Study of μmscale spatial variations in strain of a compositionally stepgraded In xGa1−x As/GaAs(001) heterostructureK. Rammohan, D. H. Rich, R. S. Goldman, J. Chen, H. H. Wieder, and K. L. Kavanagh Citation: Applied Physics Letters 66, 869 (1995); doi: 10.1063/1.113414 View online: http://dx.doi.org/10.1063/1.113414 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/66/7?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Cathodoluminescence wavelength imaging of μm-scale energy variations in InAs/GaAs self-assembled quantumdots Appl. Phys. Lett. 76, 3597 (2000); 10.1063/1.126718 Modulationdoped In0.53Ga0.47As/In0.52Al0.48As heterostructures grown on GaAs substrates using stepgradedIn x Ga1−x As buffers J. Vac. Sci. Technol. B 14, 3035 (1996); 10.1116/1.589060 Dislocation behavior in InGaAs step and alternating stepgraded structures: Design rules for buffer fabrication Appl. Phys. Lett. 67, 3632 (1995); 10.1063/1.115341 Lattice tilt and dislocations in compositionally stepgraded buffer layers for mismatched InGaAs/GaAsheterointerfaces J. Vac. Sci. Technol. B 10, 1820 (1992); 10.1116/1.586205 GaInAs solidus isotherms developed by the stepgrading technique J. Appl. Phys. 51, 5413 (1980); 10.1063/1.327495

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Study of mm-scale spatial variations in strain of a compositionallystep-graded In xGa12xAs/GaAs(001) heterostructure

K. Rammohan and D. H. Richa)Photonic Materials and Devices Laboratory, Department of Materials Science and Engineering,University of Southern California, Los Angeles, California 90089-0241

R. S. Goldman, J. Chen, H. H. Wieder, and K. L. KavanaghDepartment of Electrical and Computer Engineering, University of California at San Diego, La Jolla,California 92093-0407

~Received 17 March 1994; accepted for publication 1 December 1994!

The relaxation of strain in compositionally step-graded InxGa12xAs layers grown on GaAs~001! hasbeen examined with cathodoluminescence~CL! wavelength and linearly polarized imagingapproaches. A polarization anisotropy in CL is found, and this correlates with spectral shifts in thepeak positions of excitonic luminescence. Varying asymmetries in misfit dislocation densities fromtransmission electron microscopy are found to be consistent with themm-scale spatial variations instrain that is deduced from the CL. ©1995 American Institute of Physics.

The interest in lattice-mismatched III–V semiconductormaterials is driven, not only by the possibility of creatingoptoelectronic devices such as light modulators, lasers, anddetectors with tunable energy sensitivity, but also by the pos-sibility of integrating existing III–V devices with current Sitechnology. The approach is to create a defect-filtering bufferlayer that is grown between the surface device structure andthe substrate. Recent experiments with relatively thin~lessthan;1 mm thick! compositionally step- and linearly gradedbuffer layers have been successful in producing close to100% relaxed layers with threading dislocation densities lessthan;106 cm22. Such results have been reported for a va-riety of lattice-mismatched systems including Ge/Si,1,2

In0.5Ga0.5As/GaAs,3–5 and In0.4Ga0.6P/GaP.

6 However, withincomplete strain relaxation, such systems can exhibit an an-isotropic in-plane strain relaxation as measured by multiple-crystal x-ray diffraction5 and deduced from the nonuniformand anisotropic misfit dislocation densities that have beenobserved in plan-view transmission electron microscopy~TEM! studies.7

In this letter, we have performed an examination of spa-tial variations in strain and alloy composition of a step-graded InxGa12xAs/GaAs buffer layer heterostructure usingtwo new variations in the cathodoluminescence~CL! imag-ing technique. A unique combination of scanning linearlypolarized CL~LPCL!8 and CL wavelength imaging~CLWI!9

measurements were performed. In CLWI, the wavelength@lm(x,y)#, at which there is a peak in the intensity of aluminescence spectrum, is determined as a function of thespatial (x,y) position, and a false-color or greyscale imagedirectly mapping these wavelengths is generated.9 A NorthCoast EO-817 Gep- i -n detector was used to measure thesignal dispersed by a 0.25 m monochromator. An electronbeam energy of 20 keV and a beam current of 10 nA wereused to probe the sample, maintained at 87 K, for the CLmeasurements.

The sample studied was grown by solid source molecu-

lar beam epitaxy on a GaAs~001! wafer offcut 2° toward~011!. The structure consists of a four step-gradedInxGa12xAs buffer layer, each step dopedn-type~1018 cm23! and grown 2000 Å thick with nominal In molefractions of x50.05, 0.10, 0.15, and 0.20, respectively.Plan-view TEM was used to determine misfit dislocationdensities.

A CLWI micrograph of the step-graded structure isshown in Fig. 1~a!. The mapping oflm into the greyscalerepresentation is shown by the grey bar indicating the wave-

a!Author to whom correspondence should be addressed.

FIG. 1. CL wavelength imaging in~a! and local CL spectra in~b! for twodifferent positions. A scale showing the mapping of wavelengths of peak CLintensity into shades of grey is shown in~a!. The blue- and red-shifted localspectra in~b! were obtained from the spatial positions labeled B and R,respectively, with arrows in~a!.

869Appl. Phys. Lett. 66 (7), 13 February 1995 0003-6951/95/66(7)/869/3/$6.00 © 1995 American Institute of Physics

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length scale. Local CL spectra are shown in Fig. 1~b!; thesespectra were obtained while fixing the electron beam at typi-cal blue- and red-shifted positions, as indicated by the grey-scale representation forlm in the image of Fig. 1~a!. A shiftof ;14 nm ~;19 meV! is seen between these blue- andred-shifted regions. The full-width at half-maximum of bothspectra is;47 nm ~;64 meV!, and this large width resultsfrom CL contributions stemming from the different layers inthe buffer region, each of which has a different contributionto the overall spectra. The excitonic transitions occurring ineach of the four InxGa12xAs buffer layers are not resolved asa result of inhomogeneous broadening caused by localsub-mm random strain variations, a large density of defectsin the underlying InxGa12xAs layers, and fluctuations in al-loy composition.

Long streaks of constant grey shade are found to runalong the high symmetry110& directions in Fig. 1~a!. Thesestreaks correlate with the orientation and position of darkline defects~DLDs! of this sample, as observed in the LPCLimages of Figs. 2~a! and 2~b!. DLDs are typically observedin the monochromatic CL imaging of partially relaxedInGaAs films grown on GaAs.10 The LPCL images of Figs.2~a! and 2~b! were taken with the polarizer rotated to detectemission of light withE'@110# andEi@110# detection orien-tations at a wavelength of 956 nm~1296 meV!, whereE isthe electric field of the light. In order to emphasize polariza-tion variations in luminescence, the ratio of these images isdisplayed in Fig. 2~c!. The pixels in the ratio image at a(x,y) position are represented as log@I'(x,y)/Ii(x,y)#, whereI' andI i are the pixel intensities underE'@110# andEi@110#detection orientations, normalized to a 256 level greyscale.

The bright and dark regions in Fig. 2~c! correspond to inten-sity ratios,I' /I i , of ;0.9 and;0.6, respectively. The aver-age value ofI' /I i is 0.83, as measured from integratedLPCL spectra taken while the electron beam is rapidly scan-ning the entire region shown in Fig. 2~c!. It is our hypothesisthat the presence of bright and dark streaks~i.e., a nonuni-form intensity! in Fig. 2~c!, running parallel to the DLDs inFigs. 2~a! and 2~b!, reveals a polarization anisotropy causedby mm-scale variations in strain.

The strain-induced splitting of the heavy-hole~hh! andlight-hole ~lh! valence bands atk50 can be studied by ex-amining the polarization and energy dependence of theluminescence.8,11 The energy change,DE, of the excitonicluminescence involving thej53/2 valence bands induced bythe strain is given by the following solution of the orbital-strain Hamiltonian fork50:11

DE52a~exx1eyy1ezz!

6 12A4d2exy2 1b2~2ezz2exx2eyy!

213b2~exx2eyy!2,

~1!

where exx5eyy5(e1101e110)/2, exy5(e1102e110)/2,and ezz522exxC12 /C11; e110 and e110 are the strainsalong@110# and@110# directions, respectively. The constantais the hydrostatic deformation potential;b andd are uniaxialdeformation potentials associated with strains of tetragonaland rhombohedral symmetries, respectively, which removethe degeneracy of the bands as indicated by the6 sign;C11 and C12 are elastic constants; these constants forInxGa12xAs are found by interpolating between values forGaAs and InAs.12

We have examined the In0.15Ge0.85As/In0.20Ga0.80As in-terface with plan-view TEM, as shown in Fig. 3. The misfitdislocation distribution, most of which are of the 60° type,5,7

was examined at several different regions of the interface.Figures 3~a! and 3~b! show linear misfit dislocation densitiesof 6.13104 and 8.03104 cm21 along @110# and6.53104 and 1.33105 cm21 along @110#, respectively.For 60° misfit dislocations, an average strain relaxation of0.02% occurs for linear dislocation density of 13104 cm21.7 The resulting in-plane strains,e110 and e110,in the In0.20Ga0.80As film relative to a relaxed In0.15Ga0.85Asfilm are, respectively, 0.219% and 0.227% in Fig. 3~a! and0.189% and 0.091% in Fig. 3~b!. Application of Eq.~1! givesa DE of 19.367.4 and 12.165.1 meV for the regions of

FIG. 2. Monochromatic linearly polarized CL images for same regionshown in Fig. 1~a! at l5956 nm. The polarization detection conditions ofE'@110# andEi@110# are shown in~a! and~b!, respectively. The ratio imageof log(I' /Ii) is shown in~c!, revealing themm-scale polarization anisotropy.

FIG. 3. Plan-view TEM showing two different regions of theIn0.15Ga0.85As/In0.20Ga0.80As interface which exhibits different dislocationdensities and strain relaxation along both^110& directions in~a! and ~b!.

870 Appl. Phys. Lett., Vol. 66, No. 7, 13 February 1995 Rammohan et al.

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Figs. 3~a! and 3~b!, respectively; the center of the strain-splitbands is separated by;7 meV. It is, therefore, evident thatregions of isotropic and anisotropic relaxation are both foundin this sample. The regions of Figs. 3~a! and 3~b! representtypical variations sampled with TEM. The CL images repre-sent a sampling over a much larger area, thereby enablingmeasurements of variations in transition energy@as, e.g., the;19 meV shift seen in the CL spectra of Fig. 1~b!# which aregreater than those estimated from the TEM analysis and Eq.~1!.

For an in-plane biaxial stress~resulting inexy50), nopolarization of either hh- or lh-excitonic emissions is ex-pected for emission normal to the~001! surface plane. For apure uniaxial stress along the@110# direction, mixing of hhand lh characters in the strain-split bands is negligible, andhh ~lh! excitonic emission normal to the~001! surface planeis totally ~partially! linearly polarized perpendicular~paral-lel! to @110#.11 Since the interface exhibits varying degrees ofrelaxation along both110& directions, there will be varyingdegrees of mixing of hh and lh characters in the strain splitbands, leading to only a partial linear polarization for exci-tation emission. The regions of uniform bright and dark con-trast in Fig. 2~c! indicate variations from nearly biaxial touniaxial compressive stress, respectively, as the system re-laxes preferentially along the@110# direction. Such aniso-tropic relaxation would create regions of quasiuniaxial stresswhich are observed to run along both^110& directions in Fig.

2~c!. The bright streaks in Fig. 2~c! indicate regions wherethe intensity ratioI' /I i , is closest to unity, revealing regionsclosest to biaxial stress. The dark streaks, likewise, run alongboth ^110& directions, yield minima ofI' /I i , and reveal re-gions closest to a uniaxial stress.

A further correlation of the CLWI image of Fig. 1~a!with the LPCL image of Fig. 2~c! is shown with a peakwavelength andI' /I i ratio versus distance histogram in Fig.4, taken along an arbitrary@110#-oriented line. The histogramshows that the blue- and red-shifted regions in CLWI corre-spond to the regions of reduced- and enhanced-polarizationanisotropy @bright and dark regions in Fig. 2~c!#, respec-tively, in the LPCL imaging. This correlation confirms thatthe spatial variation in emission wavelengths, as shown inFig. 1~a!, is caused primarily by variations in in-plane strainas opposed to composition which would not yield a polariza-tion anisotropy. The regions of anisotropic relaxation~qua-siuniaxial! correspond to regions of primarily enhanced re-laxation along@110#. These regions also correspond to areduced total compressive stress along@110# which results ina red-shifted luminescence that is spatially correlated with apolarization anisotropy, as observed in Fig. 4.

In conclusion, we have studied the strain relaxation ofcompositionally step-graded InxGa12xAs layers using LPCL,CLWI, and TEM. We have observed localmm-scale varia-tions in compressive stress ranging from nearly uniaxial tobiaxial, resulting in a marked polarization anisotropy con-comitant with a variation in luminescence transition energy.

This work was supported in part by a grant from theCharles Lee Powell Foundation, NSF~PYI-DMR!, NSF~RIA-ECS!, ARO, and the NSF-ICAS center at UCSD.

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FIG. 4. Histogram of the CL wavelength imaging, CLWI, andI' /I i ratio fora line scan along@110#. The spatial correlation of regions with a red shiftand an increased polarization anisotropy~regions of nearly uniaxial com-pressive stress! and regions with a blue shift and a reduced polarizationanisotropy~regions of nearly biaxial compressive stress! is observed.

871Appl. Phys. Lett., Vol. 66, No. 7, 13 February 1995 Rammohan et al.

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