Erratum: “Photoluminescence Emission Efficiency Analysis Methodology by Integrating Raman Spectroscopy of the A₁(LO) and E₂(high) Phonons in a GaInN/GaN Heterostructure” [Physica Status Solidi B, 2024, 2400057]

There was a mistake in solving Equation 4a.4a (Formula presented.) 4b (Formula presented.) We show corrected Figure 11 and, resultantly, related Figures 13, and 14. Areas marked with asterisks and circles in Figure 11a are discussed in conjunction with Figure 14. We reconsider and revise the carrier recombination process. The temperature increase was obtained using the shift in the E₂(high) mode energy (E_E2H) by increasing laser power from zero to 9 mW. E_E2H at the zero-power limit was given by the intersection of the linear function fitted to the dependence of the experimental plots. 11 Figure (Figure presented.) Examples of images of temperature increase in the Ga_0.95In_0.05N layer obtained from ΔE_E2H using the parameter sets (a, b) for GaN of (−1027, −597): a) and (−742, −715): b). 13 Figure (Figure presented.) Histogram of effective LOPC+ energy shift by irradiating the 9 mW laser, a) (a, b) = (−1027, −597), b) (a, b) = (−911, −852), and (c) (a, b) = (−742, −715) for GaN. The negative values occupy 10%, 25%, and 40% of pixels in the images of ΔE_LOPC for (a), (b), and (c) respectively. 14 Figure (Figure presented.) Mapping images of ΔE_LOPC when increasing the laser power to 9 mW, a) for (a, b) = (−1027, −597) and b) for (a, b) = (−742, −715) for GaN, c) n_e, and d) PL emission intensity per electron when using (a, b) = (−1027, −597). In the published article, we described that the increase in the Raman peak energy of the LO phonon–plasmon coupling (LOPC) mode by increasing the laser power (ΔE_LOPC) was negative in 47% of the measured region when taking the deformation potentials set (a, b) = (−742, −715) for GaN. In the revised images, 40% region was found to have negative values. When using (a, b) = (−1027, −597), the negative value region occupies 14%. The revised Figure 13 shows that the region with negative ΔE_LOPC values increases as a value decreases. The parameter set of (a, b) = (−1027, −597) is recommended for GaN by a statistical consideration of the inclusion of an unreliable negative value area as stated in the published paper. Figures 14a,b show the revised images of the distribution of ΔE_LOPC. In Figure 14c, the mapping image of n_e for (a, b) = (−1027, −597) is exhibited, where the center region has a high electron density, which is the same property as shown in the previous version. The corrected PL emission efficiency I_PL/n_e shown in Figure 14d in this region is lower than the values in the surrounding area. This is the same feature as published. Figure 6a suggests the higher ΔE_E2H in the center region, but the contrast in ΔT obtained from the E_E2H at the zero-power limit is ambiguous. This is attributed to the high uncertainty of ΔT (σ_ΔT) as shown in Figure 15, which is obtained from the uncertainty of the slope of the fitted linear function of E_E2H. On the other hand, the regions with extremely high and low ΔT areas marked in Figure 11a show a correlation with I_PL/n_e in Figure 14d, excluding the regions at (x, y) = (2.5, 0.4), (0.4, 0), and (0, 0). At (2.5, 0.4), σ_ΔT is significantly high. At (0.4, 0), ΔE_LOPC is negative. Thus, we can exclude these regions from the discussion. The point of (0, 0) has a low σ_ΔT and a positive ΔE_LOPC, and thus there is no reason to exclude this point. As n_e at this point is lower than that in the center region, the nonradiative recombination rate is possibly higher, while the emission efficiency is not so low. At present, we have no clear reason for this point. However, the low rate of carrier escape from this region and high nonradiative recombination rate possibly affect it. Further analysis of carrier transport using Boltzmann equation is considered to be required. For other regions of extremely high and low ΔT, the correlation is good. In conclusion, even though the unclear correlation between ΔT and I_PL/n_e at a glance because of the high uncertainty of ΔT, the correlation is identified for the regions with extremely high and low ΔT regions beyond the uncertainty. It is considered that temperature increase takes place in the region of low PL emission efficiency. 15 Figure (Figure presented.) Uncertainty of temperature increase. This method allows us to discuss local carrier dynamics by integrating PL emission efficiency as the intensity per electron, temperature increase related to local nonradiative carrier recombination, the potential energy of carriers, strain, and alloy composition.