雙載子異質接面電晶體的熱穩定最佳化設計

Abstract

本論文的研究目標為多指電晶體的熱穩定壓艙電阻設計，當在高功率操作時，元件因為熱耦合效應的影響將會變的不穩定，壓艙電阻通常會被用來避免多指電晶體發生熱不定的情形，如何壓艙電阻設計是元件熱穩定的主要議題。熱阻是熱問題最主要的參數，論文中討論了熱阻的理論計算以及熱阻與元件幾何形狀之間的關係，並解釋溫度相依的基板熱導對熱流方程式及熱阻所造成的影響，熱偶合現象的發生可由耦合電流電壓方程式的推導來解釋，可使用線性化的能隙溫度關係來簡化熱電迴授係數及耦合電流電壓方程式，我們並發展使用牛頓法求解耦合電流電壓方程式的程序。 使用簡單模型來分析使用非均勻壓艙電阻的多指電晶體，可得到熱穩定最佳化壓艙電阻分佈的解析公式，與傳統均勻壓艙電阻設計作比較，新的最佳非均勻設計可以大幅增加元件穩定操作時的電流大小，使用此理想壓艙電阻分佈，可經由求解特徵分程式得到絕對穩定的最佳壓艙電阻值，第二大的正特徵值就是此最佳壓艙電阻值。多指電晶體熱穩定分析可由簡單模型拓展至準確模型，並可將溫度相依的基板熱導效應一併考慮，如此可以得到兩個熱穩定最佳化壓艙電阻分佈的設計流程，分別為均勻電流設計與均勻溫度設計，我們可以利用此兩設計流程在設定的電流或溫度之下設計最佳的熱穩定壓艙電阻值。

In this dissertation, the design of ballasting resistors for thermally stable operation of multi-finger transistors was investigated. When the devices are operated at high powers, devices will become unstable due to the phenomenon of the thermal coupling effect. To prevent the thermal instability of multi-finger transistors, ballasting resistors are often used. How to design the ballasting resistors is key issue of the thermal stability. The thermal resistance is the most importance parameter of thermal problem. Theoretical calculation of the thermal resistance was shown and the properties of the thermal resistance dependent on device geometry were discussed. The effect of temperature dependent thermal conductivity on the heat flow equation and the thermal resistance were also explained. The coupled current-voltage equations were derived and discussed to explain the origin of the thermal coupling effect. A linearized temperature dependent band-gap energy expression is used to simplify the definition of the thermal-electrical feedback coefficient and the coupled current-voltage equations. The procedure utilized to solve the coupled current-voltage equations by using the Newton-Raphson method was developed. Multi-finger transistors with nonuniform distribution of ballasting resistance have been analyzed by using the simple model. Analytical formulas for the best ballasting resistance distribution for optimum thermal stability operation were derived. Comparing to conventional method of using uniform ballasting resistance, the new schemes with optimized design could result in a significant increase in the device current under stable operation. With the ideal ballasting resistance distribution, the optimum ballasting resistance for absolutely stable operation was obtained by solving an eigenvalue equation. The second largest real positive eigenvalue of this eigenvalue equation is the optimum ballasting resistance. A design procedure for the thermally stable optimum design was developed. By extending the works on the multiple-finger transistor thermal stability from the simple thermal-electrical feedback equations to the accurate model equations and taking the temperature dependence of the thermal conductivity into account, two design flows, uniform current design and uniform temperature design, of the best ballasting resistance distribution for optimum thermal stability operation were developed. Using these design flows, we could design the best ballasting resistance needed for thermally stable operation under the specified current level or junction temperature.