A test for the applicability of the field emission law to studying multitip field emitters by analysis of the power index of the preexponential voltage factor

A test for the correspondence of experimental current–voltage $(I-U)$ characteristics to the regime of cold field emission is described. The proposed method is based on the variation of voltage power index in semilogarithmic coordinates $\ln(I/U^{k})-1/U$ and the statistical analysis of fluctuations in experimental data. It is established that $I-U$ characteristics obtained by the method of fast high-voltage sweep provide a better correspondence to the field emission law than do the characteristics measured using slow voltage sweep. The test sample was a multitip nanocomposite field emitter based on carbon nanotubes in a polymer matrix. Experimental data have been processed in modified Fowler–Nordheim coordinates with power exponent $k$ = 1.24.