Reassessment of the intrinsic carrier density in crystalline silicon in view of band-gap narrowing

Abstract

The commonly used value of the intrinsic carrier density of crystalline silicon at 300 K is ni = 1.00×1010 cm–3. It was experimentally determined by Sproul and Green, J. Appl. Phys. 70, 846 (1991), using specially designed solar cells. In this article, we demonstrate that the Sproul and Green experiment was influenced by band-gap narrowing, even though the dopant density of their samples was low (1014 to 1016 cm–3). We reinterpret their measurements by numerical simulations with a random-phase approximation model for band-gap narrowing, thereby obtaining ni = 9.65×109 cm–3 at 300 K. This value is consistent with results obtained by Misiakos and Tsamakis, J. Appl. Phys. 74, 3293 (1993), using capacitance measurements. In this way, long-prevailing inconsistencies between independent measurement techniques for the determination of ni are resolved.