Validating Raman spectroscopic calibrations of phonon deformation potentials in silicon single crystals: A comparison between ball-on-ring and micro-indentation methods

摘要

Of main interest in the present work is a quantitative comparison between the phonon deformation potential (PDP) values determined for silicon single crystals by two different calibration methods: (i) a macroscopic method exploiting the stress field developed in a ball-on-ring (biaxial) bending configuration; and (ii) a microscopic method using the residual stress field stored around an indentation print. A comparison between the two methods helps to establish the reliability limits for experimental stress analyses in the (001), (011), and (111) planes of silicon devices by means of polarized Raman spectroscopy. Emphasis is also placed on evaluating the degree of precision involved with using a closed-form equation (i.e., as proposed by other authors), which describes the stress state when different crystallographic planes of the Si sample are loaded in the ball-on- ring jig. A comparison between stress profiles obtained by such equations and those computed by the finite element method (FEM) in the loaded disk reveals a clear discrepancy for the (011) plane. Such a discrepancy could be attributed to elastic coupling and anisotropic effects (particularly relevant along the (011) direction), which can lead to errors up to 15% in computing the stress field stored in the silicon lattice.