利用波茲曼傳輸方程式所推導出之超短基區少數載體的傳輸理論

Abstract

在本篇論文中，我們提出了一個新的理論來描述擁有超短基區的雙載子電 晶體中少數載體的密度分佈及電流密度的分佈情形。我們要解的基本方程 式是波茲曼傳輸方程式；其中的一個邊界條件是下在從射極和基極的空乏 區邊緣向內算少於一個平均自由路徑的距離，在那邊少數載體的分佈函數 是呈 Maxwell 的分佈；另一個邊界條件是下在基極和集極的空乏區邊緣 ，在那邊少數載體的分佈函數是假設為零。結果顯示，當基區寬度越來越 窄時，傳統的擴散傳輸會逐漸地轉變成為彈道傳輸 ballistic transport ）。由於不均勻的離子佈植所造成的內建電場會造成少數載體在每一點的 濃度都減少；我們也證明了對以現今技術已可達成的短基區而言，傳統的 擴散理論都會高估了電流密度。所以，為了要能準確地預測一個雙載子電 晶體的特性，我們必須以新的傳輸理論來取代現有的理論。 In this thesis, a new theory to describe the minority- carrier density distribution and current density distribution for bipolar junction transistors with ultra-short bases is proposed. The basic transport equation to be solved is the Boltzmann transport equation. One of the boundary conditions is given at the position less than a mean free path from the emitter-base depletion region edge, where the minority-carrier distribution function is a Maxwell distribution function. The other boundary condition is given at the base-collector depletion region edge, where the minority-carrier distribution function is assumed to be zero (perfect sink). The results show that the conventional diffusive transport will gradually transform into the ballistic transport as the base widths decrease. The built-in field due to nonuniform-base doping will cause a reduction of carrier density at every point in the base. We also can prove that for short bases that is available in modern technology, conventional diffusion model always overestimates the current density. Therefore, a complete transport theory should replace the old one in order to make predictions accurately.