Theory of One-Carrier, Space-Charge-Limited Currents Including Diffusion and Trapping

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Abstract
The theoretical problem of one-carrier, space-charge-limited current flow is beyond the reach of analytical solutions when trapping and diffusion are included in the analysis. Nonetheless, the problem for the semiinfinite solid very generally lends itself to rather simple numerical solution on a digital computer. An interesting feature of the machine solution is that it is based on a universal geometric property of the one dimensional, planar current flow. Detailed solutions are obtained for several special cases of the trap-filled insulator problem which plays a fundamental role in the space-charge-limited current measurement of trap densities in insulators. A comparison of these exact solutions with the analytical solutions neglecting diffusion indicates that an error of a factor of two might be made in a trap density determination for the typical case which is completely studied. A brief discussion of the problem of extending the technique to the finite solid with an anode constraint is given. Also a few computer results for the Ohm's law problem are given.