以第一原理計算深入探討鈀鍺化物與 鍺(001)接面之能隙中央態密度

Abstract

本論文利用第一原理對「鈀鍺合金/鍺」蕭特基介面進行研究，根據文獻指出，鈀鍺合金/鍺接面存在大量態密度，而在TCAD模擬時引入缺陷輔助穿隧模型，可以解釋在逆偏電流明顯上升的行為，這是僅用熱離子發射理論無法解釋的，利用低掠角X-射線繞射檢測，發現隨著退火溫度上升鈀鍺合金之晶面組成趨於穩定，利用這些資訊建立原子尺度結構，從實驗樣本的低掠角 X-射線繞射檢測訊號中，確認鈀鍺合金元素組成比例與晶面，並在模擬計算上初步考慮在400℃退火時兩個訊號強度較強的晶面。經由考量每一種晶面匹配所需的計算資源後，最後選定並建構出PdGe(011)/Ge與PdGe(010)/Ge兩種適合計算的接面結構，來表示實驗上的結構。 透過第一原理計算出接面的電子結構，利用態密度圖、波函數平方機率分布圖與瓦尼爾方程，幫助分析材料特性，態密度圖幫助我們了解能隙中態密度分布，波函數平方機率分布圖並進一步分析其分布，之後進一步利用瓦尼爾方程計算在介面間的躍遷參數，透過了解接面態密度來源組成，分析常見金屬鍺化物，Ni、Pt、Ge之鍺化物與鍺接面之間的差異。 計算結果發現三種合金都會在介面形成態密度，然而在鈀鍺化物的能隙態密度觀察中，發現在能隙中央形成一明顯態密度分布，以波函數機率密度圖，發現其貢獻集中於介面區，而非一般介面常見的由金屬塊材做為主要貢獻。在利用極大局域化之瓦尼爾方程進一步分析此種介面態是否會對介面間之躍遷參數有所影響，進一步了解此種介面行為，希望能深入了解介面的能係態是否會對載子傳輸有某種程度的影響，能夠對之後使用更完整之傳輸機制來全面了解此類元件之電性。 綜合以上結果，第一原理模擬計算可幫助我們初步探究不同接面合金晶面的電子結構，計算能係態與波函數，觀察能係態在介面間的躍遷扮演的角色。我們預期這樣的理論計算能夠為實際製程之電性量測提供部分解釋。

In this thesis, I perform first-principles calculations to study the PdGe/Ge Schottky junction. The previous experiments suggest that there are a great number of gap states localized at the PdGe/Ge interface. A follow-up TCAD (Technology Computer Aided Design) calculation by including the trap-assisted tunneling model shows that the off current is significantly enhanced comparing to that with merely the Thermionic model. The temperature dependence of the Grazing Incidence X-ray Diffraction spectra shows that the Pd-germanide peaks of particular crystalline planes are almost unchanged as the annealing temperature increases. In constructing the atomistic model of a Pd-germanide/Ge interface, I consider the two crystalline planes associated with the dominated Grazing Incidence X-ray Diffraction peaks of the sample annealed at the temperature 400℃; they are PdGe(011)/Ge and PdGe(010)/Ge. I further determine the supercells along the parallel by balancing the accuracy and computational resources. I calculate, from first principles, the electronic structures of the above modeled interfaces, including density of states, wavefunctions, and Wannier functions. The density of states helps in determining the energy positions of the gap states. The wavefunctions further provide their spatial distributions and localizations. I finally apply the Wannier functions to calculate the hopping parameters across the PdGe(011)/Ge interface. I also compare three different widely used metal-germanides, the Ni-, Pt-, Ge-germanide, as they form contacts with Ge(001). My calculations find that all above three metal-germanides give rise to gap states. However, only the PdGe(011)/Ge has a significant midgap state, which is identified to be a true interface state rather than a metal bulk state. We use the maximally localized Wannier functions to find out whether the midgap state plays an essential role in the interfacial hopping parameters. All these results can help experimentalists further understand the transport mechanism across the interfaces. In summary, first-principles calculations can help us find out the energy positions of the gap states, calculate their wavefunctions, and eventually determine the role of the midgap states to the hopping through the interfaces. We expect that such calculations can provide additional explanations to the I-V characteristics in realistic fabrications.