以線性系統理論分析IC封裝導線之系統特性

Abstract

IC封裝有兩個主要目的：除了保護矽晶片免於外力，諸如水、濕氣、灰塵乃至於化學物質之破壞與腐蝕之外；在電性方面，封裝導線還要把晶片內部的訊號經過封裝導線傳送到外界系統。在早期IC封裝佈線密度尚低、晶片工作頻率未達數百MHz時，封裝的主要考量並未著眼於電性問題，多為考慮封裝材料的特性，例如封裝結構的散熱效能與熱應力分析。然而，現今IC的體積愈來愈小，工作頻率的要求已達數百兆赫(MHz)，甚至是千兆赫(GHz)等級，使得封裝電性問題成為一重要課題。 本論文以高密度的BGA(ball grid array)封裝基板為研究對象，把基板導線視為一系統，以線性系統理論分析其傳輸特性。利用電磁分析軟體Ansoft SI4.0建立基板導線的等效電路模型並求得等效電路中各元件的參數，並求出系統轉移函數，透過分析時域和頻域響應，並整理出不同的變因(導線的線長、線寬和折線角度)與響應之間的關係。從諸多系統模擬中歸納出若干IC封裝傳輸線的特性公式，利用這些公式可預測傳輸線的時域和頻域響應。最後我們以阻抗匹配的方式改善系統響應，同時也提出最佳的匹配阻抗。

It has been known that IC packages have two primary uses. In view of mechanical protection, the IC packages can be used to protect the silicon dies from being damaged or corroded by external substances, such as water, humid air, dust, or even chemicals. For the electric use the conductors in the IC packages are used to transmit signals be-tween the inner die and outer chips. In the past the density of the connectors in the IC packages was not dense and the operation frequency was not as high as hundreds mega hertz. The key considerations of the IC packages were focused on the material problems, such as heat dissipation capability, thermal stresses rather than the electric performance. Nowadays, the size of the IC packages becomes smaller and the operation frequency is demanded up to hundreds mega hertz and even giga hertz. The electric problem of the signal transmission becomes serious. Therefore, the studying the electric performance of the transmission lines in the IC packages becomes important issue. In this thesis, the high dense packaging technology, ball gate array (BGA), is consid-ered as a study target. The linear system theory is employed to analyze the transmis-sion performance of the connectors in BGA. The transmission connectors are trans-ferred to equivalent circuits by using Ansoft SI 4.0. The parameters of the transfer functions of the transmission systems are extracted from the equivalent circuits. The systems are studied by analyzing both the time and frequency responses. Some impor-tant factors of the systems, such as wire lengths, wire widths, bending angles, and dis-tance between wires, which affect the system responses, are studied and analyzed. From many system analyses in this thesis we have concluded several valuable formulae of the transmission lines in IC packages. Those formulae can be used to predict the transmission time and frequency responses and even find the best matching resistance to improve the transmission responses.