An extended ambipolar model: Formulation, analytical investigations, and application to photocurrent modeling

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Abstract
An extended development of the ambipolar transport equation is presented with a thorough investigation of the commonly omitted terms and conventional approximations. An analytical technique of integrating the fully inclusive steady‐state ambipolar equation is reported. This technique can yield closed form solutions for the frequently used recombination functions (Shockley–Read–Hall, band‐to‐band, and/or Auger models) that describe electron‐hole recombination in indirect or direct band‐gap semiconductors. The ensuing results are potentially applicable to many areas of current research. One such application is demonstrated by constructing a model for the photocurrent response of the reverse‐biased silicon p‐n junction in the presence of uniformly imposed external generation of excess carriers. The model is found to be in excellent agreement with numerical simulations. The extended ambipolar equation is shown to significantly improve the ability to model the current response due to excess carriers. Terms that are ignored or uncritically approximated in the conventional treatment of the ambipolar equation are found to have important consequences for modeling Dember‐related second‐order current response, as well as the asymptotic behavior of the photocurrent of a reverse‐biased junction.