Breathing Mode’s Temperature Coefficient Estimation and Interlayer Phonon Scattering Model of Few-Layer Phosphorene

The breathing mode’s Raman characteristic is a key parameter that estimates the number of layers and helps to determine interlayer thermal coupling in multilayer phosphorene. However, its temperature coefficient is not investigated yet, probably due to phosphorene’s ambient instability, difficulties in capturing its Raman modes, and relatively weak temperature sensitivity than the corresponding primary intralayer Raman modes. Here, we captured the breathing modes’ Raman scattering in multiple phosphorene flakes at different temperatures and estimated the corresponding first-order temperature coefficient. The captured modes show a negative temperature coefficient of around −0.0025 cm^–1/K. Besides, we have explored a unique feature of the breathing mode phonon scattering with temperature. The modes closely follow the dominant three-phonon process and four-phonon process scattering phenomena at low- and high-temperature ranges. The three-phonon process scattering is dominant below ∼100 K, shifting to the dominant four-phonon process scattering beyond ∼150 K. Moreover, the phonon modes show anomalous behavior of blue shift with temperature during 100–150 K, probably due to transition in the scattering process. Our study shows the significant dependency of the breathing modes over temperature, which helps to understand and model phosphorene’s interlayer thermal and mechanical properties. The study also reflects that phosphorene has significant interlayer heat transport capability due to three- and four-phonon scattering features.