The elasticity method: A new approach to determine recombination parameters from injection dependent carrier lifetimes of silicon wafers

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Original languageEnglish
Article number113823
JournalSolar Energy Materials and Solar Cells
Volume292
Early online date4 Jul 2025
Publication statusPublished - 15 Oct 2025

Abstract

The elasticity E of a function f(x) is a mathematical operator, which can be understood as the slope of the function plotted in a log-log-plot. We analyze the elasticity E(τ −1(Δn + Ndop)) of injection-dependent lifetime measurements τ(Δn + Ndop) as a function of the majority carrier density Δn + Ndop. The value of the elasticity provides information on the recombination mechanism in the respective injection range. For example, at injection levels where E = 1, surface recombination characterized by a surface recombination current density J0 is limiting the overall recombination. Furthermore, Shockley-Read-Hall (SRH) recombination via a deep-level impurity state within the silicon bulk always leads to E(τSRH(Δn + Ndop)) > 0 and for Δn approaching zero, the elasticity exactly equals the ratio of capture time constants Q and hence provides an alternative way for its determination within a narrow injection range. Two different cases are studied experimentally: (i) Very low J0 values (1 fA/cm2) are analyzed on silicon wafers symmetrically passivated with polycrystalline silicon layers on ultrathin silicon oxide, where the analysis of the injection-dependent lifetime curves is performed in the elasticity range (1.0 ± 0.1). (ii) Two different types of light-induced bulk defects, namely the boron-oxygen center (BO) and the light- and elevated-temperature-induced degradation (LeTID) defect are investigated. The extracted Q values show excellent agreement with those values determined from fitting the SRH equation to the complete τ(Δn) curves.

Keywords

    Carrier lifetime, Defects, Elasticity, Recombination, Silicon, Solar cell, Surface passivation

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The elasticity method: A new approach to determine recombination parameters from injection dependent carrier lifetimes of silicon wafers. / Beck, Daniel; Winter, Michael; Schmidt, Jan.
In: Solar Energy Materials and Solar Cells, Vol. 292, 113823, 15.10.2025.

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abstract = "The elasticity E of a function f(x) is a mathematical operator, which can be understood as the slope of the function plotted in a log-log-plot. We analyze the elasticity E(τ −1(Δn + Ndop)) of injection-dependent lifetime measurements τ(Δn + Ndop) as a function of the majority carrier density Δn + Ndop. The value of the elasticity provides information on the recombination mechanism in the respective injection range. For example, at injection levels where E = 1, surface recombination characterized by a surface recombination current density J0 is limiting the overall recombination. Furthermore, Shockley-Read-Hall (SRH) recombination via a deep-level impurity state within the silicon bulk always leads to E(τSRH(Δn + Ndop)) > 0 and for Δn approaching zero, the elasticity exactly equals the ratio of capture time constants Q and hence provides an alternative way for its determination within a narrow injection range. Two different cases are studied experimentally: (i) Very low J0 values (1 fA/cm2) are analyzed on silicon wafers symmetrically passivated with polycrystalline silicon layers on ultrathin silicon oxide, where the analysis of the injection-dependent lifetime curves is performed in the elasticity range (1.0 ± 0.1). (ii) Two different types of light-induced bulk defects, namely the boron-oxygen center (BO) and the light- and elevated-temperature-induced degradation (LeTID) defect are investigated. The extracted Q values show excellent agreement with those values determined from fitting the SRH equation to the complete τ(Δn) curves.",
keywords = "Carrier lifetime, Defects, Elasticity, Recombination, Silicon, Solar cell, Surface passivation",
author = "Daniel Beck and Michael Winter and Jan Schmidt",
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T2 - A new approach to determine recombination parameters from injection dependent carrier lifetimes of silicon wafers

AU - Beck, Daniel

AU - Winter, Michael

AU - Schmidt, Jan

N1 - Publisher Copyright: © 2025

PY - 2025/10/15

Y1 - 2025/10/15

N2 - The elasticity E of a function f(x) is a mathematical operator, which can be understood as the slope of the function plotted in a log-log-plot. We analyze the elasticity E(τ −1(Δn + Ndop)) of injection-dependent lifetime measurements τ(Δn + Ndop) as a function of the majority carrier density Δn + Ndop. The value of the elasticity provides information on the recombination mechanism in the respective injection range. For example, at injection levels where E = 1, surface recombination characterized by a surface recombination current density J0 is limiting the overall recombination. Furthermore, Shockley-Read-Hall (SRH) recombination via a deep-level impurity state within the silicon bulk always leads to E(τSRH(Δn + Ndop)) > 0 and for Δn approaching zero, the elasticity exactly equals the ratio of capture time constants Q and hence provides an alternative way for its determination within a narrow injection range. Two different cases are studied experimentally: (i) Very low J0 values (1 fA/cm2) are analyzed on silicon wafers symmetrically passivated with polycrystalline silicon layers on ultrathin silicon oxide, where the analysis of the injection-dependent lifetime curves is performed in the elasticity range (1.0 ± 0.1). (ii) Two different types of light-induced bulk defects, namely the boron-oxygen center (BO) and the light- and elevated-temperature-induced degradation (LeTID) defect are investigated. The extracted Q values show excellent agreement with those values determined from fitting the SRH equation to the complete τ(Δn) curves.

AB - The elasticity E of a function f(x) is a mathematical operator, which can be understood as the slope of the function plotted in a log-log-plot. We analyze the elasticity E(τ −1(Δn + Ndop)) of injection-dependent lifetime measurements τ(Δn + Ndop) as a function of the majority carrier density Δn + Ndop. The value of the elasticity provides information on the recombination mechanism in the respective injection range. For example, at injection levels where E = 1, surface recombination characterized by a surface recombination current density J0 is limiting the overall recombination. Furthermore, Shockley-Read-Hall (SRH) recombination via a deep-level impurity state within the silicon bulk always leads to E(τSRH(Δn + Ndop)) > 0 and for Δn approaching zero, the elasticity exactly equals the ratio of capture time constants Q and hence provides an alternative way for its determination within a narrow injection range. Two different cases are studied experimentally: (i) Very low J0 values (1 fA/cm2) are analyzed on silicon wafers symmetrically passivated with polycrystalline silicon layers on ultrathin silicon oxide, where the analysis of the injection-dependent lifetime curves is performed in the elasticity range (1.0 ± 0.1). (ii) Two different types of light-induced bulk defects, namely the boron-oxygen center (BO) and the light- and elevated-temperature-induced degradation (LeTID) defect are investigated. The extracted Q values show excellent agreement with those values determined from fitting the SRH equation to the complete τ(Δn) curves.

KW - Carrier lifetime

KW - Defects

KW - Elasticity

KW - Recombination

KW - Silicon

KW - Solar cell

KW - Surface passivation

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