鉍薄膜於 Si(111) 基板上的類凡德瓦磊晶行為與奈米線的量子侷限效應研究

Abstract

本論文探討鉍（Bi）薄膜於 Si(111) 基板上的類凡德瓦磊晶成長特性，結合 EBSD、TEM 與變溫 XRD 量測，分析其在低維尺度下的結構性質，並進一步延伸至奈米線製程與能帶模擬，探討尺寸與晶向對其量子侷限與電子傳輸行為的影響。 在實驗與量測分析部分，本研究採用分子束磊晶技術於 Si(111) 基板上沉積 Bi 薄膜，透過低溫成長條件（5–120 °C）與超高真空環境（~10⁻⁹ Torr）控制原子層級的成長行為。為配合低溫條件，於樣品載台表面鍍上一層 1 µm 厚的 GaAs 層，以改善輻射熱交換、穩定溫度並提升重現性。成長過程中使用反射式高能電子繞射（RHEED）進行 in-situ 觀測，確認薄膜在初期即展現二維層狀的生長模式，並與基板形成明確的晶向對齊關係。 薄膜沉積後，利用 EBSD、SAED 與高解析 X 光繞射等方法，觀察 Bi 薄膜在 Si(111) 表面的類凡德瓦磊晶堆疊特性。結果顯示，薄膜於垂直方向主要沿 Bi(0001) 成長，水平方向則傾向與基板形成 Si[–110] || Bi[–1–120] 的對齊關係，對應 6×6 Bi : 7×7 Si 的重合點晶格（coincidence site lattice）。另亦觀察到約 4.7° 偏轉的次穩排列模式，對應 3√3 × 3√3 Bi : √37 × √37 Si 的重合晶格，反映 Bi/Si 的對齊關係存在多種可能。水平方向亦觀察到孿晶與晶界的形成，其中較薄樣品更常出現晶向旋轉偏差，顯示薄膜堆疊行為受到基板表面週期的影響，呈現類凡德瓦磊晶特徵性的界面特性。 本研究亦擬合 Bi 薄膜的 bilayer 厚度與層間距比值（b/d），結果顯示各樣品皆穩定維持在 0.404–0.407 範圍，顯示雙層厚度 b 會隨垂直應變略為調整，並與堆疊週期保持比例一致，反映 Bi 薄膜可在類凡德瓦磊晶條件下穩定維持其層狀結構。此外，垂直與水平方向的晶格應變關係，顯著偏離 bulk Bi 的彈性響應，顯示晶界與基板對齊對薄膜應變行為具關鍵影響。 在能帶特性部分，本研究以鉍奈米線為模型系統，結合 Lax 模型與有限差分法，模擬不同寬度與晶向下的量子侷限效應。模擬結果指出，薄膜侷限條件下的能隙主要由電子能帶抬升主導，而在奈米線結構中，電洞能帶亦出現顯著變化。此外，特定傳輸方向（如沿 binary 軸）的電子因其橫向有效質量較大，較不易受到侷限作用，導致整體能隙開啟受限。然而該方向雖難以開啟能隙，但由於傳輸有效質量較小，反而具備較佳的載子傳輸特性，顯示出量子侷限與導通性能間的取捨關係。 為驗證上述模型，本研究採用由實驗室學弟蔡連晉製備並完成電性量測之 Bi(11-20) 奈米線陣列樣品，其厚度由 MBE 磊晶控制為 12 nm，通道寬度則以氦離子束微影定義於 20–500 nm。實驗結果顯示，當線寬縮小至 20–30 nm 時，片電阻與等效能隙會顯著上升，其中 20 nm 元件擬合得 ΔE 約為 360 meV。本研究以此實驗結果為依據進行能帶模擬，所得趨勢與實測資料高度一致，驗證本模型對 Bi 奈米線量子侷限行為的預測能力。 整體而言，本研究建立從薄膜磊晶至奈米線能帶調控的實驗與模擬架構，說明 Bi 材料於矽基平台中因侷限與方向性所導致的結構與電子性質變化，並為鉍的低維元件設計提供物理依據。

This dissertation investigates the quasi–van der Waals epitaxial growth characteristics of bismuth (Bi) thin films on Si(111) substrates. By combining EBSD, TEM, and variable-temperature X-ray diffraction (XRD) measurements, we analyze the structural properties of Bi films at low dimensional scales. The study further extends to nanowire fabrication and band structure modeling to explore how size and crystallographic orientation influence quantum confinement and electronic transport behavior. For experimental analysis, Bi thin films were deposited on Si(111) substrates via molecular beam epitaxy (MBE) under low-temperature (5–120 °C) and ultra-high vacuum (~10⁻⁹ Torr) conditions to control atomic-scale growth. A 1 µm GaAs layer was coated on the sample holder to improve radiative heat exchange and ensure thermal stability. In-situ reflection high-energy electron diffraction (RHEED) confirmed that the films adopted a two-dimensional layered growth mode and formed a well-aligned epitaxial relationship with the substrate. Post-growth structural characterization using EBSD, SAED, and high-resolution XRD revealed that the Bi films predominantly grow along the Bi(0001) direction, with an in-plane alignment of Si[–110] || Bi[–1–120], corresponding to a 6×6 Bi : 7×7 Si coincidence site lattice (CSL). In addition, a metastable configuration with ~4.7° rotation was observed, matching a 3√3 × 3√3 Bi : √37 × √37 Si CSL, indicating the presence of multiple interface arrangements. Twin domains and grain boundaries were found, especially in thinner films, suggesting that the periodicity of the substrate surface affects the stacking behavior, consistent with characteristics of quasi–van der Waals epitaxy. We analyzed the ratio between bilayer thickness and interlayer spacing (b/d) across multiple diffraction planes. All samples maintained a stable b/d of 0.404–0.407, indicating that bilayer thickness adjusts slightly under out-of-plane strain while preserving a consistent stacking proportion. This suggests that Bi films retain a stable layered structure under quasi–van der Waals conditions. The strain coupling between out-of-plane and in-plane lattice constants deviates markedly from bulk elastic predictions, underscoring the roles of grain boundaries and epitaxial alignment in thin-film Bi. To examine band structure characteristics, Bi nanowires were modeled using the Lax model and finite difference method, evaluating quantum confinement for various widths and orientations. Simulations show that in confined Bi films, bandgap opening is mainly driven by conduction band shifts, whereas in nanowires, valence band shifts also become significant. Certain transport directions (e.g., the binary axis) exhibit larger transverse effective masses, leading to weaker confinement and smaller bandgap openings, but also smaller transport masses and higher mobility—revealing a trade-off between confinement and conductivity. For model validation, Bi(11-20) nanowire arrays fabricated by our lab member Lien-Chin Tsai were grown via MBE to 12 nm thickness and patterned by helium ion beam lithography into 20–500 nm channels. Electrical measurements showed a pronounced increase in sheet resistance and effective bandgap for widths below 30 nm, with the 20 nm device yielding ΔE ~ 360 meV. Simulations closely matched these trends, confirming the model’s predictive capability for Bi nanowire quantum confinement. This work integrates experimental and modeling approaches, linking thin-film epitaxy with band structure modulation in Bi nanowires, and clarifies structure–property relationships governed by dimensional confinement and crystallographic orientation, providing a solid basis for low-dimensional Bi-based device design.