Correlation analysis of vibration modes in physical vapour deposited Bi₂Se₃ thin films probed by the Raman mapping...

In this work, the Raman spectroscopy mapping technique is used for the analysis of mechanical strain in Bi₂Se₃ thin films of various (3-400 nm) thicknesses synthesized by physical vapour deposition on amorphous quartz and single-layer graphene substrates. The evaluation of strain effects is based on the correlation analysis of in-plane (E² _g) and out-of-plane (A² _1g) Raman mode positions. For Bi₂Se₃ films deposited on quartz, experimental datapoints are scattered along the line with a slope of ∼0.85, related to the distribution of hydrostatic strain. In contrast to quartz/Bi₂Se₃ samples, for graphene/Bi₂Se₃ heterostructures with the same thicknesses, an additional negative slope of ∼-0.85, which can be associated with the distribution of the in-plane (a-b) biaxial tensile strain due to the film-substrate lattice mismatch, is observed. The algorithm of phonon deformation potential (PDP) calculation based on the proposed strain analysis for the 3 nm thick Bi₂Se₃ film deposited on the graphene substrate, where the strain is considered to be coherent across the thickness, is demonstrated. The PDPs for biaxial in-plane strain of the Bi₂Se₃ 3 nm film in in-plane and out-of-plane modes are equal to -7.64 cm^-1/% and -6.97 cm^-1/%, respectively.