Ang L K, Kwan T J T, Lau Y Y
School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Republic of Singapore.
Phys Rev Lett. 2003 Nov 14;91(20):208303. doi: 10.1103/PhysRevLett.91.208303. Epub 2003 Nov 12.
This paper presents a consistent quantum mechanical model of Child-Langmuir (CL) law, including electron exchange-correlation interaction, electrode's surface curvature, and finite emitter area. The classical value of the CL law is increased by a larger factor due to the electron tunneling through the space-charge potential, and the electron exchange-correlation interaction becomes important when the applied gap voltage Vg and the gap spacing D are, respectively, on the order of Hartree energy level, and nanometer scale. It is found that the classical scaling of Vg(3/2) and D(-2) is no longer valid in the quantum regime, and a new scaling of Vg(1/2) and D(-4) is established. The smooth transition from the classical regime to the quantum regime is also demonstrated.
本文提出了一种自洽的量子力学模型来描述Child-Langmuir（CL）定律，该模型包括电子交换关联相互作用、电极表面曲率和有限发射极面积。由于电子隧穿空间电荷势，CL定律的经典值会以更大的因子增加，并且当施加的间隙电压Vg和间隙间距D分别处于哈特里能级量级和纳米尺度时，电子交换关联相互作用变得重要。研究发现，Vg(3/2)和D(-2)的经典标度在量子 regime 不再有效，并且建立了Vg(1/2)和D(-4)的新标度。还展示了从经典 regime 到量子 regime 的平滑过渡。
