Space Charge Effects on the I-V Characteristics of Field Emission Arrays

In recent years, the wide applications of vacuum electronic devices call for a well development of field emission cathodes. Field emission arrays are a good candidate for the use as a field emitter. The electronic property, or the emission behavior, of an emitter is characterized by the I-V curves. The field emission due to quantum mechanical tunneling is described by the well-known Fowler-Nordheim (FN) equation. The FN plots are widely employed to fit the experimental data. With the advancement in the fabrication technology, the emission current density of a field emission array achieves even higher and higher values than ever before. In recent experiments of field emission arrays, the FN plots show that the results are apart from the FN fits. In this work, we study the space charge effects on the I-V characteristics of the field emission arrays that may be operated at high current density. Within the framework of the effective work function approximation, the FN equation is modified with an effective work function. The effective work function characterizes the surface properties of the field emission array. A self-consistent FN equation including the space charge effects of the field emission electrons is demonstrated to be a good fit to the I-V characteristics of field emission arrays. The theoretical results show good agreement in comparisons with some experimental results