電晶體等效電路模型參數萃取之研究

Abstract

電晶體等效電路模型及其參數是積體電路設計與製造的關鍵橋樑。隨著金氧半場效應電晶體(MOSFET)的尺寸微縮到奈米等級，以表面電位為核心的PSP模型被認為是最接近物理原型的電晶體模型，且已被IEEE選定為45奈米以下電晶體模型的工業標準。另一方面，非晶矽(a-Si:H)與複晶矽(Poly-Si)薄膜電晶體是主動矩陣液晶顯示器(AMLCDs)的關鍵元件，RPI薄膜電晶體模型(RPI Thin Film Transistor Model)是廣泛被使用的薄膜電晶體模型。這些等效電路模型的參數必須被適當地萃取出來，等效電路模型才能反應電晶體實際的特性，使得電路模擬合理且準確。然而，市面上商用的參數萃取器價格非常昂貴，使用的萃取方法不清楚，若可以使用一套本土開發的軟體來進行學術研究，對於半導體與光電元件與電路的研究將有其正面之意義。 在本論文中，我們首先介紹本研究開發適用於PSP場效應電晶體模型與RPI薄膜電晶體模型的參數萃取器。這個萃取器有手動調整和自動萃取兩個模式。手動調整的部份，使用者可以自由選取欲調整的參數，移動視窗對話盒上的滑塊連續地調整參數值，並立即觀察到參數值變化對模擬特性曲線的影響。藉由手動調整的模式，我們整理出有效的PSP模型與RPI模型的參數萃取步驟。在PSP模型的參數萃取步驟我們會先調整部份參數對Id-Vgs曲線做最佳化，再調整另一部份參數對Id-Vds曲線做最佳化。關於RPI模型的參數萃取步驟，我們依序將線性區、次臨界電壓區、飽和區和漏電流區所對應的參數最佳化。另外，針對非晶矽薄膜電晶體閘極偏壓造成的臨界電壓漂移效應，我們也研究了建模方法，這個方法整合了臨界電壓漂移的模型及RPI模型的參數萃取步驟，藉由這個方法，在閘極偏壓下非晶矽薄膜電晶體特性隨時間的變化可以被模擬與預測。另外，我們發現非晶矽薄膜電晶體模型參數的幾何效應，提出參數MUBAND的幾何相關性模型，可幫助校估不同尺寸的非晶矽薄膜電晶體模型的電特性。除此之外，我們提出低溫多晶矽薄膜電晶體模型的改良移動率模型與相對應的參數萃取步驟，提升低溫多晶矽薄膜電晶體模型在類比電路模擬的準確性。 在自動萃取方面，使用者可以在以手動調整接近最佳解的時候，圈選I-V曲線的特定區域，以數值最佳化李文伯格-馬奎特法(Levenberg-Marquardt method)進行自動萃取。我們進一步研究了演化式最佳化演算法在PSP模型自動萃取的應用，包含了基因演算法(Genetic Algorithm)、微分演化法(Differential Evolution)及粒子群最佳化演算法(Particle Swarm Optimization)。我們提出了Hybrid DE-PSO演算法，整合差分演化法的高變異性及粒子群最佳化演算法的快速收斂性。一開始我們會將可能的解依其優劣做排序，較優的一半執行粒子群最佳化演算法，而較差的一半將會以差分演化法產生的新解替換掉。一方面保有粒子群最佳化演算法的快速收斂性，一方面藉由差分演化法的變異機制來產生可能的更好的解。經過45奈米NMOSFETs的實例驗証，結果顯示此演算法比傳統的差分演化法及粒子群最佳化演算法具有更好的準確性和效率性。 總之，本論文已經跨出第一步研究出台灣本土第一套的電晶體參數萃取器，同時研究PSP模型與RPI模型的參數萃取技術，本參數萃取器將有利於我國奈米級積體電路與薄膜電晶體液晶顯示器電路的設計與製造。

A set of semiconductor device model and parameters bridges the communities between circuit design and chip fabrication. With the aggressive down-scaling technologies, the surface-potential-based PSP model has been regarded as the advanced one and has been selected a standard compact model for 45-nm CMOS technology and beyond. On the other hand, a-Si:H and poly-Si thin-film transistors have become essential devices for active matrix liquid crystal displays (AMLCDs). RPI model is the most widely used model for TFTs. The parameters of both PSP MOSFET model and RPI TFT model are required to be carefully extracted so that the results of circuit simulation are reasonable and accurate. However, the commercial parameter extraction tools are very expensive and there is no free parameter extraction tool for academic research use. In this thesis, the developed extraction CAD tool for PSP MOSFET model and RPI TFT model parameter extraction is introduced. The tool possesses manual adjustment mode and automatic extraction mode. In manual adjustment mode, users can select model parameters desired to be optimized. By tuning the corresponding slider box in the window dialog, the effects of parameter variation on the I-V curves can be seen simultaneously. By using the manual adjustment mode, the effective parameter extraction procedures for PSP MOSFET model and RPI TFT model are proposed. For PSP model parameter extraction procedure, we first optimize some parameters with respect to Id-Vgs curves then we optimize the other part of parameters with respect to Id-Vds curves. Regarding the RPI model parameter extraction procedure, we sequentially optimized the parameters related to linear region, subthreshold region, saturation region, and leakage region. Besides, we investigate the threshold voltage shift caused by bias stressing in a-Si:H TFT and its modeling technique. Combined with threshold voltage shift model and RPI a-Si:H TFT model parameter extraction technique, the current-voltage characteristics variation over time can be simulated and predicted. Besides, we find the geometry dependence effect in RPI a-Si:H TFT model and propose a model for parameter MUBAND. The MUBAND model will help the simulation of TFTs with various dimensions. Furthermore, we present a new SPICE-compatible mobility function together with parameter extraction procedure which give more accurate results than conventional RPI mobilty model for excimer laser annealed LTPS TFTs. Concerning automatic parameter extraction, users can select a limited region of I-V curves and perform automatic extraction with numerical optimization Levenberg-Marquardt method when good enough approximate solution is obtained. We further investigate the application of evolutionary based algorithms on PSP model parameter extraction, including genetic algorithm (GA), differential evolution (DE), and particle swarm optimization (PSO). We propose a hybrid DE-PSO algorithm which combines the advantages of high diversity from DE and fast convergence from PSO. Individuals in the population are first sorted according to their fitness values. The better half of population proceeds as PSO and the worse half of population are replaced by new individuals generated by DE. This algorithm maintains the fast convergence of PSO and creates good potential solutions by the differential operation from DE. Good accuracy and efficiency are obtained by several sub-45 nm NMOSFET testing cases. In summary, the parameter extraction and modeling techniques for PSP MOSFET model and RPI TFT models will benefit nano-CMOS and TFT-LCD panel circuit design and fabrication.