It is shown that the traditional approach for consideration of recombination under condition of steady-state current in the absence of external carrier generation is internally contradictory. Sometimes the approach leads to obviously incorrect results. Such situations are demonstrated and a new method for consideration of recombination is proposed. In the present paper we would like to consider some internal inconsistencies in the conventional description when we have carrier recombination under condition of steady-state current. Practically all text-books 1,2,3,4,5 present technique to solve the given problem based on the solution of a set of continuity equations:where n and p are the electron and hole concentration, j n,p are the current of electrons and holes, R n,p are the electron and hole recombination rate respectively. Here we consider the absencens of external generation of carriers (by light, etc.). Thus the nonequilibrium carriers are a result of injection or accumulation of carriers near potential barriers at interfaces. For small concentration of non-equilibrium carriers δn ≡ n − n 0 ≪ n 0 , δp ≡ p − p 0 ≪ p 0 (where n 0 , p 0 are concentration of electrons and holes without the current) the recombination rates are widely assumed to be of the following form:where τ n , τ p are life times of electrons and holes respectively. Obviously, by virtue of charge preservation law an extra conditionshould hold. Although it is not mentioned in the literature that Eq. (2) makes the system overdetermined. Some authors 3 use the latter expression as an equation to find the carrier concentration or to reduce by one the number of unknowns in the problem. However, such approach seems to be incorrect because the Eq. (2) is not a new condition for the concentration of non-equilibrium carriers, rather it is the criterion for correctness of the recombination description, and should fulfill identically at any concentration of non-equilibrium carriers. Probably due to this reason other approach frequently is used, 1,2,3,4,5,6,7 assumingwhere δp means the non-equilibrium concentration of minority carriers. Just this approach is classical and is used widely both in text-books, and in papers devoted to kinetic phenomena in semiconductors. This description possesses a serious inconsistency. It becomes especially obvious if we consider injection of majority carriers. From physical reasons it is evident: injected non-equilibrium majority carriers should recombine. While from a formal point of view, as far as non-equilibrium minority carriers do not occur (δp = 0) the recombination rates are
