## 2 Literature Review
### Overview of Low-Voltage Delay Elements for Cold Start-Up Ring Oscillator  
To achieve a fully integrated cold start-up scheme for DC energy sources (i.e., thermal and light sources), several low-voltage delay elements for cold start-up ring oscillators have already been reported [5; 6; 7; 8; 9; 10; 11; 12; 15]. Table 1 summarizes these works and the reported cold start voltage. The reported minimal cold start voltage in the literature is 36 mV [15]. Compared with other non-fully integrated solutions [2; 3; 4], this minimal cold start voltage is still not enough to meet a practical situation.  
As shown in Figure 3a, to ensure the low voltage operation of an inverter, a Schmitt trigger (ST) logic inverter has been proposed [21; 22; 23; 24]. The output signal was used to steer out the leakage current from the signal path so that the voltage between the drain and the source \(V_{ds}\) was minimized to zero. Thus, the leakage current caused by \(V_{ds}\) was reduced and the signal swing was improved. However, as the output voltage \(V_{out}\) always lagged the change of input voltage \(V_{in}\), the state change of the internal nodes in this structure was suppressed due to the feedback signal. To solve this issue, a new delay element, termed selective ST logic, was proposed [6], as presented in Figure 3b. Transistors MN4 and MP4 were inserted and controlled by the input signal, so that the feedback signal would be disabled when the input signal changed. With this configuration, the drawback of the ST logic inverter was overcome. In Figure 3c, the authors [8] proposed a stacked inverter which removed the feedback path and corresponding transistors MN3 and MP3 in Figure 3b, so that both the pull-up transistor MP2 and pull-down transistor MN2 were floated by two input signal controlled inverters between the supply rail and the ground rail. To obtain a better \(i_{on}\)/\(i_{off}\) at a lower supply voltage, two stacked inverters were used to replace the two input signal controlled inverters in Figure 3c, as indicated in Figure 3d [9]. Although a larger output swing was achieved with this configuration, the loading condition of the input signal also increased and the switching speed was sacrificed. To further enhance the performance of the ultra-low voltage delay element, a novel delay element is proposed in the next section, where a voltage level shifter (VLS) is inserted to assist the body biasing. Thus, the high voltage from the battery in the battery-assistance DC energy harvesting system is used to bias the body, and the threshold voltage of the core inverter is dynamically adjusted with the input signal. Finally, the charging current is enhanced and \(i_{off}\)/\(i_{on}\) is improved.  
\begin{table}
\begin{tabular}{c c c} \hline
**Ref.** & **Process (nm)** & **Cold Start Voltage (mV)** \\ \hline
[5] & 65 & 95 \\
[6] & 180 & 70 \\
[7] & 180 & 60 \\
[8] & 65 & 68 \({}^{\text{A}}\)/150 \({}^{\text{B}}\)/210 \({}^{\text{C}}\) \\
[9; 10; 11; 12] & 180 & 37 \({}^{\text{B}}\)/57 \({}^{\text{C}}\) \\
[15] & 180 & 36 \({}^{\text{B}}\) \\ \hline \end{tabular} \({}^{\text{A}}\) Schematic-level simulation; \({}^{\text{B}}\) post-layout simulation; \({}^{\text{C}}\) measurement.  
\end{table}
Table 1: Summary of the cold start-up ring oscillator.  
Figure 3: _Cont._