New Method to Determine the Schottky Barrier in Few-Layer Black Phosphorus Metal Contacts

Schottky barrier height and carrier polarity are seminal concepts for a practical device application of the interface between semiconductor and metal electrode. Investigation of those concepts is usually made by a conventional method such as the Schottky-Mott rule, incorporating the metal work function and semiconductor electron affinity, or the Fermi level pinning effect, resulting from the metal-induced gap states. Both manners are, however, basically applied to the bulk semiconductor metal contacts. To explore few-layer black phosphorus metal contacts far from the realm of bulk, we propose a new method to determine the Schottky barrier by scrutinizing the layer-by-layer phosphorus electronic structure from the first-principles calculation combined with the state-of-the-art band unfolding technique. In this study, using the new method, we calculate the Schottky barrier height and determine the contact polarity of Ti, Sc, and Al metal contacts to few-layer (mono-, bi-, tri-, and quadlayer) black phosphorus. This gives a significant physical insight toward the utmost layer-by-layer manipulation of electronic properties of few-layer semiconductor metal contacts.