X-ray diffraction (XRD) is a critical tool for characterizing thin films and epitaxial layers, providing detailed information about crystal structure, strain, thickness, and crystallographic orientation. Unlike bulk materials, thin films present unique challenges due to their reduced thickness, interfacial effects, and epitaxial constraints. XRD techniques such as rocking curves, reciprocal space mapping, and texture analysis are tailored to address these challenges, offering insights into thin-film properties with high precision.

Thin films often exhibit lattice mismatch with substrates, leading to strain that influences their electronic and mechanical properties. XRD measures strain by analyzing deviations in lattice parameters from their bulk values. The out-of-plane lattice parameter is determined from the Bragg peak position, while in-plane strain is assessed using asymmetric reflections or reciprocal space mapping. For epitaxial layers, the strain state can be tensile or compressive, depending on the substrate-film lattice mismatch. By comparing measured lattice parameters with relaxed reference values, the strain tensor can be fully resolved.

Rocking curves are essential for evaluating crystal quality and mosaicity in thin films. The technique involves rocking the sample around the Bragg angle while measuring diffracted intensity. A narrow full width at half maximum (FWHM) indicates high crystallinity, while broadening suggests defects or dislocations. In epitaxial films, rocking curves reveal threading dislocations and tilt misorientations. For instance, GaN films grown on sapphire often exhibit rocking curve widths below 500 arcseconds for high-quality material, while defective films may exceed 1000 arcseconds.

Reciprocal space mapping (RSM) provides a comprehensive view of strain relaxation and crystal coherence in thin films. By scanning both the Bragg angle and azimuthal orientation, RSM distinguishes between pseudomorphic (fully strained) and relaxed layers. The maps display diffuse scattering from defects and peak splitting from partially relaxed regions. For heteroepitaxial systems like SiGe on Si, RSM quantifies the degree of relaxation by comparing peak positions along the in-plane and out-of-plane directions. Fully strained films align vertically in reciprocal space, while relaxed films shift horizontally due to lattice parameter recovery.

Texture analysis determines the preferred crystallographic orientation in polycrystalline thin films. XRD pole figures measure the distribution of crystal planes by rotating the sample through multiple angles. Thin films deposited by physical vapor deposition often exhibit fiber textures, where certain planes align preferentially with the substrate normal. For example, sputtered Al films typically show a strong (111) texture due to surface energy minimization. Quantitative texture coefficients, such as the Lotgering factor, rank the degree of orientation relative to a random powder sample.

Film thickness is another critical parameter accessible through XRD. In epitaxial layers, thickness fringes appear around Bragg peaks due to interference between X-rays reflected from the film surface and substrate interface. The fringe spacing is inversely proportional to film thickness, allowing precise measurement down to a few nanometers. For polycrystalline films, the Scherrer equation relates peak broadening to crystallite size, though it requires correction for instrumental and strain effects. Grazing-incidence XRD enhances sensitivity for ultra-thin films by increasing the interaction volume at shallow angles.

Crystallographic orientation in epitaxial films is determined by phi-scans, where the sample is rotated around the surface normal. Peaks appear at specific angles corresponding to the symmetry of the crystal structure. For instance, a (001)-oriented cubic film exhibits four-fold symmetry in a (111) phi-scan, while a hexagonal film like GaN shows six-fold symmetry. Misoriented domains or twinning can be identified from additional peaks in the scan.

XRD also detects phase purity and secondary phases in thin films. Minor phases with distinct lattice parameters produce separate Bragg peaks, enabling identification even at low concentrations. In perovskite solar cells, for example, XRD distinguishes between the photoactive phase and unwanted lead iodide impurities. High-resolution XRD with synchrotron radiation enhances detection limits for trace phases.

In summary, XRD is indispensable for thin-film characterization, offering non-destructive, quantitative analysis of strain, thickness, orientation, and crystal quality. Rocking curves assess mosaicity, reciprocal space maps resolve strain states, and texture analysis reveals preferred orientations. These techniques are vital for optimizing growth processes and ensuring device performance in applications ranging from semiconductors to optoelectronics. Advances in XRD instrumentation, such as high-brilliance sources and fast detectors, continue to push the limits of thin-film metrology.