Measuring Temperature-Dependent Activation Energy in Thermally Activated Processes: A 2D Arrhenius Plot Method

Thermally activated processes are characterized by two key quantities, activation energy (E_a) and pre-exponential factor (v₀), which may be temperature dependent. The accurate measurement of E_a, ₀, and their temperature dependence is critical for understanding the thermal activation mechanisms of non-Arrhenius processes. However, the classic 1D Arrhenius plot-based methods cannot unambiguously measure E_a, v₀, and their temperature dependence due to the mathematical impossibility of resolving two unknown 1D arrays from one 1D experimental data array. Here, we propose a 2D Arrhenius plot method to solve this fundamental problem. Our approach measures E_a at any temperature from matching the first and second moments of the data calculated with respect to temperature and rate in the 2D temperature-rate plane, and therefore is able to unambiguously solve E_a, v₀, and their temperature dependence. The case study of deep level emission in a Cu (In,Ga) Se₂ solar cell using the 2D Arrhenius plot method reveals clear temperature dependent behavior of E_a and ₀, which has not been observable by its 1D predecessors.