臺灣博碩士論文加值系統

在半導體的領域中，鉍的結構相當特殊，不屬於常見的立方晶格，而是屬於菱形晶格，且可使用六方晶格描述，因此我們想在盡可能不破壞晶體的前提下，透過X光繞射的技術瞭解鉍的結構、晶格常數、積分強度等。
我們的樣品是成長在矽(111)方向的鉍(0003)薄膜，且樣品屬於多晶的結構，因此增加了分析的難度。我們的做法先從與鉍(0003)同方向的面間距求取值，即c軸方向，此方式可先去除a軸的影響得到精確度較高的c，發現c與薄膜的厚度存在相關性且不同的繞射面所能推得c的精確度也存在著差異，值得特別進行討論，之後再求取其他方向的面間距來推得a。我們還發現有些樣品的半寬具有特殊的規律與關係，藉此我們可以求取薄膜的厚度與儀器半寬對樣品影響的程度。
本文還特別分析了鉍結構中兩個子晶格間的距離。首先，由X光繞射的積分強度公式著手，因積分強度公式中有結構因子，而結構因子中有子晶格間的距離與c軸的關係式。接下來因積分強度中存在其他因子，而透過不同繞射面的積分強度比較並代入德拜-沃勒因子擬合，由消光效應判斷去除不合理的值，最後得出關係式，並觀察不同樣品間關係式的變化趨勢。

In the field of semiconductors, the structure of bismuth is quite special. It is not a common cubic lattice, but a rhombohedral lattice and can be described by a hexagonal lattice. Therefore, we want to pass through technology of X ray diffraction without destroying the crystal as much as possible to understand the structure of bismuth, lattice constant, integral intensity, etc.
Our sample is grown on the silicon (111) direction Bi (0003) thin film, and the sample has a polycrystalline structure, which increases the difficulty of analysis. In our approach, we first obtain the value from the interplanar spacing in the same direction as the bismuth (0003), that is, the c-axis direction. This method can first remove the influence of the a-axis to obtain a more accurate c and find that c is correlated with the thickness of the film. The accuracy of c, which can be deduced by different diffraction plane, is also different. This is worthy of special discussion. Then the interplane spacing in other directions can be calculated to derive a. We also find that the full width at half maximum of some specimens has special laws and relationships, so we can obtain the the thickness of the film and influence of the FWHM of the instrument on the specimen.
This paper also analyzes the distance between two sub-lattices in the bismuth structure. First, we start with the integral intensity formula of X-ray diffraction because there is a structure factor in the integral intensity formula and the structure factor has the relationship between the distance between the sub-lattices and the c-axis. Next, because there are other factors in the integrated intensity, the integrated intensity of different diffraction plane is compared and use the Debye-Waller factor to fit. The unreasonable value is judged by the extinction effect and remove it. Finally, the relationship is obtained and the changing trend of the relationship between samples is observed.

口試委員會審定書……………………………………………………...…I
誌謝……………………………………………………………………......II
中文摘要………………………………………………………...……….III
英文摘要………………………………………………………………….IV
目錄…………………………………………………………………...…...V
圖目錄…………………………………………………………………...VII
表目錄…………………………………………………………………......X
第一章 序論…………………………………………………………...…..1
1.1 研究背景與動機…………………………………………………....…………1
1.2 論文架構…………………………………………….…………………...……2
第二章 X光繞射和鉍的晶體結構………………………...……………..3
2.1 X光繞射(X-Ray Diffraction, XRD)………………………..………..………...3
2.2鉍的實空間晶格……………………………………………………………….5
2.3密勒指數(Miller indices)…………………………………………...………….7
2.4倒晶格向量…………………………………………………………..………...7
2.5 結構因子(structure factor) ……………………………………………………9
第三章 c軸、a軸與半寬…………………..………………………...…10
3.1鉍的 c軸定義………………………………………………………..............10
3.2 c軸與厚度的關係……………………………………………………………11
3.3 c軸的精確度…………………………………………………………….……13
3.4 c軸與a軸………………………………………………………………….….16
3.5半寬(FWHM)與厚度………………………………………………………….18
3.6半寬(FWHM)與探測器狹縫(detector slit)………………………..………….22
第四章 b/d與c軸的關係………….........................................................33
4.1 X光繞射的積分強度(integrated intensity)……………………………..........33
4.2積分強度說明與推導………………………………………………...………34
4.3積分強度擬合………………………………………………………….……..36
4.4子晶格間距與c軸的關係…………………………………………………...40
第五章 結論…………………………………………………...…………44
第六章 樣品數據整理…………………………...………………………45
6.1 說明………………………………………………………………...………...45
6.2 樣品薄膜厚度與基板整理……..……………………………………………45
6.3穿透式電子顯微鏡資料(TEM)整理. ……………………………..…...…….46
6.4 c軸整理………………………………………………………………...…….48
6.5 X光繞射圖…………………………………………………………………...53
6.5.1 X光繞射圖說明……………………………………………………….53
6.5.2 X光繞射圖(家同步輻射研究中心TPS09A)…………………………53
6.5.3 X光繞射圖(國立臺灣師範大學)………………………………….….65
參考文獻……………………………………………………...…………..77

[1] Y. -M. Lin, X. Sun, and M. S. Dresselhaus, "Theoretical investigation of thermoelectric transport properties of cylindrical Bi nanowires," Physical Review B, vol. 62, pp. 4610-4623, 2000.
[2] B.D. Cullity, S.R. Stock, "Elements of X-Ray Diffraction," 3rd ed. Pearson, 2014, pp.91-97.
[3] D. Schiferl and C. S. Barrett, "The crystal structure of arsenic at 4.2, 78 and 299°K," Journal of Applied Crystallography, vol. 2, pp. 34,1969.
[4] I. Aguilera, C. Friedrich, S. Blügel, "Electronic phase transitions of bismuth under strain from relativistic self-consistent GW calculations", Physical Review B, vol. 91, 125129, 2015.
[5] C. Kittel, "Introduction to Solid State Physics", 8th ed. Wiley, 2004, pp. 11.
[6] B.D. Cullity, S.R. Stock, "Elements of X-Ray Diffraction," 3rd ed. Pearson, 2014, pp. 133-138.
[7] A. G. Bluman, "Elementary Statistics-A Step By Step Approach", 10th ed. McGraw-Hill, 2018, pp. 3-40.
[8] B.D. Cullity, S.R. Stock, "Elements of X-Ray Diffraction," 3rd ed. Pearson, 2014, pp. 171-174.
[9] B.D. Cullity, S.R. Stock, "Elements of X-Ray Diffraction," 3rd ed. Pearson, 2014, pp. 125-161.
[10] C. S. Barrett, "The structure of bismuth at low temperatures", Australian Journal of Physics, vol. 13, pp. 209,1960.
[11] A. G. Bluman, "Elementary Statistics-A Step By Step Approach", 10th ed. McGraw-Hill, 2018, pp. 3-30.
[12] P. Cucka, C.S. Barrett, The crystal structure of Bi and of solid solutions of Pb, Sn, Sb and Te in Bi, Acta Crystallographica, vol. 15, pp. 865-872, 1962.
[13] P. Fischer, I. Sosnowska and M. Szymanskit, "Debye-Waller factor and thermal expansion of arsenic, antimony and bismuth", Journal of Physics C: Solid State Physics, vol. 11, pp. 1043-1051, 1978.
[14] Ph. Hofmann, "The surfaces of bismuth: Structural and electronic properties," Progress in Surface Science, vol. 81, pp. 191-245, 2006.