Exact Evaluation of K. Jensen’s General Thermal-Field-Photoemission Integral

Jensen has developed a general expression for the current density JGTF emitted from a surface by thermal or field emission, or by a combination of these processes; he has also shown how the same expression may be analytically extended to compute the current density due to photoemission. JGTF is expressed as a single integral, which Jensen evaluates analytically in certain limits and numerically outside those limits. In this paper, we show how the integral may be expressed generally as convergent series that are easily evaluated numerically for all values of the physical parameters. No real or apparent singularities, like those that appear in the function Z defined by Jensen occur in the series obtained here.