Collection velocity of excess minority carriers at metal-semiconductor contacts in solar cells

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Abstract
An expression for the collection velocity S of excess minority carriers at metal‐semiconductor contacts is derived analytically for both the Schottky barrier and the Ohmic contact. Short‐circuit conditions are assumed, appropriate to the collection of optically generated minority carriers by Schottky barriers or Ohmic contacts in solar cells or photodetectors. This analysis is then applied to the calculation of S for the materials of primary interest in solar cells (Si, GaAs, and CdS). It is found that S increases with the minority‐carrier mobility and with the doping concentration according to S∼μp N1/2d (for the contact: metal–n‐type semiconductor), but is independent of the barrier height φb or diffusion potential Vdo, provided qVdo≳ few KT. This means that, for Ohmic contacts, S depends on whether the contact is achieved by using high Nd (for which S?109 cm/s for Si cells) or by low φb but moderate Nd (S?107 cm/s for Si cells). More generally, S varies between ?106 cm/s (for CdS cells, low Nd) and ?1010 cm/s (p‐type GaAs cells, high Nd). Also defined are the conditions under which the finite collection velocity at the contact limits the collected minority‐carrier current.