  The Mott-Gurney equation (Child's law) has been frequently applied to measure
the mobility of carrier transport layers. One of the main assumption in the
Mott-Gurney theory is ignoring the diffusive currents. It was not obvious,
however, whether the diffusive currents can be ignored for thin carrier
transport layers. We obtained the current-voltage relation using analytical
solutions of drift-diffusion equation coupled with the Poisson's equation. The
integration constants were numerically determined using nonlinear equations
obtained from boundary conditions.A simple analytical relation between the
voltage and current was also derived. The analytical equation improved over the
Mott-Gurney equation when the voltage is between 0.1 and 2 [V] at room
temperature. By using published data, we show that both the mobility and the
layer thickness can be simultaneously obtained by applying the analytical
expression. The effect of diffusion on the current-voltage relation is
explained by the movement of the virtual electrode formed by space charge
accumulation.
