TOPICAL COLLECTION: 59TH ELECTRONIC MATERIALS CONFERENCE 2017

Mapping of Lattice Strain in 4H-SiC Crystals by SynchrotronDouble-Crystal X-ray Topography

JIANQIU GUO ,1,3 YU YANG,1,4 BALAJI RAGHOTHAMACHAR,1,5

MICHAEL DUDLEY,1,6 and STANISLAV STOUPIN2,7

1.—Department of Materials Science and Engineering, Stony Brook University, Stony Brook,NY 11794, USA. 2.—Cornell High Energy Synchrotron Source, Cornell University, Ithaca,NY 14850, USA. 3.—e-mail: jqguo123@gmail.com. 4.—e-mail: yu.yang@stonybrook.edu. 5.—e-mail:balaji.raghothamachar@stonybrook.edu. 6.—e-mail: michael.dudley@stonybrook.edu. 7.—e-mail:stoupin@cornell.edu

The presence of lattice strain in n-doped 4H-SiC substrate crystals grown by aphysical vapor transport method can strongly influence the performance ofrelated power devices that are fabricated on them. Information on the leveland the variation of lattice strain in these wafer crystals is thus important. Inthis study, a non-destructive method is developed based on synchrotron dou-ble-crystal x-ray topography to map lattice strains in 4H-SiC wafers. Mea-surements are made on two 4H-SiC substrate crystals—one is an unprocessedcommercial wafer while the other was subject to a post-growth high-temper-ature heat treatment. Maps of different strain components are generated fromthe equi-misorientation contour maps recorded using synchrotron monochro-matic radiation. The technique is demonstrated to be a powerful tool in esti-mating strain fields in 4H-SiC crystals. Analysis of the strain maps also showsthat the normal strain components vary much more significantly than do theshear/rotation components, indicating that lattice dilation/compression ratherthan lattice tilt is the major type of deformation caused by both the incorpo-ration of nitrogen dopants and the nucleation of basal plane dislocations.

Key words: Silicon carbide, double-crystal x-ray topography, lattice strain

INTRODUCTION

Residual stress is often observed in n-doped 4H-SiC substrate crystals after physical vapor trans-port (PVT) growth and/or high-temperature heattreatments. Since perfect crystals should be free ofstress at a homogeneous temperature, the presenceof residual stress at room temperature is usually aresult of lattice strain brought about by the exis-tence of lattice imperfections such as inhomoge-neous distribution of point defects/dopants,dislocations, low-angle grain boundaries, precipi-tates, inclusions, etc. Such lattice strain will have asignificant impact on the homogeneity of the epi-taxial layers grown subsequently, thus affecting the

functionality and reliability of the related devicestructures.1 It is therefore important to estimate thelevel and variation of lattice strain in these crystals.Double-crystal x-ray topography is a highly strain-sensitive technique for imaging single crystals.2

With angular resolutions as low as a few seconds ofarc, the technique yields a strain sensitivity of 10�6

level. Stress/strain measurements based on thistechnique have already been successfully applied todifferent single-crystal systems such as Si,3 GaAs,4,5

Nb,6 CdZnTe,7 InP,8 diamond9,10 which are primar-ily single crystals with cubic structures. In thisstudy, we demonstrate that this technique is alsoextremely useful in estimating the strain level inhighly anisotropic 4H-SiC substrate crystals.

(Received July 13, 2017; accepted September 1, 2017;published online September 20, 2017)

Journal of ELECTRONIC MATERIALS, Vol. 47, No. 2, 2018

DOI: 10.1007/s11664-017-5789-x� 2017 The Minerals, Metals & Materials Society

903

THEORY

When a single crystal is illuminated by monochro-matic x-ray radiation of a certain divergence, only alimited region will diffract. This is due to theexistence of lattice deformation (effective misorien-tation) that deviates the rest of the crystal fromperfect Bragg condition by Dx, and thus only asmall region is accepted for diffraction. With asingle exposure, a so-called equi-misorientationcontour can be obtained on the recording plate, asshown in Fig. 1a. In order to image the rest of thecrystal, a small rotation of the same amount Dxabout the x axis is applied to the crystal so that adifferent region will be accepted for diffraction andanother contour will be obtained, as shown inFig. 1b. A contour map can therefore be generatedby rocking the crystal through the perfect Braggcondition with small steps of angular rotation andtaking an exposure at each step. According toBragg’s Law, for an arbitrary location in the crystalreferenced to a perfect lattice, the deviation fromperfect Bragg condition is due to the convolutedeffect of local lattice dilation/compression (@ui=@xi)and lattice shear/rotation (@ui=@xk). This can beexpressed in the following equation6:

xxi xjð Þ ¼ @ui

@xitanhB þ @ui

@xkð1Þ

where xxi xjð Þ denotes the angular deviation fromperfect Bragg condition and, if a reference point is

selected in the crystal to be free of strain, xxi xjð Þequals the amount of angular movement one has toapply to shift the equi-misorientation contour fromthe reference point to the location of interest byrotating the diffracting plane xi about xj axis. hB isthe perfect Bragg angle. In order to deconvolutethese two strain components, an additional contourmap is needed with diffraction taking place on thesame lattice plane but with an opposite diffractionvector (�~g). This can be done practically by firstrotating the crystal about the diffraction planenormal by 180� and recording another contourmap in the same manner. In the �~g contour map,the local deviation from perfect Bragg’s condition isgiven by:

x�xi xjð Þ ¼ @ui

@xitanhB � @ui

@xkð2Þ

where the shear/rotation component @ui=@xk makesan opposite contribution to the deviation in the �~gmap and thus has a negative sign in front of it.Simple addition and subtraction of Eqs. 1 and 2yield:

@ui

@xi¼ xxi xjð Þ þ x�xi xjð Þ

2tanhBð3Þ

@ui

@xk¼ xxi xjð Þ � x�xi xjð Þ

2ð4Þ

The values of these two strain components for anylocation in the crystal can thus be quantitativelyestimated. The complete set of strain tensors(eij ¼ 1=2 @ui=@xi þ @ui=@xj

� �) can be accessed from

various �~g contour maps which are obtained byrotating different diffracting planes about differentaxes.

EXPERIMENTAL

In this study, two different silicon carbide sam-ples were analyzed. The first sample was a 75-mmn-doped 4H-SiC commercial wafer. SynchrotronMonochromatic x-ray topography was carried outat Beamline 1-BM in the Advanced Photon Source(APS) in the Argonne National Laboratory. A dou-ble-crystal setup with a Bragg/Bragg+� setting wasused in which the first crystal was a highly asym-metric Si (331) beam expander and the secondcrystal, the silicon carbide wafer, was diffractingwith ~g ¼ 0008ð Þ in reflection geometry.11 A sche-matic of the diffraction geometry is shown inFig. 2a. The þ~g contour map was obtained byrocking the wafer about the �1100

� �axis through

the perfect Bragg condition and the �~g map wasobtained in the same fashion after the wafer wasrotated about the 0001½ � axis by 180�. The diffractionimage was recorded on high-resolution x-ray filmswhich were placed 30 cm from the sample andparallel with the sample surface for minimumimage distortion. The sample was mounted on themotorized goniometer without adhesive tape so thatno additional stress was applied to the wafer duringthe experiment.

The second sample we analyzed was a5 mm 9 5 mm piece cut from a 150-mm n-doped4H-SiC commercial wafer. This sample was subjectto a special high-temperature heat treatment inwhich a large thermal gradient was created byheating the sample on a local spot up to 1600�C. Ahigh strain center was expected in this sample.Synchrotron monochromatic x-ray topography wascarried out at Beamline C1 in the Cornell HighEnergy Synchrotron Source (CHESS). A similardouble crystal set-up10 was used except that thesample was diffracting in transmission geometry, asshown in Fig. 2b. Two sets of �~g contour maps wererecorded; the diffraction vectors were 11�20

� �and

�1100� �

, respectively. For both measurements, thesame orthogonal coordinate system is used wherethe x1, x2, and x3 axis represents 11�20

� �, �1100� �

and0001½ � crystal direction, respectively.

RESULTS AND DISCUSSION

Figure 3a and b shows the 0008 and 000�8 contourmaps recorded from the 75-mm 4H-SiC commercialwafer. The reference point (marked in red) isselected in the very center of the wafer and assumed

Guo, Yang, Raghothamachar, Dudley, and Stoupin904

to be free of strain. In both maps, adjacent contoursare 3.6 s of arc in angular rotation from each other.In order to extract quantitative information, eachcontour map is divided into large numbers of smallsquare boxes of equal size (more than 6000 boxes inthe current case). Each box is identified with thevalue of angular rotation difference between the

region where the box is located and the regionwhere the reference point is located. Therefore, twoquantitative maps of angular rotation can be gen-erated from þ~g and �~g contour maps, respectively(xx3 x2ð Þ and x�x3 x2ð Þ in this case). Values of straincomponents @u3=@x3 and @u3=@x1 for any location inthe wafer can be estimated via Eqs. 3 and 4.

Fig. 1. (a) Equi-misorientation contour is obtained when the crystal is illuminated by monochromatic radiation but only a limited region diffracts.(b) When the crystal is rotated with a tiny step Dx about x axis, another region reaches Bragg condition and diffracts, making the contour shift toa different position.

Mapping of Lattice Strain in 4H-SiC Crystals by Synchrotron Double-Crystal X-rayTopography

905

Corresponding strain maps are then plotted usingMATLAB� and shown in Fig. 4.

In Fig. 4a, @u3=@x3 shows a significant variationacross the 75-mm wafer. With the reference point atthe center of the wafer, the relative strain valueranges from �1:578 � 10�4 in the bottom right to1:429 � 10�4 in the top left. @u3=@x3 is equivalentto the normal strain component e33, which repre-sents the dilation or compression in the latticeparameter, c. It is obvious that the variation of e33

matches very well with the distribution of thecontours, indicating that in 0008 reflection, thelattice dilation/compression makes a predominantcontribution to the local deviation from perfectBragg condition. In contrast, the level of straincomponent @u3=@x1 is almost two orders of magni-tude lower (�10�6 which is close to the sensitivitylimit). Under plane stress assumption (wafer diam-eter � thickness), e13 ¼ e31 ¼ 0, so @u3=@x1 repre-sents the lattice tilt about x2 axis, u x2ð Þ, which is aminimum according to the strain map. This againconfirms that lattice dilation/compression is themajor form of effective misorientation in this wafer.The origin of the strain variation in this wafer is

believed to be the non-uniformity in nitrogen dopingconcentration. According to Jacobson’s model,12

when the isotropic lattice strain varies byDe ¼ 3 � 10�4 from one end of the wafer to another,the nitrogen doping concentration differencebetween the two ends will be at leastDn ¼ 6 � 1018cm�3, which is a reasonable valuefor heavily doped SiC crystals (1018 or 1019 level).

Similar analysis has been carried out on thesecond sample and four strain maps obtained fromthe two sets of �~g contour maps recorded, as shownin Fig. 5a–d. With the reference point selected atthe top-right corner of this 5 mm 9 5 mm sample, astrain center is observed. The strain value in thisregion goes as high as 4:704 � 10�3 for e11 andalmost doubled for e22 (9:870 � 10�3). The origin ofthis strain center is obviously the plastic deforma-tion which occurred during the post-growth high-temperature heat treatment. Synchrotron whitebeam x-ray topograph (SWBXT) recorded from thesame region confirms that a large numbers of basalplane dislocations (BPDs) have been nucleated andaccumulated in the vicinity of heat center. Thetopographic image is shown in Fig. 6. The local BPD

Fig. 2. Geometric set-ups for double-crystal x-ray topography in (a) reflection mode (APS) and (b) transmission mode (CHESS).

Guo, Yang, Raghothamachar, Dudley, and Stoupin906

density near the strain center is above 105cm�2

level. Lattice distortion induced by these BPDsapparently causes the stress concentration. Again,the lattice tilt about x2 and x1 axes, @u1=@x3 and@u2=@x3 respectively, shows insignificant variations(10�5 level) compared to the normal strains accord-ing to the strain maps, indicating that the presenceof dislocations mainly causes lattice dilation/com-pression instead of lattice tilt.

SUMMARY

A non-destructive method has been developedbased on double-crystal x-ray topography to esti-mate the level and variation of lattice strain in 4H-SiC substrate crystals. This technique is capable ofmapping different components of strain tensors at a

large scale (maximum 75 mm in diameter in APS),and the strain sensitivity is as good as the 10�6

level. Such a method is particular useful in reveal-ing the strain field near stress centers and can beeasily applied to different single-crystal substrateand epitaxy systems. The selection of the referencepoint is critical since the strain measured via thismethod is just relative values with respect to thereference point rather than the absolute strain.Demonstration of this technique shows that latticedilation/compression, rather than lattice tilt, turnsout to be the major type of deformation brought byboth nitrogen dopants and BPDs.

ACKNOWLEDGEMENTS

This research used resources of the AdvancedPhoton Source, a U.S. Department of Energy (DOE)Office of Science User Facility operated for the DOE

Fig. 3. Synchrotron double-crystal x-ray topographic contour mapswith diffraction vector (a) ~g ¼ 0008ð Þ and (b) ~g ¼ 000�8

� �. Red dot

denotes the reference point (Color figure online).

Fig. 4. Strain maps of different strain components: (a) @u3=@x3 and(b) @u3=@x1.

Mapping of Lattice Strain in 4H-SiC Crystals by Synchrotron Double-Crystal X-rayTopography

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Office of Science by Argonne National Laboratoryunder Contract No. DE-AC02-06CH11357. Thiswork is based upon research conducted at the Cor-nell High Energy Synchrotron Source (CHESS)which is supported by the National Science Foun-dation and the National Institutes of Health/Na-tional Institute of General Medical Sciences underNSF award DMR-1332208. We would like to spe-cially acknowledge Dr. Ken Finkelstein for his greathelp in experimental setup and useful discussionregarding this work. The Joint Photon SciencesInstitute at SBU provided partial support for traveland subsistence for access to APS.

REFERENCES

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Fig. 5. Strain maps of four different strain components: (a) @u1=@x1 (b) @u2=@x2 (c) @u1=@x3 and (d) @u2=@x3.

Fig. 6. SWBXT image recorded from the same sample showing thenucleation of large numbers of basal plane dislocations near thestrain center. The density of dislocations is too high to resolve asingle dislocation image.

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Mapping of Lattice Strain in 4H-SiC Crystals by Synchrotron Double-Crystal X-rayTopography

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