Statistical Mechanics of Grain Boundary Scattering and Its Impact on Electrical Conductivity of Polycrystalline Transparent Conducting Oxides for Solar Cell Applications

Background: Transparent conducting oxides including indium tin oxide and zinc oxide are critical components of solar cells, with grain boundary scattering being a dominant mechanism limiting electrical conductivity in polycrystalline films. A statistical mechanical framework for grain boundary scattering in these materials under Nigerian high-temperature deposition conditions is absent. Aim: This study developed a statistical mechanical model of grain boundary scattering in polycrystalline transparent conducting oxide films and validated it against experimental data from films deposited by RF sputtering under varied conditions. Methods: A statistical mechanical framework incorporating grain size distribution statistics, grain boundary potential barrier distributions, and thermal carrier distribution functions was formulated analytically. ITO and AZO films were deposited by RF magnetron sputtering at substrate temperatures from 150 to 400 degrees Celsius. Electrical, structural, and optical properties were measured as functions of deposition conditions. Hall effect mobility and grain size data were used for model validation. Results: The model accurately predicted Hall effect mobility as a function of grain size and carrier concentration with mean absolute error of 8.3 cm2/Vs across 64 film variants. Grain boundary barrier height was found to decrease with increasing deposition temperature, explaining the mobility-temperature relationship. Optimised AZO films achieved 42 ohm/square sheet resistance at 87% optical transmittance. Conclusion: The statistical mechanical framework provides predictive capability for TCO film optimisation and is recommended as a design tool for Nigerian solar cell fabrication programmes. Keywords: transparent conducting oxide, grain boundary scattering, statistical mechanics, solar cell, ITO.