Space charge limited current in a gap combined of several kinds of medium

Summary form only given. For high current transport in a medium, where the space charge effects of injected current are important, it is generally termed as space charge limited (SCL) current. In the one-dimensional planar gap, the SCL current density is given by the classical Child-Langmuir law. The corresponding SCL current in a trap-free solid is known as Mott-Gurney law, while the trap-limited current density for a trap-filled solid with exponentially distributed traps is described as the Mark-Helfrich law. In a recent paper, an experiment was performed to understand the physical mechanism of the nitrogen incorporation in the high-k dielectric hafnium oxide (HfO₂). It was reported that SCL conduction was measured by using the scanning tunneling microscopy. In this paper, we present two cases respectively. For the first case, we show the SCL electron injections into the free space region first before entering the trap-filled dielectric solid, new scaling of current vs. voltage is found. For the second case, the SCL current in the solid contend two kinds of dielectric is derived and it is found that one can still use the MG Law to describe a dielectric formed by two different medium with a effective dielectric constant and mobility. Our model can also be helpful to determine the electron mobility and the permittivity of the dielectric hafnium oxide.