Fig. 3: Space charge region formation and local redistribution of majority charge carriers in multilayer BP close to the flake surfaces.

a Schematic diagram depicting an electrically contacted BP multilayer on a SiO₂ substrate capped with a PMMA protective layer. b Valence band energies within BP with layer number varied from 30 to 10. The dashed grey line denotes the VB position expected in bulk BP as a reference. For clarity, the flake heights are normalised as indicated by the double arrow. c Layer number dependence of the VB bottom energies (orange) and associated with it the augmentation of local carrier density within the central layers of BP flakes. d Examples of local distribution of carriers within BP flakes of different layer numbers (flake heights normalised as in (b) and e the corresponding colour maps depicting local carrier densities within BP flakes as a function of height/layer number. As the layer number is reduced, the majority of charge carriers become confined to the innermost layers. Already for flakes with heights of 10 nm, the free holes are electrically confined into the innermost 1–2 layers, with the carrier-depleted layers not contributing to the charge transport. In all calculations, the average carried density of 2 × 10¹⁸ cm⁻³ was used.