Quantitative Nanoscale Imaging of Lattice Distortions in Epitaxial

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Quantitative nanoscale imaging of lattice distortions in epitaxial semiconductor heterostructures using nanofocused x-ray Bragg projection ptychography Stephan O. Hruszkewycz, Martin V. Holt, Conal E. Murray, John Bruley, Judson Holt, Ashish Tripathi, Oleg G. Shpyrko, Ian McNulty, Matthew Highland, and Paul H Fuoss Nano Lett., Just Accepted Manuscript • Publication Date (Web): 21 Sep 2012 Downloaded from http://pubs.acs.org on September 24, 2012

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Quantitative nanoscale imaging of lattice distortions in epitaxial semiconductor heterostructures using nanofocused x-ray Bragg projection ptychography S. O. Hruszkewycz,∗,† M. V. Holt,‡ C. E. Murray,¶ J. Bruley,¶ J. Holt,§ A. Tripathi,k O. G. Shpyrko,k I. McNulty,‡ M. J. Highland,† and P. H. Fuoss† Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA, Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439, USA, IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, USA, IBM Semiconductor Research and Development Center, Hopewell Junction, NY 12533, USA, and Department of Physics, University of California San Diego, San Diego, California 92093, USA E-mail: [email protected]

KEYWORDS: Bragg projection ptychography, strain imaging, x-ray nanodiffraction, ptychography, SiGe / SOI epitaxy Abstract We imaged nanoscale lattice strain in a multilayer semiconductor device prototype with a new x-ray technique, nanofocused Bragg projection ptychography. Applying this technique ∗ To

whom correspondence should be addressed Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA ‡ Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439, USA ¶ IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, USA § IBM Semiconductor Research and Development Center, Hopewell Junction, NY 12533, USA k Department of Physics, University of California San Diego, San Diego, California 92093, USA † Materials

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to the epitaxial stressor layer of a SiGe-on-SOI structure, we measured the internal lattice behavior in a targeted region of a single device and demonstrated that its internal strain profile consisted of two competing lattice distortions. These results provide the strongest nondestructive test to date of continuum modeling predictions of nanoscale strain distributions.

In modern nanotechnology, a fundamental parameter available to manipulate materials properties and performance is strain. For example, in current silicon devices, strain distributions are deliberately introduced to locally modify the band structure and optimize device performance. 1–4 Control and prediction of these lattice responses is challenging because they depend on the complete environment and processing history of the device. Measurement and visualization of these lattice distortions is therefore necessary to fully understand the link between structure and performance in nanoelectronic and other functional nanocrystalline materials, 5 and must be done in operando without perturbing the device boundary conditions. This is especially challenging in nanomaterials technologies that rely on locally confined and strained material volumes at size scales between continuum models and the atomic scale – where prediction, measurement, and control of strain is difficult. For example, current and future ultra large scale integration silicon devices 6,7 employ epitaxial SiGe features as a stressor material in which lattice mismatch with the adjacent Si channel regions imparts strain to tailor specific elastic and electronic properties. Inducing sufficiently large values of strain, through a combination of stressor composition and geometry, improves device carrier mobility while allowing for greater device density through miniaturization. Because this trend can be maintained only so long as mechanisms that degrade the strain transfer (such as plastic relaxation and delamination) are mitigated, characterizing the elastic deformation within these structures at the nanoscale is critical. To address this challenge, we devoloped a new coherent x-ray imaging approach – Bragg projection ptychography (BPP) – and used it to image lattice distortions near the edge of a partially embedded epitaxial Si0.8 Ge0.2 on silicon-on-insulator (SOI) prototype device. Using the resulting quantitative high-resolution BPP strain map, together with complementary experimental and modeling techniques, we determined the strain contributions 2 ACS Paragon Plus Environment

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from epitaxial lattice mismatch and from device processing in a targeted area of the device, and demonstrated that thin film linear elastic modeling remains valid to within tens of nanometers of a material edge discontinuity. Bragg projection ptychography is based on coherent x-ray nanodiffraction, and is capable of imaging diffracting films at sub-20 nanometer spatial resolution and with strain resolution relevant to applied nanoscale devices – an important step towards in operando structural measurements of buried functional nanoelectronic materials. Major advances in x-ray optics and sources have now enabled the development of x-ray diffraction microscopy techniques aimed at this challenge by minimizing the size of a focused beam, 8–10 and by utilizing the coherence of the beam for strain imaging. 11,12 Bragg ptychographic imaging techniques have been under development that combine aspects of nanodiffraction and coherent imaging, 13–16 yielding a robust imaging approach that is sensitive to lattice strain and is capable of resolving features much smaller than the x-ray beam dimensions. Recently, Bragg ptychography has been successfully demonstrated in 3D, 14 and with the rapid throughput, high-resolution 2D imaging capabilities presented here, it emerges as a premier structural characterization tool for functional nanocrystalline materials and devices. The device prototype studied in this work was a rectangular multilayer heterostructure consisting of a 15 nm etched SOI layer capped with a 65 nm thick epitaxial SiGe stressor layer, embedded in the surrounding SiO2 oxide layer (depicted schematically in Figure 1a). Of interest in this study was the in-plane edge of the device, where the truncated multilayer meets the surrounding oxide (TEM cross section shown in Figure 2a). The x-ray intensity at the (004) SiGe specular diffraction peak was measured with 11.2 keV x-rays focused to an 85 nm diameter spot by the zone plate optic at the Hard X-ray Nanoprobe (operated by the Center for Nanoscale Materials at the Advanced Photon Source). The beam was scanned in a rectangular grid along the sample surface with a step size of 25 nm (Figure 1a), yielding a set of coherent (004) SiGe area diffraction patterns with 70% spatial overlap, suitable for ptychographic imaging. Diffraction patterns, like those in Figure 2b, were collected at every point for Bragg projection ptychography, while simultaneously collecting scanning probe Ge Kα fluorescence. (See Supporting Information (SI) for more sample


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and experimental details.) a)

q(004) Incident x-ray wave vector ki

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Projection along kf y′ x

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Figure 1: X-ray Bragg projection ptychography from thin film heterostructures (a) A schematic of the thin film heterostructure studied in this work is shown, composed of layered SiGe (65 nm), SOI (15 nm), and SiO2 films on a Si substrate. The incident coherent x-ray beam was focused down to an 85 nm diameter spot size using a Fresnel zone plate and diffraction patterns from the SiGe layer were measured with an area detector in the far field at the (004) Bragg condition. Also depicted in (a) are a focused beam footprint and overlapping grid points (to scale) at which diffraction patterns were collected for Bragg projection ptychography imaging of the device edge. The calculated focused beam amplitude in the SiGe layer projected along kf is shown in (b), and its 2D Fourier transform amplitude is shown in (c). This simulated diffraction pattern replicates the envelope and pattern of the experimental diffraction measured far from the edge, where the film is fully constrained in a biaxial stress state. This Fourier relationship between the beam projection and the far field area diffraction plane enables Bragg projection ptychography (See SI for more details). Bragg coherent x-ray diffraction imaging techniques, including Bragg ptychography, utilize the structural information encoded in a coherent crystalline Bragg peak for nondestructive strain imaging. 17 The shape of a coherent Bragg peak used for image reconstruction depends on the local crystal density and strain, the scattering geometry, and the x-ray illumination. The diffraction observed in this work (with an area detector) was a slice through the three-dimensional (004) SiGe Bragg peak at the exact Bragg condition. In such a case, the measured intensity encodes information about a specific projection of the locally illuminated crystal – the projection along the exit wave vector kf . 18–20 Using this principle, Bragg diffraction patterns have been used to reconstruct projections of nanocrystals by designing experiments in which a plane wave uniformly illuminates an isolated nanocrystal. 20 Thus, the projection of the unknown crystal determines the intensities 4 ACS Paragon Plus Environment

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at the detector, and the sample projection can be reconstructed with standard CXDI methods by assuming that the illumination is an infinite plane wave apertured by the complex sample shape funciton. Here, we exploit this Fourier relationship between a real space sample projection and the associated Bragg diffraction pattern in a new way to image an extended crystal with tightly focused x-rays that define a local nanoscale scattering volume. A Bragg diffraction pattern in this experiment will not only encode information about the shape and strain of the illuminated region of the crystal, but also the projected complex amplitude and phase distribution of the focused beam (see Figure 1b-c and SI). With Bragg projection ptychography, we demonstrate that, though they are convolved in reciprocal space, the complex contributions of the projected focused beam can be separated from those related to the density and internal strain field of the sample. Ptychography is based on iteratively phasing coherent diffraction patterns from spatially overlapping regions of a sample to reconstruct a complex-valued sample and beam that are consistent with the measured scattering. Using a combination of 2D ptychography algorithms (the Ptychographic Iterative Engine 23 and the Difference Map 21,22 ), we have reconstructed the projected incident nanoprobe beam and a projection of the SiGe lattice displacement field and diffracting density in a targeted region of the multilayer heterostructure (see SI for more details). The resulting image, shown in Figure 3a, is the first of its kind and provided high-resolution structural information near the edge of this prototype device. Simultaneously, the projected nanoprobe beam (Figure 3e) was reconstructed and determined to be 85 nm in size (effective full width at half maximum of intensity profile along dotted line in Figure 3e). The reconstructed SiGe film projection contains information about both the diffracting SiGe film density and its lattice displacement, distinguishable in the complex image as amplitude and phase respectively. 24 Because the film edge is a step function along x and uniform along y, we use line profiles like the one shown in Figure 3b to analyze the film. We separately consider phase and amplitude to characterize the SiGe lattice response in this prototype device and to determine the resolution of this focused beam Bragg projection ptychography measurement. The phase in a Bragg coherent diffraction image is given by the scalar dot product (Ghkl · u), 24


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a)

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Grid points (25 nm step size) Beam diameter (85 nm)

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Figure 2: Focused beam Bragg diffraction near the device edge. (a) Cross-sectional TEM image of the near-edge multilayer region shows the geometry of the film structure (image taken after xray measurements were done). One row of the ptychography raster scan is schematically depicted above the TEM image representing the 25 nm steps taken along x with an 85 nm diameter beam. Selected SiGe (004) diffraction patterns observed at a subset of the ptychographic scan positions along x are shown in (b) (colors of the labels in (b) correspond to colored scan positions in (a) ). For ptychographic imaging, the complete 101 × 3 set of diffraction patterns was used.


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Ptychographic reconstruction x

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Derivative Manual fit

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−0.8 −0.6 −0.4 −0.2 0 Distance x from edge (μm)

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Figure 3: Reconstruction of the near-edge SiGe lattice. The reconstructed SiGe film amplitude and phase are shown in (a). In the amplitude image, green dots indicate the position of ptychography scan points rastered with the beam shown in (e). The edge of the film is clearly visible in the amplitude image, and an amplitude line profile from the reconstruction is shown in (b) plotted alongside the Ge fluorescence scanning probe profile (measured concurrently). The reconstructed object phase map in (a) was unwrapped and converted to units of lattice displacement. The resulting displacement map is shown in (c) together with a line profile along the white dotted line. The derivative of (c) in the x direction is shown in (d) and represents the local slope in an average (001) SiGe lattice plane approaching the edge. In (a),(c),and (d), the shaded regions of the area maps and the light grey regions of the line profiles correspond to areas outside the density envelope of the film where reconstructed phase has no meaning. The reconstructed projected beam is shown in (e) in terms of both amplitude and phase.


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where Ghkl is the diffraction vector of the Bragg peak and u is the local lattice displacement vector. Since the specular (004) SiGe Bragg diffraction condition was used to reconstruct this image, the 2D phase map in Figure 3a is sensitive to the out-of-plane displacement of an average (001) lattice plane. The reconstructed phase map in the illuminated field of view is equivalent to the volumetric (G(004) ·u) distribution projected along kf , and represents a superposition of all lattice displacement fields that have non-zero components along G(004) . Therefore, the sample phase image contains strain information including both lattice curvature and out-of-plane lattice parameter changes. To quantify these lattice features, the reconstructed phase was unwrapped 25 and converted to nanometers, 26 yielding the projected SiGe lattice response near the film edge. A line profile (Figure 3c) shows that the average (001) plane in the SiGe near the device edge is displaced along G(004) by as much as 2.7 nm relative to the film microns away from the edge. The derivative of this displacement (Figure 3d) describes the (001) lattice slope as a function of distance. This slope was independently calculated from the raw data by nanodiffraction analysis (see SI), and the two measurements agree well at distances beyond 200 nm from the edge. This comparison independently verified the quantitative nature of the phase reconstruction, but was limited by the fact that conventional nanodiffraction analysis cannot be applied to points very near the edge because of the broad coherent scattering observed there (Figure 2b). The asymmetric peak in the reconstructed SiGe lattice slope profile (Figure 4e) suggests the presence of two diverging lattice responses of different sign, length scale, and physical origin. A positive lattice slope dominates at distances of −1.2 µm to −200 nm, but near the edge, a competing slope emerges. The micron-scale positive lattice slope in the SiGe film is a result of the physical displacement and curvature of the underlying SOI layer. This curvature, introduced during the high temperature cleaning that preceded SiGe deposition, is seen in Figure 2a and was measured as a function of position with high angle annular dark field (HAADF) scanning TEM using geometric phase analysis 27,28 after the x-ray measurements were completed (see SI). The HAADF TEM SOI lattice curvature measurement, shown with the reconstructed slope in Figure 4, was fitted to an exponential decay function and matches the reconstructed SiGe slope at


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distances greater than 500 nm from the edge, verifying that the SOI curvature was transmitted to the epitaxial SiGe film. This accounts for the micron-scale positive slope in the SiGe ptychography reconstruction, but does not adequately describe the behavior of the SiGe lattice within 500 nm of the edge. 10

Lattice Slope (mrad)

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HAADF TEM

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Figure 4: Lattice behavior of SiGe. The lattice slope of SiGe measured with focused beam x-ray Bragg projection ptychography is shown (black), and is analyzed in terms of two distinct lattice distortion phenomena. The rotation of the SOI lattice beneath the SiGe was measured with crosssectional HAADF TEM (blue crosses) and fitted to a negative exponential (blue curve). Elastic boundary element method modeling near the edge of a differentially stressed film was also done to give a net out-of-plane intrinsic lattice response (green curve). The sum of the fitted SOI lattice curvature and the calculated SiGe near-edge film mismatch response quantitatively account for the asymmetric SiGe lattice slope profile observed with Bragg projection ptychography. In a continuous epitaxial SiGe/SOI film system, the stresses induced by in-plane lattice mismatch are elastically accommodated by an out-of-plane expansion of the equilibrium SiGe unit cell. 8,29 Near an in-plane edge, the SiGe unit cell gradually approaches its stress-free state, 30,42 resulting in both crystal lattice rotation and out-of-plane unit cell contraction (relative to the biaxially constrained film far from the edge). Both of these lattice distortion fields contribute to the reconstructed phase map and can be modeled with linear elastic models such as the boundary element method (BEM). 31,32 The geometry of the edge region, the magnitude of in-plane lattice mismatch, and the elastic constants of Si, SiO2 , and Si0.8 Ge0.2 were used in a BEM model to generate a prediction of the net elastic lattice displacement and slope in the h001i direction of a partially embedded, epitaxially strained SiGe film. The calculated near-edge lattice slope in an average (001) SiGe plane, including the effects of both rotation and unit cell contraction averaged through the 9 ACS Paragon Plus Environment

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film thickness, is shown in Figure 4 (green curve), and has a negative curvature consistent with the compressive in-plane strain state of epitaxial SiGe on SOI. (see SI for more model details). The sum of the calculated SiGe lattice response to epitaxial mismatch and the measured SOI curvature (red curve in Figure 4, labeled SOI + BEM) quantitatively matches the reconstructed lattice slope from focused beam BPP (black curve), thus accounting for the opposing components of the out-of-plane SiGe lattice response in this prototype device. As we have shown, the phase of the reconstruction can quantitatively and accurately resolve lattice displacement and slope along the scattering vector, allowing for accurate extraction of subtle lattice distortions without disturbing the device structure. Furthermore, the SiGe lattice response was mapped at a spatial resolution higher than is achievable with other nondestructive strain mapping techniques, such that we could demonstrate the validity of linear elastic approximations to within 16 nm of this edge discontinuity. Previous measurements of elastic lattice distortions in device nanostructures done with convergent beam electron diffraction, 33–35 nanobeam electron diffraction, 36 and high-resolution TEM 37,38 were determined at the nanometer scale, but with destructive sample preparation that potentially changes the sample lattice, leading to uncertainty in the measurements. TEM techniques such as dark-field holography 5 have been developed to image thicker samples to mitigate strain relaxation, but still preclude in operando device studies. Nondestructive micro-Raman, 39,40 x-ray nanodiffraction, 8,41,42 and electron backscatter diffraction 43,44 studies that are sensitive to local lattice strain have provided a means to compare experimental and theoretical strain distributions in engineered nanostructures at spatial resolutions limited by the size of the beam (150-1000 nm for micro-Raman, 80-250 nm for x-ray diffraction, 20-50 nm for EBSD), with x-rays being the most applicable for studying buried device features. In this work, the SiGe film edge was aligned with the vertical scattering plane so that its projection along kf was as sharp as possible, providing a convenient means by which to estimate the spatial resolution of the measurement. The resolution of the reconstruction was determined to be 16 nm by fitting multiple density profiles and subtracting the contribution of the native edge width (see SI). This resolution is higher than that of the Ge fluorescence profile measured at the same time with the same beam (85 nm) and demon-


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strates that focused beam BPP resolution is not limited by the beam width (85 nm) as other strain determination techniques are. Recently developed x-ray focusing optics have the capability to focus hard x-rays to sub-50 nm length scales with diffractive, 45,46 reflective, 47 and refractive 48 optics, which promise to further improve the spatial resolution of scanning probe nanodiffraction measurements by decreasing the focused beam diameter. The resolution of focused beam BPP, as with all CXDI techniques, is dictated not by the beam size, but by the maximum angle at which photons are detected away from the Bragg condition (corresponding to a diffraction-limited resolution of 7 nm in this work). Focused beam BPP utilizes the size of the coherent nanofocused beam to limit the diffracting volume at each scan point, effectively resolving the position of local strain and density in an extended crystal to within a beam diameter. Ptychography is then used to resolve features in the beam and sample at length scales below the beam size, disentangling the contributions of sample morphology, lattice strain, and the focused beam that are convolved in each coherent diffraction pattern. Sub-beam size resolution is the major advantage of ptychography, and in this nanofocued BPP experiment, it allowed for the use of a higher efficiency zone plate optic with a focal length of 43 mm and a beam size of 85 nm to be used to image thin film lattice features with 16 nm spatial resolution. To reach the potential diffraction-limited resolution of our data (7 nm) with scanning probe microscopy at the same beamline, an optic with a working distance of 8 mm would need to be used to achieve a source demagnification to 7 nm. State-of-the-art hard x-ray optics are approaching this capability, but such short working distances make practical in operando measurements of devices and functional materials in a Bragg geometry much more challenging. Furthermore, the ptychographic approach separates the real space sample image from the fine features of the focused beam, including those due to lens aberrations, that are otherwise entangled in scanning probe images. This is made possible by the point-to-point differences in the coherent diffraction, which are maximized when the beam size matches the length scale of the features imaged in the sample. Because ptychographic reconstructions are most robust and accurate when this condition is satisfied, 13 BPP will benefit from smaller nanofocused beam diameters as the features we image also shrink, so


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long as issues with diffracted signal, focusing geometry, and sample damage can be addressed. The observed multi-scale contributions to lattice distortions near an in-plane heterogeneous interface in this layered SOI/SiGe thin film prototype device underscore the complexities involved in controlling strain in dense functional nanoelectronic systems subject to multiple processing steps. Intrinsic sources of crystal strain, such as lattice mismatch, couple with extrinsic processing artifacts to produce complex lattice responses in functional nanoscale devices. Observing and verifying the various sources of nanoscale lattice distortions and tracking how they couple under working conditions requires the high-resolution, nondestructive strain imaging available with nanofocused x-ray Bragg projection ptychography. Our imaging approach, capable of rapidly imaging planar projections of nanocrystalline lattice distortion and diffracting density, can be extended to in-operando studies of functional nanocrystals and fully encapsulated devices, and also to three dimensional imaging. 16 The combination of recently demonstrated 3D Bragg ptychography, 14 improvements in coherent nanofocusing x-ray optics, and the rapid focused x-ray strain projection imaging capabilities presented here creates a versatile and powerful nanocrystal imaging capability.

Acknowledgement Special thanks go to David Vine, Jesse Clark, and Ross Harder for valuable discussions. This work, including the use of the Center for Nanoscale Materials and the Advanced Photon Source, was supported by the U. S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. Work at the University of California San Diego was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under contract DE-SC0001805. Sample manufacture was performed by the Research Alliance Teams at various IBM Research and Development facilities. S.O.H., M.J.H. and P.H.F. were supported by U.S. DOE, Basic Energy Sciences, Materials Sciences and Engineering Division.


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Supporting Information Available Here we provide additional details regarding focused beam Bragg projection ptychography theory and measurement, sample details, transmission electron microscopy measurement and analysis, and the linear elastic modeling of the SiGe epitaxial film near the edge of the multilayer heterostructure prototype device studied in this work. This material is available free of charge via the Internet at http://pubs.acs.org/.

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Quantitative Nanoscale Imaging of Lattice Distortions in Epitaxial

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