中文摘要：

讨论电场使电子从纳米厚度的金属片经过量子隧穿进入真空的过程．忽略金属片的厚度，通过共形变换，使得真空电势和电子波函数满足简单的边界条件，从而得到严格的电势分布和近似的电子波函数解，给出发射电流密度空间分布的表达式．

英文摘要：

Electrons of a metallic nano-sheet tunneling into vacuum via the electric field is studied. Ignoring the thickness of the sheet, the boundary surfaces of the cathode and anode are mapped into two planes respectively through a conformal transformation, thereby, the electrostatic potential barrier is obtained rigorously and the Schroedinger equation is solved analytically. Analytical expressions for the electron wavefunction and the emission current density are given.