RETRACTED: A correlation study between size and etching time in Ge mesoporous toward the incorporation of phonon dispersion effect in PCM

Abstract

In this work, a new correlation study based on the phonon confinement model (PCM) and some advanced characterization tools was performed to extract the size of germanium (Ge) nanocrystals (NCs) fabricated by bipolar electrochemical etching. The PCM was established by incorporating simultaneously the size distribution and phonon dispersion effects. A correlation study of Raman spectroscopy with Atomic force microscopy (AFM), and High-resolution scanning transmission electron microscope (HRSTEM) was confirmed the presence of a spherical core with an average size of 8 nm and very small crystallites of 3 nm. This study confirms that the phonon dispersion has an excellent contribution to the broadness and the shifting of the Raman lines of Ge NCs. In addition, an observation of the breaking down and deviation of the PCM model due to the presence of crystallites in the range of [1–5 nm] is confirmed. • Strong contribution of phonon dispersion effect to quantum confinement effect in Ge nanocrystals. • AFM and Raman spectroscopy as powerful probing tools for tuning the synthesis parameters of Ge porous layers. • Limitations of phonon confinement model (PCM) is confirmed in the size range of [2–5 nm].