The surface of two GaN films grown under Ga-rich conditions by molecular beam epitaxywas characterized using x-ray reflectivity, assuming a self-affine/fractal surface morphology. The surface height fluctuations were similar for both samples at the largest lateral length scales at which the fractal description is valid, although this lateral length was significantly greater and the “jaggedness” significantly smaller for the sample grown under higher Ga flux. Previous atomic force microscopy images revealed a higher density of large features on the surface for the sample grown under lower Ga flux. The lateral size of the features are dominated by a convolution of the atomic force microscopy tip shape and the actual features on the surface, which precludes an accurate determination of the surface structure at length scales smaller than the tip radius. This study illustrates the importance of using different techniques to evaluate the film surface morphology at different length scales

Lederman, D

Myers, T H

Richards-Babb, Michelle

Yu, Zhonghai

English

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Faculty & Staff Scholarship 1997 Surface Morphology of GaN Films Determined From Quantitative X-ray Reflectivity D Lederman West Virginia University Zhonghai Yu West Virginia University T H. Myers West Virginia University Michelle Richards-Babb West Virginia University, Michelle.Richards-Babb@mail.wvu.edu Follow this and additional works at: https://researchrepository.wvu.edu/faculty_publications  Part of the Chemistry Commons Digital Commons Citation Lederman, D; Yu, Zhonghai; Myers, T H.; and Richards-Babb, Michelle, "Surface Morphology of GaN Films Determined From Quantitative X-ray Reflectivity" (1997). Faculty & Staff Scholarship. 863. https://researchrepository.wvu.edu/faculty_publications/863 This Article is brought to you for free and open access by The Research Repository @ WVU. It has been accepted for inclusion in Faculty & Staff Scholarship by an authorized administrator of The Research Repository @ WVU. For more information, please contact ian.harmon@mail.wvu.edu. Appl. Phys. Lett. 71, 368 (1997); https://doi.org/10.1063/1.119539 71, 368© 1997 American Institute of Physics.Surface morphology of GaN filmsdetermined from quantitative x-rayreflectivityCite as: Appl. Phys. Lett. 71, 368 (1997); https://doi.org/10.1063/1.119539Submitted: 27 December 1996 . Accepted: 17 May 1997 . Published Online: 04 June 1998D. Lederman, Zhonghai Yu, T. H. Myers, and M. R. Richards-BabbARTICLES YOU MAY BE INTERESTED INThe influence of inversion domains on surface morphology in GaN grown by molecular beamepitaxyApplied Physics Letters 71, 3486 (1997); https://doi.org/10.1063/1.120367A positive temperature coefficient of resistivity effect from a paraelectric thin-film capacitorApplied Physics Letters 71, 371 (1997); https://doi.org/10.1063/1.119540The effect of atomic hydrogen on the growth of gallium nitride by molecular beam epitaxyApplied Physics Letters 69, 2731 (1996); https://doi.org/10.1063/1.117693Surface morphology of GaN films determined from quantitative x-rayreflectivityD. Lederman,a) Zhonghai Yu, and T. H. MyersDepartment of Physics, West Virginia University, Morgantown, West Virginia 26506-6315M. R. Richards-BabbDepartment of Chemistry, West Virginia University, Morgantown, West Virginia 26506-6045~Received 27 December 1996; accepted for publication 17 May 1997!The surface of two GaN films grown under Ga-rich conditions by molecular beam epitaxy wascharacterized using x-ray reflectivity, assuming a self-affine/fractal surface morphology. The surfaceheight fluctuations were similar for both samples at the largest lateral length scales at which thefractal description is valid, although this lateral length was significantly greater and the‘‘jaggedness’’ significantly smaller for the sample grown under higher Ga flux. Previous atomicforce microscopy images revealed a higher density of large features on the surface for the samplegrown under lower Ga flux. The lateral size of the features are dominated by a convolution of theatomic force microscopy tip shape and the actual features on the surface, which precludes anaccurate determination of the surface structure at length scales smaller than the tip radius. This studyillustrates the importance of using different techniques to evaluate the film surface morphology atdifferent length scales. ©1997 American Institute of Physics.@S0003-6951~97!02029-9#It is well known that the surface structure can have asignificant impact on a thin film’s physical properties. Be-cause of this, a significant portion of the recent work on GaNthin films has focused on their structural characteristics.Technological applications resulting from GaN films, includ-ing optoelectronic devices, will have to overcome constraintsresulting from surface defects. Studies have generally fo-cused on the effects of defects on the optical and transportproperties of GaN using a variety of techniques, includingx-ray diffraction, atomic force microscopy, scanning electronmicroscopy, and others.In this letter, we analyze the x-ray reflectivity~XRR! ofGaN films, grown under different Ga flux conditions, using aself-affine/fractal description of the surface.1,2 This methodhas been previously used in for various types of thin films,3–6liquid crystal polymer superlattices,7 semiconductorsuperlattices,8 and metallic superlattices.9,10 Previously,atomic force microscopy~AFM! studies indicated that Ga-rich molecular beam epitaxy~MBE! growth close to, butbelow the Ga condensation point, results in smooth, feature-less surfaces indicative of two-dimensional growth.11 This isconsistent with reflection high energy electron diffraction,indicating that Ga-rich conditions are a requirement for two-dimensional growth.12 In this letter, we study two samplesgrown under nominally identical conditions except for theGa flux. Although the surface height fluctuations at the na-nometer scale are similar for the two samples~'2.4 nm!, thelateral roughness coherence length is significantly larger andthe fractal dimension, or jaggedness, is smaller for thesample grown under a high Ga flux. This agrees with theprevious interpretation of the AFM data. AFM images, how-ever, also reveal the presence of large vertical features thattend to mask the surface characteristics at the nanometerlength scales. The XRR is insensitive to the large features,but is able to obtain information at small length scales. Ingeneral, surface roughness measurements must be performedwith different techniques to accurately characterize the sur-face.The MBE growth of GaN films has been describedpreviously.11,13 Briefly, two samples were grown via MBEon c-plane sapphire substrates at 730 °C. A standard MBEsource provided the Ga flux. A cryogenically cooled rfplasma source was used to produce the active nitrogen flux.All growth parameters were nominally the same for the filmsanalyzed in this letter, except for their Ga flux. Film GaN1was grown at a Ga flux of 531027 Torr ~BEP!, which rep-resents the onset of Ga-rich growth, while film GaN2 wasgrown at 731027 Torr BEP, which is just before the onsetof Ga condensation under these growth conditions.XRR was measured using a 18 kW rotating Cu anodex-ray generator with a four-circle diffractometer in a moder-ate resolution configuration.14 A variable slit, placed imme-diately before the sample, was wide enough to accept theentire width of the specular peak. The angular resolution was0.12° for the detector slits and 0.05° for the sample slits. Theslits along they direction were left wide open, thus averag-ing over k space along they axis. Three types of scans wereperformed: specular, diffuse near specular, and transverse~rocking curves!. For the specular scans, the wave vectortransferq was perpendicular to the surface normal, for thediffuse near specular scansq was misaligned by 0.1° withrespect to the specularq, and for the transverse scans themagnitude ofq was constant but its direction rocked aboutthe surface of the sample. The diffuse near specular scan wassubtracted from the specular scan to obtain the true specularintensity.The true specular intensity was fit to a low-angle opticalmodel which takes into account the finite film thickness(t f).10,15The analysis was sensitive to both the average sur-face height fluctuations and the film thickness. In order tofit the data, the substrate/film interface roughness had to be&0.1 nm, and was therefore fixed at 0.1 nm. The results area!Electronic mail: dlederma@wvu.edu368 Appl. Phys. Lett. 71 (3), 21 July 1997 0003-6951/97/71(3)/368/3/$10.00 © 1997 American Institute of Physicsshown in Fig. 1. The parameters obtained (s152.4860.1nm, t f15467660 nm; and s252.3860.1 nm,t f25467660 nm for GaN1 and GaN2, respectively! weresimilar within the numerical uncertainties, determined bymonitoringx2 when the relevant parameter was fixed at dif-ferent values while the rest were allowed to vary. The fitswere significantly improved by taking into account thesubstrate-epilayer interface,16 and hence the results provide arough estimate of the film thickness. This estimate agreeswith the average thickness obtained with contact profilom-etry at the edge of the film~700 nm! and transmission elec-tron microscopy micrographs obtained near the center of thefilm ~230 nm!. Finally, the electron density obtained from thefit was within 5% of the theoretical value calculated fromthe volume of the unit cell~0.438 electrons/Å3).The near-specular and transverse scans were analyzedusing the distorted wave Born approximation.2 The diffusescattering functionSd(q) ~proportional to the intensity! wasmodeled asSd~q!5AuT~a!u2uT~b!u2uqz2ue20.5s2~ q̄ z21 q̄ z*2!3E2`1`dx~eu q̄ zu2C~x!21!e2 iqxx, ~1!whereA is a scaling factor,s is the average height fluctua-tion obtained from the true specular data,T(a) is the trans-mission coefficient of the surface for a grazing angle inci-dencea (b is the corresponding angle for the outgoingbeam!, q̄ z is the wave vector transferinsidethe film.17 Equa-tion ~1! assumes that the intensity alongqy is averaged bykeeping the slits in that direction wide open.C(x) is theheight-height correlation function, modeled asC(x)5s2 exp(2uxu/j)2h, which is applicable to self-affinefractal surfaces with a cutoff.2 j is the cutoff length of theheight fluctuations andh determines the surface ‘‘smooth-ness.’’ Small values ofh result in ‘‘jagged’’ surfaces whileh;1 indicates ‘‘smooth’’ hills and valleys. At small lengthscalesuxu&j, the surface is self-affine/fractal in nature witha fractal dimensionDs532h.2 For uxu*j, the fractal heightfluctuations saturate at a value equal tos.2,6 This could oc-cur because the fractal description is limited by the averagefilm grain size.Transverse scans were obtained at aboutqzo51.422 andqzo52.134 nm21 and fit only forqx.0 so that the reflectedbeam was smaller than the detector slit.14 The calculationwas convoluted with the instrumental resolution,14 and thespecular peak nearqx50 was modeled as a gaussian whosewidth corresponds to the instrumental resolution. The heightof the specular peak was also fit because it includes the sharpcontribution from the smooth substrate surface. The best pa-rameters were found by self-consistently fitting Eq.~1!, withs fixed to the values obtained from the true specular inten-sity ~Fig. 1!, to the transverse and diffuse near-specularscans. The integral in Eq.~1! was calculated numerically bybreaking it down into several integrals,18 each of which wascalculated by decomposing the integrand into Chebyshevpolynomials, and each of the Chebyshev terms was calcu-lated by a fast fourier transform.19 Hence, there were fivefitting parameters:j, h, A, the height of the specular peak,and a small background intensity.FIG. 2. Diffuse near-specular reflectivity obtained by misorienting thesample by 0.1° with respect to the specular peak. The solid curves representfits to Eq. ~1!. For GaN1,h50.4060.05,j5323.7650, ands52.48 nm.For GaN2,h50.6060.05,j5515.7650, ands52.38 nm.FIG. 1. True specular reflectivity obtained by subtracting a diffuse near-specular scan from a specular scan for samples GaN1~low Ga flux! andGaN2 ~high Ga flux!. The solid curves represent fits to a low angle opticalmodel~Ref. 10!. The results for the height fluctuationss and film thicknesst f are labeled on the figure.369Appl. Phys. Lett., Vol. 71, No. 3, 21 July 1997 Lederman et al.The results are shown in Figs. 2 and 3. The peaks atlarge values ofqx in Fig. 3 correspond to angles wherea orb are close to the critical angle, and are commonly known as‘‘Yoneda wings.’’20,17For even largerqx , the intensity dropsbecause the sample blocks the beam. Qualitatively, the GaN1transverse scans depend more strongly onqx than the GaN2scans because the character of their height fluctuations in thelateral direction is different. Quantitatively, the parametersobtained from these fits areh150.4060.05 andj15323.7650 nm; andh250.6060.05 andj25515.7650nm. Assuming thatj is proportional to the average grainsize, and because higher values ofh mean a lower fractaldimension, sample GaN2, grown at a higher Ga flux, issmoother in the sense that the average grain size is larger andthe surface of each individual grain is smoother. The growthof GaN2 is therefore more two-dimensional than that ofGaN1.Previous qualitative AFM work on these samples11 mea-sured large features on the surface, approximately 200 nmwide and 250 nm high. The number of features/area wassignificantly lower for the higher Ga flux sample GaN2. Aquantitative analysis of the average height fluctuations be-tween the features founds51.660.2 nm for GaN1 ands51.960.5 nm for GaN2. The two values ofs are the samewithin their uncertainties, although lower than the value ob-tained from the XRR~2.4 nm!. This discrepancy could bedue to the significant size of the AFM tip used~200 nmradius!, which combined with the roughness present in thesample, makes a quantitative analysis of the AFM imagesunreliable without taking into account the shape of the tip.21The x-rays seem to probe the surface morphology betweenthe large features, since the height fluctuations of the twosamples was similar, even though the AFM indicated thatapproximately 5% of the surface of GaN1 contained thelarger features with an average separation of 1000 nm. Thex-rays may also probe the surface of these large features,although this contribution is probably small and proportionalthe surface area of the sample they occupy~i.e., 5%!. Theseresults indicate that a complete surface analysis must includea combination of techniques which are sensitive to roughnessat different length scales.In conclusion, the surface roughness of GaN films grownunder different Ga flux conditions was quantitatively ana-lyzed using XRR. Although the two samples used in thisstudy had similar surface height fluctuations along thegrowth direction, the lateral character of the roughness wasdifferent. The sample grown at a higher Ga flux had signifi-cantly larger grain sizes and a lower fractal dimension thanthe sample grown at a lower Ga flux, consistent with increas-ingly two-dimensional growth. This study confirms prior in-terpretations of AFM images and presents a new way ofanalyzing the surface roughness of GaN films. A completeanalysis of the surface morphology must include differenttechniques, such as AFM and XRR, which are sensitive toroughness at different length scales.The authors thank Dr. Linda Romano at Xerox PARCfor the TEM imaging. This work was supported by the AlcoaFoundation~DL! and the Office of Naval Research~TM!under Grant No. N00014-94-1-1149.1For a review of fractal description of surfaces, seeDynamics of FractalSurfaces, edited by F. Family and T. Vicsek~World Scientific, Singapore,1991!.2S. K. Sinha, E. B. Sirota, S. Garoff, and H. B. Stanley, Phys. Rev. B38,2297 ~1988!.3C. H. Lee, K. S. Liang, F. S. Shieu, S. L. Sass, and C. P. Flynn, Mater.Res. Soc. Symp. Proc.209, 679 ~1991!.4C. Thompson, G. Palasantzas, Y. P. Feng, S. K. Sinha, and J. Krim, Phys.Rev. B49, 4902~1994!.5J. Nogue´s, D. Lederman, and I. K. Schuller, Appl. Phys. Lett.68, 3186~1996!.6V. Nitz, M. Tolan, J.-P. Schlomka, O. H. Seeck, J. Stettner, W. Press, M.Stelzle, and E. Sackmann, Phys. Rev. B54, 5038~1996!.7R. E. Geer, R. Shashidhar, A. F. Thibodeaux, and R. S. Duran, Phys. Rev.Lett. 71, 1391~1993!.8S. K. Sinha, M. K. Sanyal, A. Gibaud, S. K. Satija, C. F. Majkrzak, and H.Homma, inScience and Technology of Nanostructured Magnetic Materi-als, edited by G. C. Hadjipanayis and G. A. Prinz~Plenum, New York,1991!, p. 145; S. K. Sinha, M. K. Sanyal, S. K. Satija, C. F. Majkrzak, D.A. Neumann, H. Homma, S. Szppala, A. Gibaud, and H. Morkoc¸, PhysicaB 198, 72 ~1994!.9D. E. Savage, J. Kleiner, N. Schimke, Y.-H. Phang, T. Jankowski, J.Jacobs, R. Kariotis, and M. G. Lagally, J. Appl. Phys.69, 1411~1991!.10E. E. Fullerton, J. Pearson, C. H. Sowers, S. D. Bader, X. Z. Wu, and S.K. Sinha, Phys. Rev. B48, 17 432~1993!.11M. Richards-Babb, S. L. Buczkowski, Z. Yu, and T. H. Myers, Mater.Res. Soc. Symp. Proc.395, 237 ~1996!.12T. D. Moustakas, Mater. Res. Soc. Symp. Proc.395, 111 ~1996!.13Z. Yu, S. L. Buczkowski, N. C. Giles, T. H. Myers, and M. R. Richards-Babb, Appl. Phys. Lett.69, 2731~1996!.14J. D. Shindler and R. M. Suter, Rev. Sci. Instrum.63, 5343~1992!.15E. E. Fullerton, I. K. Schuller, H. Vanderstraeten, and Y. Bruynseraede,Phys. Rev. B45, 9292~1992!.16B. Vidal and P. Vincent, Appl. Opt.23, 1794~1984!.17S. K. Sinha, J. Phys.~France! III 4, 1543~1994!.18M. Blakemore, G. A. Evans, and J. Hyslop, J. Comput. Phys.22, 352~1976!.19W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling,Numerical Recipes in C: The Art of Scientific Computing~CambridgeUniversity Press, Cambridge, 1992!, p. 190.20Y. Yoneda, Phys. Rev.131, 2010~1963!.21S. M. Paik, S. Kim, and I. K. Schuller, Phys. Rev. B44, 3272~1991!.FIG. 3. Transverse~rocking curve! scans measured aboutqzo51.422 andqzo52.134 nm21. The solid curves represent fits to Eq.~1!. For GaN1,h50.4060.05, j5323.7650, and s52.48 nm. For GaN2,h50.6060.05,j5515.7650, ands52.38 nm.370 Appl. Phys. Lett., Vol. 71, No. 3, 21 July 1997 Lederman et al.

Surface Morphology of GaN Films Determined From Quantitative X-ray Reflectivity

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Surface Morphology of GaN Films Determined From Quantitative X-ray Reflectivity

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