Double Injection in Semiconductors with Multivalent Trapping Centers

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Abstract
A numerical solution based on the general equations of conduction and recombination is used to calculate the current‐voltage characteristics of p‐``i''‐n diodes in which the ``i'' region contains multivalent trapping centers. The theory is based on the assumption that the current is entirely field driven in the ``i'' region. The solution includes calculation of important properties of the conduction mechanism, such as the space charge and carrier density distributions. The results are a considerable improvement over more approximate analytical solutions, since the present method allows for important effects such as variations in the carrier lifetimes with injection level. Calculations are presented for the case of the Zn impurity in Si and are compared with previously published results for Au in Si. We discuss a space‐charge neutrality approximation which gives reasonable agreement with the exact calculations for certain ranges of the J‐V characteristic and which provides useful insight into the conduction process in the p‐``i''‐n. Comparisons are made between the present work and previous theoretical models based on more restrictive approximations.