Corrected Approximation Model for Semiconductor Field Emission Based on Voltage Drop

For semiconductor field emission, the field emission characteristics do not conform to the Fowler–Nordheim (F–N) theory. It makes the field emission characteristics not be evaluated correctly. This paper presents a corrected approximation model for semiconductor field emission, which is particularly suitable for zero emission current scenarios. The model introduces a correction factor γ for the electric field in the F–N theory and accounts for the influence of the partial voltage across the semiconductor sample on the field emission performance. The correction factor is derived from three key factors: the vacuum electrode spacing, sample thickness, and relative permittivity of the sample. The effectiveness of the correction is validated through electrostatic simulations and experimental verification. To validate the simulation, structural parameter independence was verified and the electric field intensity at the sample surface and electrode spacing was assessed under three conditions, with and without correction. Experimentally, the correction’s efficacy was demonstrated by varying the vacuum electrode spacing, sample layer count (indicating thickness), and conductive sample type to analyze field emission performance pre- and postcorrection. The correction elucidates the discrepancy between experimental findings in the low-current domain of semiconductor field emission and the Fowler–Nordheim theory. This adjustment effectively mitigates the effect of the three influencing factors on field emission characteristics, aligning experimental observations more closely with theoretical expectations. The adjusted turn-on electric field intensity rectifies the systematic error introduced by the sample’s partial voltage, rendering it a more appropriate metric for assessing field emission performance.