高頻半導體元件電路時域模擬之研究

Abstract

為了模擬射頻穩態電路問題 (意即：高頻週期性電路) ，在本論文中，我們發展了一個新的時域數值方法，用來解如雙調交互調頻失真 (two-tone intermodulation distortion) 之電路問題。傳統類似SPICE 之時域電路模擬器中的暫態分析 (transient analysis) 並不適用於解高頻穩態電路問題。由於計算時域解高頻穩態電路問題的嚴苛限制條件，驅使我們發展屬於自己的時域非線性電路模擬器。此新的電路模擬器必須符合穩定、有效率的條件，並且可以處理如：半 導體元件等效電路模型之強烈非線性電路問題。為此，我們成功的 結合了波形分散法 (waveform relaxation method)、單調疊代法(monotone iterative method) 與 Runge-Kutta 法 (一種常微分方程式積分法)，用之於解時域電路常微分方程式 (ordinary differential equations) ，並且可以符合上述模擬高頻穩態電路之要求。此電路模擬器所用之數值方法已被證明可以收斂並於本論文中揭示其收斂特性曲線。

為了要從模擬出來的時域數值資料之擷取出有用的頻域資訊，我 們也做了如離散Fourier 轉換法 (discrete Fourier transform) 等之後續分析。在本論文中， 我們使用自己發展出來的數值解題法與 Gummel-Poon 大訊號電路模型來模擬異質雙接面電晶體(heterojunction bipolar transistors, HBTs) 。于論文中，我們討論了直流電路計算、時域模擬、頻域分析與交互調頻失真特性分析 (intermodulation distortion characterization) 之結果。我們也進一步對不同的電路模擬器 (包括了我們發展的模擬器、HSPICE 與ADS) 之模擬結果與量測數據做了相互的比較，以說明所發展的數值模擬方法是準確且有效率的。

對於操作在高偏壓與高功率的HBT 而言，熱效應主導了元件之行為特徵。為此，我們將電熱交互作用的方程式包含到所發展的數值計算方法之中，如此可以進一步增進數值模擬之真實性。在論文的內文中詳盡討論了考慮與不考慮熱效應的電路模擬之不同處。我們也另行模擬了一個多指 (multi-finger) HBT 上所發生之熱偶合效應(thermal coupling effect) ，與此效應對HBT 之直流、射頻功率與交互調頻失真等多項特性之影響。

在附錄中， 我們介紹了金氧半導體場效電晶體 (metal-oxide semiconductor field-effect transistors, MOSFETs) 之EPFL-EKV 大訊號電路模型，並且用所發展的模擬器模擬了相關的電路。此外，我們也進一步的闡述了在本論文中所提出之數值方法的收斂特性。如本論文所言，我們所發展之數值計算方法不但可以用來解時域電路之非線性常微分方程，也可以推廣應用到包含更多數量及更多種類的半導體元件之高頻電路模擬上。

In order to solve the radio-frequency (RF) steady-state, that is ,high-frequency periodic circuit problem, such as intermodulation distortion, we develop a new numerical solution technique in this dissertation to simulate circuits in time-domain. Traditional transient analysis in SPICE-like time-domain solver is not suitable for RF steady-state solution. The tough criteria for solving steady-state problem in time- domain drive us to build our own time-domain circuit solver. This solver should be stable, efficient, and able to handle strongly nonlinear circuits, for instance, the large-signal models for semiconductor devices. Combining the waveform relaxation (WR) method, monotone iterative (MI) method, and Runge-Kutta (RK) method, we succeeded in solving the circuit ordinary differential equations (ODEs) in time domain that satisfies the criteria of the RF steady-state analysis. The convergence of our developed algorithms has been proved and demonstrated in this dissertation.

We also perform subsequent analysis, such as the discrete Fourier transform (DFT), to extract the frequency-domain information from simulated time-domain data. In this dissertation, we use our numerical solution techniques to simulate the characteristics of heterojunction bipolar transistors (HBTs) with the Gummel-Poon (GP) model. The results of DC circuit calculation, time-domain simulation, frequency-domain analysis and intermodulation distortion characterization are presented. Furthermore, we compare the results of various simulators (our solver, HSPICE and ADS) with measured data to show the accuracy and efficiency of the developed method.

For HBTs under high bias and high power operation, the thermal effects dominate the behavior of the device. Therefore, we include the electrical-thermal interactive equations in our numerical solution technique to further improve the reality of the simulation. The difference between the simulations with and without thermal effects is well discussed in the context of this dissertation. In additional, we describe the thermal coupling effects of an multi-finger HBT and its influence on DC, RF power and intermodulation distortion characteristics.

In the appendixes, the EPFL-EKV compact model of the metal-oxide semiconductor field-effect transistors (MOSFETs) is discussed and the related circuits are simulated by the proposed method and HSPICE. The convergence properties of the utilized algorithms are presented in these appendixes.

According to the discussion in this dissertation, the developed approach is not only an alternative computational technique for the time-domain solution of nonlinear circuit ODEs but also can be generalized for high-frequency circuits simulation including more and variant kind of semiconductor devices.