# Energy and Charge Transport in 2D Atomic Layer Materials: Raman-Based Characterization
## 7 Concluding Remarks and Outlooks  
As Raman spectroscopy can be used to characterize the energy and charge transport in 2D materials, many different Raman-based techniques have been developed over the last decade. Steady state Raman can be used to measure the thermal conductivity and interface thermal resistance. However, both temperature calibration and laser absorption measurement, which induce large errors, are needed. To overcome this drawback, techniques involving time resolving, which include TD-Raman and FR-Raman, are proposed. For TD-Raman, it is not appropriate for studying very fast thermal transport phenomena. Though FR-Raman can be used for fast thermal transport, a large number of measurements under different frequencies are required for the data fitting process. Then, FET-Raman technique, with a fixed frequency, was developed to characterize the thermal properties by studying the Raman shift change against laser power. For all the Raman-based techniques mentioned above, the hot carrier diffusion effect is not considered. By constructing different energy transport states in both time and space domains, ET-Raman techniques are proposed. For supported samples, a picosecond laser and a CW laser are combined to realize the simultaneous measurement of \(\kappa\), \(D\), and \(R\). To reduce the heat accumulation effects in suspended samples, a nanosecond laser and a CW laser are used together to measure \(\kappa\) and \(D\). As all Raman-based techniques share the similar energy transport process, the neglect of temperature nonequilibrium among different energy carriers can also introduce errors in the thermal property characterization. The nanosecond ET-Raman technique is further developed to study the energy coupling between OP and AP. The corresponding coupling factors are determined, and a much more accurate thermal conductivity is also obtained. This breakthrough is expected to move the Raman-based energy transport probing to an unprecedented level. In summary, Raman-based techniques show excellent suitability and performance in characterizing the energy and charge transport of 2D materials. Additionally, since 2D materials are extremely thin, the beam scattering techniques (e.g., XRD) cannot obtain sound diffraction signal and determine the in-plane lattice size. On the other hand, using thermal diffusivity (\(\alpha\)) measured by Raman spectroscopy, we can measure the thermal diffusivity at different temperatures. Then by using the thermal refusivity theory, we can extend to obtain the thermal refusivity at the 0 K limit, and obtain the structure domain size. The thermal refusivity model of phonons is expressed as:  
\[\Theta= \frac{1}{\alpha}=\frac{3}{\
u^{2}}\bigg{(}\frac{1}{\tau_{\text{phonon} }}+\frac{1}{\tau_{\text{defect}}}\bigg{)}=\Theta_{0}+C\cdot e^{-B/T}, \tag{13}\]  
where \(\
u\) is the average group velocity, \(\tau_{\text{phonon}}\) and \(\tau_{\text{defect}}\) are the electron-phonon scattering time and defect scattering time, respectively. \(\Theta_{0}\) is the thermal refusivity at the 0 K limit, and is entitledas residual thermal refrusivity, \(B\) is a constant proportional to the material's Debye temperature. Based on Equation (13), \(\Theta\) decreases with the decrease of temperature and reaches \(\Theta_{0}\) at the 0 K limit. Furthermore, the defect scattering intensity from grain boundary, lattice imperfections, chemical impurities, rough edges, and amorphous structures, etc. can be reflected by \(\Theta_{0}\). In addition, the lattice vibration also weakens and the phonon population decreases as temperature goes down. From Equation (13), \(\Theta_{0}\) can be written as \(\Theta_{0}=3/(vl_{0})\), where \(l_{0}\) is the mean free path limited by defect scattering. \(l_{0}\) is called structure thermal domain size, which is actually an effective domain size combining the effect from three-dimensional crystallite [38; 39; 40].