臺灣博碩士論文加值系統

本研究利用銅單晶製成晶向為 [011](12-2) / [011](-12-2) 傾斜對稱 (tilt symmetry) 之人工雙晶, 利用高分辨電子顯微鏡 (high resolution transmission electron microscope, HRTEM) 呈現原子影像的能力, 觀察分析晶界的原子結構。研究發現, 銅的Σ = 9 [011]/(-17-7)(7-55) 傾斜非對稱晶界與Σ = 9 [011]/(12-2) 傾斜對稱晶界同時存在並互相連接。偏離(12-2)L / (1-22)R對稱晶界25.24 °的 (-17-7)L / (7-55)R 非對稱晶界, 無論在LJ或EAM的結構模擬中, 都是可以穩定存在, 而且是 (12-2)L / (1-22)R晶界過渡到最低能量的 (-5-11)L / (11-1)R 非對稱晶界所必需的中間晶界。
在Σ = 9 [011]/(12-2) 傾斜對稱晶界的部份, 由HRTEM觀察的結果證實其為滑移鏡面對稱的晶界結構, 與實驗觀察到的Al, Si及Ge的Σ = 9 [011]/(12-2) 傾斜對稱晶界中的滑移鏡面對稱晶界結構類似, 亦與Seidman等人利用EAM模擬所得的結構相同。依據EAM的原理, 銅具有較大的dΦij(Rij) / dRij 值及剛性模數, 代表在金屬鍵的平衡長度附近, 原子間的鍵結位能曲線將較為陡峭, 銅原子的互相接近, 將引起相對較大的能量升高, 而Al則不然。因此本研究並未發現類似Mills在Al中所發現的鏡面對稱結構。
銅的滑移鏡面對稱結構, 其晶界膨脹, δV / A, 經測量為0.0036 nm, 代表兩邊晶粒的距離稍微大於兩個 {244} 晶面間距。由晶界附近原子的位移地圖 (displacement map) 可以看出五邊形週期結構的頂端的原子具有最大的鬆弛位移, 其鬆弛方向皆指向晶界中心。而最接近晶界中心的原子, 其鬆弛位移皆是偏離晶界中心, 因為此處的原子最容易受到對面晶粒庫倫斥力的影響。當賦予滑移鏡面對稱結構的原子在 [011] 方向上的高度, 發現經由原子的鬆弛位移方向及鍵結長度所推論出的晶界結構, 與Seidman等人所提出的模型相違背。
滑移鏡面對稱結構之晶界, 經過台階結構後, 轉變為 ‘擬鏡面對稱結構’ (modified mirror symmetric structure), 同時晶界向左平移了大約4至5個 {244} 平面間距。本研究所發現的擬鏡面對稱結構, 與Mills 在Al的Σ = 9 [011]/(12-2) 傾斜對稱晶界所觀察到的鏡面對稱結構並不相同。
台階結構包含一DSC部份差排, 其Burgers 向量b, 為兩個部份DSC向量之和, b = a/18 [12-2]L + a/36 [-41-1]L = a/36 [25-5] L , 或b = a/18 [1-22]R + a/36 [41-1]R = a/12 [2-11]R。依據DSC晶格的原理, 若晶體的剛體位移不是DSC向量的整數倍, 則晶格點將不會位移到DSC的晶格位置。而台階結構上的DSC部份差排, 其Burgers 向量在DSC晶格上的分量, 僅為DSC向量的一半, 因此, 滑移鏡面對稱結構經過DSC部份差排的晶格轉移, 並不會回復到原來的滑移鏡面對稱結構, 而是形成擬鏡面對稱結構。
在DSC部份差排額外原子平面的區域, 滑移鏡面對稱結構的晶界膨脹 (δV / A) 為-0.0024 nm, 小於遠離差排處, 同樣是滑移鏡面對稱結構的晶界膨脹值0.0036 nm, 與DSC刃差排額外原子平面的區域為壓應力場的理論相符。相對地,擬鏡面對稱結構之晶界膨脹值為0.0322 nm, 與DSC刃差排非額外原子平面的區域為張應力場的理論相符。擬鏡面對稱晶界結構, 與Mills 在Al發現之鏡面對稱結構有少許相異之處。如同EAM原理與等效電荷觀念所探討的, Al比Cu更能可以忍受兩原子的迫近, 迫近後所增加的斥力能並不大﹐證明Cu無法和Al一樣, 形成鏡面對稱結構, 只能形成擬鏡面對稱結構。由擬鏡面對稱結構的鬆弛位移地圖及DSC晶格的特性, 可以推論出擬鏡面對稱結構中, 兩邊晶粒的晶格點有a/4 [011] 的相對落差, 而此一模型在文獻中尚未有任何記載。
由Co之EDX成份分析能譜得知, 晶界處並未有Co偏析的現象, 定量分析後發現Co濃度分別為0.8 at% 與0.7 at%。摻雜Co之Cu的Σ = 9 [011]/(12-2) 傾斜對稱晶界結構, 證實為鏡面對稱結構, 與純Cu之擬鏡面對稱結構不同, 但與Mills在Al的Σ = 9 [011]/(12-2) 傾斜對稱晶界所觀察到的鏡面對稱結構極為相似。
Co摻雜的Cu晶界中所發現的台階結構, 與純Cu或與Mills在Al晶界所觀察到的台階結構皆不同。晶界經過台階後, 向左平移了6個 {244} 平面間距。兩晶粒相對位移一個完整DSC向量, 同時保持與原來相同的鏡面對稱結構。伴隨台階結構的二次晶界差排, 其Burgers 向量也等於一個完整的DSC向量, 成為 ‘完全DSC差排’。此一剛體位移並未產生晶界的多重性。
台階上的DSC完全差排b在DSC1及DSC2方向上的分量, 各為a/9 [1-22]L // a/9 [12-2]R 及 a/18 [-41-1]L // a/18 [41-1]L , 皆為完整的DSC向量。此一完全DSC差排的Burgers 向量為a/18 [-25-5] L 或a/6 [2-11]R。
在摻雜Co的Cu晶界, 兩組鏡面對稱結構的晶界膨脹值分別為0.0614 nm及0.0681 nm。在δV / A接近半個DSC向量的情況下, 原子半徑較小的Co有可能會介入較為鬆散的晶界中心位置, 並且成為兩方晶粒晶格點的另一重合位置。

Abstract
Copper (Cu) is one of the most popular fcc metals in recent researches and applications. The smaller the electronic devices become, the more important is to study the structures and properties of grain boundaries in Cu in order to yield better performances for the processes of semiconductor production. In this research, an artificial Cu bicrystal with a symmetric tilt misorientation of [011](12-2) / [011](-12-2) was made and then the atomic structure of the grain boundary (GB) of the bicrystal was investigated using high resolution transmission electron microscope (HRTEM). Σ = 9 [011]/(-17-7)(7-55) asymmetric tilt grain boundary and Σ = 9 [011]/(12-2) symmetric tilt one were found to be connected. Corresponding to the simulations of Lennard-Jones (LJ) or embedded atomic method (EAM), the asymmetric tilt grain boundary of (-17-7)L / (7-55)R which is deviated from the symmetric tilt one of (12-2)L / (1-22)R by 25.24 °can exist stably and become an essential transitional grain boundary for the transition from high-energy (12-2)L / (1-22)R grain boundary to the lowest-energy (-5-11)L / (11-1)R one.
The boundary structure in the segment of Σ = 9 [011]/(12-2) symmetric tilt grain boundary (STGB) was analyzed using HRTEM to be a glide-mirror symmetric structure which is the same as those observed in Al, Si and Ge. Simultaneously, the structure is also corresponding to the structural model of EAM which was simulated by Seidman et al. On the principle of EAM, the larger values of dΦij(Rij) / dRij and bulk modulus of Cu imply a steep bonding-energy curve near the equilibrium position. The repulsive energy in Cu may increase more dramatically than in Al if the atoms come closer. In other words, Al may have more tolerance for two atoms being closer than their equilibrium distance to make the mirror symmetric structure present (observed by Mills), but it has not been found in this research.
The volume expansion per unit GB area, δV / A, of the Σ = 9 [011]/(12-2) GB in Cu can be obtained as 0.0036 nm, which represents a little wider gap between both grains than 0.1205 nm, twice the lattice spacing of {244}. Compared to the dilation of Σ = 3 [011]/(11-1) STGB in Cu-Bi alloy, δV / A = 0.04 ±0.005 nm, and that of Σ = 3 [011]/(11-1) STGB in Cu, δV / A = 0.001 ±0.004 nm, it is reasonable to postulate that the glide-mirror symmetric structure is a stable structure without any alloy atom interfered in the GB core. According to the displacement map of the glide-mirror symmetric structure, it is apparent that the atoms at the tops of the periodic pentagons have relatively large displacements and relax towards the core of the GB. Large displacement of these atoms may have something to do with missing of a {244} plane in the boundary core. The atoms, however, next to the core of the GB relax outwards the core because they are highly influenced by the Coulomb’s repulsive force of the opposite grain. These atoms possess relatively small relaxation displacements because of the positiveδV / A . If the levels of the atoms of the glide-mirror symmetric structure in the [011] direction were considered, the glide-mirror symmetric structure interpreted by relaxation displacements and bonding lengths would be conflicting with that proposed by Seidman et al.
The glide-mirror symmetric structure translates into modified mirror symmetric structure through a step structure. As a result of that, the boundary plane shifts to left for four to five {244} spacings. The modified mirror symmetric structure is somewhat different from that observed in Al by Mills.
The borderline between both grains in the step structure is measured as (11-1)L[-21-1]L and (-1-33)R[6-11]R and is similar to (75-5)L / (-1-77)R with deviations of 7.5 °and 9.4 °, respectively. It is the same as (-17-7)L / (7-55)R asymmetirc tilt GB which holds relatively low GB energy.
There is a partial displacement-shift-complete (DSC) dislocation in the step structure. The Burgers vector of this partial DSC dislocation is the combination of two mutually perpendicular partial DSC vectors of the Σ = 9 [011]/(12-2) STGB. b = a/18 [12-2]L + a/36 [-41-1]L = a/36 [-25-5]L, or b = a/18 [1-22]R + a/36 [41-1]R = a/12 [2-11]R. Due to the nature of DSC, the lattice points will not occupy the DSC lattice sites if the rigid-body translation is not the multiple of perfect DSC vectors. The translation in the step structure does not preserve the glide-mirror symmetric structure but forms modified mirror symmetric one because the components of the Burgers vector of the DSC dislocation are only half the perfect DSC vectors.
The dilation (δV / A) of the glide-mirror symmetric structure near the step is measured as —0.0024 nm and is smaller than that of the same structure far away from the step, 0.0036 nm. It means that a compressive stress field is endured in this area where the glide-mirror symmetric structure is above the partial DSC positive edge dislocation. On the other hand, the dilation of the modified mirror symmetric structure is evaluated as 0.0322 nm which is corresponding to a tensile stress field. The modified mirror symmetric structure is different from that observed by Mills in Al. Based on the principle of EAM and the concept of effective charge, Al has more tolerance than Cu to get closer with little elevation of repulsive energy. The mirror symmetric structure can exist in Al, but only modified mirror symmetric one can be present in Cu.
The atomic model of the modified mirror symmetric structure of which both grains have a relative translation of a/4 [011] were proposed according to the relaxation displacements and the DSC lattice.
From the EDX information of Co, no Co segregation was found in the Σ = 9 [011]/(12-2) STGB in Cu. The concentrations of Co in the GB and near the GB were determined as 0.7 at% and 0.8 at%, respectively, by means of EDX spectroscope. The grain boundary structure of the Co-doped Σ = 9 [011]/(12-2) STGB in Cu was verified to be mirror symmetric structure, which is very similar to that in Al proposed by Mills, but is different from the modified mirror symmetric one.
The mirror symmetric structure of the Co-doped Σ = 9 [011]/(12-2) STGB in Cu translates into another mirror symmetric structure through a step structure. The step structure is also different from that either in pure Cu or in Al. As a result of that, the boundary plane shifts to left for six {244} spacings. The orientation of the step is close to (-5-11)L / (11-1)R, which is of the lowest energy among all of the Σ = 9 [011]/(12-2) symmetric and asymmetric tilt GB. The step structure is also influenced by the Co doping.
Both grains translate each other by a perfect DSC vector, maintain the same mirror symmetric structure and then induce a secondary grain boundary dislocation (SGBD) at the step. The components of the Burgers vector, a/18 [-25-5]L or a/6 [2-11]R, of the SGBD in the axes of DSC lattice are both perfect DSC vectors. The multiplicity of the Co-doped Σ = 9 GB was not formed by the rigid-body translation.
The GB dilation,δV / A, of two set of mirror symmetric structures are calculated as 0.0614 nm and 0.0681 nm, respectively. BecauseδV / A is close to half a DSC vector, Co atoms with smaller atomic size may insert into the looser sites at the core of the GB, and then are treated as secondary coincident sites.

封面
中文摘要
英文摘要
目錄
表目錄
圖目錄
第一章前言
第二章文獻回顧
2-1重合位置對稱晶界的意義
2-2面心立方（FCC）之Σ=9[011]/（122）傾斜對稱晶界之原子結構模型
2-3二次晶界差排與晶界結構的關係
2-4Σ=9[011]/（122）傾斜對稱晶界的能量及原子結構模型
2-5 Si,Ge及Al之Σ=9[011]/（122）傾斜對稱晶界結構
2-6合金元素與晶界結構之關係
第三章實驗步驟
3-1銅單晶製作
3-2求取銅單晶之（122）與（011）介面
3-3製作Σ=9[011]/（122）傾斜對稱雙晶
3-4TEM試片製作與觀察
3-5決定HRTEM晶格像之原子位置
3-6分析摻雜Co之Σ=9[011]/（122）傾斜對稱雙晶
第四章銅的Σ=9[101]/（122）傾斜對稱晶界結構
4-1Σ=9[011]/（177）（755）傾斜非對稱晶界結構
4-2Σ=9[011]/（122）傾斜對稱晶界結構
4-3結論
第五章二次晶界差排對銅的Σ=9[011]/（122）傾斜對稱晶界結構的影響
5-1晶界平移、臺階結構與擬鏡面對稱結構
5-2二次晶界排排的觀察
5-3晶界結構的多重性
5-4結論
第六章摻雜Co之Cu的Σ=9[011]/（122）傾斜對稱晶界結構
6-1 Co在晶界附近的分佈
6-2摻雜Co形成之鏡面對稱結構
6-3臺階結構與二次晶界差排
6-4摻雜Co對晶界原子鬆弛的影響
6-5結論
第七章總結論
第八章參考文獻

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