A mathematical model for deep ion implantation depth profiling by synchrotron radiation grazing-incidence X-ray fluorescence spectrometry

Abstract

Synchrotron based grazing incidence X-ray fluorescence (GIXRF) spectrometry is usually applied to obtain shallow depth distributions (less than 25 nm) using information from the X-ray standing wave (XSW). In this paper a new XSW-free mathematical model is proposed that allows the quantitative derivation of much deeper depth distributions. The model was validated with three test Si(111) wafers deeply implanted with 200 keV argon ions of nominal doses of 10¹⁵ to 10¹⁶ at. per cm². Ar ion retained doses determined with our XSW-free GIXRF model agreed well with nominal quantities, additionally cross-checked by ion beam analysis (IBA) techniques. Deduced depth profiles of Ar ions are critically discussed in comparison with the Monte Carlo simulation of Ar ion transport in amorphous silicon. The developed model provides a robust quantification GIXRF methodology to study deeply implanted dopants in semiconductors, expanding the applicability of GIXRF spectrometry in new fields with emerging technological interest.