## 2 Theory  
### Heat Flux Calculation Method  
Heat fluxes are compared using two models. First, the model can be expressed as follows [29]. \[\dot{H}_{\rm s}=C_{\rm s}\left(\frac{\partial T_{\rm surf}}{\partial t}\right)_{ t=0} \tag{1}\]  
where \(\dot{H}_{\rm s}\) denotes the total heat influx, \(C_{\rm s}\) denotes the heat capacity of the wafer, and \(T_{\rm surf}\) denotes surface wafer temperature. The total heat flux value is calculated using the difference between the initial wafer temperature and the temperature after the process, and the heat capacity of the wafer. In this calculation, energy transfer efficiency is considered to substantially apply the ion bombardment energy transfer from plasma to the wafer [30]. The energy transfer efficiency from ions of a specific gas to the wafer is given as follows. \[\eta=\frac{4\mu}{\left(\mu+1\right)^{2}} \tag{2}\]  
where \(\eta\) denotes the energy transfer efficiency, and \(\mu\) denotes the mass ratio of bombarding ion (\(M_{\rm ion}\)) to Si atom (\(M_{\rm Si}\)), as presented in the following equation. \[\mu=\frac{M_{\rm ion}}{M_{\rm Si}} \tag{3}\]  
In addition, the effect of energy transfer due to the angle at which ions enter the wafer cannot be ignored, and the angle of incidence is assumed to be \(\theta=90^{\circ}\) through the low-pressure condition. The second model calculates the heat flux incident from the plasma to the wafer and can be expressed as follows. \[Q_{\rm in}=\int_{A_{\rm surf}}J_{\rm in}dA \tag{4}\]  
where \(Q_{\rm in}\) denotes the total plasma heat flux incident on the wafer, \(J_{\rm in}\) denotes the total energy influx, and \(A_{\rm surf}\) denotes wafer surface area. The total energy influx parameter should be comprehended and calculated to determine the plasma heat flux. Total energy influx is expressed as follows. \[J_{\rm in}=J_{\rm i}+J_{\rm e}+J_{\rm inter}+J_{\rm SP}+J_{\rm chem} \tag{5}\]  
where \(J_{\rm i}\) denotes energy flux due to ion, \(J_{\rm e}\) denotes energy flux due to electron, \(J_{\rm inter}\) denotes energy flux of neutrals due to electron and vibration excitation, \(J_{\rm SP}\) denotes energy flux of reactions associated with other gas phases, and \(J_{\rm chem}\) denotes energy flux due to chemical reaction in wafer surface. However, this study considers only the physical reaction of ions, which is the main parameter of anisotropic etching and increasing wafer temperature required according to HAR. Therefore, only ion heat flux is considered in this paper. The term summarizing the ion energy flux is as follows. \[J_{\rm in}=J_{\rm i}^{\rm kin}+J_{\rm i}^{\rm rec} \tag{6}\]  
where \(J_{\rm i}^{\rm kin}\) denotes kinetic energy of ion, and \(J_{\rm i}^{\rm rec}\) is energy balance of the substrate due to recombination. The two terms can be expressed as follows. \[J_{\rm i}^{\rm kin}=j_{\rm i}E_{\rm i}=j_{\rm i}e_{0}\big{(}V_{\rm P}-V_{\rm bias }\big{)}=0.6n_{\rm e}\sqrt{\frac{kT_{e}}{m_{i}}}~{}e\big{(}V_{\rm P}-V_{\rm bias }\big{)} \tag{7}\]  
\[J_{\rm i}^{\rm rec}=j_{\rm i}E_{\rm rec} \tag{8}\]Kinetic energy of ion consists of ion flux density \(j_{\rm i}\) and ion mean energy \(E_{\rm i}\), and the recombination energy of ion is replaced by ionization energy \(E_{\rm iz}\) instead of ion mean energy. The expression of ion flux density is used according to the pressure or other conditions. The Bohm-flux equation expressed in Equation (9) was utilized since it is used in the target process at a low-pressure level (<10 Pa). In addition, ion mean energy may be expressed as a difference between plasma potential \(V_{\rm P}\) and bias potential \(V_{\rm bias}\), as shown in Equation (10). \[j_{\rm i}=0.6n_{\rm e}\sqrt{\frac{kT_{\rm e}}{m_{\rm i}}} \tag{9}\]  
\[E_{\rm i}=e_{0}\big{(}V_{\rm P}-V_{\rm bias}\big{)} \tag{10}\]  
\[\eta=\frac{4\mu}{\left(\mu+1\right)^{2}} \tag{2}\]0  
With reference to Figure 1, the plasma characteristics for potential leak (\(kT_{\rm e}/2e\)) are considered and applied [31].