Details
| Original language | English |
|---|---|
| Article number | 113823 |
| Journal | Solar Energy Materials and Solar Cells |
| Volume | 292 |
| Early online date | 4 Jul 2025 |
| Publication status | Published - 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
ASJC Scopus subject areas
- Materials Science(all)
- Electronic, Optical and Magnetic Materials
- Energy(all)
- Renewable Energy, Sustainability and the Environment
- Materials Science(all)
- Surfaces, Coatings and Films
Sustainable Development Goals
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In: Solar Energy Materials and Solar Cells, Vol. 292, 113823, 15.10.2025.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The elasticity method
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
UR - http://www.scopus.com/inward/record.url?scp=105009627729&partnerID=8YFLogxK
U2 - 10.1016/j.solmat.2025.113823
DO - 10.1016/j.solmat.2025.113823
M3 - Article
AN - SCOPUS:105009627729
VL - 292
JO - Solar Energy Materials and Solar Cells
JF - Solar Energy Materials and Solar Cells
SN - 0927-0248
M1 - 113823
ER -