Two Dimensional Collisional Child-Langmuir Law

Summary form only given. The paper presents a two dimensional (2D) model of space-charge-limited (SCL) flows in a planar gap with an applied voltage of V and gap spacing D, including the effects of collisions. It is found that the 2D collisional Child-Langmuir (CL) law (in terms of the 1D classical CL law with no collisions) is in the form of 1+(4F/pi(W/L)), where F measures the mean position of the injected electrons from a emitting strip with finite width W. Depending on the degree of collisions, the parameter F changes from F=1/3 (collision-dominated) to F=1/4 (ballistic). Note that the model is immediately applicable for the SCL electron flows in a trap free solid, or the so called Mott-Gurney (MG) law. By setting F=1/3, our analytical model agrees very well with a semiconductor device simulation. The extension of the model to include the effects of traps in the solid will be discussed.