Unipolar space-charge-limited current in solids with nonuniform spacial distribution of shallow traps

Models and analyses of unipolar space-charge-limited current (sclc) in the presence of traps usually assume that the distribution of the traps is uniform in space. It is demonstrated here that this assumption can be a critical one. Simple models with shallow traps are analyzed in detail to establish the fact. Planar, cylindrical, and spherical geometries receive equal attention. The results show that traps in the bulk of the base outside of the immediate vicinity of the emitter are of little significance to the V–I characteristic. The origin of this effect is discussed. A simple approximate treatment is derived. The results imply that the dc characteristic alone is an ambiguous tool for characterizing traps and their physical origin. Included as a byproduct are complete solutions of the V–I characteristics of trap-free sclc in all five distinct cases of the planar, cylindrical, and spherical geometries. Results are given both analytically as well as graphically.