Nanoscale Disentangling of Strain and Doping in Monolayer Graphene Grown on Cu-Based Growth Template and Transferred onto Si Substrate by Combining TERS, Raman Correlation Analysis, and PCA.

Understanding and decoupling the effects of strain and doping in graphene remains a central challenge in Raman spectroscopy, as far-field measurements inherently average local variations. In this work, we combine conventional Raman spectroscopy, tip-enhanced Raman spectroscopy (TERS), G-2D bands correlation analysis, and principal component analysis (PCA) to investigate graphene grown on copper (Cu) and transferred onto silicon (Si) substrates, with the aim of probing substrate-dependent spectral variability across different length scales. Far-field Raman measurements show distinct but relatively compact spectral distributions for graphene on Cu and Si, with trends that can be qualitatively associated with mixed strain- and dopinglike contributions. These measurements primarily reflect a spatially averaged response, which masks local variations. In contrast, TERS reveals a significantly broader and spatially heterogeneous spectral behavior, particularly for graphene on Cu, whereas graphene on Si exhibits a more compact distribution. These differences indicate that substrate-dependent interactions and transfer processes influence not only the average spectral response but also its local variability. Correlation analysis based on G-2D trends provides a qualitative framework to identify dominant spectral tendencies, while PCA enables a data-driven description of spectral variability without relying on peak fitting. PCA distinguishes the main substrate-dependent contribution from additional sources of variability and, through spatial mapping of principal components, reveals that these variations are spatially structured at the nanoscale in TERS measurements, whereas Raman maps remain comparatively smooth. Overall, the combined approach demonstrates that TERS does not simply enhance the Raman signal locally but provides access to the distribution of local spectral variations that are averaged out in far-field measurements. This methodology offers a robust framework for the nanoscale investigation of graphene and can be extended to other two-dimensional materials, where local heterogeneity plays a key role in determining macroscopic properties.