I. C. Noyan

High-resolution strain mapping in heteroepitaxial thin-film features

Heteroepitaxial thin-film features that are lattice matched to the underlying substrate undergo elastic relaxation at the free edges of the feature. To characterize the degree of elastic relaxation, we employed synchrotron-based x-ray diffraction techniques to map the change in lattice spacing in the thin film at a submicron resolution. Measurements were conducted on 0.24‐μm thick, heteroepitaxially grown SiGe strips of various widths on Si (001). A comparison of the SiGe diffraction peak positions across the features provides a real-space mapping of the extent of elastic relaxation as a function of linewidth. The resultant in-plane normal film stress measurements were compared to calculated values from several elastic mechanical models to assess their validity in predicting stress distributions within the features.

A Rigorous Comparison of X-ray Diffraction Thickness Measurement Techniques using Silicon-on-insulator Thin Films

Thickness data from semiconductor-grade silicon-on-insulator thin-film samples determined from high-resolution X-ray diffraction (HRXRD) data using the Scherrer equation, rocking-curve modeling, thickness fringe analysis, Fourier analysis and the Warren–Averbach method, as well as with cross-sectional transmission electron microscopy and X-ray reflectivity measurements, are presented. The results show that the absolute accuracy of thin-film thickness values obtained from HRXRD data is approximately 1 nm for all techniques if all sources of broadening are correctly identified, while their precision is one or two orders of magnitude smaller. The use of multiple techniques is required to determine the various contributions to peak broadening.

Submicron mapping of silicon-on-insulator strain distributions induced by stressed liner structures

Strain distributions within a silicon-on-insulator (SOI) layer induced by overlying compressively stressed Si3N4 features were measured using x-ray microbeam diffraction. A comparison of analytical and numerical mechanical models of the depth-averaged strain distributions to the measured strain profiles in the SOI layer indicated a blanket film stress of −2.5 GPa in the Si3N4 features. A two-dimensional boundary element model, implemented to analyze thin film/substrate systems, reproduced the observed strain distributions better than an edge-force formulation due to the incorporation of loading along the Si3N4/Si interface.

Differentiating between elastically bent rectangular beams and plates

We report x-ray microdiffraction curvature measurements of a (100)-type Si single crystal loaded in four-point bending and provide experimental verification of a procedure for differentiating between anisotropic, elastically bent beams and plates. In general usage, beam and plate components are distinguished by dimensions alone. In mechanics, however, beams and plates are differentiated based on their flexural rigidity and stress state. Since current textbooks do not provide a quantitative technique for selecting the proper constitutive equations for these two types of structures, we suggest the extension of an analysis for isotropic materials originated by Searle [G. F. C. Searle, Experimental Elasticity (Cambridge University Press, Cambridge, 1908), pp. 40–58] and expanded on by Ashwell [D. G. Ashwell, J. R. Aeronaut. Soc. 54, 708 (1950)]. We demonstrate that, by varying the degree of bending of an anisotropic strip, a single specimen can behave as both a beam and a plate, as is predicted by this analysis.

Strain measured in a silicon-on-insulator, complementary metal-oxide-semiconductor device channel induced by embedded silicon-carbon source/drain regions

The strain imparted to 60 nm wide, silicon-on-insulator (SOI) channel regions by heteroepitaxially deposited, embedded silicon-carbon (e-SiC) features was measured using x-ray microbeam diffraction, representing one of the first direct measurements of the lattice parameter conducted in situ in an SOI device channel. Comparisons of closed-form, analytical modeling to the measured, depth-averaged strain distributions show close correspondence for the e-SiC features but 95% of the predicted strain in the SOI channel. Mechanical constraint due to the overlying gate and the contribution of SOI underneath the e-SiC in the diffracting volume to the measurements can explain this difference.

Nanoscale silicon-on-insulator deformation induced by stressed liner structures

Rotation and strain fields were mapped across silicon-on-insulator (SOI) regions induced by overlying stressed Si3N4 features using x-ray nanobeam diffraction. The distribution in SOI tilt exhibited an antisymmetric distribution with a maximum magnitude of 7.9 milliradians, representing one of the first direct measurements of the lattice tilt conducted in situ within buried layers using a spot size of less than 100 nm. The measured rotation distribution corresponds to simulated values generated by boundary element method modeling, indicating that the strain transfer into the underlying SOI primarily induces elastic deformation.

Diffraction profiles of elastically bent single crystals with constant strain gradients

This work presents a set of equations that can be used to predict the dynamical diffraction profile from a non-transparent single crystal with a constant strain gradient examined in Bragg reflection geometry with a spherical incident X-ray beam. In agreement with previous work, the present analysis predicts two peaks: a primary diffraction peak, which would have still been observed in the absence of the strain gradient and which exits the specimen surface at the intersection point of the incident beam with the sample surface, and a secondary (mirage) peak, caused by the deflection of the wavefield within the material, which exits the specimen surface further from this intersection point. The integrated intensity of the mirage peak increases with increasing strain gradient, while its separation from the primary reflection peak decreases. The directions of the rays forming the mirage peak are parallel to those forming the primary diffraction peak. However, their spatial displacement might cause (fictitious) angular shifts in diffractometers equipped with area detectors or slit optics. The analysis results are compared with experimental data from an Si single-crystal strip bent in cantilever configuration, and the implications of the mirage peak for Laue analysis and high-precision diffraction measurements are discussed.

Mapping local strain in thin film/substrate systems using x-ray microdiffraction topography

The authors report experimental data and modeling results for reflection microbeam x-ray topographs from a Si substrate strained by an overlying pseudomorphic SiGe film edge. The diffracted x-ray intensity from the Si substrate is strongly asymmetric as a function of distance from the film edge. A model of the diffracted intensity based on the classical Ewald–von Laue dynamical diffraction theory for an antisymmetric strain distribution indicates that the asymmetry in the diffracted beam profile is only due to the scattering process; individual intensity maxima in the intensity profile cannot be uniquely ascribed to individual features in the local strain distribution.

Modeling of kinematic diffraction from a thin silicon film illuminated by a coherent, focused X-ray nanobeam

A rigorous model of a diffraction experiment utilizing a coherent, monochromatic, X-ray beam, focused by a Fresnel zone plate onto a thin, perfect, single-crystal layer is presented. In this model, first the coherent wave emanating from an ideal zone plate equipped with a direct-beam stop and order-sorting aperture is computed. Then, diffraction of the focused wavefront by a thin silicon film positioned at the primary focal spot is calculated. This diffracted wavefront is propagated to the detector position, and the intensity distribution at the detector plane is extracted. The predictions of this model agree quite well with experimental data measured at the Center for Nanoscale Materials nanoprobe instrument at Sector 26 of the Advanced Photon Source.

A Quantitative Analysis of Room Temperature Recrystallization Kinetics in Electroplated Copper Films using High Resolution X-ray Diffraction

Time-resolved in situ x-ray diffraction measurements were used to study the room-temperature recrystallization kinetics of electroplated copper thin films with thicknesses between 400 and 1000 nm. The thinnest films exhibited limited recrystallization and subsequent growth of grains, while recrystallized grains in the thicker films grew until all as-plated microstructure was consumed. For all films, recrystallized grains that belonged to the majority texture component, ⟨111⟩, started growing after the shortest incubation time. These grains exhibited volumetric growth until they achieved the film thickness. After this point the growth mode became planar, with the ⟨111⟩-type grains growing in the plane of the film. Grains with the ⟨100⟩ direction normal to the film surface started growing after the ⟨111⟩-type grains switched to planar growth. However, the planar growth of this texture component finished at the same time as the growth of the ⟨111⟩ grains. Profile fitting of the 111 peak permitted the separat...