應變鉍薄膜的結構特性

Abstract

本論文研究~10 nm等級厚度的鉍薄膜的結構特性；10 nm範圍為鉍薄膜以分子束磊晶法成長於Si (111)基板時，由原子團簇連接成連續平整層面後的初步階段。鉍薄膜在此厚度範圍具有可觀的量子侷限效應，其平整性也具有元件的應用性。我們針對此厚度範圍的鉍薄膜進行了高解析X光繞射、穿透式電子顯微鏡、電子背向散射繞射等分析。 所成長的鉍薄膜樣品基本上是由沿著c軸成長之孿晶晶粒構成，晶粒的尺寸在微米以上。我們採用高解析X光繞射量測(0003)、(0006)、(0009)、(00012)及(00015)面的繞射峰以干涉函數來擬合並獲取晶格常數c、薄膜的厚度。同時也以考慮結構因子、勞侖茲極化因子、德拜-瓦勒因子及X光吸收的X光繞射強度公式擬合各繞射面的積分強度，以求出鉍雙層的厚度b與德拜-瓦勒因子。我們也對(01-14)、(11-26)、(11-29)、(01-110)等傾斜面進行高解析X光繞射量測，並配合c晶格常數求取a晶格常數。我們發現同一樣品中由不同面所求取的晶格常數c其標準差大都在0.01 Ǻ以下，顯示c有相當好的一致性。晶格常數c大於文獻上鉍塊材之值，且有隨著厚度的減小而變大的趨勢，顯示薄膜在水平方向受有應力，致使垂直方向呈現伸張性的應變。雙層厚度b與c/3的比值則與文獻上塊材之值接近，顯示雙層厚度b隨著c比例變化。所求得的德拜-瓦勒因子中之Bz項略大於文獻值，顯示鉍薄膜的晶格在垂直方向維持接近塊材的有序性。在水平方向，我們發現所求得的同一樣品的a常數則散佈在\frac{7}{6}\frac{a_{Si}}{\sqrt2}與a_{Bi}塊材值之間的區間內，顯示鉍雙層在水平方向受到複雜的應力，其來源可能包括晶粒邊界的鬆弛、內部的缺陷及Si基板的影響。垂直方向則可能因為鉍雙層間準凡得瓦鍵結間隙的緩衝，使晶格常數c與b具有較好的有序性；而鉍雙層由具方向性的共價鍵組成，故晶格常數a易受應力影響而較為紊亂。 我們以穿透式電子顯微鏡拍攝之晶格影像進行快速傅立葉轉換後的倒空間之晶格結構，發現鉍薄膜與矽基板兩者晶格點具有相類似的排列，顯示兩者在水平面具有方向對準的關係。再透過選取Bi (0003)、Si (111)雙晶格點進行逆快速傅立葉轉換後，利用影像強度分布圖證實了從高解析X光繞射實驗擬合取得的厚度；而Bi (01-14)與Si (220)的逆快速傅立葉轉換後的強度分布圖則顯示7個矽原子堆疊6個鉍原子的關係。 針對準凡得瓦磊晶中磊晶層與基板在水平方向的相關性，我們也就Bi (01-14)與Si (220)傾斜面進行高解析X光繞射的φ scan。發現鉍主要孿晶晶粒與矽基板峰值的角度差大都在0.1°以下，確實具有對準的磊晶關係。晶粒尺寸在10微米等級樣品的φ scan中，除了與矽對準的鉍繞射峰之外，還伴隨著另一個差距2°至3.5°的繞射峰。我們以矽最密堆積面優選位置與7:6間距關係的模型來解釋雙繞射峰的現象。這個現象顯示準凡得瓦磊晶仍然有其晶格匹配的原則。由於準凡得瓦鍵結遠比共價鍵結微弱，此現象在10微米等級的晶粒中才能排除其他的應力而顯現出來。

In this thesis, the structural properties of Bi thin films with a thickness in the 10 nm range are studied. The 10 nm range is the initial stage after the Bi atomic clusters, grown on Si (111) substrates by molecular beam epitaxy, connect to form a continuous smooth layer. Bi films have a considerable quantum confinement effect in this thickness range, and their flatness also allows the applications to devices. The grown Bi films are composed of twinning grains along the c-axis with a size beyond micrometers. We performed high-resolution X-ray diffraction (HRXRD) for (0003), (0006), (0009), (00012) and (00015) planes. The interference function was used to fit and obtain the lattice constant c and the thickness of the films. Meanwhile, the integrated intensities of the planes were fitted by the X-ray diffraction intensity formula considering the structure factor, Lorentz polarization factor, Debye-Waller factor, and X-ray absorption to obtain the bilayer thickness b and the Debye-Waller factor. We also performed HRXRD on tilting planes (01-14), (11-26), (11-29), and (01-110) to obtain the lattice constant a. We found that the standard deviations of lattice constant c obtained from different planes were mostly below 0.01 Ǻ, showing that the c-axis had a quite good consistency. While samples’ lattice constant c’s are larger than the value of the bulk Bi in the literature and tend to increase with the decreasing thickness, suggesting the existence of compressive strain. Furthermore, the ratio of the bilayer thickness b to c/3 is close to the value of the bulk bismuth in the literature, showing the dependency of b on c. The obtained Bz terms in the Debye-Waller factor are slightly larger than the literature value, indicating that our films maintain an order close to that of the bulk one along the growth direction. In the horizontal direction, we find that the obtained a for the same sample are scattered between \frac{7}{6}\frac{a_{Si}}{\sqrt2} and a_{Bi} bulk values, showing that the bilayers undergo complicated stresses in the horizontal direction. The stresses could result from the relaxation of grain boundaries, internal defects, and the influence of the substrate. The quasi-van der Waals gap between the Bi bilayers along the c-axis could play a role of buffers, resulting in an order of lattice constants c and b; while the Bi atoms in the bilayer are connected by directional covalent bonds, thus resulting in disordered a. In addition, we performed a fast Fourier transform on the TEM lattice image to obtain the diffraction pattern for a Bi film and found that the lattice points of the Bi film and the Si substrate have similar arrangements, showing that the two have alignment in the horizontal direction. Then the Bi (0003) and Si (111) lattice points were selected for inverse Fourier transform, and the interplanar spacings were used to confirm the thickness obtained from the HRXRD. Besides, the contrast profile of Bi (01-14) and Si (220) shows the relationship of 7 silicon atoms stacked with 6 bismuth atoms. Aiming at the correlation between the epitaxial layer and the substrate in the horizontal direction in the quasi-van der Waals epitaxy, we also performed a φ scan of the Bi (01-14) and Si (220). It is found that the angle difference between the main twin peak of bismuth and that of the silicon substrate is mostly less than 0.1°, suggesting a well epitaxy. In addition, the φ scan of the samples with grain size in the 10-μm range samples are accompanied by another diffraction peak that is 2° to 3.5° apart. We use a model of the relationship between the preferential site of the silicon closest-packed plane and the 7:6 spacing to explain the phenomenon of double diffraction peaks. This phenomenon shows that the quasi-van der Waals epitaxy still has its rule of lattice matching. Since the quasi-van der Waals bond is much weaker than the covalent bond, this phenomenon can only be manifested in samples with grains size large enough to exclude other stresses.