Quantum-continuum framework for the limiting charge of metal nanoparticles in contact with substrates

A hybrid theoretical approach is proposed to estimate the maximum charge that a metal nanoparticle can acquire due to tunneling contact with a conducting semiconductor substrate. The method combines analytical relations and self-consistent Kohn–Sham calculations of the electron work function, ionization potential, and critical charge of an isolated particle embedded in a dielectric medium. These quantities were obtained within the framework of density functional theory (DFT) using the free electron model and subsequently adapted for noble metals. The particle capacitance is estimated using the Johnson–Kendall–Roberts contact mechanics model for both rigid and compliant dielectric spacers. It is shown that the dielectric contact region can significantly modify the ionization potential, especially for soft spacer layers. An analytical expression is derived for the maximum number of electrons that can be transferred to the particle, defining the range of attainable excess charges as a function of the spacer elastic properties. The theoretical predictions are compared with experimental data obtained from Kelvin probe force microscopy measurements of charged nanoparticles. The physical origin of the contact potential difference in Kelvin probe experiments is also discussed.