Quadratic recombination in silicon and its influence on the bulk lifetime
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RONIC AND OPTICAL PROPERTIES OF SEMICONDUCTORS
Quadratic Recombination in Silicon and Its Influence on the Bulk Lifetime A. V. Sachenko^, A. P. Gorban, V. P. Kostylev, and I. O. Sokolovskiœ Lashkarev Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, Kiev, 03028 Ukraine ^e-mail: [email protected] Submitted May 17, 2006; accepted for publication September 5, 2006
Abstract—The coefficient of nonradiative excitonic recombination by the Auger mechanism involving deeplevel centers in n-Si was determined by comparing the theoretical dependence of the effective bulk lifetime on the doping level with the experimental dependence. It is shown that this mechanism controls the bulk lifetime in silicon at doping levels on the order of or above 1016 cm–3. This mechanism is more pronounced at shorter bulk lifetimes τv0 and low doping levels. The dependences of the bipolar diffusion length in n-Si on the doping level (using the parameter τv0) were calculated. PACS numbers: 71.55.Cn, 72.20.Jv DOI: 10.1134/S1063782607030074
1. INTRODUCTION It is well known that nonlinear recombination mechanisms, in particular quadratic recombination and band-to-band Auger recombination, begin to manifest themselves in silicon under high-intensity, e.g., laser, excitation [1]. Until 1987, it was believed that quadratic recombination in silicon is associated only with radiative band-to-band recombination; in particular, such a viewpoint is outlined in published monographs and textbooks (see, e.g., [2]). In [3–5], it was shown that quadratic recombination associated with nonradiative recombination of excitons by the Auger mechanism involving deep recombination centers can occur in silicon under certain conditions. On the one hand, a fraction of excited electron–hole pairs is bound into excitons. Since the exciton concentration is proportional to the product of the concentrations of excess electrons and holes, this fraction is large even at room temperature at sufficiently high-intensity excitation or high doping levels. On the other hand, the hole–electron distance in the exciton, equals (on the order of magnitude) to the Bohr radius of the exciton in silicon, is so short that the probability of the Auger process significantly increases in this case. Therefore, the probability of room-temperature nonradiative recombination of excitons by the Auger mechanism involving deep recombination centers will dominate in a certain range of excitation or doping levels in comparison to the probabilities of Shockley–Read–Hall, radiative, and band-toband Auger recombination types. In [5], the quadratic-recombination coefficients A in silicon were determined for samples with a wide range of initial bulk lifetimes τv by fitting the theoretical dependence of the inverse lifetime on the excitation level to corresponding experimental dependences. The
correlation coefficient for this fitting was from 0.97 to 0.99, and the relative determination error for the quadratic-recombination parameter did not exceed 60%. It was shown that, in particular
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