P4-23: Determination of the field enhancement factor distribution of field emitter nanoemission matrix from emission investigation

It is shown that current take-off of matrix field nanoemitters, taking into account a statistical nature of the field enhancement factor distribution of separate emitters, can be written in the form of the Fredholm equation of the first kind. A method for determination of statistical function of the field enhancement factor distribution of the matrix field emission nanostructures is proposed from emission test results. Since the current take-off equation is the Fredholm equation of the first kind from product of arguments, an inverse task of the determination of the field enhancement factor distribution from the emission test results is ill-posed. The effective algorithm connected to the Fourier transform of the Tikhonov functional is proposed for solving the inverse task. The correctness of solution, its stability, and convergence to the exact solution are shown when an error of source information tends to zero. The numerical simulation results of the solution of the direct and inverse tasks are shown.