In fabricating advanced silicon (Si)-based metal–oxide semiconductors, the ability to inspect dopant distribution in Si ultrathin films (tens of nm) is crucial for monitoring the amount of dopant diffusion. Here, we perform an anisotropic reflective second harmonic generation (SHG) measurement to demonstrate the sensitivity of SHG to phosphorus (P) concentration within the range of 2.5×1017 to 1.6×1020 atoms/cm3. In addition, we propose an analysis method based on a simplified bond-hyperpolarizability model to interpret the results. The bond vector model that corresponds to the P vacancy clusters is built to calculate the SHG contribution from substitutionally incorporated P atoms. The effect of incorporating P into the Si lattice is reflected in the effective hyperpolarizability, lattice tilt, and deformation of this model. The fitting results of the intuitively defined coefficients exhibit a high correlation to the P concentration, indicating the potential of this model to resolve the properties in complex material compositions. Finally, a comparison with Fourier analysis is made to evaluate the advantages and disadvantages of this model. Combined anisotropic reflective SHG (Ani-RSHG) and the simplified bond-hyperpolarizability model (SBHM) can analyze the crystal structure of doped ultrathin films and provide a non-destructive nanophotonic way for in-line inspection.

Si/SiGe stacked multilayers are key elements in fabrication of gate-all-around (GAA) structures and improvement of electrical properties, with the evolution of the Si/SiGe interfaces playing a crucial role. In this work, a model is developed based on the simplified bond hyperpolarizability model (SBHM) to analysis the anisotropic reflective second harmonic generation (Ani-RSHG) on a three-period stacked Si/Si1−xGex multilayer, which builds on Si(100) diamond structures. The C4v symmetry of the Si(100) structure enables the second harmonic generation (SHG) contribution from the bonds to be simplified and the effective hyperpolarizabilities of the interfacial and bulk sources to be obtained. The effective interface dipolar and bulk quadrupolar SHG hyperpolarizabilities in the Si1−xGex sample with various Ge concentration profiles are modeled by interpreting the concentration of a component element as the probability of the element occupying an atomic site. On the basis of the developed model, the Ani-RSHG spectra of the as-grown samples with various Ge ratios for each layer and the samples annealed at 850 °C and 950 °C are analyzed to inspect the change in Ge distribution and its gradient in depth. The Ani-RSHG analysis on as-grown samples showed difference in Ge distribution in samples with the multi Si/SiGe structure, which is not well observed in synchrotron X-ray diffraction (XRD) spectra. For the annealed samples, the response to changes in Ge concentration and its gradient in depth reveal the Si/Si1−xGex interface intermixing. Results of high-angle annular dark-field scanning transmission electron microscopy and energy dispersive X-ray spectroscopy agree well with the Ani-RSHG with SBHM findings. Compared with the Raman and synchrotron XRD spectra, the Ani-RSHG with SBHM simulation result demonstrates much better response to changes in compositions of the Si/Si1−xGex stacked multilayered structures, verifying the potential for characterizing the concentration distribution in stacked multilayered thin films for GAA structures.