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

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∼μ_p N^1/2_d (for the contact: metal–n‐type semiconductor), but is independent of the barrier height φ_b or diffusion potential V_do, provided qV_do≳ few KT. This means that, for Ohmic contacts, S depends on whether the contact is achieved by using high N_d (for which S?10⁹ cm/s for Si cells) or by low φ_b but moderate N_d (S?10⁷ cm/s for Si cells). More generally, S varies between ?10⁶ cm/s (for CdS cells, low N_d) and ?10¹⁰ cm/s (p‐type GaAs cells, high N_d). Also defined are the conditions under which the finite collection velocity at the contact limits the collected minority‐carrier current.