In this paper, an analytical threshold voltage model of the strained gate-all-around MOSFET fabricated on the Si1-xGex virtual substrate is presented by solving the two-dimensional Poisson equation. The impact of key parameters such as the strain, channel length, gate oxide thickness and radius of the silicon cylinder on the threshold voltage has been investigated. It has been demonstrated that the threshold voltage decreases as the strain in the channel increases. The threshold voltage roll-off becomes severe when increasing the Ge content in the Si1-xGex virtual substrate. The model is found to tally well with the device simulator.

A novel auto-tuning digital DC--DC converter is presented. In order to reduce the recovery time and undershoot, the auto-tuning control combines LnL, conventional PID and a predictive PID with a configurable predictive coefficient. A switch module is used to select an algorithm from the three control algorithms, according to the difference between the error signal and the two initially predefined thresholds. The detection and control logic is designed for both window delay line ADC and $Sigma Delta$ DPWM to correct the delay deviation. When the output of the converter exceeds the quantization range, the digital output of ADC is set at 0 or 1, and the delay line stops working to reduce power consumption. Theoretical analysis and simulations in the CSMC CMOS 0.5,$mu$m process are carried out to verify the proposed DC--DC converter. It is found that the converter achieves a power efficiency of more than 90% at heavy load, and reduces the recovery time and undershoot.