# Energy and Charge Transport in 2D Atomic Layer Materials: Raman-Based Characterization
## 2 Steady State Raman  
For steady state Raman, an electrical current or a continuous-wave laser is applied to the 2D materials to realize steady state heating. Meanwhile, the sample is irradiated by an excitation laser and the corresponding Raman signal is collected. Based on the temperature-dependence characteristic Raman signal, the interface resistance between the sample and the substrate or the thermal conductivity of the sample can be determined. Yue et al. developed an electrical heating method for the interfacial thermal resistance measurement of epitaxial graphene on 4H-SiC [18]. As shown in Figure 1, the steady state heating of the sample is achieved with an electrical current passing through. Furthermore, a confocal Raman system is used to obtain the Raman signal with an excitation laser irradiating the graphene. Then, the temperature of graphene and SiC can be differentiated based on the corresponding Raman signals. Finally, the interfacial thermal resistance between these two materials can be derived based on \(R_{\text{tc}}=(T_{\text{graphene}}-T_{\text{SiC}})\cdot A/(I^{2}\cdot R)\), where \(A\) is the graphene area, \(R\) is the electrical resistance of graphene, and \(I\) is the applied current. Due to the large uncertainty originated from a single temperature point, a linear fitting of the relation between the temperature and input power of Joule heating is conducted. The equation for determining thermal resistance can be rewritten as \(R_{\text{tc}}=(T^{\prime}_{\text{graphene}}-T^{\prime}_{\text{SiC}})\cdot A\), where \(T^{\prime}_{\text{graphene}}\) and \(T^{\prime}_{\text{SiC}}\) are the temperature against input power slopes shown in Figure 2.  
Though the heating level can be controlled accurately by adjusting the electrical current, the results can be affected by the contact resistance between the electrode and the sample. Additionally, precise positioning of the laser is also important for Raman-based temperature measurement. To overcome these drawbacks, Tang et al. developed a dual laser Raman-based thermal probing method with a superior spatial resolution [19; 20]. In this method, two lasers are used: one is for thermal probing, and the other one is for heating. In this work, the interfacial energy coupling across graphene/substrate interfaces is characterized, and the experimental setup is shown in Figure 3. The sample is placed on a nanostage, which is controlled by a piezoelectric actuator. As the stability is improved dramatically and the positioning resolution could be down to as small as 5 nm, the noise level in Raman spectra is greatly reduced. Figure 1: Illustration of the sample under electrical heating for measuring interface thermal resistance. The top figure depicts the Raman spectrum of epitaxial graphene on 4H-SiC. Reproduced from [18], with permission from John Wiley and Sons. Figure 2: The relationship between temperature and heating power. Reproduced from [18], with permission from John Wiley and Sons. During calibration and real interface measurement, 2D materials experience different stress effect. In calibration, the temperatures of the 2D material and the substrate are the same. However, the temperature of the 2D material is higher than the substrate in actual experiment. Additionally, the 2D material has different thermal expansion coefficient from the substrate. Therefore, it does not mean the temperature is determined precisely in experiment, even with high quality calibration. Furthermore, during experiment, the local spacing at the interface will significantly affect the laser absorption, which could probably lead to very high error in laser absorption calculation. All these issues need to be resolved in order to obtain high-level understanding of the energy transport in 2D materials interface. Raman shift, which is related to temperature and stress, has a higher sensitivity to temperature than Raman linewidth. Based on this, for the first time, Tang et al.