# Energy and Charge Transport in 2D Atomic Layer Materials: Raman-Based Characterization
## 4 Energy Transport State-Resolved Raman  
Similar to the modulation of laser in TD-Raman technique, the CW laser used in FET-Raman technique is also modulated with a square wave. In addition to the modulation in time domain, this energy transport design can also be extended to spatial domain to control the energy transport states. Yuan et al. reports a novel technique for non-contact simultaneous determination of interface thermal resistance (\(R\)) and hot carrier diffusion coefficient (\(D\)) of MoS\({}_{2}\) nanosheets on c-Si by varying the laser heating area [29]. In this work, the constructed two energy transport states are in spatial domain. To be fully free from the large errors of laser absorption evaluation and temperature coefficient  
Figure 11: (a) 3D numerical simulation of a 36 nm-thick MoSe\({}_{2}\) sample. (b) Comparison of in-plane \(\kappa\) values of MoSe\({}_{2}\) nanosheets from different studies. (c) The blue shift of Raman peak with the increase of sample thickness. Reprinted from [27], with permission from Elsevier, 2019. Figure 10: (a) Schematic of suspended MoSe\({}_{2}\) nanosheet. (b) Suspended MoSe\({}_{2}\) sample under CW laser and (c) under frequency-modulated CW laser heating and Raman excitation. (d) Square wave used to modulate the CW laser. Reprinted from [27], with permission from Elsevier, 2019.  
calibration, a further developed technique named energy transport state-resolved Raman (ET-Raman) is developed to determine \(R\) and \(D\)[30; 31]. In this technique, three distinct energy transport states in both spatial and time domains are constructed to probe materials' thermal response. Furthermore, a five-state ET-Raman technique is proposed to measure \(\kappa\) of MoS\({}_{2}\), and the effects of \(R\) and \(D\) are taken into consideration, and all these properties are determined simultaneously [32]. Figure 12a shows the physical principles of this technique. A laser with 532 nm wavelength is used to irradiate the sample for both laser heating and Raman probing. As the excitation energy is higher than the band gap of MoS\({}_{2}\), three physical processes take place. First, hot carriers are generated, and then diffuse in space before the electron-hole recombination. Subsequently, phonons, which receive energy from the hot carriers or electron-hole recombination, transports the energy by heat conduction. This process mainly depends on \(\kappa\) of the sample. The third process, which is determined by \(R\), is the heat conduction from MoS\({}_{2}\) to the substrate. As shown in Figure 12d-f, combined with three different objective lenses (20\(\times\), 50\(\times\), and 100\(\times\)), a CW laser is used to construct three steady states. Similar to FET-Raman, three RSCs (\(\chi_{\text{CW}_{1}}\), \(\chi_{\text{CW}_{2}}\), \(\chi_{\text{CW}_{3}}\)) can be obtained, and we have \(\chi_{\text{CW}_{3}}>\chi_{\text{CW}_{2}}>\chi_{\text{CW}_{1}}\). With the decrease of laser spot size, \(D\) and \(\kappa\) play a much more important role in determining the temperature of the sample. Based on this, the effects of \(R\), \(\kappa\), and \(D\) can be differentiated. In this technique, two transient states are designed by using a picosecond-pulsed laser with two objective lenses (50\(\times\) and 100\(\times\)), shown in Figure 12b,c, to rule out the large errors introduced by laser absorption evaluation and temperature coefficient calibration. Similarly, two RSCs under the two lenses are obtained as \(\chi_{\text{PS}_{1}}\) and \(\chi_{\text{PS}_{2}}\), respectively. Furthermore, the heat accumulation effect can be ruled out by taking the difference of these two RSCs as \(\chi_{\text{PS}_{2}}-\chi_{\text{PS}_{1}}\). Based on the five measured RSCs, three dimensionless normalized RSCs \(\Theta_{1}=\chi_{\text{CW}_{1}}/(\chi_{\text{PS}_{2}}-\chi_{\text{PS}_{1}})\), \(\Theta_{2}=\chi_{\text{CW}_{2}}/(\chi_{\text{PS}_{2}}-\chi_{\text{PS}_{1}})\), and  
Figure 12: The mechanism of five-state energy transport state-resolved Raman (ET-Raman) technique.