Using X-Ray Topography to Inspect Surfaces of Single-Crystal Components

Using X-Ray Topography to Inspect Surfaces ofSingle-Crystal Components

David Black*

NIST, Ceramics Division, Gaithersburg, MD 20899-8523

X-ray diffraction topography, which is sensitive to local strain and/or crystallographic orientation, provides a unique viewof the surface of single-crystal samples and can be used to nondestructively inspect for surface and subsurface damage. Theattributes of synchrotron-based X-ray topography as applied to inspection will be described and illustrated with examples fromrecent experiments.

Introduction

Single-crystal materials are incorporated in a widevariety of technological applications, e.g., semiconduc-tors for electronic devices, as optical elements and asstructural components. In these applications, the finalstate of the material is usually a fabricated product re-quiring substantial cutting, shaping, and polishing,many times starting from a large single-crystal boule.Inspection is a critical part of this fabrication process. Itprovides the assurance that each step in the fabricationprocess has been successful as well as providing feedbackfor process control and development. Successful inspec-tion relies on the application of characterization tools

and techniques that can provide a detailed image of thesurface of a sample and are sensitive to the damage thatresults from the fabrication process. A wide variety oftechniques are used to assess surface and subsurfacedamage, including optical microscopy,1 X-ray diffrac-tion,2 transmission electron microscopy3 and laser lightscattering.4,5 We have explored the use of X-ray diffrac-tion topography as a complementary imaging tool forapplication to single-crystal materials. Topography pro-vides a completely different view of the sample usingdiffracted X-rays to form the image. Because the re-corded topograph is very sensitive to strain and/or cry-stallographic misorientation, features such as subsurfacedamage and the strain fields around defects and fabri-cation damage are obvious in the topograph. These fea-tures can be difficult if not impossible to observe withother methods. One advantage of topography is that thehigh strain sensitivity accentuates defects and flaws. Atopograph recorded at unity magnification can revealdefects and flaws, because of the extended strain field,that are observable only at significantly higher magni-fication by other methods. Therefore, large areas, andin many cases the entire sample, can be examined in a

Int. J. Appl. Ceram. Technol., 2 [4] 336–343 (2005)

Ceramic Product Development and Commercialization

This work was supported by the Ballistic Missile Defense Organization (BMDO) through

the Air Force Metrology and Calibration Program, Heath, Ohio and by the Sapphire Sta-

tistical Characterization and Risk Reduction program, Huntsville, AL. The National Syn-

chrotron Light Source, Brookhaven National Laboratory, is supported by the U.S.

Department of Energy, Division of Materials Sciences and Division of Chemical Scienc-

es, under Contract No. DE-AC02-98CH10886.

*[email protected]

r 2005 The American Ceramic Society

No claim to original US government works

single topograph which still provides details of the crit-ical features. A combination of topography and tradi-tional characterization tools leads to a richer under-standing of the sample surface. It should be noted thatthe examples below are representative of topography aspracticed at a synchrotron radiation facility. The inten-sity and tunability of the X-rays from these sources pro-vide some capabilities not attainable with tube sources.However, many of the advantages of topography forcharacterizing surfaces of single-crystal materials couldbe implemented in a production environment. Forexample, there are commercially available instrumentsthat can scan 300 mm silicon wafers.6

Our use of X-ray topography to inspect for surfacedamage is a result of experience from the Sapphire Sta-tistical Characterization and Risk Reduction Program(SSCARR).7 This program was designed to establish afracture-strength database for sapphire and to developthe means to detect subsurface damage and to control itin single-crystal sapphire windows and domes for theinfrared seekers of antiballistic missiles. The role of theNational Institute of Standards and Technology (NIST)in this program was primarily to identify and evaluateways to nondestructively inspect for sub-surface damage(SSD). A secondary task was to investigate whetherthere was a correlation between inspection results andobservations and actual fracture performance. The re-sults of this second investigation have been reportedelsewhere.8 The discussion of X-ray topography for sur-face inspection will be conducted within the context ofthe SSCARR program. The examples shown will bemostly of sapphire components and test coupons, al-though our experience has shown that similar featuresare seen on many other single-crystal components. Ageneral review of X-ray topography will be given fol-lowed by examples of its application to surface charac-terization and inspection.

X-Ray Topography

X-ray topography is a well-established, nondestruc-tive characterization technique for imaging, by means ofX-ray diffraction, the micrometer-sized to centimeter-sized defect microstructure of single crystals.9–12 Thismethod got its name from the fact that the diffractionimage can resemble a geographical topographic mapwith the appearance of different elevations and topo-graphical contours. However, since diffracted X-raysform the image, its interpretation is not always straight-

forward. In X-ray topography, an X-ray beam illumi-nates the crystal sample and images of the diffractedbeams are recorded. The basis for the technique is thatthe diffracted intensity from any point on a sample isdetermined by the local crystal perfection at that point.In other words, the intensity diffracted from an imper-fect region of the sample will be different from thatfrom a perfect region. Imperfect regions exist aroundcrystallographic defects, surface and subsurface damageand result from long-range inhomogeneous strain. Ho-mogeneous strain fields would not change the diffrac-tion condition and therefore, not result in intensityvariations. If we record the spatial distribution of dif-fracted intensity from the sample surface, we then have amap of the distribution of defects and strain. This mapis the topograph. The experimental geometry for re-cording a surface topograph is shown in Fig. 1. Topo-graphs can be recorded in transmission through thesample, but for inspection, we need consider only sur-face topographs. A monochromatic and nearly parallel(low divergence) X-ray beam illuminates the samplecrystal. A specific set of crystallographic planes is select-ed and oriented with respect to the incident beam at theBragg angle according to the equation:

E ¼ hc=2d sin y ð1Þ

where E is the incident X-ray energy, h is Planck’s con-stant, c the speed of light, and d the lattice spacing of theselected set of planes and y defines the Bragg angle.

The diffracted beam is recorded, at 1:1 magnifica-tion, on high-resolution film, electronically from a dig-ital camera, and/or viewed in real time on X-ray-sensitive video cameras. The best spatial resolution of

Fig. 1. The experimental geometry for recording a surfacetopograph.

www.ceramics.org/ACT Topography of Single-Crystal Components 337

a topograph is about 1 mm and the depth of penetrationinto the sample can be varied from a few tens of mi-crometers to a few nanometers depending on the spe-cific diffraction conditions. Although the typical spatialresolution is only a few micrometers, much smaller de-fects can be imaged because of the extent of the sur-rounding strain field. For example, in high-qualitycrystals, individual dislocations of atomic dimensionare routinely observed with image widths typically afew micrometers. The sensitivity to local crystallograph-ic orientation is of the order of the rocking curve widthof the sample, typically of the order of a few to a fewtens of arcseconds. The strain sensitivity is also depend-ent on specific experimental conditions, but generallyDd/d � 10�4–10�5. The incident beam size can be aslarge as 140 mm� 50 mm so that large areas can beimaged. The topographs shown here were recorded atthe NIST beamline, X23A3, at the National Synchro-tron Light Source at Brookhaven National Laborato-ry.13 The incident beam was prepared using a double-crystal monochromator with asymmetrically cut Si(111) crystals.

Normally, the test coupon is placed in the beamand oriented so that the selected lattice planes satisfy thediffraction condition. The film or other imaging detec-tor is located at twice the diffraction angle. As an ex-ample, consider a sapphire crystal with the surfaceparallel to the basal plane, (0001). The lowest order al-lowed diffraction is the (0006) with a lattice spacing ofd 5 0.21652 nm. With incident X-ray energy of 8 keV,chosen for convenience since the incident energy is tun-able over a typical range from � 5 to � 30 keV, thecrystal will need to be positioned at 20.971 with respectto the incident beam to satisfy the diffraction condition.A topograph recorded in just such a condition is shownin Fig. 2. This topograph shows many of the featurestypically seen on surfaces. Individual dislocations arevisible and a subgrain boundary runs across the image asindicated. There are also fine scratches on the opticalsurface and more severe grinding damage on the sidewall.

Why these features are so prominent will be clearfrom a discussion of the contrast mechanisms that leadto the image. Contrast in X-ray topographs generally isdescribed by two mechanisms: orientation contrast andextinction contrast.14,15 To understand orientation con-trast, consider an X-ray beam incident on a sample con-taining areas that are crystallographically misoriented,such as the subgrain structure in Fig. 2 for example. Ifthe misorientation (or strain) is sufficient to be outside

the reflecting range (rocking curve) of the crystal theBragg condition cannot be satisfied and therefore, thatarea of the sample will not diffract. For somewhat lessmisorientation, the diffracted intensity can vary fromnegligible to nearly the intensity in the surroundingcrystal. This effect is seen in Fig. 2 as the contrast acrossthe subgrain varies along the length, tending to diminishnear the right side.

To understand extinction contrast consider the dif-fracted intensity from a single crystal. The intensity dif-fracted from a perfect crystal is proportional to thestructure amplitude16 of the Bragg reflection, |F |,whereas the diffracted intensity from an imperfect crys-tal is proportional to |F |2.17 Therefore, the integratedintensity diffracted from an imperfect region will belarger than that from the surrounding perfect matrix.

Fig. 2. An X-ray topograph of a portion of a large sapphirewindow. The topograph has been rotated 901 counterclockwise fromthe schematic drawing of the part. The prominent linear feature(GB) running from lower left to center right is a low angle grainboundary. Scratches (S) are visible on the optically finished surfaceand more severe grinding damage (GD) is observed on the beveledside of the window.

338 International Journal of Applied Ceramic Technology—Black Vol. 2, No. 4, 2005

This increase in diffracted intensity in the imperfect re-gions is the result of the reduction in primary extinctionand thus the term ‘‘extinction contrast’’ is used.14 Thisis exactly the case in the region around a dislocation forexample.

These contrast mechanisms explain why topogra-phy is so sensitive to fabrication and handling damageand other flaws at the surface. The fabrication processnecessarily damages the sample surface. This damagecan be in the form of cracks, dislocations and strainfields, shown schematically in Fig. 3. As the sample isfurther processed to remove damage such as a scratch, astandard inspection may indicate that the part is damagefree since no alteration/disruption of the surface ispresent, when in fact residual damage remains. This re-maining damage, dislocation loops and strain fields,may be significant, and is precisely the microstructuralfeatures that produce contrast in the X-ray topograph.

An X-ray topograph can be recorded in several dif-ferent configurations. Contrast in the image will resultfrom any deviation from long-range order that has aprojection onto the diffraction vector. Therefore, thesymmetric surface geometry of Fig. 4a, diffraction fromplanes parallel to the sample surface, is sensitive to de-partures from crystalline perfection normal to the sur-face. Whereas the asymmetric geometry of Fig. 4b,diffraction from planes inclined to the sample surface,is sensitive to both in-plane and out-of-plane features.Of particular interest with respect to damage inspectionis the extremely grazing incidence asymmetric geometry.This geometry takes advantage of the fact that for X-raywavelengths the index of refraction is less than 1, given

by n 5 1�a�ib where a is called the unit decrementand b is the imaginary part that accounts for absorption.When an X-ray beam impinges a surface at an anglebelow the critical angle, yc 5 (2a)1/2, total external re-flection occurs exactly analogous to total internal reflec-tion in visible optics. The critical angle for X-rays istypically a few tenths of a degree. By properly selectingthe diffracting planes and the incident X-ray energy, theBragg condition can be satisfied with an incidence anglethat is at or just below the critical angle. For the asym-metric diffraction shown in Fig. 4b, the incidence angleis given by yin 5 yB�31.21. By selecting an X-ray en-ergy of 9.64 keV the Bragg angle will be about 31.41and so the incidence angle will be � 0.21, which isabout the critical angle. Under these circumstances thereare no beams entering the sample, only an evanescentwave that has exponentially decreasing amplitude intothe sample. The effective penetration depth is given by18

DðyÞ ¼ ðl=4pÞf½ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðy2 � y2

cÞ2 þ 4b2

qþ y2

c

� y2�=2g�1=2

where y is the incident angle to the sample surface and lis the wavelength. For a sapphire crystal the penetrationdepth as a function of incidence angle is shown inFig. 5. Just below the critical angle the topograph will be

Fig. 3. A cross-section schematic of how fabrication leads tosubsurface damage.

Fig. 4. The symmetric and asymmetric geometry for surfacetopographs is shown in (a) and (b) respectively.


sensitive to structures within about the first 5 nm of thesample surface. This imaging condition can have a dra-matic effect on the observed microstructure as discussedbelow. In summary, by choice of lattice planes to bestudied, and the angles of incidence and diffraction andthe energy of the incident beam, it is possible to controlthe depth of penetration and therefore isolate structuresat different depths below the surface.

Examples of Surface and Subsurface Damage

One of the first and perhaps most dramatic obser-vations to come from the topographic examination ofpolished surfaces is the extent to which these pristinesurfaces are vulnerable to damage from inadvertent mis-handling of samples. This is evident in Fig. 6a, whichshows damage on a sapphire dome caused by an align-ment jig. Damage from mishandling frequently appearswith a characteristic morphology typified by a series ofparallel, often times serpentine, lines of varying severityas seen in Fig. 6a. This characteristic morphology dis-tinguishes handling damage from other microstructuralfeatures such as dislocation networks, which can also bevisible in topographs. The other typical structure asso-ciated with mishandling is a single dramatic perturba-tion on the surface as seen in Fig. 6b. It was surprising tosee the magnitude of the damage that can occur and thefrequency of occurrence. What is particularly trouble-some with this type of damage for quality control is thatit is very difficult to observe with the usual inspectiontools. Figure 7 shows another handling flaw and optical

Fig. 5. The 1/e penetration depth as a function of the ratio ofincident angle to critical angle for a sapphire surface.

Fig. 6. Typical examples of handling damage observed in X-raytopographs. The image in (a) shows the morphology where damageis characterized by a series of parallel features. Image (b) shows theother morphology of a single perturbation to the surface.


examination required a magnification of � 35 to see thelarge feature that is obvious in the topograph at unitymagnification. And even at this magnification, thesmaller parallel feature is not detectable optically. Thistype of defect can have a substantial impact on the re-sults of mechanical testing for example. Knowing beforehand that some samples have significant damage givesthe experimenter the option to eliminate them from thesample population or treat them separately, potentiallyimproving the results of the experiment. Another ex-ample of the type of surface damage that can go unno-ticed with typical inspection protocols is shown in Fig.8. The flexure strength bars shown were part of a set of39 sapphire bars fabricated to nominally identical spec-ifications for figure and finish. In fact, optical charac-terization indicated that they were identical within

typical variation of the surface finish measurement.19

However, topographic examination of the entire sampleset identified 14 bars as having considerable subsurfacedamage. The remaining bars had high-quality surfaceswith the exception of the pervasive handling damage.The effect of this type of unnoticed damage on test re-sults can be substantial. The average strength of the en-tire population of bars was 5947165 MPa (1 SD).Separating the bars based on the topographic examina-tion resulted in one set of 14 damaged bars with an av-erage strength of 4537125, and a set of 25 undamagedbars with an average strength of 6727129 MPa. Thefabrication processes used to finish the surface of manysingle crystals can lead to an extremely thin damagedregion. The grazing incidence geometry, as discussedabove, is very sensitive to damage within the first fewnanometers of the surface. Figure 9 shows the dramaticeffect that this increased surface sensitivity can have onobserved microstructure. The microstructure observedin grazing incidence from this sapphire crystal was notobserved by typical optical characterization methodssuch as noncontact interferometry or laser light scatter-ing. Similar results have also been observed on manycommercially available silicon wafers. Figure 10 showsthe structure observed from a small part of a production200 mm silicon wafer. While the specifics of the pro-duction process are not known, the concentric circularfeatures on both the sapphire and silicon crystals are asignature of the fabrication process.

Fig. 7. A comparison of topographic images and optical imagesfrom the same sapphire bend bar. The optical images required amagnification of � 35 to observe the handling damage that isobvious in the topograph at unit magnification. The weaker,secondary feature in the topograph is not visible optically.

Fig. 8. Topographs of nominally identical sapphire bend bars.Both samples have handling damage (HD). The bar on the righthas a high quality surface where individual dislocations are evident(D). Optical characterization was not sensitive to the surfacedamage seen in the bar on the left.


One of the strengths of topography when applied tosurface inspection is that the occasional outlier or raresignificant flaw can be easily detected. For example, in

the case of abrasive polishing, occasionally a particle willintroduce substantially more damage into the surfacethan is expected. Continued polishing to smaller gritsizes will remove the majority of the damage from theprevious step but not necessarily that from the unex-pected damage. This residual damage is isolated, notcommon and very difficult to identify. The sapphirecomponent in Fig. 11 shows just such damage. Smallcracks remain from the previous fabrication process thathave not been removed in the final step. These cracksare quite apparent in the topographs but were not de-tected by the standard inspection protocol for thesecomponents.

Fig. 9. An example of the dramatic effect that reduced depth ofpenetration can have on the ability to image surface and subsurfacedamage. The image on the left was recorded just above the criticalangle and the image on the right was recorded just below the criticalangle.

Fig. 10. Part of a grazing incidence topograph from a production200 mm silicon wafer. The parallel features are concentric andindicative of the fabrication process.

Fig. 11. An example of the sensitivity of topography to the residualdamage that can occur in an abrasive polishing process. An abrasiveparticle from a previous step in the fabrication process introducedmore damage into the sample as it traversed the surface as indicatedin the upper image. This damage is easily identified by topographyand can be identified as surface cracks as shown in the lower image.


Conclusion

X-ray diffraction topography is a complementarytool to inspect the polished surfaces of single-crystalmaterials. The topograph is sensitive to microstructuralfeatures, such as fabrication related subsurface damageand mishandling damage, that are often not readily ob-servable by standard inspection methods. Topographycan be a valuable part of an inspection process and whencombined with traditional methods can lead to a betterunderstanding of the microstructure of the surface.

References

1. L. R. Baker, ‘‘Standard for Surface Damage,’’ Opt. Eng., 31 [8] 1685–1689(1992).

2. V. S. Wang and R. J. Matyi, ‘‘X-Ray Diffraction Observation of SurfaceDamage in Chemical–Mechanical Polished Gallium Arsenide,’’ J. Electron.Mater., 21 [1] 23–31 (1992).

3. B. J. Hockey, ‘‘Observation by Transmission Electron Microscopy on theSubsurface Damage Produced in Aluminum Oxide by Mechanical Polishingand Grinding,’’ Proceedings 20 of the British Ceramic Society. The British Ce-ramic Society, Stoke-on-Trent, Great Britain, 95–115, 1972.

4. F. Orazio, V. M. Airaksinen, M. Hokkanen, and M. Hiltunen, ‘‘Using Op-tical Technology to Detect Subsurface Wafer Damage and its Effect on Epit-axial Layers,’’ Micro, 20 [3] 73 (2002).

5. R. M. Silva, F. D. Orazio Jr., and J. M. Bennett, ‘‘Nondestructive Measure-ments of Subsurface Structural Defects in Polished Single-Crystal Silicon,’’Opt. News, 12 10–17 (1986).

6. D. K. Bowen, M. Wormington, and P. Feichtinger, ‘‘A Novel Digital X-RayTopography System,’’ J. Phys. DA: Appl. Phys., 36 A17–A23 (2003).

7. R. Cayse, P. Lagerlof, R. Polvani, D. Harris, D. Platus, D. McClure, C. Patty,and D. Black, ‘‘Sapphire Statistical Characterization and Risk ReductionProgram.’’ Final Report, Nichols Research Corp., Huntsville, AL, SETACContract DASG60-97-D-002, April 28, 2000.

8. D. Black, ‘‘Strength Limiting Surface Damage in Single-Crystal SapphireImaged by X-Ray Topography,’’ J. Am. Ceram. Soc., 84 [10] 2351–2355(2001).

9. B. K. Tanner, X-Ray Diffraction Topography. Pergammon, Oxford, 1976.10. B. K. Tanner, ‘‘Contrast of Defects in X-Ray Diffraction Topographs,’’ X-Ray

and Neutron Dynamical Diffraction Theory and Applications. eds. A. Authier,S. Lagomarsino, and B. K. Tanner. Plenum Press, New York, 1996.

11. B. K. Bowen and B. Tanner, High Resolution X-Ray Diffractometry and To-pography. Taylor and Francis, London, 1998.

12. D. R. Black and G. G. Long, ‘‘X-Ray Topography,’’ NIST SP960-10, (2004).13. R. Spal, R. C. Dobbyn, H. E. Burdette, G. G. Long, W. J. Burdette, and M.

Kuriyama, ‘‘NBS Materials Science Beamlines at NSLS,’’ Nucl. Instrum.Methods Phys. Res., 222 189–192 (1984).

14. J. B. Newkirk, ‘‘Method for the Detection of Dislocations in Silicon by X-Ray Extinction Contrast,’’ Phys. Rev., 110 1465–1466 (1958).

15. J.-F. Petroff, ‘‘Basic Understanding of Image Formation in X-Ray Topogra-phy,’’ Applications of X-Ray Topographic Methods to Materials Science. eds. S.Weissmann, F. Balibar, and J.-F. Petroff. Plenum Press, New York, 75–96,1984.

16. B. D. Cullity, Elements of X-Ray Diffraction. Addison-Wesley, Reading,118–123, 1967.

17. B. E. Warren, X-Ray Diffraction. Addison-Wesley, Reading, 326, 1969.18. R. Feidenhans’l, ‘‘Surface Structure Determination by X-Ray Diffraction,’’

Surf. Sci. Rep., 10 [3] 105–186 (1989).19. D. Black, R. Polvani, K. Medicus, and H. Burdette, ‘‘X-Ray Topography

Study of Surface Damage in Single-Crystal Sapphire,’’ Mater. Res. Soc. Symp.Proc., 590 279–284 (2000).


Using X-Ray Topography to Inspect Surfaces of Single-Crystal Components

Documents

Transcript of Using X-Ray Topography to Inspect Surfaces of Single-Crystal Components