of ~0.5 nm). (e, f) HAADF-STEM intensity profile and Indium Lβ intensity profile inEDX analysis, along the line A-B (~1 nm wide). (g, h) HAADF-STEM intensity profile andIndium Lβ intensity profile, along the line C-D. (i) HRTEM image near the top of the specimen.White arrowhead indicates SiNx masks and black arrowheads indicate InGaN QDs (j)Enlarged image of the area enclosed by the square in (i), which insets the enlarged image ofthe area enclosed by the rectangle. (Observations were performed in Tecnai F30 (Cs=1.2mm) operated at V=300 keV. For HAADF-STEM, α=15 mrad and D= 36~181 mrad.).

516 Chiang Mai J. Sci. 2008; 35(3)

image near the top of the specimen. The darkline is identified, due to the small thermaldiffuse scattering cross-section of Si14 (andN7), as the projection of a layer composedof SiNx mask islands. The height of the SiNxmasks is roughly estimated to be less than 2nm from the thickness of the dark line. TheInx

49Ga1-x31N7 QDs are observed as bright

triangles, which look peaks in a mountainchain, in the QDs layer between two-dottedlines. Figure 18i shows an HRTEM image nearthe specimen edge, where a part of thecapping layer was removed during the ion-milling. Quite high QDs (indicated by blackarrowheads) are seen on the SiNx mask layer(indicated by an white arrowhead). The darkcontrast for the QDs may be caused bydiffraction effect of the high structure ampli-tude of In and large lattice strain. The rectangleframe in Figure 18i encloses an area containingthe SiNx layer and a QD and the square frameencloses an area in the GaN barrier layer. InFigure 18j the former area is inset on the latterarea. The SiNx mask surely has a heavilystrained lattice. The images do not allow usto determine the crystal structure and thecomposition x of the SiNx. The lattice in theQD was coherently connected with the GaNlattice in the capping layer although it was alsoheavily strained.

The QDs can be regarded as nanoislandcrystals with the {10 1} side walls and a heightof several nanometers or more. This crystalhabit can be understood in taking account ofELOG or the crystal growth through masksat lower reactor temperature [33,36]. Thus,we can propose the structure for this three-dimensional InGaN quantum dots as the insetin Figure 18a.

In conclusion, functional devices, such asquantum well lasers, tunneling devices,random access memories, and high electronmobility transistors, usually comprise nanoscalemultilayer heterostructures that exploit

quantum confinement effects. Since the in situmonitoring in most processing equipment isstill absent, atomic-scale analysis is required forunderstanding the real structure in the finalproduct, including the thickness and thecomposition of each layer. Only then canimprovement of the functional properties andcontrol of the product’s quality be carried out.HAAD-STEM has become one of the mostpowerful analytical tools for characterizationof these nanostructures because it enables usto make atomically-resolved quantitativecomposition analysis. The other part of mylectures can be acquired through our reviewpapers [61-63].

ACKNOWLEDGEMENTSThanks are owing to collaborators,

particularly, coauthors of our papers cited inreferences, and also deeply to Dr. TorraninChairuangsri, Department of IndustrialChemistry, Chiang Mai University, formotivating me to write this paper.

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