Nanometer surface gratings on Si(100) characterized by x-ray scatteringunder grazing incidence and atomic force microscopy

T. H. Metzger,a) K. Haj-Yahya, J. Peisl, M. Wendel, H. Lorenz, and J. P. KotthausSektion Physik, Ludwig-Maximilians-Universita¨t Munchen, Geschwister-Scholl-Platz 1, 80539 Mu¨nchen,Germany

G. S. Cargill IIIColumbia University, New York, New York 10027

~Received 22 April 1996; accepted for publication 15 October 1996!

During rapid melting and resolidification of As-implanted Si~100! by pulsed laser irradiation aperiodic lateral grating has been created on the Si surface. Structure and perfection of the grating isinvestigated by specular and diffuse x-ray scattering under grazing incidence and exit angles. Usingsynchrotron radiation we find sharp, off-specular diffraction rods perpendicular to the samplesurface. Their lateral separation is given by the periodicity of the grating~52261 nm!, which isnearly the same as the light wavelength~530 nm! used in laser annealing the samples. Intensitymeasurements along the diffraction rods are used to determine the detailed structure of the surfacegrating by fitting the experimental results with model calculations. A sinusoidal shape is found withan average amplitude of 661 nm. This structure is confirmed by atomic force microscopy studies.The x-ray method presented will be a unique tool also applicable in the case of buried lateralnanostructures which are not accessible by surface-sensitive techniques, e.g., scanning probemethods. ©1997 American Institute of Physics.@S0021-8979~97!05002-0#

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I. INTRODUCTION

The fabrication of periodic lateral nanostructuressemiconductor surfaces is a field of high scientific intersince low-dimensional electron systems defined by thstructures, such as quantum wires or quantum dots, aretended to have distinct properties compared to the 2D etron gas in semiconductor quantum-well systems.1 Typicallythey are produced by a combination of lithography and ptern transfer techniques.2 Recently, it has been reported thlateral structures may also be induced in such systemspulsed laser transient thermal gratings.3,4 In this case the re-sulting structures are expected to be located in the nsurface region, while the surface itself remains unstructuIn the case of technologically relevant^100&Si surface, lat-eral nanostructures have been investigated in transportinfrared experiments.5,6 Etched nanometer gratings on Si sufaces are also used as well-defined substrates to studyreplication properties of the nanostructures after they hbeen covered by other materials.7 Again these gratings havbeen fabricated by lithography and etching. It has beenported that similar structures can also be produced by linterference patterns on semiconductor surfaces8–10 with alateral periodicity close to the laser wavelength used.

In the present work we report on the characterizationlaser-induced periodic gratings on the Si~100! surface. Wehave partly adopted the x-ray scattering method used bylan et al.11 The off-specular diffuse scattering at grazing icidence and exit angles shows intensity streaks~so-calledtruncation rods! running parallel to the specular path in rciprocal space. It has been demonstrated that the coherlength necessary to obtain diffraction from such extendstructures is sufficiently large for x rays from a synchrotro

a!Electronic mail: thmetzger@lrz.uni-muenchen.de

1212 J. Appl. Phys. 81 (3), 1 February 1997 0021-8979/97

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especially in case of the present scattering geometry.12

The grating on Si^100& investigated in this work hassimilar lateral periodicity as for the above-mentioned ca~several hundred nanometers! but much smaller heights oonly some nm, with microscopic surface roughness superposed. These structures have been produced~unintentionally!during rapid thermal annealing of Si after As implantatiusing a pulsed laser beam scanning over the sample surWe do not want to speculate on the detailed mechanismcauses the evolving surface pattern, it being likely a parasinterference effect, but rather concentrate on demonstrahow the specific x-ray method applied here can be usecharacterize such a periodic perturbation of the surface.compare the resulting structure with atomic force microsco~AFM! measurements, which are only applicable with hisensitivity if the gratings are not buried under a cap laye

II. EXPERIMENTS

A. Sample preparation

Si~100! wafers, polished to industrial standard~surfaceroughness about 1 nm!, have been implanted by 100 keV Aions to a dose of 631016 cm22 at room temperature. Recrystallization of the damaged near-surface layer has beenformed by laser annealing using aQ-switched frequency-doubled Nd:YAG laser~l5530 nm!. The laser beam habeen defocused to a diameter of about 50mm resulting in asurface energy density of 2.2 J/cm2. The sample surface wascanned in near normal incidence with a raster of partiaoverlapping patches. The electrical activation procthereby obtained and the corresponding structure of theatoms in the Si matrix has been reported elsewhere togewith the details of the sample preparation.13 Further longtime furnace annealing of these samples led to electricalactivation and a new defect complex.14 It is the aim of a

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current investigation by x-ray techniques under grazing indence conditions to study the lattice structure and preciptions evolving in the long time annealed samples.15

Here we are interested in the surface grating thatevolved in all samples during laser annealing. Due tohigh energy density and the parasitic interference of the labeam, the local temperatures probably exceeded the mepoint of Si, thus resulting in stripelike evaporation patteron the Si surface. The presence of the high As concentrain the near-surface region may have favored this procsince it is known that foreign atoms increase the absorpof laser light.9

B. X-ray scattering

In order to characterize a surface grating with a periicity of some hundred nm, extremely high resolution for laeral momentum transfer is mandatory. This can onlyachieved by triple crystal diffractometry16 or by choosing thescattering geometry of grazing incidence.12 Let us assumeqxandqz , the momentum transfer parallel and perpendiculathe sample surface, be placed in the plane of incidencethe case of specular reflectivity the angle of incidenceai andexit af are the same. Information on the density profile ppendicular to the surface is obtained. If the grating is oented perpendicular to the incident x-ray beam, diffractmaxima atdqx5n* 2p/d are expected, whered is the peri-odicity of the grating. Since the grating is confined to tsample surface the diffraction maxima are extended alqz , perpendicular to the sample surface. Figure 1 showsscattering geometry together with the expected intensitytribution in reciprocal space.Daf represents the range of thexit angles covered by a position-sensitive detector~PSD!.The different orders of the diffraction rodsm521 throughm524 are expected to appear parallel to the specular p

The experiments have been performed using a 60Rigaku rotating anode x-ray generator~CuKa1 radiation!and the positron storage ring DORIS, at Hasylab, DESYHamburg at the diffractometer located at beamline D4. Tx-ray wavelengthl50.13 nm was selected by a flat Ge^111&

FIG. 1. Scattering geometry in the plane of incidence. Expected intenrodsm521 to24 for a lateral grating are indicated schematically. Besidthe Yoneda peak and the strong specular beam, different ordersm of dif-fraction rods appear. The solid curve in this schematic scattering geomat small, fixed incident angleai represents an exit angle scan as recordeda position sensitive detector alongDaf .

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monochromator crystal from the synchrotron beam afpassing a gold mirror which suppressed the higher harmonfrom the monochromator. The size of the incident beam wdefined by a horizontal slit of 1 mm and a vertical slit of 0mm. Details of the setup have been described elsewher12

The scattered intensity was recorded by a PSD that canrotated around an axis perpendicular to the plane of indence. It covers an exit angle range of about 3° with a relution of about 0.8 mrad.

In the inset of Fig. 2 the existence of diffraction rodsdemonstrated by a detector ‘‘scan’’ as measured by thesition sensitive detector. CuKa1 radiation was used. The in-cident angle was kept constant atai50.36°. If the exit angleequals the critical angle for total reflection,af5ac , the dif-fuse intensity is amplified by the transmission function~so-called Yoneda peak!. Forai5af strong specular reflection isobtained, while for exit angles larger thanai four maximaappear. They are due to different orders of Bragg diffractiom521 to m524, from the surface grating as indicateschematically in Fig. 1. The scattering anglesai andaf havebeen converted in the vector for momentum transfer usin

q5~qx,0,qz!52p/l~cosa f2cosa i ,0,sinca f1sin a i !.

Plotting the scattering intensity as a function ofqx ~Fig. 2!,we find the lateral distances between all diffraction rods toconstant. This distance corresponds to a mean lateral pericity of the grating of 52261 nm.

The orientation of the grating with respect to the planeincidence has been checked by maximizing the distancethe Bragg rods,dqx5n* 2p/deff , as a function of the azi-muthal anglev, which changes the effective periodicity according to deff5d/sinv. For v5vmax590° the grating isplaced perpendicular to the incident beam.vmax can be de-termined to an accuracy of 0.1°. Inspection of Fig. 2 shothat the width of the specular beam is smaller than for tsatellite peaksm521 to 24. From the full width at half-maximum~FWHM! of the first side peak the number of pe

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tryyFIG. 2. Scattering intensity on a logarithmic scale as a function of the eangleaf at the incident angleai50.36°~inset!. The horizontal axes from theinset are converted to lateral momentum transferqx in the main plot. Thediffraction maximam521 to m524 become equidistant. Note that theiwidths are larger than the width of the specular beam.

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riodsN contributing coherently to the interference maximuis determined according to the Laue equation

sin2@Ndqx~d/2!#/sin2 @dqx~d/2!#50.5N2.

N513 is obtained from this analysis and represents astructure effect rather than the limitation by the coherelength of the x rays. The coherently eluminated length resing from the projection of the longitudinal coherence lengon the surface reaches about 300mm.12 The grating imper-fection is presumably due to the perturbation of the lonranged periodicity created by the laser-induced lateral stturing mechanism. This perturbation will become obviousthe AFM measurements taken at different locations onsample surface~see below!.

C. Quantitative interpretation

In the following the detailed structure of the surfagrating is characterized by comparing further x-ray measuments with model calculations for the off-specular structfactor of a periodic surface ‘‘roughness’’ using the theooutlined recently by Tolanet al.11 They have shown that threal structure of a surface grating can be obtained by msuring theqz dependence of both the specular reflectivity athe satellite diffraction rods. To do so, we have performeqz scan along the first two diffraction maxima, by varyingai

and the PSD in a manner that kept the specular peak alwat the same channel number in the multichannel analywhich records the PSD signal. For intensity reasonsmeasurement was done using synchrotron radiation.background corrected integrated intensity of the first diffrtion satellite peak,m521, is shown as a function of momentum transferqz in Fig. 3 at constantqx52p/d. The circlesrepresent the measurement, while the solid line shows reof a model calculation, which is explained later. Quali

FIG. 3. Scattering intensity along the first satellite diffraction rodm521 asa function of vertical momentum transferqz . Circles represent the experment, the solid line a calculation using a sinusoidal model. The inset shthe result of the model calculation~solid line! and the surface profile asobtained from AFM measurements.

1214 J. Appl. Phys., Vol. 81, No. 3, 1 February 1997

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tively this measurement can be interpreted as follows: Tintensity maximum is again caused by the transmission fution at ai5ac and is followed by a structureless monotonintensity decay alongqz .The absence of further intensity oscillations forai.ac indicates that the grating height is mucsmaller than its periodicity. For other systems with larggrating heights pronounced oscillations have been found.11,16

From the following evaluation it becomes clear that the aplitude of the surface grating is still too large to be treateda small perturbation of the surface and thus can not bescribed by a Gaussian roughness. In addition the spepower density of the grating is quite different from a surfawith a self-affine height–height correlation function. Thdifference is now demonstrated from the analysis ofspecular reflectivity~m50! as shown in Fig. 4. Again thegrating is oriented perpendicular to the incident beam. TFresnel decay of the specular intensity is modulated bweak intensity oscillation. Using a simulation program fspecular reflectivity of layered flat samples~REFSIM by Si-emens! the experimental data have been fitted by two moels. First, a flat surface with Gaussian roughness of 2.3has been assumed. The corresponding curve in Fig. 4 cledoes not reproduce the experimental data. Second, theing is modeled by a layer with sinusoidal vertical amplitudz5h* sin~x/d! on top of the Si substrate with an averadensity smaller than Si bulk density. The corresponding cculated specular reflectivity is shown in Fig. 4 as a solid linDue to the crude assumptions made in the model the oreliable parameter in the fit is the layer thickness of 2h5661nm. It determines the location of the intensity modulatiaroundqz50.09~A21!. We conclude that the specular refletivity measurement is able to distinguish between Gaussand structured roughness even for relatively small heigFor the remainder of this subsection we want to determthe detailed structural parameter of the grating from mocalculations using the theory reported by Tolanet al.11 in thekinematic approximation. Two models have been compara sinusoidal grating profile and a periodic grating with

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FIG. 4. Specular intensity~m50! as a function of perpendicular momentumtransferqz . Open circles represent the experimental data, the dashed lia calculation using a Gaussian surface roughness of 2.3 nm. The solidshows the result of a fit for which the surface grating has been replacea sinusoidal surface layer with an average thickness of 6 nm.

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asymmetric trapezoidal shape. The simulation resulting frthe sinusoidal shaped grating is represented by a solid linFig. 3 and fits the data reasonably well. The disagreembetween the fitted and experimental curve forai smaller thanthe critical angle is caused by a trivial geometric effewhich contains no further structural information. The struture obtained by the fitting is compared to the grating promeasured directly by AFM~see inset of Fig. 3!. The mainresult from the fitting is the average grating height: 2h5661nm has been found. The model calculation is rather insetive to the periodicity of the grating. We therefore used tperiodicity d5540630 nm as obtained from averaging seeral AFM measurements. Within this error bar the mocalculations produced fits similar to the one given in Fig.

The trapezoidal model fits the measured data with silar quality ~not shown in Fig. 3! but the amplitude of thegrating is too small by a factor of about 2 as compared toAFM result.

D. AFM measurement

Finally, we present the result of AFM measuremewhich probe the surface grating in real space. They hbeen performed with a NANOSCOPE III in the tappinmode. In this mode the cantilever vibrates at its resonafrequency of about 300 kHz, resulting in an amplitude toorder of 10 nm. To obtain high topographic resolution wfabricated needlelike, electron-beam-deposited supewith a typical tip length of 1mm and a tip diameter of abou100 nm. Some of these tips were additionally sharpenean oxygen plasma, resulting in a decrease of the tip diamby a factor of 3–4. For a detailed description of the tip farication we refer to Ref. 17. An area up to 14314 mm2 hastypically been scanned in the AFM measurement. The resing topography is shown in the lower part of Fig. 5, whilethe upper the vertical section plot along the line A, Bpresented. The average periodicity of the grating is 522the amplitude in this section varies from 3 to 5 nm. Takiseveral such pictures at different locations on the samsurface we find that the grating is far from being perfectshows varying amplitudes between 2 and 10 nm and pericites between 510 and 570 nm~540630 nm!. Typical lengthscales over which the grating is reasonably perfect amoun4000–7000 nm. The number of periods within such a lenranges fromN58 to N514 and gives a similar value aobtained from the FWHM of the x-ray satellite rods~N513!.An amplified section of one of the surface profiles obtainby AFM measurements is compared to the result from x-scattering in the inset of Fig. 3.

III. DISCUSSION AND CONCLUSION

The structure of a laser-induced lateral gratingSi~100! is determined in detail by x-ray scattering at graziincidence and exit angles and in real space by AFM. Keepin mind that the averaging in x-ray scattering is performover macroscopic dimensions while the high-resolutAFM measurement images only somemm, we conclude thatthe results of both methods agree reasonably well. Inpresent scattering geometry the x-ray coherence length

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jected on the sample surface is enlarged by a factor of mthan 100 and the resolution for lateral momentum transbecomes as high as 1.531025 A21.12 Thus, lateral periodicpatterns with a periodicity of up to 10mm can be investi-gated by x rays. The lower limit of such structures iscourse determined by the atomic distances which are stilfrom being realized by current lateral patterning techniqu

We finally want to emphasize that the comparison btween the two methods will not be possible in the caseburied gratings; then diffuse x-ray scattering will be tunique tool to characterize such structures. In addition tocharacterization of periodic lateral electron density modutions as demonstrated by the x-ray methods presented hdiffraction under grazing incidence from such buried strutures will show how the corresponding atomic orderchanged by the lateral patterning of crystalline samples.

First measurements on buried lateral gratings in GaAlGaAs heterostructures revealed encouraging results.18

ACKNOWLEDGMENTS

We want to thank H. Rhan and G. Goerigk for valuabhelp during our stay at HASYLAB. One of us~K.H.! wantsto thank the DAAD for financial support and M. Tolan fofruitful discussions. Enlightening conversations withSalditt are gratefully acknowledged. We are grateful fornancial support from BMFT under Grant No. 055MAXIand from Volkswagen-Stiftung I/68769.

1W. Hansen, J. P. Kotthaus, and U. Merkt, inSemiconductor and Semimeals, edited by R. K. Willardson, A. C. Beer, and E. R. Weber~Academic,San Diego, 1992!, Vol. 35, p. 279.

FIG. 5. AFM topography of the surface grating~lower part!. Surface profilealong the section A, B~upper part!. Periodicity of 522 nm and height amplitudes between 3 and 5 nm are found.

1215Metzger et al.

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