利用模型擬合方法預測環狀振盪器之臨界電壓變異數與靜態IR壓降

Abstract

本論文提出一個統計模型擬合程序，在不增加任何額外電路到環狀振盪器的情況下，可以有效率地從環狀振盪器的輸出頻率中解析出元件的臨界電壓變異數以及供電網絡上的IR壓降。此模型擬合程序採用高斯過程迴歸作為其核心的模型擬合技術，且前處理使用逐步迴歸，用以挑選重要的預測因子。根據工業28奈米製程技術之積體電路仿真模擬程式進行實驗，研究結果顯示，基於不同外部電壓測量下的環狀振盪器輸出頻率，所提出的模型擬合程序可以同步地預測NMOS的臨界電壓、PMOS的臨界電壓以及靜態IR壓降。對於這三者的預測，最終實驗結果均可達到超過99.93%的決定係數。

This thesis presents a statistical model-fitting framework to efficiently decompose the impact of device Vt variation and power-network IR drop from the measured ring-oscillator frequencies without adding any extra circuitry to the original ring oscillators. The framework applies Gaussian process regression as its core model-fitting technique and stepwise regression as a preprocess to select significant predictor features. The experiments conducted based on the SPICE simulation of an industrial 28nm technology demonstrate that our framework can simultaneously predict the NMOS Vt, PMOS Vt and static IR drop of the ring oscillators based on their frequencies measured at different external supply voltages. The final resulting R squares of the predicted features are all more than 99.93%.