Theory of field emission

A serious barrier impedes the comparison between the theoretical prediction and the experimental observation in field emission because there is no way to measure the emission area. We introduce three dimensionless variables $\mathcal{R}_{J}$, $\mathcal{S}$ and $\mathcal{D}$ to construct a formulation for connecting directly the theoretical variables and experimental data without measuring the emission area. Based on this formulation we can analyze that the behaviors of $\mathcal{R}_{J}$ $\mathcal{S}$ and $\mathcal{D}$ with the voltages between the anode and the emitter to reveals the characteristics of current-voltage (I-V) curve and detect the physical properties of emitters. This formulation provides a way to understand the fundamental physics of I-V curve in field emission and to set up a map between the physical properties of emitters and the experimental I-V curve.