Scaling of Mott-Gurney law in the quantum regime

Summary form only given. Research finding [1] has confirmed a new scaling of Child-Langmuir (CL) law in the quantum regime. Now a new question is proposed that whether the classical Mott-Gurney (MG) still holds in the quantum regime. With this in mind, this paper presents a consistent quantum mechanical model of MG law in the configuration of planar electrode, including electron exchange-correlation interaction and potential induced by inelastic collisions. It is found that the classical MG law is no longer valid in the quantum regime and that a new scaling of Vg and D is established [2]. The smooth transition from the classical regime to the quantum regime is also demonstrated for SCL current in solid.