## 4 Results and Discussion
### Analysis of Photoluminescence Spectra
#### 4.2.1 Analysis of Optical Constants for Binary Materials in the NIR \(\rightarrow\) UV Region  
Optical constants, i.e., the real and imaginary parts of pseudo-dielectric functions [\(\widetilde{\mathrm{n}}(\mathrm{E})\)\(\left(=\sqrt{\widetilde{\epsilon}(\mathrm{E})}\right)\) and \(\widetilde{\epsilon}(\mathrm{E})\)], are numerically obtained by using the best-fitted MDF parameters (Table 2) following the methodology outlined in Section 3.3. For InSb, theoretical results of \(\mathrm{n}(\mathrm{E}),\kappa(\mathrm{E})\) and \(\varepsilon_{1}(\mathrm{E}),\varepsilon_{2}(\mathrm{E})\) in the photon energy (\(6\,\mathrm{eV}\geq\mathrm{E}\geq 0\)) range are reported (red and blue lines) in Figures 7a and 7b, respectively, and compared with the SE data of Aspnes and Studna (2018) and Seraphin and Bennett (2018) (see black and green symbols). Similar results for InP are displayed in Figure 8a,b. The perusal of Figure 7a,b revealed that the sharpest peaks in \(\mathrm{n}(\mathrm{E})\) (\(\varepsilon_{1}(\mathrm{E})\)) are related to \(\mathrm{E}_{1}\) transitions while in \(\kappa(\mathrm{E})\) (\(\varepsilon_{2}(\mathrm{E})\)), the strongest peaks are linked to \(\mathrm{E}_{2}\) transitions. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **[PERSON] et al. (a) (10 K)** & \multicolumn{6}{c}{**Our PL Data (b) (13 K)**} \\ \hline
**x (a)** & **E\({}_{\mathrm{g}}\)** & **E\({}_{\mathrm{PL}}\)** & **x (b)** & **E\({}_{\mathrm{PL}}^{\mathrm{II}}\)** & **E\({}_{\mathrm{PL}}^{\mathrm{II}}\)** & **E\({}_{\mathrm{PL}}^{\mathrm{II}}\)** & **E\({}_{\mathrm{PL}}^{\mathrm{II}As}\)** \\ \hline  
\hline \end{tabular}
\end{table} 
Table 3: Values of the fitted parameters from the absorption spectra recorded by [PERSON] et al. (2018) (bandgap E\({}_{\mathrm{g}}\) in eV) and photoluminescence peak energies (E\({}_{\mathrm{PL}}\) in eV) at 10 K. We have also reported our PL results measured at 13 K on GS-MBE-grown InP\({}_{1-\mathrm{x}}\)Sb\({}_{\mathrm{x}}\)/n-InAs samples. Figure 6: Comparison of x-dependent bandgap energies of InP\({}_{1-\mathrm{x}}\)Sb\({}_{\mathrm{x}}\)/n-InAs based on Table 3. Bandgap energies from absorption spectra (blue open circles) at 10 K (Ref. (2018)) are fitted (magenta line) using Equation (16) with a bowing parameter of 1.9 eV. We have also displayed 10 K PL results open red squares and our 13 K PL data solid black triangles, green-filled circles, and light-blue-filled squares (see text). Figure 8: (**a**) Comparison of simulated MDF results (blue and red lines) for n(E) and k(E) with experimental data (Refs. [22; 23]) for InP (indicated by symbols) in the energy range of 0–6 eV. Magenta vertical arrows indicate the critical point energies; (**b**) same key as (**a**) but for \(\varepsilon_{1}(\mathrm{E})\) and \(\varepsilon_{2}(\mathrm{E})\). Figure 7: (**a**) Comparison of simulated MDF results (blue and red lines) for n(E) and k(E) with experimental data (Refs. [22; 23]) for InSb (indicated by symbols) in the energy range of 0–6 eV. Magenta vertical arrows indicate the critical point energies; (**b**) same key as (**a**) but for \(\varepsilon_{1}(\mathrm{E})\) and \(\varepsilon_{2}(\mathrm{E})\). For InSb and InP, our calculated results of reflectance R(E) and absorption \(\alpha\)(E) coefficients displayed in Figure 9a,b and Figure 10a,b have agreed reasonably well with the experimental results [22]. Interestingly, the simulations in each category has provided distinct CP energy features of the band structures arising from the inter-band transitions (indicated by magenta vertical arrows). Like n(E) and \(\kappa\)(E), the R(E) and \(\alpha\)(E) data have also revealed appropriate shifts in the major CP energy structures. Among other features, the reflectivity R(E) spectra indicated the strongest peaks at the E\({}_{2}\) energy gaps, varying between \(\sim\)0.6 and 0.625 [see Figures 9a and 10a], in very good agreement with the observed values for the binary (InP, InSb) materials [22].