深次微米互補式金氧半可靠性重要議題:因時變化的介電崩壞與穿透漏電流

Abstract

本論文將以模型化分析探討兩項深次微米互補式金氧半技術的重要議題: 因時變化的介電崩壞與穿透漏電流。首先，在因時變化的介電崩壞的部分， 採用透析式方法模擬造成介電崩壞的陷阱生成;而穿透漏電流的部分、 則旨在建立一個解析的公式， 這其中包括針對P通道金氧半電晶體的電洞直接穿透漏電流的模型化以及針對閘- 汲極重疊區域的邊緣穿透漏電流的模型化。 由於因時變化的介電崩壞是一個包含隨機產生陷阱與路徑形成的行為 ，要建立完整的模型也必須包含說明陷阱產生機制的物理模型以及描述隨機行為的統計模型。 文獻中兩套經常被引用的模型、 因為分別採用不同的物理與不同的統計模型， 這使得兩者之間的實驗數據無法進行比較。對此、 我們針對統計模型部分進行參數相關性的研究， 發現解析式統計模型與蒙地卡羅透析模型參數間有明顯的相關性， 說明參數值的選擇應該將此相關性列入考慮以保證不同模型間的一致性。 蒙地卡羅透析模型雖然在解釋本質崩壞統計結果的面積及厚度效應上有不錯的表現， 然而，需要很長的計算時間則是其缺點，有鑑於此， 建立一個解析式的經驗公式有其實際應用上的需要。同時、 以此本質經驗公式為基礎，配合``等效厚度薄化''與兩區域競爭觀念 ，更可將公式進一步推廣應用至異質崩壞的部分， 除了原本的計算快速特性之外，經由配適實驗數據萃取所得的參數， 可用以評估介電層品質的優劣、 製程中所受到的傷害程度等。至此， 一套完整而實用並可同時應用於本質與異質崩壞區的統計模型已然成功地被建立。 加入``等效厚度薄化''觀念的蒙地卡羅透析模型被用來驗證前述模型， 在驗證過程中，由模擬的結果發現，解釋統計數據還需要注意樣本的數量， 特別是在異質崩壞的部分，有限的樣本數限制之下， 在累進損壞率圖中的最小資料點的解釋也要審慎、保守，也就是說， 這(些)資料可能並不具有統計上的意義。 在量子穿透漏電流的部分，雖然將之列入可靠性議題的範疇可能引發爭議， 但由於介電層的電流傳導主要藉由量子穿透效應，即使有高電場加速劣化 產生的陷阱輔助，其導通模型的建立，仍需側重對量子物理的了解。 因此，建立穿透漏電流的解析公式可視為 對任何劣化下的介電層導通機制探討的基礎。 首先、針對P型複晶矽閘P通道金氧半電晶體中的電洞進行解析公式的推導。 透過解析公式可以清楚了解電洞分布在各量化後次能帶的比例以及各次能帶電洞對穿透漏電流的貢獻。 這部分的研究旨在補足文獻中僅針對電子所做的類似分析。 在P型複晶矽閘P通道金氧半電晶體中， 當閘極氧化層厚度降至大約3毫微米或更薄時， 電洞穿透漏電流在沒有導帶電子穿透漏電流的情形下、 將超過價帶電子穿透漏電流成為主要的穿透漏電流。 另一方面、將前述解析公式稍作修改， 可進一步應用於閘-汲極重疊區域的穿透漏電流分析， 當閘極氧化層厚度降至2毫微米， 這部分的漏電流將因為平帶電壓的差別造成邊緣漏電流大於通道區域漏電流以及閘極引致汲極漏電流， 成為關態下電晶體的主要漏電流成分。 透過解析公式萃取出邊緣漏電流發生區域的寬度大約是60埃。

This dissertation presents modeling analysis on two reliability concerns of deep submicron CMOS gate dielectrics : time-dependent-dielectric-breakdown (TDDB) and tunneling leakage. First, percolation methods were adopted in modeling TDDB. Second, tunneling leakage through oxide, both in the channel and the gate-drain overlapped regions were formulated and discussed. Since TDDB is a behavior combining random trap generation and path formation from one side to the other, the whole model should also contain two distinct parts in series relation, and with the randomly generated traps as the linkage. To uniquely interprete the experimental, statistical results, two most commonly cited percolation models, i.e. cell-based analytical model and sphere-based Monte Carlo model, were compared and were found to be correlative. This will lay an additional restriction on the choice of parameter values but sustain the consistency by adopting either one of the above models. \indent Although sphere-based Monte Carlo simulation successfully explained the thickness and area dependence of intrinsic breakdown statistics, the large conputation efforts kept it from practical application. Empirical reproduction of Monte Carlo simulations in closed-form was thus motivated. All features including ultimate thickness prediction were preserved in the proposed model with only the calculation time greatly down to ``click-and-response''. To futher deal with the extrinsic case that is far more important in a real manufacturing process concerning the early failure, the concept of ``effective oxide thinning'' was adopted in the Monte Carlo sphere model. Different from the original introduction of ``effective oxide thinning'' concept that was a one-on-one relationship with the lower breakdown quantities, breakdown affected by the ``effective oxide thinning'' was also competing in nature, just like its intrinsic counterpart. With ``effective oxide thinning'' described by the geometric parameters as well as the percentage of occurrence among samples, the extended Monte Carlo sphere model now provides a direct way of modeling the competing nature in both the defective zone and the defect-free one. As a result, reproduction of the extrinsic or ``B'' mode characteristics can create a new picture of defective severity as well as its uniformity across wafers and lots. In addition, sample-size-limited characteristics (detailed in chapter 4) as clarified by the improved model suggest that a care be taken when evaluating extrinsic TDDB data in a real manufacturing process. Again, for practical consideration, formulating both intrinsic and extrinsic statistics in closed-form was motivated and was achieved by applying the novel two region scheme (chapter 4) with each region treated intrinsically (chapter 3) and combining them through the competing risk formulism (detailed in chapter 5). In addition to providing underlying physical picture, the proposed model was computational efficient, free from the sample size limited problems encountered during the extrinsic TDDB evaluations, and, the most attractively, its easy adoption of local acceleration effects (field, temperature, etc.). Hole direct tunneling were found to dominate the valence electron tunneling in p+ poly gate pMOSFET's with gate oxide thickness of around 3 nm or thinner. Modeling direct hole tunneling in an analytical way, we followed the steps that had been done on the electrons in the literatures. The proposed model could thus serve as a promising tools for sensitivly characterizing direct tunneling in oxides and can enable in-depth understandings of the subbands in the quantized inversion layer. On the other hand, as the gate oxide further down scaled to around 1.5 nm, the edge tunneling components of the gate tunneling leakage in off-state tended to overwhelm the channel ones. The model constructed with respect to the gate-drain overlapped region helped to extract the edge tunneling area of ~60 \AA times W (channel width). The experimental obervation also showed that the egde gate tunneling leakage was a single function of the gate-to-drain voltage difference (independent of the substrate bias), and the doping concentration adopted in the calculation was higher than 10^19 cm^-3. This high concentration implied the edge tunneling located in the deep extension region, consistent with the experimental observation. English Abstract \hfill iii \newline Acknowledgement \hfill vi \newline Figure Captions \hfill x \newline } {\bf \noindent Chapter 1 \hspace{0.5cm} Introduction \\ } {\noindent 1.1 \hspace{0.5cm} Overview \dotfill 1 \\ 1.2 \hspace{0.5cm} Time-dependent-dielectric-breakdown (TDDB) \dotfill 2 \\ 1.3 \hspace{0.5cm} Tunneling leakage \dotfill 3 \\ 1.4 \hspace{0.5cm} Dissertation organization \dotfill 4\\ \indent \hspace{0.8cm} References \dotfill 7\\ } {\bf \noindent Chapter 2 \hspace{0.5cm} Cell-based Analytic Statistical Model with Correlated Parameters for Intrinsic Breakdown of Ultra-thin Oxides \\ } {\noindent 2.1 \hspace{0.5cm} Introduction \dotfill 13 \\ 2.2 \hspace{0.5cm} Parameter correlation \dotfill 14 \\ 2.3 \hspace{0.5cm} Experimental result comparisons \dotfill 16 \\ 2.4 \hspace{0.5cm} Conclusion \dotfill 17 \\ \indent \hspace{0.8cm} References \dotfill 18\\ } {\bf \noindent Chapter 3 \hspace{0.5cm} A Trap Generation Statistical Model in Closed-Form for Intrinsic Breakdown of Ultra-thin Oxides\\ } {\noindent 3.1 \hspace{0.5cm} Introduction \dotfill 22 \\ 3.2 \hspace{0.5cm} Monte Carlo simulation and new model \dotfill 23 \\ 3.3 \hspace{0.5cm} Experiment and comparisons \dotfill 24 \\ 3.4 \hspace{0.5cm} Conclusion \dotfill 25 \\ \indent \hspace{0.8cm} References \dotfill 26\\ } {\bf \noindent Chapter 4 \hspace{0.5cm} Monte Carlo Sphere Model for ``Effective Oxide Thinning'' Induced Extrinsic Breakdown \\ } {\noindent 4.1 \hspace{0.5cm} Introduction \dotfill 39 \\ 4.2 \hspace{0.5cm} Monte Carlo simulation and new model \dotfill 40 \\ 4.3 \hspace{0.5cm} Experiment and comparisons \dotfill 43 \\ 4.4 \hspace{0.5cm} Conclusion \dotfill 44 \\ \indent \hspace{0.8cm} References \dotfill 45\\ } {\bf \noindent Chapter 5 \hspace{0.5cm} A Novel Sphere-Based Statistical Model for ``Local Oxide Thinning'' Induced Gate Oxide Breakdown\\ } {\noindent 5.1 \hspace{0.5cm} Introduction \dotfill 55 \\ 5.2 \hspace{0.5cm} Model development \dotfill 55 \\ 5.3 \hspace{0.5cm} Experimental comparisons \dotfill 57 \\ 5.4 \hspace{0.5cm} Conclusion \dotfill 58 \\ \indent \hspace{0.8cm} References \dotfill 59\\ } {\bf \noindent Chapter 6 \hspace{0.5cm} A Physical Model for Hole Direct Tunneling Current in $p^{+}$ Poly-Gate pMOSFETs with Ultrathin Gate Oxides \\ } {\noindent 6.1 \hspace{0.5cm} Introduction \dotfill 73 \\ 6.2 \hspace{0.5cm} Characterization and parameter extraction\dotfill 74 \\ 6.3 \hspace{0.5cm} Physical model \dotfill 75 \\ 6.4 \hspace{0.5cm} Calculation and dicussion \dotfill 78 \\ 6.5 \hspace{0.5cm} Conclusion \dotfill 79 \\ \indent \hspace{0.8cm} References \dotfill 80\\ } {\bf \noindent Chapter 7 \hspace{0.5cm} Edge Direct Tunneling(EDT) Induced Drain and Gate Leakage in Ultrathin Gate Oxide MOSFETs \\ } {\noindent 7.1 \hspace{0.5cm} Introduction \dotfill 92 \\ 7.2 \hspace{0.5cm} Experiment and Characterization \dotfill 93 \\ 7.3 \hspace{0.5cm} EDT Modeling \dotfill 94 \\ 7.4 \hspace{0.5cm} Conclusion \dotfill 95 \\ \indent \hspace{0.8cm} References \dotfill 96\\ } {\bf \noindent Chapter 8 \hspace{0.5cm} Conclusions \\ } {\noindent 8.1 \hspace{0.5cm} Time-dependent-dielectric-breakdown (TDDB) \dotfill 106 \\ 8.2 \hspace{0.5cm} Tunneling leakage \dotfill 107 \\ } {\bf \noindent Appendix A \hspace{0.5cm} Back-Gate Bias Enhanced Band-to-Band Tunneling Leakage in Scaled MOSFET's\\ } {\noindent A.1 \hspace{0.5cm} Introduction \dotfill 108 \\ A.2 \hspace{0.5cm} Separation and analysis \dotfill 109 \\ A.3 \hspace{0.5cm} Additional experiment \dotfill 111 \\ A.4 \hspace{0.5cm} Conclusion \dotfill 112 \\ \indent \hspace{0.9cm} References \dotfill 113\\ } {\bf \noindent Vita\\ Publiaction List }