VOLUME 82, NUMBER 17 P H Y S I C A L R E V I E W L E T T E R S 26 APRIL 1999

Montréal,

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High Resolution Radial Distribution Function of Pure Amorphous Silicon

Khalid Laaziri,1 S. Kycia,2 S. Roorda,1,* M. Chicoine,1 J. L. Robertson,3 J. Wang,4,† and S. C. Moss41Groupe de Recherche en Physique et Technologie des Couches Minces, Département de Physique, Université de

CP 6128 Succursale Centre-Ville, Montréal, Québec, Canada H3C 3J72CHESS, Wilson Laboratory, Cornell University, Ithaca, New York 14853

3Solid State Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831-63934Department of Physics, University of Houston, Houston, Texas 77204-5506

(Received 23 November 1998)

The structure factorSsQd of high purity amorphous Si membranes prepared by ion implantation wasmeasured over an extendedQ range (0.03 55 Å21). Calculation of the first neighbor shell coordination(C1) as a function of maximumQ indicates that measurement ofSsQd out to at least40 Å21 is requiredto reliably determine the radial distribution function (RDF). A 2% change inC1 and subtle changesin the rest of the RDF were observed upon annealing, consistent with point defect removal. After an-nealing at 600±C, C1 ­ 3.88, which would explain why amorphous Si is less dense than crystalline Si.[S0031-9007(99)09040-7]

PACS numbers: 61.43.Dq, 61.10.Eq

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The atomic structure of pure amorphous silicon (a-Si)is believed to be that of a roughly fourfold coordinatecontinuous random network [1–3], where the local ordis similar to that of crystalline silicon (c-Si). Becauseof the isotropic nature of amorphous materials, the mothat can be determined from a diffraction measuremeis the radial distribution function (RDF) which containonly one-dimensional information. In order to discerthe three-dimensional atomic structure, one must constrmodels and compare them with experiment. Successagreement with experiment is therefore extremely difficuto achieve, even when other data such as density andvibrational spectrum are considered. Hence, radial dtribution functions with the highest spatial resolution arneeded. The study of aa-Si is of particular interest be-cause it is the canonical system for the study of all covlently bonded amorphous materials and has long serveda test material for comparing theoretical and model calclations involving the role of order and disorder in continuous random networks. In spite of all the work that habeen done to date, many aspects of the structure ofa-Siare not well understood. For example, it is still not cleawhy a-Si is 1.7% less dense thanc-Si [4].

Currently, there are two main reasons for the lack of rliable RDF’s ofa-Si. First, most earlier experiments werdone using amorphous Si or Ge produced by deposittechniques such as vacuum evaporation or sputtering10]. Both methods can be optimized to yielda-Si layersof sufficient thickness for x-ray diffraction measurementBut such samples usually suffer from large numbersvoids or impurities in the films [8,11], resulting in a majority of the Si atoms actually having an impurity or voidas one of its “neighbors.” These problems can be ovcome if thea-Si is prepared by self-ion implantation oc-Si, which has been shown to reproducibly yield higpurity, densea-Si without any detectable voids [12]. Thesecond reason for the lack of reliable RDF’s is that e

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periments that were carried out on high quality sampledo not extend out to sufficiently highQ (­ 4pl21 sinu).The spatial resolution of the RDF is inversely proportionato theQ range (extent in reciprocal space) of the expermental data. For example, a resolution of 0.1 Å woulrequire data out to30 Å21, yet few experiments have ex-plored the range beyond25 Å21. In addition, there is therelated problem that the atomic scattering factor for silcon is not well determined beyond20 Å21. An RDF froma measurement over a restrictedQ range typically showssevere termination ripples. Such ripples can be reducby applying damping functions to the data; however, thetreatments severely degrade the resolution of the RDF.

In order to overcome these difficulties and obtainmore reliable RDF, twoa-Si membranes suitable for x-raydiffraction experiments were prepared and their chemicpurity verified [13] by ion implantation of silicon ionsinto c-Si substrates at 77 K. Thirteen different ionenergies were used, varying from 0.5 to 27 MeV, witdoses ranging from5 3 1015 to 9 3 1015 cm22. A 5 mmdiameter area on the backside of the sample was expoto a wet chemical etch (20% KOH at 80±C) in orderto remove the crystalline substrate. No etch stop wused other thana-Si itself. This procedure resulted inpure edge-supporteda-Si membranes of 10 and11 mmthickness. One of the two samples was annealed (befothe wet etch) under vacuum at a temperature of 600±Cfor 1 hour, in order to induce structural relaxation. Botmembranes were slightly buckled.

X-ray diffraction measurements were carried out usingHuber six-circle diffractometer at the Cornell High EnergSynchrotron Source (CHESS) A2-wiggler beam line. Iorder to cover an extended region inQ space from 0.5to 55 Å21 at equidistantDQ of 0.025 Å21, four x-rayenergies (13, 21, 43, and 60 keV) were used in eithtransmission, for the low-Q region from 0.5 to6 Å21,or reflection geometry. Angular scans at the differen

© 1999 The American Physical Society

VOLUME 82, NUMBER 17 P H Y S I C A L R E V I E W L E T T E R S 26 APRIL 1999

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energies were chosen in such a way as to have significoverlap between scans in reciprocal space. Multiple scwere recorded in order to average out artifacts associawith the stability of the source. A displex cryostat wamounted on the diffractometer to cool the samples to 10so as to minimize thermal effects on the diffraction patteas well as air scattering. The absorption coefficientSi was measured for each x-ray energy. Ac-Si powdersample was also measured and analyzed under the sconditions, but only in the range from 1.5 to35 Å21.

The Compton incoherent scattering could be resolvfrom the elastic coherent scattering, except for the lowQ region, by fitting the energy spectrum of the scatterbeam using theoretical Compton profiles. The methwe developed to extract the coherent scattering isscribed elsewhere [14]. The extracted elastic scatterintensity IsQd underwent a series of corrections for deatime, background, absorption, polarization, and the dettor efficiency factor. No multiple scattering correction warequired for such thin samples. The agreement amongferent scans in the overlappingQ regions was good towithin 1%. We used an iterative procedure to extend tatomic scattering factor for Si,f, to55 Å21. Details of thisprocedure and the complete data analysis will be publishelsewhere [15]. Oncef was known, the elastic scattering intensities were normalized to electron units (Ieu) [16].Results from earlier small-angle x-ray scattering (SAXmeasurements [12] were added to the actual data to acha totalQ range from 0.03 to55 Å21.

The structure factorSsQd (­ Ieuyf2) was then deter-mined for both annealed and as-implanteda-Si as shownin Fig. 1. The inset shows the corresponding interferenfunction sssFsQd ­ QfSsQd 2 1gddd. Oscillations in thestructure factors persist far intoQ space (up to40 Å21);beyond this value, statistical noise drowns out the damposcillations. A small difference can be seen between

FIG. 1. The structure factorSsQd of as-implanted (· · ·) andannealed (—)a-Si. The inset plot represents the correspondiinterference functionsFsQd of the two samples in the high-Qregion.

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two structure factors, indicative of a change in the struture during the annealing process. The Fourier transfoof the structure factorSsQd yields the RDFJsrd with

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Our data may extend to55 Å21, but that is still notthe infinite value required for a proper Fourier transformIn order to avoid interference effects caused by statistinoise in the last data point, we used only interferenfunctions which terminate with a value of 0 at the uppintegration limit. In other words, we calculated the RDonly for r values which satisfy

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This is known as the sampling method [17]. The resultinRDF of annealeda-Si is shown in Fig. 2. Every point inthe graph is the result of an unbiased Fourier transfoof the SsQd data; no damping function was used. Thnumber of points is limited because of the restrictioimposed by the sampling method, but in fact this reflecthe true spatial resolution.

Figure 2 shows the RDF of annealeda-Si as calcu-lated with the sampling method (). Significant noiseremains inJsrd due to the statistical noise inSsQd athigh Q. Noting that theSsQd data beyond20 Å21 is al-most exclusively due to first neighbors, we have adoptthe following procedure to suppress the noise: The fineighbor peak in the RDF was isolated and its contribtion to the interference function evaluated through a rverse Fourier transform. This contribution was subtract

FIG. 2. The RDF of annealeda-Si calculated before () andafter (—) filtering the noise fromSsQd at largeQ as describedin the text. The inset shows the first neighbor peak ofJsrdcalculated using various values ofQmax for the upper limit inEq. (1).

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from the total interference function, and the remaining sinal (which, beyondQ ­ 20 Å21, is essentially statisticalnoise only) is damped through multiplication by a factoexpf2asQyQmaxd2g, whereQmax ­ 55 Å21, and the con-stant a is chosen so that a satisfactory reduction of thnoise is achieved, typically6 , a , 9. The unfilteredfirst neighbor contribution is then added to the filteredata, and the resulting interference function is Fouritransformed to yield the solid line shown in Fig. 2.

A full interpretation of the RDF shown in Fig. 2 requiresextensive modeling of the atomic structure, but a few initiobservations are already secure. The absence of featufor r , 2 Å confirms that the corrections and the atomiscattering factor have been dealt with properly. The insof Fig. 2 shows and expanded view of the region arounthe first peak calculated using different values ofQmax, forthe upper integration limit in Eq. (1). Here it can be seethat the subsidiary satellites around the first peak becoless important above40 Å21. The coordination number,peak position, and width of the first neighbor peak of eacRDF were determined for both annealed and as-implantamorphous membranes as well as thec-Si powder usingvarious values forQmax. For this purpose, the peaks werefit to Gaussian distributions. In Fig. 3, the variation othe coordination number of the first peak (C1) of the RDFversusQmax is shown. The coordination number of eacsample initially decreases withQmax then approaches aconstant value around40 Å21. Although the data on thec-Si powder extend only to aQmax of 35 Å21, it is clearthat C1 approaches a value of 4. For low values ofQmax,the fit overestimatesC1 because of the contribution fromtermination ripples (see the inset plot of Fig. 2). For largQ the peak shape becomes independent ofQmax with amean valueC1 of 3.79 6 0.01 for the as-implanted sample,and 3.88 6 0.01 for the annealed sample. We believthat the undercoordination, even in annealeda-Si, is dueto vacancy-type defects (hence the density deficit) rath

FIG. 3. Coordination number of the first neighbor peak fothe as-implanted () and annealed () a-Si, and that for thec-Si powder (?) as a function ofQmax.

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than to isolated dangling bonds, as will be discusseddetail in a forthcoming publication [15]. There is a,2%increases inC1 as a result of the annealing process. Fall three samples the peak was centered at,2.35 Å. Thewidth of the first peak, due to static disorder and thermmotion, corresponds within the errors to 0.065 Å foa-Si, compared to 0.057 Å inc-Si measured with aQmax

of 35 Å21. This leads to an rms static disorder of 0.031for a-Si. BeyondQmax . 40 Å21, we believe that theintrinsic value for the position, coordination number, anwidth has been reached. This would indicate that, evfor a simple single-atom system such asa-Si, reliableRDF’s require scattering intensity data that extend toleast40 Å21.

In Fig. 4, we compare the RDF of both annealed (· · ·)and as-implanted (—)a-Si in the range of 1 to 5 Å, toexamine closely the difference between the relaxed anonrelaxed material. The first neighbor peaks of bosamples are nearly indistinguishable, the only significadifference being the 2% increase, as described aboin C1 upon annealing. Note that the height of thsecond neighbor peak increases upon thermal annealSurprisingly, the widths of the second neighbor peaare almost identical, even though one would expectsignificant sharpening of the second peak as a result ofstructural relaxation, reflecting a narrowing of the bonangle distribution. In order to verify that the annealinprocess indeed altered the structure, we performed Ramspectroscopy on the pieces ofa-Si which had beenexposed to the x rays [13], and indeed there wascharacteristic shift in position of the TO-like band in thRaman spectra. In the region between the secondthird peak, at about 4.7 Å, a small enhancement in tannealed RDF, over the as-implanted RDF, suggestsexistence of a peak (seen earlier by Moss and Gracz[5]) indicative of dihedral bond ordering [6]. We donot believe that this peak is spurious, since it appearsthe same position in all of the RDF’s calculated usin

FIG. 4. Radial distribution functionJsrd of annealed (—) andas-implanted (· · ·) a-Si.

VOLUME 82, NUMBER 17 P H Y S I C A L R E V I E W L E T T E R S 26 APRIL 1999

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different values ofQmax. It, in a sense, represents the losof the distinct (12) third neighbor peak that appears in thcrystal [5].

The 2% change inC1 upon thermal annealing is consistent with other experimental work, which has shown ththe positron spectra [18], Pd solubility and diffusivity [19]and hydrogen trapping [20] all change upon thermal anealing according to a decrease of 2 at. % of trapping siti.e., defects. The increase in the first neighbor coordintion number by the same amount leads us to believe ththe change in the second and third peak of the RDF cbe discussed in terms of point defects, instead of averamedium range order [21]. Upon thermal annealing, 2%the vacancylike defects are removed, effectively changithe first shell coordination. Before removal, each of thedefects induced a distortion in its surrounding, breaking tlocal tetrahedral symmetry, because neighboring atomsthe defect will tend to rearrange in order to eliminate broken bonds. The extent of the local rearrangements cbe estimated from the calculations of defect structuresc-Si. Several studies have shown that, inc-Si, a singlevacancy defect influences the immediate atomic enviroment by altering the interatomic distances, so that the dtance which separates silicon atoms on either side orelaxed vacancy is about 3.4 to 3.5 Å [22]. In Fig. 4, thesdistances correspond to the region (3.2 to 3.6 Å) whea shoulder or broadening of the second neighbor peakas-implanteda-Si appears. Moreover, in a fully coordi-nated random network, the second neighbor coordinatiC2 would be equal toC1sC1 2 1d. An increase inC1 dueto defect removal by thermal annealing would lead to a sinificant increase inC2, as is observed. Comparison withcomputer models is required to quantify the increaseC1 and the shoulder or broadening of the second neighbpeak. We thus conclude that all visible changes in the fiand second neighbor peaks induced by thermal annealare consistent with the annihilation of 2 at. % point defectwhich is in excellent and quantitative agreement withrange of other experiments characterizing structural relaation [18–21].

In summary, we have presented a high resolutiodetermination of the RDF of relaxed and as-implantehigh purity a-Si. X-ray diffraction measurements weremade over a wide range ofQ space (0.5 to55 Å21),and previous SAXS data were added to extend texperimental range from 0.03 to55 Å21. A new methodfor the separation of coherent and Compton scatterihas been applied [14], and the atomic scattering facof silicon has been extended beyond20 Å21 [15]. Theobserved variation of the coordination number with thvalue of Qmax indicates that data beyond40 Å21 arerequired for reliable high resolution information on locaatomic structure in amorphous materials. Followingthermal anneal, no major changes in peak positions awidths have been observed. Instead, subtle changnamely, a 2% increase in the coordination numberthe first neighbor peak, and accompanying changes

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the second neighbor peak are observed, which show tstructural relaxation ina-Si is defect mediated and not aglobal reordering. Even after thermal annealing at 600±C,the first peak coordination number is well below 4, whilthe bond length remains 2.35 Å. With the previousobserved absence of nanovoids [12], this would impthat the density deficit ofa-Si relative toc-Si is due toa fundamental undercoordination.

This work is supported by the Natural Science anEngineering Research Council of Canada (NSERC) athe Fonds pour la formation de Chercheurs et l’Aidela Recherche (FCAR). The Cornell High Energy Synchrotron Source (CHESS) is supported by the NationScience Foundation, under Award No. DMR-931177Work at the University of Houston was supported bthe U.S. DOE/BES under Contract No. DE-FG05-87E45325 and at Oak Ridge National Laboratory under Cotract No. DE-AC05-96OR 22464. It is a pleasure to thanD. L. Willamson for the SAXS measurements, and Larent Lewis, D. L. Price, A. C. Wright, and T. Egami forenlightening discussions.

*Email address: Sjoerd.Roorda@umontreal.ca†Currently with Net Explorer, Houston, TX.

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