## 6 Conclusions  
This paper introduces an in situ time-based sensor capable of characterizing the RC time constants of the BEOL routing, enabling process attestation. Leveraging inherent process variations during manufacturing, the sensor facilitates die authentication. To address the resolution issue arising from a slow clock frequency, a three-configuration measurement method is proposed. Theoretical analysis shows that utilizing two auxiliary components with 10\(\times\) resistance and capacitance values can reduce measurement error by 82%.  
An analytical model is developed to study the impacts of each component in the TCG block on the discharge cycle, including the parasitic capacitances of the MOSFET switches and those of the resistors in the discharge path. The model simplifies these parasitic capacitances while incorporating charge redistribution and clock feedthrough effects, achieving close alignment with circuit simulations.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Configuration**} & \multicolumn{2}{c}{**Simulation**} & \multicolumn{2}{c}{**Measurement**} \\ \hline \multirow{2}{*}{**R Cell**} & \multirow{2}{*}{**C Cell**} & \(\begin{array}{c}\text{$N_{\text{DC}}$ {}^{a}$}\\ \text{(\mu)}\end{array}\) & \multirow{2}{*}{**Std (\(\sigma\))**} & \(\begin{array}{c}\text{$N_{\text{DC}}$ {}^{a}$}\\ \text{(\mu)}\end{array}\) & \multirow{2}{*}{**Std (\(\sigma\))**} & \multirow{2}{*}{**Error b**} \\ \hline \(R\) & \(hC\) & 1.91 & 0.06 & 1.82 & 0.063 & 4.9\% \\ \(hR\) & \(C\) & 2.24 & 0.06 & 2.19 & 0.085 & 2.2\% \\ \(R\) & \(C\) & 3.32 & 0.07 & 3.13 & 0.069 & 6.1\% \\ \(2R\) & \(C\) & 3.45 & 0.06 & 3.42 & 0.063 & 0.8\% \\ \(R\) & \(2C\) & 5.88 & 0.10 & 5.88 & 0.15 & 0\% \\ \hline \hline \end{tabular}  
* Derived discharge cycle of \(R_{\text{metal}}C_{\text{metal}}\) from Equation (11). b Error between mean values of the simulation and measurement.  
\end{table}
Table 6: Summary of time-based sensors.  
Figure 15: Measurement results of time-based sensors. (**a,c,e,g,i**) results are from the first wafer, and (**b,d,f,h,j**) from the second wafer.  
To validate the accuracy of the time-based sensors, a DMA with identical layouts of \(R_{metal}\) and \(C_{metal}\) alongside the sensors is fabricated. The DMA enables accurate resistance and capacitance measurement using external equipment. By updating the \(R_{metal}\) and \(C_{metal}\) values in the time-based sensor simulations in accordance with the DMA results, a strong correlation between the simulations and measurements is observed, validating the effectiveness of the proposed sensor.  
In summary, the time-based sensor presented in this work offers a promising solution for process attestation, contributing to the advancement of secure and reliable hardware systems.  
Conceptualization, J.-C.H., M.K. and W.K.; Methodology, J.-C.H.; Software, D.S.S.; Validation, J.-C.H. and V.J.P.; Formal analysis, J.-C.H.; Investigation, J.-C.H. and M.K.; Resources, M.K., D.S.S., J.M., B.D. and V.J.P.; Data curation, Y.A.T.; Writing--original draft, J.-C.H.; Writing--review and editing, M.K. and Y.A.T.; Supervision, J.M. and W.K.; Project administration, W.K.; Funding acquisition, W.K. All authors have read and agreed to the published version of the manuscript.  
This material is supported by the Air Force's Center of Excellence for Enabling Cyber Defense in Analog and Mixed Signal Domain (CYAN) contract FA8650-19-1-1741.  
Not applicable.  
Data Availability Statement: Data are contained within the article.  
Authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest