臺灣博碩士論文加值系統

本論文研究電路的不匹配效應與物理模型。首先針對背閘偏壓對於次臨界區的影響，經由量測及分析不同尺寸並加以逆向及順向偏壓電晶體，觀察次臨界區存在比過臨界區更大的電特性誤差，主要的原因在於次臨界區中，電流與閘極電壓及製程參數成指數的關係影響所致，其中也發現電流誤差會隨著逆向偏壓的加劇而增大，從另一個角度去思考，電流誤差會隨著背閘順向偏壓的增大而改善，這樣的結果是由於閘控橫向電晶體低注入情況產生所致。同時我們亦推導出一個新的解析式統計模型，並成功模擬在次臨界區對不同元件在不同偏壓下所量測的結果，另外電流誤差也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，符合前人所提出的論點。
在接下來的過程中，我們利用已經萃取出來的參數做進一步的利用，並特別探討臨界電壓的變異特性，過程中利用和別人的模型做比對，一方面探討背閘偏壓對臨界電壓的影響，另一方面探討不同的汲極電壓下，所造成臨界電壓的差異，此時導致電子能階產生變化，而使元件的控制力有所升降；在其中臨界電壓變異也是探討的重點之一，如此一來便可發現元件匹配程度，並進一步得知電路設計時的限制，並設計出電子電路最適操作情況。
中間過程中，因為通道尺寸的縮小，有些前人未考慮的因子必須被考慮，如通道長度要考慮成有效的通道長度，因此在這個部份，利用EDT模型去求出重疊長度部分，並藉此確認元件的有效通道尺寸；而另一個重要的物理因子，源極以及汲極的阻抗，則利用不同背閘偏壓情況下所產生的電流特性，並加以高的電場，利用載子遷移率相同的特性而求出阻抗大小。
從一開始，我們探討元件操作在次臨界區域，並討論其中匹配特性，在最後的步驟，我們探討了元件操作在過臨界區域匹配特性，並利用一套新的背向散射理論推導出其相對應的變異模型，其中考慮到背向散射的原理，而使元件操作在飽和區，再利用之前已經得到的參數臨界電壓、汲極電壓致使位障下降因子以及新的萃取參數：背向散射係數，並加上考慮有效的通道長及源極和汲極的阻抗來建構整個不匹配模型，當然也建立背向散射係數匹配模型，並加以運用在整個電流誤差模型，也成功的達到預期中的結果。

This thesis investigates the current mismatch and derives a physical model. First, we have discussed the back-gate bias control on subthreshold circuit mismatch. We have measured the MOSFETs operated in subthreshold region with different gate widths and lengths. These MOSFETs were characterized with back-gate reverse and forward biases. We have observed that the devices operating in subthreshold region exhibited larger mismatch than those in above-threshold region. The 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. On the other hand, with the supply of back-gate forward bias, the current mismatch decreases with increasing the back-gate forward bias. The improvement in match is due to the gated lateral bipolar action in low level injection. We have also statistically derived an analytical 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. The extracted variations are shown to follow the inverse square root of the device area.
In the following work, we have used the results of extraction for different parameters. We also pay more attention to the threshold voltage fluctuation compared to different models. The substrate bias dependence of threshold voltage standard deviation was also discussed. On the other hand, we have found that drain voltage bias caused the effect of DIBL.
To reconfirm the reliability of our model, we have taken some parameters into account. In order to obtain the effective channel length, we have used the edge direct tunneling (EDT) model to gain the overlap length. On the other hand, the source/drain series resistance is also an important pole in our model. By incorporating the constant mobility criterion into the current equation under different bias conditions, the series resistance can be easily achieved.
In the beginning, we have discussed the devices operated in the subthreshold region. In the end, we have discussed the current mismatch in above-threshold regions and derived a physical model based on backscattering theory. Due to the backscattering theory, we have discussed the devices operated in saturation region. We have also derived a backscattering based mismatch model with key parameters, DIBL, threshold voltage, and backscattering coefficient. The effective channel length and series resistance were also taken into consideration to confirm the validity of the mismatch model. We have achieved that the backscattering coefficient mismatch model was feasible for our data. We have also successfully used the new mismatch model to reproduce the experimental current mismatch.

Contents

Chinese Abstract i
English Abstract iii
Acknowledgement v
Contents vi
Figure Captions viii

Chapter 1 Introduction 1
1.1 An Overview for Measured Devices 1
1.2 Matching Properties of MOS Transistors 2
1.3 Mismatch Model 3

Chapter 2 Subthreshold Operation 5
2.1 Basic Concepts about Subthreshold Operation 5
2.2 Experimental Subthreshold Operation 6
2.3 Subthreshold Mismatch Model 6
2.4 Conclusion for Devices Operated in Subthreshold 9

Chapter 3 Random Threshold Voltage Fluctuation 11
3.1 Fluctuation Model 11
3.2 Using Extraction of Mismatch Coefficient and to Derive 13
3.3 Effect of DIBL on Threshold Voltage 15
3.4 Conclusion 16

Chapter 4 Extraction of Series Resistance and Overlap Length 18
4.1 Constant Mobility Bias Conditions................................................................18
4.2 Extraction of Source/Drain Series Resistance .19
4.3 Results and Discussion of Source/Drain Series Resistance .20
4.4 Extraction of Gate-to-Source/Drain-Extension Overlap Length 20
4.5 Results 21

Chapter 5 Mismatch in above Threshold Region 22
5.1 Backscattering Theory 22
5.2 Analysis and Model 23
5.3 Devices Operated in above Threshold Region 24
5.4 Conclusion 26

Chapter 6 Summary 27

References 28
Vita 63

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