Measurements of x-ray profiles and diffuse scattering from (111), (100) single crystal Niobium films implanted with Nitrogen to average levels of 5 and 0.5 atomic percent are discussed. Theoretical analysis of the asymmetric profiles are used to determine the strain profile in the implanted films. The measured strain profile results from two factors: (1) depth distribution of implants and knock-on damage and (2) elastic constraints. Residual elastic strains develop due to the constraints imposed by a sapphire substrate. Comparison of the diffraction results with theoretical predictions of TRIM indicates the presence of measurable knock-on damage in the films. Huang and Stokes-Wilson scattering measurements made using synchrotron radiation at the ORNL beamline, Brookhaven National Laboratory, were used to reveal the identity of defects formed during the knock-on process

Claussen, J.

Grabowski, K.

Habenschuss, A.

Houska, Charles R.

Ice, G.

Rao, Satish I.

UNT Digital Library

CONF-8811161—1DE89 006685X-RAY DIFFRACTION FROM ION IMPLANTED ZONESSati.sh I. Rao, Charles R. Houska, Department of Materials Engineering, Virginia PolytechnicInstitute and Stale University, Blacksburg, Virginia 24061; K. Crabnvvski and J. Claussen, NavalResearch Laboratory, Washington, D.C., 20375; and G. Ice and A. Hahenschuss, X-14 NSLS,Brookhaven National Laboratory, Upton, NY 11973.ABSTRACTMeasurements of x-ray profiles and diffuse scattering from (III), (100) single crystal Niobiumfilms implanted with Nitrogen to average levels of 5 and 0.5 atomic percent are discussed. The-oretical anatysis of the asymmetric profiles are used to determine the strain profile in the im-planted films. The measured strain profile results from two factors: (i) depth distribution ofimplants and knock-on damage and (ii) elastic constraints. Residual elastic strains develop dueto the constraints imposed by a sapphire substrate. Comparison of the diffraction results withtheoretical predictions of TRIM indicates the presence of measurable knock-on damage in thefilms. Huang and Stokes-Wilson scattering measurements made using synchrotron radiation atthe ORNL beamline, Brookhaven National Laboratory, were used to reveal the identity of defectsformed during the knock-on process.INTRODUCTIONtkm^ontai:Primary solutions(are. under examinations-co taining single foreign interstitials whkh re-main nnclustered in octahedral sites [I] becauseoTtne choice of low implantation temperature*^An energetic interstitial atom produces damage related self interstitixls, and vacancies. Selfinterstitials and vacancies produced by damage become st^regated, due to enhanced diffusion, intoa distribution of small loops at liquid nitrogen temperature.Four implantation energies were used to produce four overlapping Gaussian distributionsof N in a 2500A Nb single crystal film deposited onto a thick (001) sapphire crystal. This givesa nonuniform concentration when superimposed giving an average of 5 at % N. Variations aboutthe average composition produce related variations in the interplanar spacing. Bragg peaks be-come broadened into intensity bands with a characteristic fine structure which is used to obtainthe distribution of interplanar spacing below the free surface. Diffraction theory was developedto allow for the rather large eiTect of static displacement fields about interstitial implants as well*s damage related defects. Kinematic theory was used throughout these developments becauseof the relatively large distortions encountered in high fluence ion-implantation problems.We flntf that the distrihintion of interplanar spacing* is 15% larger than that predicted the-oretically In TRIM. This has been shown (n he related to the excess expansion from residualDISTRIBUTION c? niir r(f.::;iMi;jT .s unn^iuuknock-on damage. Both implanted N and knock-on defect arrangements can produce a latticeexpansion and related compressive stresses. Although some stress relaxation results from fieldcancellation behveen interstitial and vacancy loops, complete cancellation does not occur for smallloops due to core effects.ELASTIC-FREE EXPANSION STRAINSConsider (he overall implanted zone to be contained within semi rigid walls and that it re-sponds elastically without relaxations associated with plastic deformation. That is, the underlyingmaterial does not allow a free expansion of the zone. The strains (and stresses) that developalong the implanted zone can he calculated using the method of strain suppression [2].In treating the purely elastic problem, the implanted zone is allowed to expand freely asuncoupled slabs of constant concentration "C," and a thickness dxj. Each slab undergoes a freeexpansion (or contraction) due to the pressure exerted by the implanted atoms and knock-ondefects. We know that a concentration "C," of one kind of point defect and orientation producesa bulk expansion of the lattice given by (3).where eM are the diagonal components of the strain tensor, expressed in terms of the cuhic coor-dinate system. Cubic symmetry is maintained by allowing each of the axes of the principal strainto he oriented along mutually perpendicular directions in equal numbers. Isotropy is normallylost when the slabs are joined continuously [4] by the method of strain suppression. The elasticstrain profile, expressed in terms of the sample coordinate system, is directly proportional to thevariation of " C . Slabs are joined together continuously making the total strain along the 1' and2' parallel to Hie free surface, essentially zero throughout the implanted zone.The normal elastic strain, at an angle x to the x.t direction, is obtained from [4J.e (x-i) = { e (x ) - e v,(x%)}sinZz + e ,.,(x-i) (2)orwhere= ' ~ Aand il relates to the transformation to the sample coordinate system (4). The total strain in theimplanted /r;ie, at tilt angle z, includes the free expansion strain and the elastic strain, i.e.~^r l> cos jTlie measured strain goes to zero linearly with a coszz dependence, at j = 90°. The ratio of thetotal strain at 7 = 0°, to the free expansion strain is flri which is a magnification factor that canbe a.v large as 2-3. At an angle x — Zo » the total strain is identically equal to the free expansioni.e.cos = > /f «r sinZ2o = - A jfThe main features of the strain equations are illustrated in Fig. 1 for one element.1V<}CC 4V\Incrcoting > .Ploitic Deformation .I I/-PiOJtiCc11110". C"*Off or mot *oo1ic Otf.\FIG. I. Plots of Eq. (6) with andwithout /*•• expansion factori.e completely elastic orcompletely relaxed by plas-tic deformation (fftl — 1).sin* XA measurement of the strain profile at various tilt angles x, allows one to separate the freeexpansion gradient from the elastic strain gradient. X-ray intensity band analysis is used to de-termine the strain profile and is discussed in a later paper.If the concentrations are sufficiently small, these results can be applied to more than onetype of defect by summing over all defect species, "\" to obtain the free expansion profile. Theprofile obtained when the sample is elastically constrained is ohtained by simply multiplying byINTENSITY DISTRIBUTION FROM ELASTICALLY CONSTRAINED ZONEIf the implanted zone is completely constrained by the underlying substrate, then the dis-placement components along at and ai directions, X,, and Ym, are identically equal to zero.Therefore, the strains «=,"„, is only a function of x3 . By introducing these simplifications, andsumming over each layer, one obtains(«N2h'2)*e-M(m,)e-M(m',) (7)where K' is constant over one intensity hand, F is the .structure factor for the normal unit cell.N t a , and N;• i2 are the dimensions of the crystal along ai and at directions parallel to the freesurface and it', = (h, — h), hi = (h2 — k) are variables in reciprocal space. Tlie exponentials con-taining M(m3) and M(mi) are static attenuation factors determined by the implants and loops[1,5]. If Niai and Nja* are taken to be large, the intensity in reciprocal space is spread onlyalong the h3 direction, and is a product of delta functions with respect to the h', and h2 dependence.The variation of the intensity along the h3 direction is obtained by numerically summing Eq. (7)over the entire implanted zone.FIG. 2. Free expansion strain pro-Hies for multiply implantedN into a 2500A (111) ori-ented Nb film on (001)sapphire. Determined from(a) TRIM simulations (b)x-ray intensity band analy-sis.ISOOtpth (NM)200 240 290 3ZOFIG. 3.(222) intensity hand fromTRIM obtained with enrrein Fig. 2(a) using Eq. (7).FIG. 4. Experimental (222) intensityband compared with the in-tensity profile obtained withthe curve in Fig. 2(b) usingE:q.(7).Figure 2(h) shows an experimentally determined strain profile along the multiply implantedNb film and the division of such a zone into connecting linear regions. The assumption of lineargradients introduces sawtooth regions in the strain profile when the strain gradient changes sign.A sinusoidal representation of the strain profile would eliminate the sawtooth discontinuities.However, under the present conditions, the end results from either analysis are not significantlyaltered.Figure 3 illustrates the (222) intensity band from strain profile Fig. 2a obtained from TRIMcalculations. Clearly, this does not fit. Also, TRIM calculations do not account for theNb sapphire interface. Figure 4 illustrates our best fit to the experimental intensity band andgives the experimental curve in Fig. 2(a). The x-ray analysis shows a strain profile that containsadditional detail near the surface and appears to go to zero near the interface. The TRIM cal-culation should not be considered beyond 160 nm. However, the peak location is in agreementwith the constrained elastic modeLA preliminary examination of a (100) Nb film implanted under the same conditions as the(111) orientation gives an intensity band which differs from the results shown with a (111) film.However, the results indicate that they are in accord with an eUstteally contrained model.The (222) planes are parallel to the free surface so that the data are obtained from a radialscan. If this is transformed to (001), bands of the type hk/ must be projected. At an angle ofinclination % corresponding to the (hk/ ) band, the projection is given by* + k2 +(8)When this holds the spread of the intensity along an (hk/) band in the "fa" direction is identicalto the distribution around the corresponding (00/) point A detailed study of six intensity bandswas used to determine the strain distribution along the implanted zone and assess whether thestrains along the 1', T directions are zero.If particle size broadening is negligible, one can show that the strain broadening is propor-tional to / [6] and one can inter-relate (hk/) distributions to the (001) distribution. The spreadin radians ts proportional to the overall strain and described byA20(rad) - 2( e cos22)tan0 (9)This gives the usual tanfl relation between a shift in d-spacing and the related angular change.The additionn! cos'x allows for the projection along an angle j . If this dependence is obeyed, thenthe purely elastic model is verified and particle size broadening is negligible. These data are ex-amined in detail in a later paper.LATTICE DAMAGEA (I M) Nb film was implanted to an average composition of 0.5% N .it LNT to reduce thed-spacing In r-;? Jetting and thereby allow diffuse scattering data to be collected. We have charac-terized the knock-on defect structures with Huang-Stokes-Wilson x-ray diffuse scattering usingLarson plots [7]. This required a difference to he taken between the data from implanted andunimplanted single crystal Nb films. Statistically meaningful data could only be obtained withsynchrotron radiation. This diffuse scattering, resulting front long range elastic displacementfields, and can be explained by vacancy and self interstitial loops of like size distributions withradii extending from 5-ISA.The displacement Meld from knock-on damage has been identified as loops on (211) planesusing an anisotropic calculation by Ohr [8]. Self interstitial and vacancy loops have like dis-placement fields except for a change in sign i.e interstitial loops give a positive displacement alongthe loop axis while vacancy loops give negative values. Although this cancels some of the dis-placement field, the cores continue to make a contribution and account for the 15% differencebetween the x-ray results and TRIM in the range from 0 to 140 nm (Fig 2).At 0.5% N, most of the expansion is due to lattice damage and this is close to the levelfound at 5%. Someplace in between these concentrations, the lattice damage appears to saturatecausing the lattice disturbance from an increasing number of interstitial N defects to dominate.Simulations using expanded versions of TRIM are capable of giving the distribution of en-ergy loss due to knock-on collisions. We were encouraged to find that this follows the samegeneral form as the excess in d-spacing which is attributed to residual knock-on damage.CONCLUSIONS1. For a 5 at % implantation of N in Nb at LNT, the dominant elastic strain is due to singleN interstitials.2. (\A/a lower level of*(0.5O at */• N) knock-on lattice damagtj^sufficiently large and different 4 " * -•flative to single interstitials to be measureable using Huang-Stokes-Wilson diffuse scatter-ing from a single crystal film^tey^hu^u^ ^ XMU) XIA***- & t-J k&s^f 0- $3. X-ray intensity band analysis provides a means of determining the strain profile along animplanted zone.4. The strains remain elastic without observable plastic deformation.ACKNOWLEDGEMENTSWe wnu!d like to acknowledge Professor D. Farkas for providing simulations of the energydeposition curves and the Office of Naval Research for sponsoring this research on Grant #N0004-83-K-P750, P00004. Research was performed in part at thr Oak Ridge National Labo-ratory Bcnm'cne X-I4 at the National Synchrotron Light Source, Brookhaven National Labors-tory, sponsored by tiie Division of Materials Science and Division of Chemical Sciences, U-S.Department of Energy and under Contract DE-AC05-840R21400 with the Martin MariettaEnergy Systems, Inc.REFERENCES1. S.I. Rao, E.J. Ssvino and C.R. Houska in 'Mat. Res. Soc Symp. Proc', V82, pl87 (1987).2. S. Timoshenko and J.N. Goodier, Theory of Elasticity (McGraw-Hill, N.Y., 1970).3. P.H. Dederichs, J. Phys. F. i 471 (1973).4. S.I. Rao and C.R. Houska, J. Appl. Phys. 52* 6322 (1981).5. M.A. Krivoglaz, Theory of X-Ray and Thermal Neutron Scattering by Real Crystals (Ple-num, New York, 1969).6. C.R. Houska, J. Appl. Phys. £L 69 (1970).7. B.C Larson and F.W. Young, Jr. in 'Point Defects and Defect Interaction in Metals' editedby Jin Ich Takamura, Masao Doyama and Michfo Kiritani, University of Tokyo Press, p.679 (1982).8. S.M. Ohr, Thys. Stat SoL 64,317 (1974).DISCLAIMERThis report was prepared as an account of work sponsored by an agency of the United StatesGovernment. Neither the United Slates Government nor any agency thereof, nor any of theiremployees, makes any warranty, express or implied, or assumes any legal liability or responsi-bility for the accuracy, completeness, or usefulness of any information, apparatus, product, orprocess disclosed, or represents that its use would not infringe privately owned rights. Refer-ence herein to any specific commercial product, process, or service by trade name, trademark,manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recom-mendation, or favoring by the United States Government or any agency thereof. The viewsand opinions of authors expressed herein do not necessarily state or reflect those of theUnited States Government or any agency thereof.

X-Ray Diffraction From Ion Implanted Zones

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X-Ray Diffraction From Ion Implanted Zones

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