Doped Colloidal InAs Nanocrystals in the Single Ionized Dopant Limit

We investigate the electronic properties of individual n-type (Cu) doped and p-type (Ag) doped InAs colloidal nanocrystals (NCs) in the 2-8 nm size range from their charge transfers toward a highly oriented pyrolytic graphite (HOPG) substrate, using ultrahigh vacuum Kelvin probe force microscopy (KPFM) with elementary charge sensitivity at 300 K. The NC active dopant concentration is measured as N_D = 8 × 10²⁰ cm^-3 and N_A > 5 × 10²⁰ cm^-3 for n- and p-type doping, respectively. The electrostatic equilibrium between the NC and the HOPG reference substrate is investigated and reveals an enhancement of the Fermi-level mismatch between the NCs and the HOPG substrate at reduced NC sizes, both for n- and p-type doping. It also shows, for n-type doped NCs with smallest sizes (-2 nm), the existence of a full depletion regime, in which smallest NCs contain single ionized dopants. Results are compared with self-consistent tight-binding calculations of the electronic structure of InAs NCs, including hydrogenoid impurities and the presence of a host substrate, in the case of n-type doped NCs. The observed enhancement of the NC-HOPG Fermi-level mismatch can be understood by considering a size-dependent electrostatic contribution attributed to dipolar effects at the NC-ligand interface. The estimated surface dipole density equals a few Debye/nm² and is increased at smallest NC sizes, which follows the enhancement of ligand densities at small NC sizes previously reported for metallic or semiconducting NCs. The results put forward the role played by the NC-ligand interface electrostatics for electronic applications.