An exact uniform theory is given for theI‐Vcharacteristic of longp‐i‐ndiodes with one trapping level. This theory does not assume a constant recombination lifetime or quasi‐neutrality, as did all previous treatments of this problem. As limiting cases, the theory gives the cube law at high injection levels, the square law for the semiconductor regime and the Ashley—Milnes regime. The theory is applied to the acceptor level of Au in Si for which case numerical solutions are given.