Field emission current from multipoint nanoemission matrix, taking into account the statistical nature of the distribution of the field enhancement factor. Determination of the statistic distribution of the field enhancement factor of anoemission matrix of field emitter from results of emission investigation

A method is considered for determining the statistical distribution function of the field enhancement factor matrix nanoscale field emission structures from the results of emission testing. The method is based on the work of academician A.N. Tikhonov, associated with the decision of inverse ill-posed problems described by the Fredholm equation 1-st kind. In deciding it was taken into account that the emission current equation is the equation of Fredholm 1-st kind on the multiplication of argument. This made it possible to use an efficient algorithm associated with the Fourier transform of the functional and unusual. The results of numerical modeling for solving direct and inverse problems are given. The correctness of the solutioning shown, its stability and convergence to the exact solution, the error of initial information tending to zero.