I–V curve investigation with regression methods

Currently, field electron emission is an indispensable tool for studying advanced materials. Analysis of the current-voltage (I–V ) dependences allows us to derive information about some characteristics of the field-emission cathode (i.e., work function or field enhancement factor values). It is known that in the Fowler—Nordheim coordinates I–V curve is linear. A linear approximation can be constructed with the method of ordinary least squares (OLS). OLS is one of the basic methods of regression analysis used to estimate unknown parameters of regression models. However, reliable confidence intervals for the regression coefficients can only be easily obtained if the model residuals are normally distributed. This is impossible to assume about the log-transformed I–V curve. The scope of this paper is modeling of I–V dependence. The random errors of I measurements are normally distributed. We have constructed estimations of the coefficients in Fowler— Nordheim law (i.e. A and B) using methods of linear and nonlinear regression and shown that those approaches give different results. Errors of determining of the coefficients A and B are presented.