Toward a comprehensive understanding of solid-state core-level XPS linewidths: Experimental and theoretical studies on theSi 2pandO 1s

High resolution X-ray Photoelectron Spectroscopy (XPS) core-level $\text{Si}\text{ }2p$ and $\text{O}\text{ }1s$ spectra of the nonconductors $\ensuremath{\alpha}{\text{-SiO}}_{2}$ (quartz) at 120 and 300 K and vitreous ${\text{SiO}}_{2}$ at 300 K were obtained with a Kratos Axis Ultra XPS instrument (instrumental resolution of $<0.4\text{ }\text{eV}$) which incorporates a unique charge compensation system that minimizes differential charge broadening on nonconductors. The $\text{Si}\text{ }2p$ and $\text{O}\text{ }1s$ linewidths at 300 K ($\ensuremath{\sim}1.1$ and $\ensuremath{\sim}1.2\text{ }\text{eV}$, respectively) are similar for all silicates (and similar to previous thin film ${\text{SiO}}_{2}$ spectra obtained previously), showing that differential charging does not contribute significantly to our spectra. At 120 K, there is a small decrease (0.04 eV) in the $\text{Si}\text{ }2p$ linewidth of $\ensuremath{\alpha}{\text{-SiO}}_{2}$, but no measurable decrease in $\text{O}\text{ }1s$ linewidth. The $\text{O}\text{ }1s$ lines are generally and distinctly asymmetric. We consider all possible sources of line broadening and show that final state vibrational broadening (FSVB) and phonon broadening are the major causes of the broad and asymmetric lines. Previous high resolution gas phase XPS studies have identified large FSVB contributions to the $\text{Si}\text{ }2p$ spectra of ${\text{SiCl}}_{4}$, ${\text{SiF}}_{4}$, and $\text{Si}{({\text{OCH}}_{3})}_{4}$ molecules, and this vibrational structure leads total $\text{Si}\text{ }2{p}_{3/2}$ linewidths of up to $\ensuremath{\sim}0.5\text{ }\text{eV}$, even with individual peak linewidths of $<0.1\text{ }\text{eV}$. The Si atom of $\text{Si}{({\text{OCH}}_{3})}_{4}$ is an excellent analog for Si in crystalline ${\text{SiO}}_{2}$ because the Si-O bond lengths and symmetric stretch frequencies are similar in both compounds. Similar vibrational contributions to the $\text{Si}\text{ }2p$ and $\text{O}\text{ }1s$ spectra of solid silicates are anticipated if the $\text{Si}\text{ }2p$ and $\text{O}\text{ }1s$ core-hole states produce similar changes to the Si-O bond length in both phases. To investigate the possibility, Car-Parrinello molecular dynamics calculations were performed and show that changes to Si-O bond lengths between ion and ground states $(\ensuremath{\Delta}r)$ for both $\text{Si}\text{ }2p$ and $\text{O}\text{ }1s$ hole states are similar for both crystalline ${\text{SiO}}_{2}$ and gaseous $\text{Si}{({\text{OCH}}_{3})}_{4}$. $\ensuremath{\Delta}r$ are $\ensuremath{-}0.04\text{ }\text{\AA{}}$ for $\text{Si}\text{ }2p$ and $\ensuremath{\sim}+0.05\text{ }\text{\AA{}}$ for $\text{O}\text{ }1s$ in both compounds. Indeed, the vibrational envelope from the $\text{Si}\text{ }2p$ spectrum of $\text{Si}{({\text{OCH}}_{3})}_{4}$, broadened to our instrumental linewidth of 0.4 eV, accounts for the majority $(\ensuremath{\sim}0.8\text{ }\text{eV})$ of the $\text{Si}\text{ }2{p}_{3/2}$ linewidth for crystalline ${\text{SiO}}_{2}$ $(\ensuremath{\sim}1.1\text{ }\text{eV})$ with phonon broadening accounting for the remainder. The results provide excellent support for the tenet that final state vibrational splitting, as seen in the gas phase molecules, similarly affects the solid-state spectra. The calculations also indicate that the $\text{O}\text{ }1s$ linewidths should be larger than the $\text{Si}\text{ }2p$ linewidths, as observed in our spectra. FSVB should also lead to small peak asymmetries, as seen in the $\text{O}\text{ }1s$ spectra. The contribution of phonon broadening to the linewidth is also evaluated and shown to be comparable to the FSVB contribution at 120 and 300 K but considerably smaller at very low temperatures.