Photogenerated Carrier Transport Properties in Silicon Photovoltaics

Abstract

Electrical transport parameters for active layers in silicon (Si) wafer solar cells are determined from free carrier optical absorption using non-contacting optical Hall effect measurements. Majority carrier transport parameters [carrier concentration (N), mobility (μ), and conductivity effective mass (m*)] are determined for both the n-type emitter and p-type bulk wafer Si of an industrially produced aluminum back surface field (Al-BSF) photovoltaic device. From measurements under 0 and ±1.48 T external magnetic fields and nominally "dark" conditions, the following respective [n, p]-type Si parameters are obtained: N = [(3.6 ± 0.1) × 10¹⁸ cm^-3, (7.6 ± 0.1) × 10¹⁵ cm^-3]; μ = [166 ± 6 cm²/Vs, 532 ± 12 cm²/Vs]; and m* = [(0.28 ± 0.03) × m_e, (0.36 ± 0.02) × m_e]. All values are within expectations for this device design. Contributions from photogenerated carriers in both regions of the p-n junction are obtained from measurements of the solar cell under "light" 1 sun illumination (AM1.5 solar irradiance spectrum). From analysis of combined dark and light optical Hall effect measurements, photogenerated minority carrier transport parameters [minority carrier concentration (Δp or Δn) and minority carrier mobility (μ_h or μ_e)] under 1 sun illumination for both n- and p-type Si components of the solar cell are determined. Photogenerated minority carrier concentrations are [(7.8 ± 0.2) × 10¹⁶ cm^-3, (2.2 ± 0.2) × 10¹⁴ cm^-3], and minority carrier mobilities are [331 ± 191 cm²/Vs, 766 ± 331 cm²/Vs], for the [n, p]-type Si, respectively, values that are within expectations from literature. Using the dark majority carrier concentration and the effective equilibrium minority carrier concentration under 1 sun illumination, minority carrier effective lifetime and diffusion length are calculated in the n-type emitter and p-type wafer Si with the results also being consistent with literature. Solar cell device performance parameters including photovoltaic device efficiency, open circuit voltage, fill factor, and short circuit current density are also calculated from these transport parameters obtained via optical Hall effect using the diode equation and PC1D solar cell simulations. The calculated device performance parameters are found to be consistent with direct current-voltage measurement demonstrating the validity of this technique for electrical transport property measurements of the semiconducting layers in complete Si solar cells. To the best of our knowledge, this is the first method that enables determination of both minority and majority carrier transport parameters in both active layers of the p-n junction in a complete solar cell.

Figure 1

Schematic of a Si wafer aluminum back surface field (Al-BSF) solar cell mounted on a magnet for optical Hall effect measurements based on terahertz (THz) range spectroscopic ellipsometry under 1 sun illumination (AM 1.5 solar irradiance spectrum)^,,. More detailed information regarding this type of experimental setup can be found in ref. .

Figure 2

Experimental (symbols) spectra measured at 0 T (top-left), +1.48 T (top-right), −1.48 T (bottom-left) and difference spectra measured at ±1.48 T (bottom-right) with their corresponding calculated models (solid lines) of m₁₂, m₁₃, m₂₁, m₂₂, m₂₃, m₃₁, m₃₂, m₃₃, m₄₁, m₄₂, and m₄₃ normalized Mueller matrix elements for the Al-BSF Si wafer solar cell at 50° angle of incidence under dark condition measurement. The unweighted error function for this fit is σ = 4.33 × 10⁻².

Figure 3

Complex dielectric function, ε = ε₁ + iε₂, spectra for the phosphorus doped n-type Si emitter layer and boron doped p-type Si bulk wafer obtained from optical Hall effect measurements of the Al-BSF Si wafer solar cell under dark condition and 1 sun illumination (AM1.5 solar irradiance spectrum) measurements. Short dotted grey lines indicate gaps in the measured spectral range with the parametric expression for spectra in ε extrapolated over those regions.

Figure 4

Experimental spectra (symbols) measured at 0 T (top-left), +1.48 T (top-right), and −1.48 T (bottom-left) and difference spectra measured at ±1.48 T (bottom-right) with their corresponding calculated models (solid lines) of the normalized Mueller matrix elements m₁₂, m₁₃, m₂₁, m₂₂, m₂₃, m₃₁, m₃₂, m₃₃, m₄₁, m₄₂, and m₄₃ for the Al-BSF Si wafer solar cell at 50° angle of incidence under 1 sun illumination (AM1.5 solar irradiance spectrum). The unweighted error function for this fit is σ = 4.29 × 10⁻².