We report a theoretical investigation of field emission from metals in n-dimension. The field-emission current density is derived as a function of the electric field in one to three dimensions. Then, the generalized field-emission current density is calculated for arbitrary n dimensions, is shown as a function of electric field for different work functions of one-, two- and three-dimensional materials, and is expressed as a function of dimension for different work functions. These analyses reveal that the current density increases as the spatial dimension increases in the conductors and work function decreases. Our study on the generalized current density can be applied to material systems with high dimensions or fractional dimensions.

我们报告了对n维金属场发射的理论研究。场发射电流密度是作为一到三个维度中电场的函数导出的。然后，计算任意 n 维的广义场发射电流密度，将其表示为一维、二维和三维材料的不同功函数的电场函数，并表示为不同维度的函数。工作职能。这些分析表明，随着导体中空间尺寸的增加和功函数的降低，电流密度增加。我们对广义电流密度的研究可以应用于具有高维数或分数维数的材料系统。