Role of work function distribution on field emission effects

Abstract

Field emission current exponentially depends on the work function of a cold surface. We consider the role of work function distribution on tunneling current. The work function distribution can arise due to nano-scale inhomogeneities of the surface as well as for collection of nano-particles with size distribution. We consider both Gaussian distribution as well as log-normal distribution. For Gaussian distribution, the field emission current, Jav, averaged over work function distribution shows Gaussian dependence, Jav∝exp(ασ2), where σ is the width of the work function distribution and α is a fitting parameter. For log-normal distribution, Jav shows compressed exponential behavior, Jav∝exp(γσn), where the exponent n>1 is a non-universal parameter. We also study in detail field emission current for various electric field strength applied to systems with high density, characterized by Fermi energy, EF≫Φ, Φ being the work function of the system as well as systems with low density characterized by EF≪Φ.