結構不完整性

1、3.2. 缺陷化學基礎缺陷化學基礎 3.3. 本征缺陷本征缺陷 (熱缺陷熱缺陷) 3.4. 非本征缺陷（雜質缺陷）非本征缺陷（雜質缺陷）3.5. 固溶體固溶體3.6. 晶體中電子結構與缺陷晶體中電子結構與缺陷3.7. 線缺陷：位錯線缺陷：位錯偏離偏離理想理想晶體晶體0 0維維: : 點缺陷點缺陷1 1維維: : 線缺陷線缺陷2 2維維: :面缺陷面缺陷3 3維缺陷維缺陷原子缺陷原子缺陷電子缺陷電子缺陷: 能級躍遷能級躍遷本征缺陷本征缺陷: : 熱缺陷熱缺陷非本征缺陷非本征缺陷: :雜質缺陷雜質缺陷( (固溶體固溶體) )非化學計量缺陷非化學計量缺陷韌形位錯韌形位錯固溶體固溶體多晶多晶(陶瓷陶瓷

2、)非晶態(tài)非晶態(tài)表面界面表面界面晶界晶界表面表面納米粉體納米粉體納米結構納米結構螺旋位錯螺旋位錯晶粒晶粒主體符號: 原子離子: Al、Mg、 空位Vacancy: V 電子electron: e 孔穴hole: h位置符號: 晶格中原有的位置: 原有晶格為Al 原有晶格間位置: interstitial sites i 電荷符號: 帶正電: , 帶負電: 電中性: x 注意: 缺陷電荷為相對電荷reletive charge, 相對原有晶格而言正常晶格: null or nil (非缺陷晶格) AlViMg【K-V符號】符號】Kroger-Vinkern Notation主體主體電荷電荷位置位置

3、AlMg? 完全由熱運動所致, 在絕對零度以上, 任何晶體中都必然產(chǎn)生。對于一定的晶體，熱缺陷的濃度是溫度的單值函數(shù)。熱缺陷的基本類型 Intrinsic point defectsVacancyFrenkelIntersticialcyDi-vacancySchottky)2()2(kTHkTgeeNn總粒子數(shù)總粒子數(shù)缺陷數(shù)缺陷數(shù)討論： 低溫時：kT 缺陷濃度急劇升高, 對研究燒結、擴散、快離子導體有重要意義注意：此處是指平衡濃度平衡濃度生成能生成能本征缺陷濃度與溫度及生成能之間的關系本征缺陷濃度與溫度及生成能之間的關系 對于一定的物質其熱缺陷生成能為常數(shù)對于一定的物質其熱缺陷生成能為常數(shù),

4、 , 故缺陷故缺陷濃度單隨溫度的變化呈指數(shù)變化濃度單隨溫度的變化呈指數(shù)變化. .無法人為控制無法人為控制.l同價雜質同價雜質 Iso-solutes incorporation 特點特點: 無電荷變化無電荷變化 l異價雜質異價雜質 Aliovalent solutes 特點特點: 涉及涉及電價補償【雜質缺陷雜質缺陷】impurity defect注意注意兩種不同的電價補償機理: l離子補償l電子補償上兩種情況可由第三式表示內(nèi)在關聯(lián)上兩種情況可由第三式表示內(nèi)在關聯(lián):“賓賓” foreign“主主” host【氧化還原缺陷】2【非化學計量化合物】 Non-stoichiometric compou

5、nd Defect structure of Fe1-xO: Nonstoichiometry【】ixOYOOrZSZrO 32)(22ioYOOrZSZrO 32)(22 263)(2YxoYVOZrSZrO密密度度Experiment shows that addition of ZrO2 to Y2O3 leads to formation of interstitial anionsZrO2Y2O3重要的固體電解質材料重要的固體電解質材料復習復習CH4fcc lattice + 復習復習a1a2a1,a2 為該元晶格的為該元晶格的基矢基矢Rn為為格矢量格矢量Rn復習復習復習復習復習復習

6、 = e i (k . r - t)i =-1 , r : 位矢位矢 position vectork: 波矢波矢,就是波數(shù)就是波數(shù) （ k = 2） 波的一般表達式：波的一般表達式：復習復習二維二維WS胞及胞及Brillouin Zone補充補充aa2baa一維倒格子及一維倒格子及Brilloin 區(qū)正格子正格子倒格子倒格子Brilloin Zonekox復習復習復習復習復習復習化學鍵復習復習金屬金屬特性金屬特性: :自由電子在離子實自由電子在離子實(ion core)(ion core)之間之間幾乎不受約束幾乎不受約束自由電子氣模型自由電子氣模型: (1900: (1900年年) ) 電子

7、完全自由電子完全自由, ,猶如理想氣體分子猶如理想氣體分子, ,被表面勢場約束在金屬內(nèi)部被表面勢場約束在金屬內(nèi)部. .電子的電子的能量是純動能的能量是純動能的. . “Electron gas in box”“Electron gas in box”離子實離子實復習復習自由電子氣模型的說明自由電子氣模型的說明:l該經(jīng)典模型至今依然有效該經(jīng)典模型至今依然有效l理論解釋理論解釋: 庫倫以外還有量子效應的附加排斥力庫倫以外還有量子效應的附加排斥力VR, 所以凈力很小所以凈力很小 Vc + VR = Vpseudo 贗勢贗勢 存在如圖勢能與動能的關系存在如圖勢能與動能的關系 由于由于Pauli exc

8、lusive priciple: 每個電子有每個電子有11 的的“勢力范圍勢力范圍”，稱為，稱為Fermi Hole 復習復習電子所電子所“看到看到”的勢場的勢場電子速度電子速度晶體中離子實周圍勢場及電子速度變化關系晶體中離子實周圍勢場及電子速度變化關系復習復習EFEFT=0kT0kEE復習復習EFEFEFf(E)EFf(E)1/211)(/ )(kTEEFeEf費米能級與費米能級與費費-狄分布狄分布的關系的關系Fermi-Dirac Distribution：T=0kT0k結論：結論：1. 費米能級處電子存在的幾率為費米能級處電子存在的幾率為1/2。 2. 費米能級不隨溫度改變。費米能級不隨

9、溫度改變。EE復復習習溫度對電子F-D分布的影響：高溫時還原成玻耳茲曼經(jīng)典分布復習復習The Brillouin zone and Fermi surface of copper復習復習)(2222222dzddyddxd)()()()4(2rErrVmhPlank 常數(shù)電子質量電子質量電子狀態(tài)函數(shù)電子狀態(tài)函數(shù), 即波形即波形. :電子分布概率密度電子分布概率密度電子量子電子量子化能量化能量電子所受電子所受勢場勢場2)(r復習復習)()()()4(2rErrVmh0)(rV對于晶體對于晶體: : 欲解欲解LLWhy?)()(nRrVrV重要推論重要推論:晶體中電子所受的勢場V(r)具有與其晶格

10、相同的周期.故, 晶體中的Rn?)()()()4(2rErRrVmhnabRn復習復習與晶格周期性相同的勢場與晶格周期性相同的勢場復習復習)()()()4(2rErRrVmhn)()(ruRru)()(ruerrk il當勢場V(r)具有晶格周期性時, 波動方程的解具 有如下形式和性質:其中:u(r r)具有與晶格相同的周期,即:rk ie其中 為一平面波(正弦波)復習復習)(ru)()(ruerrk irk ie無勢場無勢場晶格勢場晶格勢場復習復習復習復習內(nèi)層電子的能級內(nèi)層電子的能級保持不變保持不變價電子的能級價電子的能級變?yōu)槟軒ё優(yōu)槟軒土晱土曇痪S周期性勢場周期性勢場內(nèi)形成的住波Poten

11、tial EnergyaIon coreProbability densityStanding wave 1Standing wave 2復習復習)()()()4(2rErRrVmhn/a/akkEgEnergyEnergy無勢場時自由電子無勢場時自由電子一維周期性勢場一維周期性勢場下形成能隙下形成能隙Eg解解 表明表明:晶格內(nèi)會產(chǎn)生能隙晶格內(nèi)會產(chǎn)生能隙. aThe standing wave 2 piles up electrons around the positive ion cores, which means that the average potential energy wil

12、l be lower than for a free traveling wave (constant probability density). The potential energy corresponding to standing wave 1 will have higher potential energy than a free traveling wave, since it piles up electrons between the ion cores (not compensated by positive ions). The energy difference be

13、tween the standing waves is the origin to the energy gap Eg. The band diagram of Si, e.g., then assumes its standard form: 復習復習復習復習GaAs三維能帶構造三維能帶構造復習復習載流子濃度決定物質的電導特性載流子濃度決定物質的電導特性復習復習【價帶【導帶【滿帶空帶【禁帶禁帶的寬度，又稱能隙能隙 band gap能帶基本術語【金屬、絕緣體、半導體能帶結構比較金屬金屬價帶未滿，電子價帶未滿，電子無須躍過禁帶可無須躍過禁帶可直接參與電導。直接參與電導。價帶價帶導帶導帶Eg導帶導

14、帶Eg導帶導帶價帶價帶價價帶帶絕緣體絕緣體價帶滿價帶滿, 禁帶很禁帶很寬寬,電子很難進入電子很難進入導帶。導帶。半導體半導體價帶雖滿價帶雖滿, 但禁但禁帶帶較窄較窄, 一部分電子一部分電子可以跳入導帶可以跳入導帶半導體能帶寬度半導體能帶寬度0.1-2eVFermi energy, or Fermi level, EF and its meaningEF費米能級費米能級(EF)是晶體中電子能量高低的基本指示標尺, 晶體的能帶結構與EF密不可分。研究的重點是EF附近的能帶結構。遠離費米能級的能帶或能級無實際意義。EFEFT=0KT0K本征半導體能帶結構本征半導體能帶結構價帶價帶導帶導帶Eg禁帶禁帶

15、【本征缺陷濃度本征缺陷濃度 =電子濃度電子濃度=空穴濃度空穴濃度 ni = ne = nh11)(/ )(kTEEFeEfEF純鍺是本征半導體純鍺是本征半導體, 其載流子濃度隨其載流子濃度隨溫度指數(shù)變化溫度指數(shù)變化典型的半導體材料禁帶寬度典型的半導體材料禁帶寬度n-type extrinsic semiconductors and the band modelP5價磷摻雜于價磷摻雜于4價硅中形成價硅中形成 施主能級施主能級, 產(chǎn)成產(chǎn)成n半導體半導體EFp-type extrinsic semiconductors and the band modelAlAl3價鋁摻雜于價鋁摻雜于4價硅中形成受

16、主能級價硅中形成受主能級, 產(chǎn)成產(chǎn)成P半導體半導體 韌形位錯 edge dislocation 螺旋位錯 screw dislocation特點： 1. 非平衡缺陷 2. 位錯單位均為一個格矢，即b (Burgers Vector)韌形位錯 edge dislocationEdge dislocation (line defect)位錯的移動：滑移Screw dislocation (line defect)Dislocation formation by shear晶界示意晶界示意三維晶界：類似肥皂泡三維晶界：類似肥皂泡二維二維孿晶界孿晶界小角度晶界小角度晶界高分辨率點電鏡：螺旋位錯和小角度

17、晶界高分辨率點電鏡：螺旋位錯和小角度晶界1HRTEM of Screw Dislocations in a Small Angle Grain Boundary Valence Electron Energy Loss Study of Fe doped SrTiO3 and a S13 Boundary: Electronic Structure and Dispersion Forces Fe 摻雜摻雜SrTiO3晶界及其電子結構（勢壘）變化2The grains of this hypereutectoid iron-carbon alloy are packed in a simila

18、r way to the bubbles in the previous photographs. 1STEM micrographs of the LaAl - Si3N4 sample showing the four interfaces, a) IF 1 to IF 3 and b) IF 4 where SR-VEEL spectrum images were acquired. 1 nm thick Yb-Si-O-N amorphous phase special grain boundary G. Drai and M. Komac, Analytical Electron M

19、icroscopy of the Grain Boundaries in Si3N4- Yb2O3 Ceramics, Electron Microscopy, Vol. 1 (Inter- disciplinary Developments and Tools), Edts. B. Jouffrey and C. Colliex, Les Editions de Physique, p. 685, 1994晶界相界：玻璃相晶界相界：玻璃相固相焼結結果。 複數(shù)固相含系焼結過程示。材料焼結幾多物質移動過程絡合複雑現(xiàn)象、様物質移動機構取込本手法、複雑組織形成過程表現(xiàn)可能。 晶界的形成：晶界的形成：

20、計算機模擬的計算機模擬的固相燒結過程固相燒結過程液相焼結結果。 液相含系焼結時起組織形成過程示。液相固相濡性液相介物質移動、緻密化挙動焼結後粒成長挙動多大影響及。 晶界的形成：晶界的形成：計算機模擬的計算機模擬的液相燒結過程液相燒結過程三次元計算格子用複相組織 (固相+液相) 粒成長例。 (a)固相液相、(b)(a)液相取除部分示。、実材料三次元的広複雑組織中、固相連続性持明確捉可能。 晶界的形成：晶界的形成：計算機模擬的計算機模擬的固、液相共存固、液相共存Application of lateral bias and in-situ imaging increases the range o

21、f possibilities provided by scanning probe microscopy tenfold. Shown below is surface topography and surface potential for grounded, forward and reverse biased ZnO varistor surface. Surface topography shows a number of pores and dust particles. Grain boundaries can be detected as small grooves due t

22、o preferential grain boundary polishing. Potential image of the grounded surface exhibits a number of potential depressions associated with second phase inclusions. Application of lateral bias results in the development of potential barriers at the grain boundaries due to the lower resistivity of gr

23、ain boundary region compared to the grain bulk. Upon switching the lateral bias contrast inverts. Analysis of the grain boundary potential drop dependence on external bias allows transport characteristics of grain boundary to be reconstructed. ZnO變阻器晶界：變阻器晶界： 晶界勢壘隨變壓晶界勢壘隨變壓變化情況變化情況【Tea Break】 de Bro

24、glie & Nobel Prizede Broglie1892: born in France 1910: graduated with an arts degree (majored in history)1914: World War I, serving in the army （at the Eiffel Tower）1920: resuming studying theoretical physics 1924: doctoral thesis on theory of matter waves 1929: awarded with Nobel prize Background19

25、00: Planck “quantum”nhrpM2nhE hhp1905: Einstein “photon”1907: Bohr H atom structure1918 Noble Prize1921 Noble Prize1975 Noble PrizePlanck 常數(shù)常數(shù)n=1, 2, 3, 頻率電子角動量動量波爾量子化條件波爾量子化條件:電子只能在特定能級電子只能在特定能級問題：Why?rhHow de Broglie won Nobel Prize直覺一：Einstein光波光子（photon) 或許：原子中的電子 電子波？直覺二：如果電子是波，它在原子中必定是住波推導推導：是

26、住波 2r = n 又 p = h / (Einstein) 2r = n h / p 得到r p = h/2 nnhrpM2Bohr的的量子化條件量子化條件!Nobel Prize 如此簡單！如此簡單！# de Broglie 的電子波理論使SchrdingerSchrdinger & de Broglie波動方程成為可能!住波住波 standing waveA standing wave results from the interference of two or more waves along the same medium. These positions standing sti

27、ll are called nodes. Nodes are the result of the meeting of a crest with a trough. Schrdinger & de Broglie From 1921 he studied atomic structure, then in 1924 he began to study quantum statistics. Soon after this he read de Broglies thesis which became a turning point in the direction of his researc

28、h and had a major influence on his thinking. On 3 November 1925 Schrdinger wrote to Einstein:- “A few days ago I read with great interest the ingenious thesis of Louis de Broglie, which I finally got hold of. .” On 16 November, in another letter, Schrdinger wrote:- “I have been intensely concerned t

29、hese days with Louis de Broglies ingenious theory. It is extraordinarily exciting, but still has some very grave difficulties.” One week later Schrdinger gave a seminar on de Broglies work and a member of the audience, a student of Sommerfelds, suggested that there should be a wave equation. Within

30、a few weeks Schrdinger had found his wave equation. The work was indeed received with great acclaim. Planck described it as:- “. epoch-making work.” 【Tea Break】 Measuring the circle of the earth with a stick about experiment 歷史上十大著名實驗1 Youngs double-slit experiment applied to the interference of sin

31、gle electrons 2 Galileos experiment on falling bodies (1600s) 3 Millikans oil-drop experiment (1910s) 4 Newtons decomposition of sunlight with a prism (1665-1666) 5 Youngs light-interference experiment (1801) 6 Cavendishs torsion-bar experiment (1798) 7 Eratosthenes measurement of the Earths circumf

32、erence (3rd century BC) 8 Galileos experiments with rolling balls down inclined planes (1600s) 9 Rutherfords discovery of the nucleus (1911) 10 Foucaults pendulum (1851) 米利肯（米利肯（Millikan）的電子電量測定實驗裝置的電子電量測定實驗裝置What Millikan did was to put a charge on a tiny drop of oil, and measure how strong an appl

33、ied electric field had to be in order to stop the oil drop from falling. Since he was able to work out the mass of the oil drop, and he could calculate the force of gravity on one drop, he could then determine the electric charge that the drop must have. By varying the charge on different drops, he noticed that the charge was always a multiple of -1.6 x 10 -19 C, the charge on a single electron. This meant that it was electrons carrying this unit charge.xOiAlAlxOAlOxOAlOMgMgMgOVOMgMgOVOMgMgO3232333222 MgO-FeO完全固溶相圖Al2O3-Cr2O3完全固溶相圖A-B有限固溶相圖BaTiO3