Test for compliance with the cold field emission regime using the Elinson–Shrednik and Forbes–Deane approximations (Murphy–Good plot)

A test is described in the paper, which allows one to determine the correspondence of experimental data to the classical field dependence. The test is presented in two versions: using the Elinson–Shrednik approximation to the current-voltage characteristics in the classical Fowler–Nordheim coordinates, as well as the modern Forbes–Deane approximation with modified Murphy–Good plot. The application of the test is shown by the example of a study of a multi-tip emitter based on carbon nanotubes. The technique of online calculation of the effective parameters of the emitter and the test is presented.