The equivalent circuit model in solid-state electronics—Part I: The single energy level defect centers

Abstract

The equivalent circuit model is developed in this series of papers and applied to solid-state junction devices. In this paper, the exact equivalent circuit of a single energy level defect center in a semiconductor is developed based on the Shockley-Read-Hall model. It is then applied to the calculation of the steady-state lifetimes of electrons and holes and to the transient decay time constants. The transient decay time constants are obtained for arbitrary nonequilibrium, but steady-state, conditions and are presented as a function of the steady-state electron and hole concentrations by means of contour maps. Simple examples and gold in silicon are used for the construction of these maps. The general criteria of trapping, recombination, and generation are also obtained using the single energy level defect center model which divides the carrier concentration plane log <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10</inf> N versus log <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10</inf> P into four quadrants centered at the equality carrier concentrations p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">*</sup> and n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">*</sup> . At this equality point, the four rates of electron or hole capture or emission at the defect center are equal and the four quadrants represent regions where recombination, generation, electron trapping, or hole trapping dominates.