Revisiting the Valence and Conduction Band Size Dependence of PbS Quantum Dot Thin Films

We use a high signal-to-noise X-ray photoelectron spectrum of bulk PbS, GW calculations, and a model assuming parabolic bands to unravel the various X-ray and ultraviolet photoelectron spectral features of bulk PbS as well as determine how to best analyze the valence band region of PbS quantum dot (QD) films. X-ray and ultraviolet photoelectron spectroscopy (XPS and UPS) are commonly used to probe the difference between the Fermi level and valence band maximum (VBM) for crystalline and thin-film semiconductors. However, we find that when the standard XPS/UPS analysis is used for PbS, the results are often unrealistic due to the low density of states at the VBM. Instead, a parabolic band model is used to determine the VBM for the PbS QD films, which is based on the bulk PbS experimental spectrum and bulk GW calculations. Our analysis highlights the breakdown of the Brillioun zone representation of the band diagram for large band gap, highly quantum confined PbS QDs. We have also determined that in 1,2-ethanedithiol-treated PbS QD films the Fermi level position is dependent on the QD size; specifically, the smallest band gap QD films have the Fermi level near the conduction band minimum and the Fermi level moves away from the conduction band for larger band gap PbS QD films. This change in the Fermi level within the QD band gap could be due to changes in the Pb:S ratio. In addition, we use inverse photoelectron spectroscopy to measure the conduction band region, which has similar challenges in the analysis of PbS QD films due to a low density of states near the conduction band minimum.