Optimization of the X-ray incidence angle in photoelectron spectrometers

TL;DR

This paper analyzes how the optimal X-ray incidence angle in photoelectron spectrometers varies with energy, showing it becomes more grazing at higher energies to maximize signal, with practical design implications.

Contribution

It provides a comprehensive calculation of the optimal X-ray incidence angle across a wide energy range, informing spectrometer design.

Findings

Optimal angle decreases from tens of degrees at 50 eV to about one degree at 3.5 keV.

Photoelectron signal can increase by up to a few tens of times with optimal angle.

Trend is largely material independent.

Abstract

Interplay of the angle dependent X-ray reflectivity and absorption with the photoelectron attenuation length in the photoelectron emission process determine the optimal X-ray incidence angle which maximizes the photoelectron signal. Calculations in a wide VUV through hard-X-ray energy range show that the optimal angle goes with energy progressively more grazing from a few tens of degrees at 50 eV to about one degree at 3.5 keV accompanied by the intensity gain increasing up to a few tens of times as long as the X-ray footprint on the sample stays within the analyzer field of view. This trend is fairly material independent. The obtained results bear immediate implications for design of the (synchrotron based) photoelectron spectrometers.