## 2 Materials and Methods
### Use Rate of Gas (\(U_{i}\))
#### 2.3.2 Research on Improving the Use Rate of Gas (\(U_{i}\)) Measurements  
In the case of measuring the use rate of gas (\(U_{i}\)), no research method or standardized method has been proposed. Accordingly, this study proposes various methods that can be used to measure the use rate of gas (\(U_{i}\)) and compare the measurement results.  
The first method of measuring the use rate of gas (\(U_{i}\)) involves installing a sampling port at the inlet of the point-of-use (POU) scrubber and measure the FCs or N\({}_{2}\)O gas volume flow rate in the plasma (on/off state) of the main process using measurement equipment (QMS and FT-IR), as shown in Figure 5.  
\[\mathrm{F}_{on,off}=\frac{S_{f(on,off)}}{\mathrm{C}_{Kr(on,off)}\times 10^{-6}} \tag{6}\]  
\(\mathrm{F}_{on,off}\): the inlet volume flow rate at on/off plasma (L/min);  
\(S_{f(on,off)}\): the volume flow rate of tracer gas injected using an MFC at plasma (on/off state) (L/min);  
\(C_{Kr(on,off)}\): the measured concentration of the tracer gas using the QMS at plasma (on/off state) (umol/mol).  
The volume flow rate of FCs or N\({}_{2}\)O gas is calculated from the estimated inlet volume flow rate.  
\[V_{on,off}=\mathrm{C}_{(on,off)}\times F_{on,off}\times 1000 \tag{7}\]  
\(V_{on,off}\): the inlet volume flow rate of FCs or N\({}_{2}\)O gas at plasma (on/off state) (sccm);  
\(C_{(on,off)}\): the measured concentration of FCs or N\({}_{2}\)O gas using the QMS at plasma (on/off state) (umol/mol).  
Therefore, the use rate of gas (\(U_{i}\)) is determined using Equation (8).  
\[U_{i}=\frac{V_{off}-V_{on}}{V_{off}}\times 100\ (\%) \tag{8}\]  
\(U_{i}\): the use rate of gas (\(\%\));  
\(V_{off}\): FC or N\({}_{2}\)O gas volume flow rate of plasma (off state) in the process chamber (sccm);  
\(V_{on}\): FC or N\({}_{2}\)O gas volume flow rate of plasma (on state) in the process chamber (sccm).  
Figure 5: Diagram of measuring device installation for measuring the use rate of gas (\(U_{i}\)) [Method 1].  
The second method of measuring the use rate of gas (\(U_{i}\)) involves calculating and comparing the volume flow rate of the chamber using an MFC with FCs or N\({}_{2}\)O gas volume flow rate measured at the inlet of the removal facility (POU scrubber) during the operating process (Figure 6).  
\[F=\frac{S_{f}}{C_{Kr}\times 10^{-6}} \tag{9}\]  
\(F\): the inlet volume flow rate (L/min);  
\(S_{f}\): the volume flow rate of tracer gas injected using an MFC (L/min);  
\(C_{Kr}\): the measured concentration of tracer gas using the QMS (\(\mu\)mol/mol).  
The volume flow rate of GHG emissions at the inlet is estimated from the calculated inlet volume flow rate.  
\[V_{in}=C\times F\times 1000 \tag{10}\]  
\(V_{in}\): the volume flow rate of FCs or N\({}_{2}\)O gas at the inlet (sccm);  
\(C\): the measured concentration of FCs or N\({}_{2}\)O gas at the inlet (\(\mu\)mol/mol).  
Therefore, the use rate of gas (\(U_{i}\)) can be determined using Equation (11).  
\[U_{i}=\frac{V_{s}-V_{in}}{V_{s}}\times 100\ (\%) \tag{11}\]  
\(U_{i}\): the use rate of gas (\(\%\));  
\(V_{s}\): FCs or the N\({}_{2}\)O gas volume flow rate of GHGs from the main process (sccm);  
\(V_{in}\): FCs or the N\({}_{2}\)O gas volume flow rate of GHGs at the inlet (sccm).  
The non-steady state process in Method 1 is approximately equal to the actual process gas supplement in Method 2. Therefore, Method 1 can be applied when the amount of GHGs supplied during the measurement time in the facility's main process is provided and verified, and Method 2 can be applied when the number of FCs or the amount of N\({}_{2}\)O gas is impossible to provide.