## 4 Layout and Post-Layout Experimental Results
### Post-Layout Experimental Result Comparison of Ring Oscillator with Two Different Delay Elements  
A post-layout transient experiment was conducted to validate the proposed delay element by the minimal system (cold start-up ring oscillator) under different VDD. The accuracy of the transient analysis was set as conservative with the max strep of 0.1 \(\upmu\)s.  
Figure 7 shows the simulated cold start-up ring oscillator based on the proposed low voltage delay element and comparison with the stacked inverter based ring oscillator. As shown in Figure 7a, in contrast to the schematic-level simulation presented in Figure 4e, the cold start-up ring oscillator cannot oscillate under VDD = 23 mV and VDDH = 100 mV at a typical corner with room temperature; and Figure 7b shows that the oscillation starts under VDD = 24 mV and VDDH = 100 mV. Under  
Figure 6: Post-layout experimental results of VTC and DC gain under different VDD with VDDH = 100 mV: (**a**) VTC under VDD = 24 mV; (**b**) DC gain under VDD = 24 mV; (**c**) VTC under VDD = 30 mV; (**d**) DC gain under VDD = 30 mV; (**e**) VTC comparison between the proposed delay element and the stacked delay element; (**f**) gain comparison between the proposed delay element and the stacked delay element. VDD = 30 mV and VDDH = 100 mV, the cold start-up ring oscillator based on the proposed delay element can still sustain oscillation, as shown in Figure 7c. A comparison with the stacked inverter based ring oscillator is shown in Figure 7d. It indicates that a 55% improvement in output voltage swing is obtained under VDD = 40 mV. Figure 7: Experimental results of the proposed cold start-up ring oscillator and the stacked cold start-up ring oscillator: (**a**) post-layout transient simulation with VDD = 23 mV and VDDH = 100 mV at a typical corner under room temperature; (**b**) post-layout transient simulation with VDD = 24 mV and VDDH = 100 mV at a typical corner under room temperature; (**c**) post-layout transient simulation with VDD = 30 mV and VDDH = 100 mV at a typical corner under room temperature; (**d**) post-layout transient simulation with VDD = 40 mV and VDDH = 100 mV at a typical corner under room temperature. Figure 8 presents the output swing histogram of MC simulation for the cold start-up ring oscillator based on the proposed low voltage delay element under different VDD from 100 samples. As indicated in Figure 8a, the MC simulation result indicates that the oscillation may fail with the consideration of the process variation. However, with the increase of VDD, the failed cases decline and the normalized standard deviation (\(\sigma/\mu\)) becomes smaller, as shown in Figure 8b,c. In particular for VDD = 40 mV (Figure 8c), the failed cases almost disappear. Table 3 shows a performance comparison of the cold start-up ring oscillator based on the proposed delay element with previous works. Compared with other non-fully integrated schemes [2; 3; 4], the cold start-up voltage of the proposed solution is close to the cold start-up voltage of the LC-based oscillator previously reported [4]. Among the ring oscillators from the aspect of simulation results [9; 10], the proposed solution obtains the minimal cold start-up voltage. Compared to a previous study [15] using body dynamical control to achieve a low voltage ring oscillator in a cold start-up minimal system, a VLS is inserted in each delay element to assist the body control in this paper. As the VLS can transfer the oscillation waveform in the low voltage domain into the oscillation waveform in the high voltage domain, a wider body dynamical control range is thus obtained to bias the body of the corresponding delay element in the low voltage ring oscillator. Although the proposed solution in this paper requires an extra high power supply (VDDH) to realize a wider body dynamical control range, it can realize a fully integrated cold start-up ring oscillator with the minimal cold start-up voltage.