Layer-Dependent Raman Spectroscopy Study of 3R-Phase MoS₂

Layered transition metal dichalcogenides (TMDs) have attracted extensive interest due to their remarkable electronic, optical, and mechanical properties. Among them, molybdenum disulfide (MoS₂) exhibits two main stacking polytypes: the centrosymmetric 2H phase and the non-centrosymmetric 3R phase. The latter has recently drawn attention for its spontaneous polarization, piezoelectricity, band modulation, and possible topological features, but its lattice dynamics and phonon-related properties remain far less understood. To address this gap, we present a comprehensive study of the layer-dependent Raman phonon characteristics of 3R-phase MoS₂ and systematically compare them with those of the 2H phase. Experimentally, we employed confocal Raman spectroscopy and polarization-resolved second-harmonic generation (SHG) to probe vibrational modes and stacking-dependent nonlinear responses of samples ranging from monolayer to bulk. SHG measurements provided an unambiguous means of distinguishing the stacking orders: while the SHG signal vanishes in even-layer 2H samples due to inversion symmetry, it persists strongly in 3R samples of any thickness. Raman spectra in the low-frequency region revealed distinct shear and breathing modes whose evolution with layer number was analyzed using both the linear chain model (LCM) and the more refined force constant model (FCM). While the LCM qualitatively captures the layer-dependent shifts of interlayer vibrations, the FCM provides quantitative agreement with experiments by explicitly incorporating nearest- and next-nearest-neighbor interactions as well as surface corrections. To further interpret the relative intensities of interlayer Raman modes, we introduced the bond polarization model (BPM), which links mode-dependent scattering strength to the symmetry and orientation of chemical bonds. Our BPM analysis revealed pronounced asymmetry in charge redistribution for 3R stacking, leading to weaker interlayer binding energy compared to 2H (0.111 eV vs. 0.113 eV), and consequently a lower sliding barrier, consistent with the observed propensity of 3R crystals for interlayer slip. In the high-frequency region, both stacking types show characteristic in-plane and out-of-plane modes; however, the peak separation in 3R-phase MoS₂ demonstrates stronger sensitivity to the layer number, making it a more reliable spectroscopic fingerprint for thickness identification. Importantly, we found that surface effects play a critical role in reproducing experimental high-frequency shifts in 3R samples, reflecting their weaker interlayer coupling and enhanced surface contributions. In summary, this work establishes a complete picture of the phonon behavior in 3R-phase MoS₂, bridging experiment and theory. Our results demonstrate that Raman spectroscopy combined with SHG provides a powerful toolkit for identifying stacking order and thickness in layered MoS₂. By benchmarking LCM, FCM, and BPM models, we clarify the roles of interlayer coupling, stacking symmetry, and surface effects in shaping vibrational properties. These insights not only advance the fundamental understanding of lattice dynamics in non-centrosymmetric TMD polytypes, but also lay the groundwork for exploiting 3R-phase MoS₂ in next-generation optoelectronic, piezoelectric, and quantum devices.