Space-charge-limited bipolar flow in a nano-gap

This paper presents a quantum model of space-charge limited (SCL) bipolar flow in a nano-sized planar gap, including the effects of electron tunneling and exchange-correlation. It is found that the classical scaling of the SCL bipolar flow is no longer valid when the gap spacing $D$ is comparable or smaller than the electron’s de Broglie wavelength at gap voltage $Vg$⁠. The classical value of the SCL bipolar electron flow is greatly enhanced due to the electron tunneling through the space-charge electric potential created by both the electrons and ions. The space-charge effect of ions is less significant (compared to electron tunneling) in the deep quantum regime that the quantum SCL bipolar flow is nearly identical to the unipolar electron flow (or quantum Child-Langmuir law).