Li Jian V, Johnston Steven W, Yan Yanfa, Levi Dean H
National Renewable Energy Laboratory, Golden, Colorado 80401, USA.
Rev Sci Instrum. 2010 Mar;81(3):033910. doi: 10.1063/1.3361130.
Thermally activated processes are characterized by two key quantities, activation energy (E(a)) and pre-exponential factor (nu(0)), which may be temperature dependent. The accurate measurement of E(a), nu(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), nu(0), 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), nu(0), and their temperature dependence. The case study of deep level emission in a Cu(In,Ga)Se(2) solar cell using the 2D Arrhenius plot method reveals clear temperature dependent behavior of E(a) and nu(0), which has not been observable by its 1D predecessors.
热激活过程由两个关键量来表征，即激活能（E(a)）和指前因子（nu(0)），它们可能与温度有关。准确测量E(a)、nu(0)及其温度依赖性对于理解非阿仑尼乌斯过程的热激活机制至关重要。然而，基于经典一维阿仑尼乌斯图的方法由于无法从一个一维实验数据阵列中解析出两个未知的一维阵列，因而无法明确测量E(a)、nu(0)及其温度依赖性。在此，我们提出一种二维阿仑尼乌斯图方法来解决这一基本问题。我们的方法通过在二维温度-速率平面中匹配相对于温度和速率计算的数据的一阶矩和二阶矩，在任何温度下测量E(a)，因此能够明确求解E(a)、nu(0)及其温度依赖性。使用二维阿仑尼乌斯图方法对铜铟镓硒（Cu(In,Ga)Se(2)）太阳能电池中的深能级发射进行的案例研究揭示了E(a)和nu(0)明显的温度依赖性行为，这是其一维前身所无法观测到的。
