Two-dimensional analytical Mott-Gurney law for a trap-filled solid

The letter presents a two-dimensional analytical model of the space charge limited (SCL) current injection in a solid with exponentially distributed trap energy state. By considering that the electrons are injected from an infinitely long emission strip of width W, the one-dimensional SCL current density is enhanced by a factor of 1+F(4/pi)/(W/L), where F=1/(l+2) measures the mean position of the injected electrons in the solid of length L, and l is the ratio of the distribution of the traps to the free carriers. The analytical formula is verified by using a two-dimensional device simulator. (c) 2007 American Institute of Physics.