To solve this problem, we will extend the BET model with complex DOS by intro-ducing site-selective temperature-dependent non-radiative recombination rates [8]. At low temperatures, non-radiative losses can be neglected so that previous results for low-temperature linewidth shrinkage are not altered. At higher temperatures, however, the non-radiative losses strongly influence the temperature dependence of the Stokes shift and of the PL linewidth. The core assumption here is that complex exponential-plus-Gaussian DOS corresponds to two types of impurity sites with strongly different temperature-dependent none-radiative rates.
The importance of the non-radiative recombinations depends on the recombination mechanism. In Ref. [7] the recombination of free carriers from the extended states was assumed to be the dominant loss mechanism [19]. In this case, the non-radiative recombination plays only a minor role for the temperature dependence of the Stokes shift and of the PL linewidth. Therefore, it is not surprising that the BET model with two types of impurity sites failed to reproduce the experimental data.
The alternative approach [26] is to assume that the exciton captured on a localized site can recombine either radiatively or non-radiatively, depending on whether or not the temperature is high enough to overcome the exciton binding energy. Therefore, we can assume that the non-radiative recombination rates are strongly site-selective.
Such assumption is motivated by the two-peak shape of the experimentally observed PL spectra shown in Fig.2.2. As one can see, the two peaks in the PL spectra have different contributions at different temperatures. At low temperatures, only the high-energy peak is visible. With increasing temperature, the second, low-energy peak becomes discernible in the PL spectra. At T ≈ 120 K both peaks exhibit equal contributions.
A further increase in temperature diminishes the high-energy peak and, at T &200 K, only the low-energy peak remains. We attribute the high-energy peak to type-I localized states that are generated by the alloy disorder and that are distributed according the exponential part of the complex DOS given by Eq. (2.5). The low-energy peak arises from the type-II localized states in the nitrogen clusters whose energy is distributed according the Gaussian term in the combined DOS.
The approach with two types of localized states resolves the apparent discrepancy be-tween the values of the energy scale of disorder, as extracted from the different PL features using the universal relations given in Table 2.1. Indeed, these relations were obtained on the basis of the conventional BET model with a pure exponential DOS and a single energy scale. The conventional BET applies to semiconductor heterostruc-tures where clusters are absent. In semiconductor compounds with clusters, such as Ga(NAsP) or Ga(BiAs), however, the situation is qualitatively different.The alternative approach [26] is to assume that the exciton captured on a localized site can recombine either radiatively or non-radiatively, depending on whether or not the temperature is high enough to overcome the exciton binding energy. Therefore, we can assume that the non-radiative recombination rates are strongly site-selective.
Such assumption is motivated by the two-peak shape of the experimentally observed PL spectra shown in Fig.2.2. As one can see, the two peaks in the PL spectra have different contributions at different temperatures. At low temperatures, only the high-energy peak is visible. With increasing temperature, the second, low-energy peak becomes discernible in the PL spectra. At T ≈ 120 K both peaks exhibit equal contributions.
A further increase in temperature diminishes the high-energy peak and, at T &200 K, only the low-energy peak remains. We attribute the high-energy peak to type-I localized states that are generated by the alloy disorder and that are distributed according the exponential part of the complex DOS given by Eq. (2.5). The low-energy peak arises from the type-II localized states in the nitrogen clusters whose energy is distributed according the Gaussian term in the combined DOS.
The approach with two types of localized states resolves the apparent discrepancy be-tween the values of the energy scale of disorder, as extracted from the different PL features using the universal relations given in Table 2.1. Indeed, these relations were obtained on the basis of the conventional BET model with a pure exponential DOS and a single energy scale. The conventional BET applies to semiconductor heterostructures where clusters are absent. In semiconductor compounds with clusters, such as Ga(NAsP) or Ga(BiAs), however, the situation is qualitatively different. As one can see from the experimentally observed temperature dependence of the Stokes shift shown by circles in Fig. 2.3, the Stokes shift almost jumps near its minimum. This sharp increase results from the switch between the different peaks in the PL spectra shown in Fig. 2.2. The corresponding maximum in the experimental temperature dependence of the spectral
Excitons recombination in disordered materials 34 linewidth is equally sharp. This temperature dependence of the PL spectra indicates that the extrema in the temperature dependence of the Stokes shift and of the spectral linewidth are caused by the interplay of the PL emission intensities from localized states of different types. In contrast to the standard BET model, the hopping dynamics and the thermal distribution of localized carriers is not the primary source for the observed temperature dependence of the PL spectra. Therefore, the universal relations given in Table 2.1 are not relevant for the PL features of semiconductor compounds where the impurity atoms tend to cluster.
As one can see from the experimentally observed temperature dependence of the Stokes shift shown by circles in Fig.2.3, the Stokes shift almost jumps near its minimum. This sharp increase results from the switch between the different peaks in the PL spectra shown in Fig. 2.2. The corresponding maximum in the experimental temperature de-pendence of the spectral linewidth is equally sharp. This temperature dede-pendence of the PL spectra indicates that the extrema in the temperature dependence of the Stokes shift and of the spectral linewidth are caused by the interplay of the PL emission intensities from localized states of different types. In contrast to the standard BET model, the hopping dynamics and the thermal distribution of localized carriers is not the primary source for the observed temperature dependence of the PL spectra. Therefore, the uni-versal relations given in Table 2.1are not relevant for the PL features of semiconductor compounds where the impurity atoms tend to cluster.
Thus, in order to describe experimental results let us consider the following model:
1. Sites are distributed with complex DOS, according to Eq. (2.5);
2. Two different types of LS are corresponding to exponential (Type-I) and Gaussian (Type-II) components of the DOS;
3. Exciton can recombine radiativelly or non-radiativelly at any site, while prob-abilities of radiative and non-radiative recombination processes is temperature dependent, and differs for different types of LS;