以密度泛函理論研究鐿矽及鐿鍺接觸的蕭特基位障

Abstract

鍺有比矽更高的載子遷移率，未來當傳統矽金氧半場效電晶體達到微縮極限的時候，可用鍺取代矽做為下一世代的通道材料，使元件效能得以繼續提升。但是鍺與金屬的接面存在嚴重的費米能級釘札，接面費米能級被釘札在鍺價帶頂端附近，使金屬-鍺接觸對電子呈現蕭基特接觸，而非適合做成電極的歐姆接觸。本所合作的實驗室提出用鐿(Yb)金屬在鍺基板上做歐姆接觸的方法，但從實驗上並不清楚該接面由何種機制改善釘札問題。 本研究根據X光繞射結果提出一種泛用的接面建造方法，據此建造YbSi2-x(100)/Si(100)、Yb3Ge5(111)/Ge(101)、Yb3Ge5(302)/Ge(101)三種單晶接面。使用密度泛函理論進行接面結構弛豫，計算接面的蕭特基位障高度。討論接面結構的變化對位障的影響。YbSi2-x(100)/Si(100)的位障計算結果符合實驗，而Yb3Ge5(111)/Ge(101)與Yb3Ge5(302)/Ge(101)的位障計算結果都不符合實驗。分析Yb3Ge5/Ge接面未鍵結電子加入H原子的位障計算，得知計算與實驗的誤差源於計算的Yb3Ge5/Ge中存在相當多的懸鍵。 由密度泛函理論的假設與半導體物理的接面模型，解釋了模擬接面與實際接面的能帶排列不同的原因。此外，以態密度來串聯接面的位障算法比另外兩種位障算法需要更厚的接面，使用上計算量更大。不過該方法中，以相關係數對齊態密度的技巧可以用來過濾表面態，幫助判斷能帶邊界。另外，在用來建造接面的計算技巧上，我們發現可以根據晶格的週期特性，提出調整應力與晶胞變換的方法，用來篩選重複結構，提升計算效率。

The carrier mobility of Ge is higher than that of Si. Such a semiconductor will very likely be the next-generation channel material to replace Si as the traditional Si-based MOSFET is approaching its scaling limit. This new development promises to continue the enhancement of device performance. However, the contact between Ge and a metal has strong Fermi-level pinning (to the valence band edge of Ge). As a result, the contact becomes the Schottky type rather than Ohmic, which is needed to serve as an electrodes. Our collaborated experimentalists report a method to achieve an Ohmic contact with a YbGe alloy-type metal, but their cannot reveal the mechanism of resolving the pinning issue. In this thesis, we report a general method to model the interface atomistic structures based on the X-ray diffraction result. We build ideal, perfectly crystallized interface structures YbSi2-x(100)/Si(100), Yb3Ge5(111)/Ge(101), and Yb3Ge5(302)/Ge(101). Then we employ density functional theory to simulate these systems, relaxing atomic positions and calculating the Schottky barrier height. We analyze how the interface structure affects the Schottky barrier height. By comparing the simulated results with the experimental data, we find that they agree each other only in the case YbSi2-x(100)/Si(100), while inconsistency arises in the other two, Yb3Ge5(111)/Ge(101) and Yb3Ge5(302)/Ge(101). We further study the effect of saturating the dangling bonds of the Yb3Ge5/Ge interface by appropriately adding H atoms, which indicates the calculation-experiment inconsistency may result from the dangling bonds at the Yb3Ge5/Ge simulated interfaces. We also discuss the difference of the band-alignment pictures between the first-principles simulation and the realistic system based on semiconductor device physics. We also show that in calculating the Schottky barrier heights, the density-of-state lineup method requires thicker layers of both Ge and YbGe. Although this method consumes more computational resources, it helps determine the band edges by excluding the interface states. In the technical aspect of constructing interface atomistic structures, we can identify the seemingly different but identical structures by figuring out the rules of the matrices of 〝strains〞 and 〝cell transforms〞, which reduces unnecessary repeating work.