Extracting Mobility-Lifetime Product in Solar Cell Absorbers Using Quantum Efficiency Analysis
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Extracting Mobility-Lifetime Product in Solar Cell Absorbers Using Quantum Efficiency Analysis Jeremy R. Poindexter1, Riley E. Brandt1, Niall M. Mangan1, Tonio Buonassisi1 1
Massachusetts Institute of Technology, Cambridge, MA 02139, USA
ABSTRACT The long-wavelength quantum efficiency (QE) response of photovoltaic absorbers is determined by the length scales for minority carrier collection. However, extracting quantitative measurements of minority carrier mobility-lifetime product (μτ) is complicated by uncertainty in other factors such as the depletion width, electric field, and the absorption coefficient. We apply previously developed methods to obtain estimates for μτ in a tin(II) sulfide (SnS) solar cell. We compare three analytic models for the minority carrier collection probability as a function of absorber depth to determine which model most accurately captures the behavior in our devices. For models in which multiple parameters are unconstrained, a random numerical search is used to optimize the fit to experimental QE for SnS. To identify sources of error, we perform a sensitivity analysis by fitting with SCAPS-1D. Our analysis shows that changes in absorption most strongly affect estimates for μτ, highlighting the need to obtain accurate, device-specific absorption data. Further modeling and experimental constraints are required to obtain selfconsistent values for μτ that correspond to actual device performance. INTRODUCTION Quantum efficiency (QE) analysis has proven a useful tool for evaluating minority carrier collection in many photovoltaic (PV) absorbers, as QE directly relates to the minority carrier mobility-lifetime product, μτ. In particular, an increase in μτ for a given material typically results in an increase in the long-wavelength region of the QE spectrum (i.e., close to the band gap of the material). For materials that exhibit diffusion-dominated collection of minority carriers (e.g., silicon), increases in long-wavelength QE are directly related to increases in μτ through a linear relationship [1–3]: (1)
where Leff is an effective diffusion length and α is the absorption coefficient. The approximation in equation (1) holds for αt >> 1 and t/Leff >> 1 (where t is absorber thickness). For diffusiondominated collection, Leff ≈ Ldiff, the minority carrier diffusion length. Ldiff is related to μτ based on the Einstein relation: (2)
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where kB is Boltzmann’s constant, T is absolute temperature, and q is elementary charge. Many “thin film” PV absorbers exhibit a mix of drift-assisted and diffusion-assisted minority carrier collection, complicating the extraction of μτ and invalidating the relationship described in equation (1). These materials absorb strongly in the visible and have depletion widths comparable to absorber thickness. Other factors can affect the long-wavelength QE response in devices based on these materials, including changes in depletion width and electric field, uncertainty in the absorption coefficient, and recombination at interfaces and surfaces. We investigate sever
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