An analytical heat transfer model for transient Raman thermometry analysis

Transient Raman thermometry improves on its steady-state counterpart by eliminating the error-prone steps of temperature calibration and laser absorption measurement. However, the accompanying complex heat transfer process often requires numerical analysis, such as the finite element method, to decipher the measured data. This step can be time-consuming, inconvenient, and difficult to derive a physical understanding of the heat transfer process involved. In this work, the finite element method is replaced by fitting the measured data to an analytical three-dimensional heat transfer model. This process can be completed in a few seconds. Using this approach, the in-plane thermal conductivity of two bulk layered materials and the interfacial thermal conductance between two-dimensional materials and quartz have been successfully measured. Based on our model, we performed an analytical quantitative sensitivity analysis for transient Raman thermometry to discover new physical insights. The sensitivity of the in-plane thermal conductivity of bulk layered materials is dictated by the ratio between the spot radius and heat spreading distance. The sensitivity of the interfacial thermal conductance between two-dimensional materials and quartz is determined by its conductance value. In addition, the uncertainty of the measured value contributed by the uncertainty of the input parameters can be efficiently estimated using our model. Our model provides an efficient data and sensitivity analysis method for the transient Raman thermometry technique to enable high throughput measurements, facilitate designing experiments, and derive physical interpretations of the heat transfer process.