Equation (19), however, describes also situations where two crossover points in the log-log plot are observed. Equation (20) describes most experimental situations, where a nonlinear log-log plot is observed with only one crossover excitation ϕ 0. For high excitation ( ϕ ≫ ϕ 0), the 1 in the denominator can be neglected and the power law exponent converges to k = k low − ( k low − k high ) = k high. For low excitation ( ϕ ≪ ϕ 0), the power law exponent converges to k = k low. It not only applies to a donor-acceptor pair transition but also to a free-to-bound or exciton transition where the values for k low and k high are different. This equation can be used to fit a curved log-log plot with the crossover excitation at ϕ 0. 26 To detect this nonlinear behavior, it is very important to measure the excitation dependence over several orders of magnitude. Several models exist for the analytical or numerical description of nonlinear log-log plots. Furthermore, it is often observed that the log-log plot of PL intensity vs excitation intensity is not linear. 17,19 For example, we will show in the following that, for certain cases, the PL intensity of a shallow donor-acceptor pair transition can increase with a superlinear power law if deep recombination centers are present. 1–15 However, it has been shown that the attribution can be erroneous if deep levels are present as well. This model is used in the literature to distinguish between excitonic and defect related transitions. The power law exponent k is between 1 and 2 for free- or bound-exciton transitions and below 1 for free-to-bound or donor-acceptor pair transitions. The excitation power density ϕ is varied over several orders of magnitude. It is shown that the intensity of the photoluminescence transitions follows a power law behavior with I PL ∝ ϕ k in simplified cases. 1, a description of the transitions with rate equations is given as well as numerical results and experimental measurements on CdTe. 1–22 The different transitions are generally identified by measuring the photoluminescence intensity in dependence of the laser power. The saturation effects of defects by excess carriers as well as the influence of deep recombination centers can be extracted with the help of the presented model, which extends existing theories.Įxcitation-dependent photoluminescence measurements are often used as a tool to distinguish excitons, free-to-bound or donor-acceptor-pair transitions in semiconductors. Model functions for the analytical description of these transitional excitation dependencies are derived and the analysis is applied to chalcopyrite thin films and to numerical data. Power law exponents different from n / 2 can result from the transition region between two limiting cases of linear power laws. Defect levels can saturate at high enough excitation intensities, leading to one or several crossover points from one power law behavior to another. The values depend on the availability of additional recombination channels. We show that the exponent k takes on values of multiples of 1 / 2. Generally, it is observed that the photoluminescence intensity I PL follows a power law I PL ∝ ϕ k with the excitation intensity ϕ. We have extended existing models based on rate equations to include the contribution of deep defects. Excitation-intensity-dependent measurements at low temperatures are typically analyzed to distinguish between exciton and defect related transitions. Photoluminescence characterization of semiconductors is a powerful tool for studying shallow and deep defects.
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