Thermionic Field Emission Explanation for Nonlinear Richardson Plots

Accurate extraction of the Schottky barrier height (SBH) is imperative to the development of low-resistance contacts. Nonlinearity in the Richardson plot generates errors in the extraction of the SBH. Without invoking generation-recombination currents, defect-assisted tunneling, or even inhomogeneity, nonlinearity of the Richardson plot can be explained by thermionic field emission (TFE) and can be evidenced even in lightly doped diodes. An analytical model is proposed whereby the extracted barrier height is actually related to the peak energy of the energy distribution of the emitted electrons and can be extracted from a typical Richardson plot using polynomial regression. A comparison of the proposed model with the conventional model and a popular inhomogeneous model that uses a Gaussian distribution of barrier heights concludes that the proposed TFE model extends the doping range of an accurate extraction of the SBH.