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.

Models for numerical device simulations of crystalline silicon solar cells—a review

“…4(b). It implies that BGN starts to have an effect at very low dopant densities, so Sproul and Green's experiment yielded n i,eff instead of n i , and n i turned out to be n i = 9.65(3) × 10 9 cm −3 [83], consistent with the value of Misiakos and Tsamakis [82]. The fact that Schenk's BGN model was successful had two further implications.…”

“…Adjusting n i to the lower value of 9.65(3) × 10 9 cm −3 [83] necessitates an adjustment of the effective masses of Fig. 7 Left: The surface recombination velocity parameter S p at phosphorus-diffused surfaces passivated with SiO 2 or bare, extracted from J 0 measurements using Fermi-Dirac statistics or Boltzmann statistics (crosses), and a parameterization [99].…”

“…Klaassen's parametrization [108,109] of the minority mobility is shown as solid lines, and of the majority mobility as dashed lines finite-temperature full random-phase approximation (RPA), hence it is a rigid shift model. It was extended to the full RPA contribution on the basis of the statically screened ladder approximation (SSLA) in [83,122], showing no significant effects at N dop < 2 × 10 19 cm −3 .…”

PC1Dmod 6.1 – state-of-the-art models in a well-known interface for improved simulation of Si solar cells

“…The Schenk BGN model takes part in a collection of state-of-the-art models for (highly doped) c-Si which were chosen for use in cmd-PC1D 6.0 [3] as suggested by Altermatt et al [5] [8]. This set of models also includes Sproul and Green's model for the temperature-dependent intrinsic carrier density i,0 ( ) [9], which has been linearly scaled by a constant factor 0.9677 to match the latest value of 9.65 × 10 9 cm -3 at 300 K as reported by Altermatt et al [10], as well as the extensive and commonly used mobility model by Klaassen [11], [12]. Furthermore, we have also implemented the latest parameterisation of intrinsic recombination by Richter et al [13], which was derived using F-D statistics and Schenk's parameterization for BGN, and is based on a large set of empirical data, taking the latest advances in material quality and surface passivation into account.…”

Excellent passivation of highly doped p-type Si surfaces by the negative-charge-dielectric Al2O3

“…where eff is the measured effective excess carrier lifetime, Auger the intrinsic Auger lifetime, 12 SRH the defect-related bulk lifetime, N d the base doping level, n i the intrinsic carrier concentration of c-Si, 13 q the elementary charge, ⌬n the excess carrier density, and W the sample thickness.…”