背閘偏壓對於次臨界區電路不匹配效應之控制與其物理模型

Abstract

本論文研究背閘偏壓對於次臨界區的電路不匹配之效應與物理模型。我們已經量測及分析不同大小的電晶體，這些電晶體都被加以逆向及順向偏壓。我們首先觀察到，在次臨界區存在著比過臨界區更大的誤差。此種現象是因為在次臨界區中，電流與閘極電壓及製程參數成指數關係的結果。如將背閘逆向偏壓加入考慮，我們發現電流誤差隨著背閘逆向偏壓的加劇而增大，在次臨界區此一現象更加明顯。另一方面，電流誤差會隨著背閘順向偏壓的增大而改善。此種改良是因為閘控橫向電晶體在低注入情況下作用的結果。隨著分析從不同大小的電晶體所量測的結果，我們發現小尺寸的電晶體不只存在著更大的誤差，並且對於背閘偏壓更加敏感。從實驗的結果我們提出兩點建議：(一)次臨界區的電路需小心設計以免誤差；以及(二)閘控橫向雙載子電晶體的作用可以被利用來改善誤差。 除了實驗外，我們亦推導出一個新的解析式的統計模型。此一模型可以成功地重現在次臨界區對不同元件在不同偏壓下所量測的結果。在此模型中，電流誤差被表達成以製程參數變動為因子的函數。所萃取出的參數變動值與元件面積平方根的倒數成正比，符合前人所提理論。對於在元件面積與誤差間的取捨，我們以一些例子來顯示，以背閘順向偏壓為參數此一模型可被利用來當成一種量化的最佳化設計工具。

This thesis investigates the back-gate bias control on subthreshold circuit mismatch as well as its physical model. We have measured the MOSFETS operating in subthreshold (or called weak inversion) to above-threshold regions with different gate widths and lengths. These MOSFETS were characterized with back-gate reverse and forward biases. The first observation is that the devices operating in subthreshold region exhibit larger mismatch than those in above-threshold region. This is due to the exponential dependence of current on gate and bulk voltages as well as process variations. In the case of back-gate reverse bias, we have found that current mismatch increases as the magnitude of back-gate reverse bias increases. This phenomenon is more pronounced in subthreshold region than in above-threshold region. On the other hand, with the supply of back-gate forward bias, the current mismatch deceases with increasing the back-gate bias in all operation regions. The improvement in match is due to the gated lateral bipolar action in low level injection. With the data measured from devices with different sizes, we have found that small size devices not only exhibit larger mismatch, but also are more sensitive to the back-gate bias. Two suggestions are drawn from the experiment data: (i) subthreshold circuits should be carefully designed to suppress the mismatch; and (ii) the gated lateral bipolar action can be utilized to improve the matching property of MOSFET’s. Besides the experiment, we have also derived a new simple analytical statistical model that has successfully reproduced the mismatch data in weak inversion for different back-gate biases and different device dimensions. With this model, the current mismatch can be expressed as a function of the variations in process parameters, namely, flat-band voltage and body effect coefficient. The extracted variations are shown to follow the inverse square root of the device area. Some examples have been given to demonstrate that the model is capable of serving as the quantitative design tool for the optimal design between the mismatch and device size with the back-gate forward bias as a parameter.