A simplified and improved model of ideal and almost ideal silicon p-n junctions: The role of oxygen

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Abstract
Properly gettered and annealed silicon p‐n junctions are either well described by Shockley’s diffusion theory (the ideal case) or they have (the almost ideal case) a reverse voltage–current characteristic constituted by three parts: a voltage‐independent contribution Ir, smaller than the saturation diffusion current, and by two contributions, one, igr, of generation–recombination and the other, ioh, ohmic, which are both due to the same defect centers characterized by equal activation energy and by a null charge. In a recent work we have shown that such experimental findings may be ascribed to four‐state traps (FST) which contain a ion dipole and which may be empty of carriers (the ground state), or filled by an electron or a hole, or both (the stimulated state), and to different Frenkel–Poole effects for electron and hole in their field‐assisted thermal emission from trap states. Here, firstly, the model is simplified and improved (i) by considering the most likely emission (capture) of a carrier from (into) the only states containing (empty of) it, (ii) by taking into account that the transition between the ground and the stimulated states is thermally activated and assisted by both the electric field and the tunnel effect, and (iii) by considering the effects on the current of the dispersions Dλ and Dθ of the length and direction, respectively, of the ion dipole and of that DVm of the energy barrier height crossed by the electron in the above mentioned tunnel transition. In this way, the FST kinetic equations are greatly simplified, the whole model is improved and generalized and, at the same time, the physical meaning of the analytical results becomes more simple and straightforward. As a matter of fact we find that (a) Ir is due to the field‐assisted tunnel effect in the transition between the ground and the stimulated states and it depends on Dλ, Dθ, and DVm, (b) igr and ioh derive from the Frenkel–Poole effect on the carrier emission from the stimulated state and the (ioh, practically) are independent of Dλ, Dθ, and DVm and (c) the activation energies of igr and ioh are equal and the value is given by the smallest of the energies required to bring each of the carriers from the ground state, through the stimulated state, into the respective band. Finally, the physical origin of the FSTs is found in groups of localized states with different positions and energy levels, due to the oxygen, whose donor levels, related to SiyOx clusters of a few hundred atoms of oxygen, are destroyed and generated at the annealing temperature of 650 and 800 °C, respectively, at which the ideal and almost ideal p‐n junctions are obtained, respectively.