We used Raman spectroscopy to investigate phonon modes of single InP-InAs core-shell nanowire with a pure wurtzite phase to reveal the embedded strained state. Raman spectra show that the InP core exhibits tensile strain and the InAs shell exhibits compressive strain due to the radial heterostructure growth. Using different polarization excitation configurations, we identified distinct A1 (TO) and E1 (TO) modes, atomic vibrations along and perpendicular to the  direction, respectively. We also identified E2h phonon modes in wurtzite InP and InAs, lattice vibration along with the  direction, a fingerprint to distinguish a wurtzite phase from a zinc-blende phase. The Raman spectra changes reveal the resonance effects of InP and InAs between the E0+Δ0 energy level and the E1 gap by varying excitation energy, which indicates Γ7c-Γ6v transition consists of a split-off valence band and a band-gap transition along  directions of the Brillouin zone. The polar patterns show the Raman A1 (TO) mode of InP only predominates in the x(yy)x¯ configuration, indicating the InP A1 (TO) phonon is sensitive to excitation polarization, suggesting the resonant Raman spectroscopy with specific polarization offers a direct way for characterizing wurtzite InP. Our findings deepen the understanding of strain in wurtzite-phase core-shell nanowire, providing a significant reference for engineering strain in core-shell nanowire to control optical and electric properties.
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