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Tomographic Mapping Analysis in the Depth Direction of High-GeContent SiGe Layers with Compositionally Graded Buffers Using Nanobeam X‑ray Diffraction Kazuki Shida,† Shotaro Takeuchi,*,† Yasuhiko Imai,‡ Shigeru Kimura,‡ Andreas Schulze,§ Matty Caymax,§ and Akira Sakai*,† †

Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, Osaka 560-8531, Japan Research & Utilization Division, Japan Synchrotron Radiation Research Institute (JASRI), Sayo, Hyogo 679-5198, Japan § IMEC, Kapeldreef 75, 3001 Leuven, Belgium ‡

S Supporting Information *

ABSTRACT: A high-Ge-content Si1−yGey/compositionally graded Si1−xGex-stacked structure grown on Si(001) is now considered to be an important platform for the realization of advanced nanometerscale complementary metal oxide semiconductor devices with highmobility channel materials, such as III−V materials and Ge, and monolithically integrated photonic modules. The performance of such advanced devices is critically influenced by crystalline inhomogeneity in the stacked structure; therefore, precise characterization of the crystallinity is important. In particular, the development of a characterization method not only for in-plane crystallinity but also for in-depth crystallinity is strongly required. This is because the crystalline quality of the constant composition Si1−yGey is sensitively dependent on that of the compositionally graded Si1−xGex layers underneath. Here, we have demonstrated in-depth tomographic mapping of a high-Ge-content Si1−yGey/compositionally graded Si1−xGex-stacked structure using position-dependent ω− 2θ map measurement using nanobeam X-ray diffraction. This mapping technique is based on the correspondence of each 2θ value in the ω−2θ map to the lattice constant of stacked layers in the depth direction. Application of the proposed analytical procedure provides tomographic maps of the local variation in lattice plane tilting (VLPT) from the obtained ω−2θ maps. It is quantitatively verified that the local crystallinity in the layer at a certain depth is strongly influenced by that underneath the layer. The correlation between the local VLPT and real structural defects in the stacked structure is also discussed in detail. KEYWORDS: compositionally graded SiGe strain-relaxed buffer layer, high Ge content, structural inhomogeneity, tomographic mapping, nanobeam X-ray diffraction

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INTRODUCTION

and dislocation distribution, has been characterized using appropriate tools. Cross-sectional transmission electron microscopy (TEM) has been frequently used to reveal the distribution of dislocations;7−9 however, quantitative evaluation of the crystallinity, except for the estimation of the threading dislocation density, remains a difficult task. On the other hand, nanobeam X-ray diffraction (nanoXRD)5,6,10−12 has been recognized as a powerful tool to analyze the local crystallinity nondestructively, focusing on the lattice plane morphology. In particular, the in-plane microstructures of films, such as the local variation in lattice spacing and tilting, can be quantitatively characterized using nanoXRD. However, in the case of graded SRB, the crystallinity is also predicted to change along the

High-Ge-content SiGe layers on Si(001) substrates are indispensable to realize complementary metal oxide semiconductor (CMOS) devices with advanced active layers, such as high-mobility channels of III−V materials for nMOS and Ge for pMOS and monolithically integrated photonic modules.1 Compositionally graded Si1−xGex strain-relaxed buffers (graded SRBs)2−6 with a ramped Ge content up to 70−100% fabricated on Si(001) are often used and play an important role in the compensation of the lattice mismatch strain between the highGe-content SiGe layers and the substrate. The performance of the active layers is critically dependent on the crystallinity of the high-Ge-content SiGe layer/graded SRB-stacked structures; therefore, structural characterization of these stacked structures is an important issue. In this research field, the crystallinity of graded SRB, including the surface roughness, lattice plane morphology, © 2017 American Chemical Society

Received: January 25, 2017 Accepted: March 29, 2017 Published: March 29, 2017 13726

DOI: 10.1021/acsami.7b01309 ACS Appl. Mater. Interfaces 2017, 9, 13726−13732

Research Article

ACS Applied Materials & Interfaces

(BL13XU) in the Super Photon Ring, 8 GeV (SPring-8) with a photon energy of 8 keV, and an energy resolution of 10−4 using a Si(111) double-crystal monochromator. The primary X-ray nanobeam focused by a zone plate was 360 nm (vertical) × 400 nm (horizontal). The estimated angular divergence was 0.04°, although a 2θ resolution at each pixel in the 2D-CCD X-ray detector was 0.01°. The detailed optical setup of the nanoXRD measurement was described in ref 12. Figure 2 shows the diffraction geometry for asymmetric SiGe 224

depth direction because the Ge content gradually increases with the thickness of the layer. Therefore, the development of quantitative analysis methods is strongly required for the characterization of not only the in-plane microstructure but also the variation thereof in the depth direction of the SiGe-stacked structure. In this study, a tomographic investigation of the crystallinity in the high-Ge-content constant-composition Si1−yGey layer (CC-SG)/graded SRB structure was performed using positiondependent ω−2θ map measurements of nanoXRD. Application of the analytical procedure proposed in this paper enabled successful three-dimensional tomographic mapping of the variation in lattice plane tilting (VLPT) ranging from 10 × 10 × 1 μm3 (expressed in terms of [110] × [11̅0] × [001] directions) in the sample.

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EXPERIMENTAL SECTION

A CC-SG/graded SRB-stacked structure was grown on a Si(001) wafer using chemical vapor deposition. During the growth procedure, the Ge content in the graded SRB was ramped to 70% within a thickness of 4.3 μm. The Ge content in the CC-SG with a thickness of 1 μm was also set to be 70%. The Ge-content depth profile in the sample was analyzed using secondary-ion mass spectrometry (SIMS) measurements. A schematic diagram and a cross-sectional TEM image of the sample are shown in Figure 1. From the TEM result, misfit

Figure 2. Schematic overview of the experimental setup for asymmetric ω−2θ map measurements with nanoXRD for SiGe 224 Bragg reflections and the scanning area of the ω−2θ map measurement.

Bragg reflections for a position-dependent ω−2θ map measurement. The trace of the incident and diffracted X-ray beams on the sample surface was set to be parallel to the [110] direction. The projected beam spot size on the measured surface was 360 × 410 nm2. In this case, the penetration depth of the X-ray nanobeam, defined as the distance from the sample surface, was 16.4 μm. By moving the sample stage at 1 μm intervals along the [110] (defined as X-axis) and [11̅0] (defined as Y-axis) directions, an area of 10 × 10 μm2 was measured, where the total number of sampling positions was 121 points. In addition, laboratory-based high-resolution X-ray diffraction (HRXRD) using a Bruker D8 Discover diffractometer was performed to characterize the degree of strain relaxation (DSR) of the CC-SG/ graded SRB-stacked structure by using SiGe 224 and 004 Bragg reflections. In this case, the projected beam spot sizes on the measured surface were 1.0 × 1.0 mm2 for SiGe 224 Bragg reflections and 1.0 × 1.8 mm2 for SiGe 004 Bragg reflections.

Figure 1. Schematic diagram (left panel) and a cross-sectional TEM image (right panel) of a constant-composition Si1−yGey/compositionally graded Si1−xGex/Si(001)-stacked structure. Dislocations in the graded SRB propagating along the [11̅0] and [110] directions can be seen as representatively indicated by red and yellow arrows, respectively. Lines indicated by white arrows are boundaries due to overlapping two TEM images and do not come from inherent defects in the sample.

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RESULTS AND DISCUSSION In each ω−2θ map obtained by position-dependent nanoXRD measurement of the CC-SG/graded SRB-stacked structure, information is obtained on both the crystallinity in the depth direction and in the in-plane direction. This is because the continuous variation in 2θ value in each map directly reflects the continuous variation in the lattice constants along the depth direction in the graded SRB. Thus, the assignment of each 2θ value to each depth in the sample allows tomographic analysis of the CC-SG/graded SRB-stacked structure. To accomplish this, the Ge content in the depth direction of the sample must first be accurately determined. Figure 3 shows a depth profile of the Ge content measured using SIMS, where the Ge content in the CC-SG was estimated to be 0.686 as the average of values measured at sample depths from 0 to 1 μm. In addition, the Ge content in the graded SRB at sample depths from 1 to 2 μm was found to decrease linearly from 0.686 to 0.617, where the gradient was then determined to be 0.0691/μm using leastsquares fitting.

dislocations propagating along the [11̅0] and [110] directions in the graded SRB can be seen as representatively indicated by red and yellow arrows, respectively. They are inhomogeneously distributed in in-plane and in-depth directions. On the other hand, there are few misfit and threading dislocations in the CC-SG. In this sample, the threading dislocation density in the CC-SG was estimated to be on the order of 106 cm−2. It is well-known that the misfit strain in the graded SRB/Si(001) system is mainly relaxed by generating 60° dislocations propagating along the [110̅ ] and [110] directions.13−15 Because extra half-planes are inserted between the {111} planes by the generation of 60° misfit dislocations, these dislocations have a potential to induce the VLPT to the lattice planes. In this case, the VLPT can be quantitatively estimated by using X-ray rocking curve (XRC) measurements because the full width at half-maximum (FWHM) of measured XRC directly reflects the VLPT of measured lattice planes in SiGe films. In addition, it is well-known that the 60° misfit dislocation density and the associated strain field are closely related to the FWHM measured from XRC.16 To investigate the VLPT locally and quantitatively, the nanoXRD measurements were taken at the hard X-ray undulator beamline 13727


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(iii) The redefined 2θ value is assigned to the depth in the sample. From the SIMS measurements shown in Figure 3, the Ge content in the graded SRB was determined to have a linear relationship with the depth in the range of focus. Thus, the depth D is expressed in the following equation using the composition gradient α, which is 0.0691/μm for the graded SRB in the present sample D=

y′ − x′ y−x = α α

(1)

Here, y′(x′) is the Ge content of the CC-SG (graded SRB) measured using SIMS and y(x) is the Ge content of the CC-SG (graded SRB) measured using XRD. In the present experiment, we have determined y from the 2θ value for the CC-SG, 2θy, in the measured ω−2θ map and the DSR of the CC-SG, βy, by solving a nonlinear equation including 2θy and βy. Detailed analytical procedures are shown in the Supporting Information. A similar manner can be applied to derive the Ge content of the graded SRB, x, by taking the DSR of the graded SRB, βx, into account. Here, DSRs of the CC-SG and the graded SRB were estimated using laboratory-based HRXRD measurements. From the ω−2θ mapping results for SiGe 224 Bragg reflections, both the CC-SG and graded SRB were found to be fully strainrelaxed, and thus both βy and βx can be determined to be 1. The Ge content of the CC-SG was measured as 0.688, which corresponds well with that obtained using SIMS within the measurement error. Detailed results of this analysis are also shown in the Supporting Information. In the practical nanoXRD measurements, we have often measured 2θ values slightly scattered position-by-position in the CC-SG, which is likely due to the measurement scale on which nanoXRD is used to analyze local microscopic regions. Such scattering causes errors in the identification of D at each sampling position. Thus, it is meaningful to estimate the depth error ΔD in the present procedure. Because local variations in both Ge content and strain cause the variation in the 2θ value, they give rise to the variation in y, resulting in ΔD according to eq 1. The variation in y caused by the local strain variation can

Figure 3. SIMS depth profile for the Ge content. The thicknesses of the CC-SG and graded SRB are 1.0 and 4.3 μm, respectively.

A tomographic investigation was attempted for the sample until a depth of 1 μm from the CC-SG/graded SRB interface, where the Ge content decreased linearly. Figure 4a shows a representative ω−2θ map obtained at the sampling position of (X, Y) = (0, 0). A diffraction spot from the CC-SG was clearly observed, while broad diffraction intensities from the graded SRB lie on the high-angle side. The tomographic mapping analysis procedure was as follows. (i) Each ω−2θ map obtained at each sampling position is resolved into several XRCs within the 2θ values ranging from 85.0° to 87.0°. In this regard, each XRC is obtained by integrating the diffraction intensity within a range of 0.08°, which corresponds to twice the angular divergence of the primary X-ray nanobeam. Here, the 2θ position for each XRC is redefined as the central value in the integration range of 2θ. (ii) Figure 4b−d shows typical XRCs derived from the representative 2θ positions in Figure 4a. The XRC with the maximum peak intensity, shown in Figure 4b, comes from the CC-SG, and those at the higher angle side of 2θ, shown in Figure 4c,d, come from the graded SRB. The FWHM from each obtained XRC, which corresponds to the degree of the VLPT of SiGe(224) caused by 60° misfit dislocations, was also determined using Gaussian fitting.

Figure 4. (a) Representative ω−2θ map around SiGe 224 Bragg reflections. Representative XRCs derived from (b) CC-SG and (c,d) graded SRB. 13728


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ACS Applied Materials & Interfaces be estimated to be approximately ±0.1%, which then results in ΔD of approximately ±15 nm, when using the value of 0.06% obtained in ref 5. On the other hand, it was found that the above-mentioned scattering of 2θ values cannot be accounted for solely by the local strain variation of 0.06%. In other words, the local Ge content variation largely contributes to the variation in y, which is estimated to be ±0.21% as the standard deviation and then results in ΔD of approximately ±31 nm. (iv) The primary X-ray nanobeam direction is not parallel to the surface normal, as shown in Figure 5; therefore, correction

Fn′(D) = Fn + 1(D) − {Fn + 1(D) − Fn(D)} × (0.5 + D) tan(12.1°)

(2)

These procedures are applied to all sampling positions. (v) Using all redefined FWHM values at all sampling positions and depths, in-plane FWHM maps can be formed for the sampling area as a function of the sample depth. Figure 6 shows three representative characteristic profiles of the redefined FWHM values as a function of depth at three different positions that were selected from the data processed for all sampling positions after step (iv). The value at depth 0 corresponds to the FWHM of the CC-SG. Figure 6a shows a sudden decrease in FWHM, that is, a reduction in VLPT was observed at shallower depths in one position but at greater depths in the other position (Figure 6b). Figure 6c shows that the VLPT was gradually reduced approaching the CC-SG. Therefore, the depth at which an improvement in the crystallinity occurs and the associated process are critically dependent on the in-plane position in the sample. Figure 7a shows a series of tomographic maps of the FWHM value showing the VLPT, which consists of a map of the CCSG and maps apart from the CC-SG/graded SRB interface in units of approximately 125 nm. Comparison of all maps through the depth direction reveals that the shallower the depth is, the smaller the FWHM values are, indicating the reduction in the VLPT on approaching the CC-SG. Note that the local FWHM values in the CC-SG are strongly influenced by those of the graded SRB. For example, a striped pattern that runs mainly along the [11̅0] direction in the CC-SG map, indicated by black arrows, was observed up to approximately 250 nm in the depth direction. This striped pattern reflects the in-plane spatial VLPT around the [110̅ ] direction. Considering the diffraction geometry used in the present experiment, the VLPT caused by the edge (screw) component of the 60° misfit dislocations propagating along the [11̅0] ([110]) direction can be detected. Therefore, the observed large VLPT is probably

Figure 5. Schematic diagram to indicate the correction of the sampling position. Taking the incident angle of the primary X-ray nanobeam into account, the values at the red dots are obtained by linear interpolation of the FWHM values at two neighboring positions (the black dots).

is necessary to have an exact correlation between adjacent images in tomography. This was achieved by linear interpolation of the FWHM values for two neighboring positions at the same depth to obtain a value, as shown schematically for the red dot-dashed line in Figure 5. When Fn(D) is defined as the FWHM value at the sampling position X = n and at the depth D, the redefined FWHM value Fn′(D) is written as

Figure 6. Three characteristic profiles of the redefined FWHM vs the sample depth plots, where crystallinity is (a) improved at shallower depths, (b) improved at greater depths, and (c) gradually improved as indicated by blue arrows. 13729


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Figure 7. Tomographic FWHM mapping result (a) in units of approximately 125 nm around the CC-SG/graded SRB interface. Black arrows indicate positions of the striped pattern. (b) Tomographic maps in units of approximately 62 nm around depths from 0 to 997 nm. Black-dotted boxes indicate positions where the FWHM locally changes in the mapping area of the nanoXRD measurement.

Figure 8. Cross-correlation (a) between the CC-SG and the layers below it and (b) between adjacent layers with intervals of 62 nm (black), 125 nm (red), and 187 nm (blue). Each schematic diagram shows the correlation of the layers from which R was derived. Dotted lines in (b) are shown as a guide to the eye.

caused by the existence of several 60° misfit dislocations propagating along the [110̅ ] direction and the associated strain field, both of which are components of the cross-hatched pattern17,18 and distributed in the depth direction up to approximately 250 nm in the graded SRB. To conduct a more detailed analysis of such a correlation in the depth direction, many tomographic VLPT maps were drawn in units of approximately 62 nm depth. The results are shown in Figure 7b, and the similarity of the FWHM pattern is qualitatively confirmed in the neighboring maps. A cross-correlation analysis was used to investigate this correlation quantitatively. The quantitative correlation can be evaluated by calculation of the cross-correlation coefficient R

R=

∑ (ξ − ξ ̅ )(η − η ̅ ) ∑ (ξ − ξ ̅ )2 ∑ (η − η ̅ )2

(3)

where ξ and η are the redefined FWHM data sets at one depth and at another depth, respectively, and ξ̅ and η̅ are averages of the redefined FWHM values in the respective data sets. Figure 8a shows R for the CC-SG and the layers located underneath it as a function of depth, where ξ and η in eq 3 are selected from the redefined FWHM data set of the CC-SG and that of the layers at depth, respectively. Note that the R values are greater than 0.9 until a depth of approximately 100 nm, which indicates that the local VLPT of the CC-SG is strongly influenced by that of the graded SRB. R then rapidly decreases and positive R values are observed until a depth of approximately 200 nm. Cross-correlations of the FWHM values between adjacent 13730


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the FWHM showing the VLPT for SiGe(224) was successfully demonstrated using nanoXRD data taken from the sample. The cross-correlation analysis of the tomographic FWHM maps has quantitatively revealed that the local VLPT of the CC-SG and layers at certain depths in the graded SRB is strongly influenced by that of the underneath layer, which directly corresponds to the distribution of the 60° misfit dislocations in the in-plane and the depth directions in the graded SRB. This nanoXRDbased tomographic mapping analysis can open the way to the characterization of not only in-plane microstructures but also the variation in the depth direction for other types of samples with compositionally graded structures, such as the Al1−xGaxN19 and InxAl1−xAs20 systems.

layers with three-depth intervals are shown in Figure 8b, where ξ and η in eq 3 are the redefined FWHM data set at a certain depth and that at greater depths by 62, 125, and 187 nm, respectively. The R values obtained for 62 nm interval plot are greater than 0.6, which means that the FWHMs in over half of the mapping area are correlated with each other, although such a cross-correlation becomes smaller with larger intervals. This result quantitatively indicates that the cross-correlation is dependent on the interval between adjacent layers and that the VLPT of the layers in the graded SRB is influenced by the crystallinity of the adjacent layers. In Figure 8b, two remarkable features of the R value variation are observed: the local minimums at the sample depths of approximately 200 and 700 nm and the plateau between them. The former feature reflects the sudden changes in the FWHM values as shown in Figure 6. This is also observable in the maps shown in Figure 7b, where the sudden changes in the FWHM values occur at the position surrounded by black-dotted boxes, which leads to the decrease in the R value at around the depths. On the contrary, in between the depths, the change in the FWHM pattern is observed to be rather gradual, which therefore leads to the plateau of the R value variation. To investigate the relationship between these features and real structural defects in the sample, TEM observations have been performed. Figure 9 shows a typical cross-sectional TEM image

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsami.7b01309. Details of the analytical procedure to derive the Ge content of y and x in the CC-SG and graded SRB, respectively; details of the DSR measurement using laboratory-based XRD; and reciprocal lattice space plot of SiGe 224 diffraction spots in the CC-SG/compositionally graded SRB-stacked structure (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. Phone: +81 6 6850 6302. Fax: +81 6 6850 6341 (S.T.). *E-mail: [email protected]. Phone/Fax: +81 6 6850 6300 (A.S.). ORCID

Shotaro Takeuchi: 0000-0002-3919-9083 Shigeru Kimura: 0000-0003-1064-7572 Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Figure 9. Cross-sectional TEM image around the interface between the CC-SG and graded SRB. Dislocations in the graded SRB propagating along the [11̅0] direction can be seen as indicated by white arrows.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The nanoXRD measurements were performed at the BL13XU of SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (Proposal no. 2014B1549). This work was partially supported by JSPS KAKENHI grant number JP16H06423. We thank P. Storck of Siltronic AG for supplying the measurement sample for nanoXRD and the result of SIMS measurement.

around the interface between the CC-SG and the graded SRB. It is clearly observed that 60° dislocations were introduced in the graded SRB parallel to the CC-SG/graded SRB interface. Note that the dislocations are distributed not homogeneously but at a few to several hundred nanometer intervals along the depth direction as indicated by white arrows in Figure 9. Such dislocation distribution allows us to deduce that the local VLPT abruptly changes at the depth position where the dislocations are introduced while that gradually changes at the rest of the depth position. This simultaneously explains the observed features of the R values of the FWHM maps depending on the depth.

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REFERENCES

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CONCLUSIONS The correlation of the local VLPT in the depth direction of a high-Ge-content CC-SG/graded SRB structure was investigated using position-dependent ω−2θ map measurements with nanoXRD. Three-dimensional tomographic mapping of 13731


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