Static disorder in soft X-ray angle-resolved photoemission spectroscopy: theory and application to ion-bombarded InAs(110)

Angle-resolved photoemission spectroscopy (ARPES) is one of the most ubiquitous characterization techniques utilized in the field of condensed matter physics. The resulting spectral intensity consists of a coherent and incoherent part, whose relative contribution is governed by atomic disorder, where thermal contribution is expressed in terms of the Debye-Waller factor (DWF). In this work, we present a soft-X-ray study on the sputter-induced disorder of InAs(110) surface. We define a new quantity, referred to as the coherence factor FC, which is the analogue of the DWF, extended to static disorder. We show that FC alone can be used to quantify the depletion of coherent intensity with increasing disorder, and, in combination with the DWF, allows considerations of thermal and static disorder effects on the same footing. Our study also unveils an intriguing finding: as disorder increases, the ARPES intensity of quantum well states originating from the conduction band depletes more rapidly compared to the valence bands. This difference can be attributed to the predominance of quasi-elastic defect scattering and the difference in phase space available for such scattering for conduction-band (CB) and valence-band (VB) initial states. Specifically, the absence of empty states well below the Fermi energy (EF) hinders the quasi-elastic scattering of the VB states, while their abundance in vicinity of EF enhances the scattering rate of the CB states. Additionally, we observe no noticeable increase in broadening of the VB dispersions as the sputter-induced disorder increases. This observation aligns with the notion that valence initial states are less likely to experience the quasi-elastic defect scattering, which would shorten their lifetime, and with the random uncorrelated nature of the defects introduced by the ion sputtering.