Evaluating the Field Emission Properties of N-Type Black Silicon Cold Cathodes Based on a Three-Dimensional Model

Black silicon (BS), a nanostructured silicon surface containing highly roughened surface morphology, has recently emerged as a promising candidate for field emission (FE) cathodes in novel electron sources due to its huge number of sharp tips with ease of large-scale fabrication and controllable geometrical shapes. However, evaluating the FE performance of BS-based nanostructures with high accuracy is still a challenge due to the increasing complexity in the surface morphology. Here, we demonstrate a 3D modeling methodology to fully characterize highly disordered BS-based field emitters randomly distributed on a roughened nonflat surface. We fabricated BS cathode samples with different morphological features to demonstrate the validity of this method. We utilize parametrized scanning electron microscopy images that provide high-precision morphology details, successfully describing the electric field distribution in field emitters and linking the theoretical analysis with the measured FE property of the complex nanostructures with high precision. The 3D model developed here reveals a relationship between the field emission performance and the density of the cones, successfully reproducing the classical relationship between current density J and electric field E (J-E curve). The proposed modeling approach is expected to offer a powerful tool to accurately describe the field emission properties of large-scale, disordered nano cold cathodes, thus serving as a guide for the design and application of BS as a field electron emission material.