考慮薛丁格和帕松方程式聯立解之 Au/Bi/Si金屬半金屬半導體接面特性研究

Abstract

本論文研究Au/Bi/Si 金屬/半金屬/半導體 三層結構。考慮鉍薄膜在不考慮MIGS (Metal Induced Gap States)以及鉍的表面態下所受之量子侷限效應，並以薛丁格方程式與帕松方程式聯立計算在各種偏壓以及不同鉍薄膜厚度時的結構能帶圖、鉍薄膜上的總載子濃度分布、由電子電洞基態能量差所得的等效能隙等重要特性。 本研究計算發現在鉍薄膜等效能隙轉正變成半導體時，鉍區載子濃度約在10^20 cm^(-3)，接觸電阻極小，是製作歐姆接觸的一種潛力材料，而其載子的貢獻的電場數量級約在10^6 V/cm，遠大於Bi/Si接面的10^2 V/cm，本研究認為在此情況下鉍區並不像一般的半導體異質接面一樣會分掉電壓。此外由於量子效應，電洞都被趕到了遠離半導體端的位置，而電子受到抬升後與半導體能隙重疊的區域減少，會穿透到半導體端的狀態數量便會大減，本研究認為這與鉍薄膜能夠減少與矽形成接面時的MIGS有關。 由於鉍量子井會受到內部載子強大的電場而改變其形狀，操縱量子侷限效應能夠使鉍矽接面特性在歐姆與蕭特基之間切換。Au/Bi/n-Si在平衡的條件下，隨著鉍薄膜的厚度由1 nm增加到8 nm，Si的接面附近會由inversion轉變為depletion。當厚度再增加到21 nm時會再由depletion轉變為accumulation，對於實驗樣品中發現的逆偏異常上升電流，我們也提出表面反轉電荷的計算模型進行解釋。 Au/Bi/p-Si在平衡的條件下，隨著鉍薄膜的厚度由1 nm增加到17 nm， Si的接面附近會由accumulation轉變為depletion；當厚度再增加到51 nm 時會再由depletion轉變為inversion，與本實驗室團隊的實驗樣品量測結果大致符合，理論與實驗的誤差方面我們以接面不理想電荷的模型做解釋，進一步驗證本研究理論計算的正確性。

This paper investigates the Au/Bi/Si metal/semimetal/semiconductor trilayer structure. Considering the quantum confinement effects on bismuth films and neglecting MIGS and surface states of bismuth, the Schrödinger and Poisson equations are solved simultaneously to compute band diagrams and total carrier distributions as well as concentrations on bismuth films under various biases and thicknesses. Additionally, important characteristics such as the effective band gap derived from the energy difference of electron and hole ground state energies are analyzed. Our study reveals that when the effective bandgap of bismuth thin films becomes positive and transitions to a semiconductor, the carrier concentration in the bismuth region is approximately 10^20 cm^(-3), which is promising in the application of Ohmic contact, contributing to an electric field magnitude of around 10^6 V/cm which is significantly greater than the 10^2 V/cm typically found at the Bi/Si interface. Under these conditions, we argue that the bismuth region does not exhibit the typical voltage drop seen in conventional semiconductor heterojunctions. Furthermore, due to quantum effects, the holes are pushed far from the semiconductor edge and the overlap region decrease since electrons states are lifted above. Consequently, the number of states penetrating into the semiconductor edge decreases. We attribute this effect to the ability of bismuth thin films to reduce the Metal-Induced Gap States (MIGS) formed at the silicon interface. Bismuth quantum well undergoes shape changes due to the strong electric fields generated by internal carriers. Manipulating quantum confinement effects allows the characteristics of the bismuth-silicon interface to switch between Ohmic and Schottky behaviors. For Au/Bi/n-Si under equilibrium conditions, as the thickness of the bismuth film increases from 1 nm to 8 nm, the Si interface transitions from inversion to depletion. Increasing the thickness further to 21 nm changes the Si interface from depletion to accumulation. To explain the observed anomalous reverse-bias current in experimental samples, we propose a model based on surface inversion charge calculations. For Au/Bi/p-Si under equilibrium conditions, as the bismuth film thickness increases from 1 nm to 17 nm, the Si interface transitions from accumulation to depletion. Increasing the thickness further to 51 nm changes the Si interface from depletion back to inversion. These findings roughly correspond to measurements from our laboratory's experimental samples. Discrepancies between theory and experiment are explained using a model that considers non-ideal charges at the interface, further validating the accuracy of our theoretical calculations in this study.