鉍薄膜於矽基基板之微觀結構分析

Abstract

本論文利用XRD與EBSD研究鉍薄膜的晶粒尺寸及其中的微應變。我們以鉍薄膜的(0003)、(0006)、(0009)及(00012) XRD繞射譜為基礎，分別以Williamson-Hall (W-H)方法及Halder-Wagner (H-W)方法分析各樣品的縱向平均晶粒尺寸及微應變。此外，我們也建構譜型分析法，此方法考慮具厚度分佈的XRD干涉函數(Interference Function)與微應變高斯函數進行摺積以擬合XRD繞射譜型，藉以求取鉍薄膜厚度的平均值及標準差以及微應變。 我們發現垂直方向的平均晶粒尺寸大於40 nm；當薄膜厚度小於40nm時所求得的晶粒尺寸受限於薄膜厚度。我們也發現，所求得的微應變與應變大致呈正相關。當薄膜厚度超過40 nm之後，鉍薄膜已經鬆弛，此時微應變降至10-4的範圍。選擇晶粒尺寸受限於薄膜厚度的樣品與TEM量測厚度比較發現，W-H及H-W方法所得結果與其較為接近，而譜形分析法所得之結果較前兩種要小。 接著，我們以EBSD進行水平方向晶粒尺寸研究。從band contrast圖進行截距法分析及調整AZtecCrystal分析軟體的不同閾值角(Threshold Angle)設定，藉以求取水平方向的平均晶粒尺寸。我們發現，大部分樣品的閾值角在10°或15°左右，而具有高應變及高微應變的樣品其閾值角低至1°與5°。這顯示高應變樣品中的低角度晶界已出現嚴重缺陷，進而使其在band contrast圖中能被辨識為晶界。 最後，我們對樣品的水平方向晶粒尺寸分佈進行對數常態分佈的Kolmogorov-Smirnov(K-S)檢定。大部分樣品的p-value均在0.134以上，僅有兩個生長於SiO2基板的樣品其p-value小於0.063，經進一步分析其分佈型態，發現它們均呈雙峰(bimodal)分佈，其為對數常態與常態分佈組成的混合型態，若改以該混合分佈進行檢定，其p-value則升至0.196以上。我們也發現在基板溫度(Ts)為5°C的樣品中，p-value隨膜厚增加而上升，顯示樣品越厚其晶粒分佈越趨近於對數常態分佈。

This study investigates the grain size and microstrain in bismuth (Bi) thin films using X-ray Diffraction (XRD) and Electron Backscatter Diffraction (EBSD). Based on the (0003), (0006), (0009), and (00012) XRD diffraction patterns of the bismuth thin films, the Williamson-Hall (W-H) and Halder-Wagner (H-W) methods were employed to analyze the vertical average grain size and microstrain of each sample. Additionally, a profile analysis method was developed. This method involves the convolution of an XRD interference function (considering thickness distribution) with a Gaussian function representing microstrain to fit the XRD diffraction profiles, thereby determining the mean thickness, standard deviation, and microstrain of the bismuth thin films. The results indicate that the average vertical grain size is greater than 40 nm; for films thinner than 40 nm, the calculated grain size is limited by the film thickness. We also observed a positive correlation between the calculated microstrain and the strain. When the film thickness exceeds 40 nm, the bismuth thin films undergo relaxation, and the microstrain decreases to the range of 10-4. Comparing sample where grain size is limited by thickness with Transmission Electron Microscopy (TEM) measurements, we found that the results from the W-H and H-W methods are relatively close to the TEM data, whereas the profile analysis method yielded smaller values than the former two. Subsequently, the lateral grain size was investigated using EBSD. The lateral average grain size was determined by performing intercept method analysis on band contrast maps and adjusting the threshold angle settings in the AZtecCrystal analysis software. We found that the threshold angle for most samples is approximately 10° or 15°, whereas samples with high strain and microstrain exhibited threshold angles as low as 1° and 5°. This suggests that low-angle grain boundaries in high-strain samples possess severe defects, allowing these boundaries to be identified in band contrast maps. Finally, a Kolmogorov-Smirnov (K-S) test for log-normal distribution was performed on the lateral grain size distribution of the samples. The p-values for most samples were above 0.134, while only two samples grown on SiO2 substrates showed p-values less than 0.063; further inspection of their distribution patterns revealed that both exhibited a bimodal distribution, which consists of a mixture of log-normal and normal distributions. When re-evaluated using this mixture distribution, the p-values significantly increased to above 0.196. Furthermore, in samples with a substrate temperature (Ts) of 5°C, the p-value increased with film thickness, indicating that as the film becomes thicker, the grain size distribution more closely approaches a log-normal distribution.