## 5 Concluding Remarks  
In conclusion, systematic assessments of phonon and optical characteristics are achieved both experimentally and theoretically for comprehending the vibrational, structural, and electronic behavior of high-quality GS-MBE-grown InP\({}_{1-x}\)Sb\({}_{x}\)/n-InAs (001) epilayers (0.1 \(\leq\) x \(\leq\) 0.48). To estimate the composition-dependent phonons, we have employed a Reinshaw InVia Raman spectrometer using a DPSS 532 nm laser as an excitation source. For bulk InP and InSb, the observed separations of (\(\omega_{\rm LO}-\omega_{\rm TO}\)) modes are 50 cm\({}^{-1}\)[48] and 8 cm\({}^{-1}\)[49], respectively. In each InP\({}_{1-x}\)Sb\({}_{x}\)/n-InAs (001) sample, our RSS measurements have identified InP-like (\(\omega_{\rm LO}^{\rm InP},\omega_{\rm TO}^{\rm InP}\)) doublet and a DAO mode while revealing (Figure 2) InSb-like DALA, A\({}_{1g}\) Sb-impurity mode, and an unresolved broad optical band near \(\sim\)195 cm\({}^{-1}\) with FWHM \(\sim\) 10 cm\({}^{-1}\). For x = 0.48, while the separation (see Figure 4) between InP-like (\(\omega_{\rm LO}-\omega_{\rm TO}\)) modes decreases, the split in InSb-like phonons increases, but only slightly. Our calculated separation between InSb-like (\(\omega_{\rm LO}-\omega_{\rm TO}\)) modes stays much smaller (\(\sim\)3-4 cm\({}^{-1}\)\(<<\) FWHM) than the observed broad bandwidth--thus, resolving the \(\omega_{\rm TO}^{\rm InP}\) mode in InP\({}_{1-x}\)Sb\({}_{x}\) is quite difficult [24; 25; 26; 27]. Although the observed Raman line shapes of ternary InP\({}_{1-x}\)Sb\({}_{x}\) alloys are signified as the optical phonon density of states exhibiting two-phonon-mode behavior, no LVM (InSb\(:\)P\(:\)x \(\rightarrow\) 1) and gap mode (InP\(:\)Sb; x \(\rightarrow\) 0) have been perceived near the limiting values of x. Our ATM-GF calculations [59], providing accurate values of the impurity vibrational modes, have offered further support for the \"two-phonon-mode behavior\". Accurate results of bandgaps are achieved using PL measurements by calibrating the radiation lines of a Xe lamp and exploiting the SPEX 500M monochromator with a 532 nm DP-SSL excitation source. Although the earlier studies [26; 27] on InP\({}_{1-x}\)Sb\({}_{x}\) epilayers suggested large miscibility gaps from x = 0.02 to 0.97, our careful HR-XRD and PL results on E\({}^{\rm PL}\) energy gaps have indicated attaining high-quality, single-phase epilayers around x \(\sim\) 0.3, ascribed to the effect of lattice match. A complete set of model dielectric functions is methodically achieved by using [PERSON]'s MDF approach [37; 38] for calculating the optical dispersion relations of both the binary InP, InSb and ternary InP\({}_{1-x}\)Sb\({}_{x}\) alloys. For InP, InSb materials, the detailed analyses of optical constants (viz., n(E), \(\kappa\)(E); \(\epsilon_{1}\)(E), \(\epsilon_{2}\)(E); \(\alpha\)(E), and R(E)) over the photon energy range 0 \(\leq\) E \(\leq\) 6.0 eV have exhibited reasonably good agreement with the SE experimental data [22; 23]. The extension of MDF methodology to InP\({}_{0.67}\)Sb\({}_{0.33}\) alloy has provided the lowest energy bandgap value E\({}_{0}\)\(\sim\) 0.46 eV, in very good agreement with the existing first-principles calculation [18] and PL measurements. We strongly feel that our systematic study, using RSS and PL measurements along with the MDF simulations of optical constants, has provided valuable information on the vibrational and optical characteristics of InP\({}_{1-x}\)Sb\({}_{x}\)/n-InAs (001) epilayers which can be extended to many other technologically important materials. D.N.T., Conceptualization, methodology, investigation, simulations, writing the original draft. H.-H.L., Supervision, GS-MBE growth of the InAs\({}_{1-x}\)N\({}_{x}\)/InP (001) samples, experimental data acquisition, editing. All authors have read and agreed to the published version of the manuscript. This research received no external funding. The data that support the findings of this study are available from the corresponding author upon reasonable request.