脈衝雷射沉積法製作 [Co(100) / Cu(100)]x /H-Si(100)多層膜磁性行為研究

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(1)National Taiwan Normal University Department of Physics Master Thesis. Magnetic Behaviors of PLD Grown [Co(100) / Cu(100)]x /H–Si(100) Multilayer. 脈衝雷射沉積法製作 [Co(100) / Cu(100)]x /H-Si(100)多層膜磁性行為研究. Author:. 黃凱雋. Kai-Jyun Huang. Supervisor: 盧志權博士. Jan 2015. Dr. C.K. Lo.

(2) Acknowledgements. 畢業在即，回首此片校園，細數過往在實驗室的時光，心中真是五味雜陳，實驗雖偶遇障礙，但摸索的過程中總有貴人相助，其中不得不提及 PLD 機台開台聖王 spintronics 的晉鴻學長、總會能夠化危機為奇蹟 AMDL 的嘉良、TSMC 最猛的彥成、無數個日子裡一起在 DMS Lab 挑燈鍍膜的承佑以及必定堅持戰到最後一刻且使命必達的含章哥，最後是指導教授盧志權老師以及傳授了我相當多 PLD 相關知識 DMS Lab 駱芳鈺老師的引導下，此篇論文才能順利完成。每當想起這些曾經幫助過我、即將各奔前程的英雄好漢，心中除了充滿無限感激以外更由衷希望各位都能在自己有興趣的領域闖出一片天。. I.

(3) 摘要. 我們成功地在室溫及攝氏 350 度下以脈衝雷射沉積法於氫鈍化矽(100)基板上磊出高品質的鈷(100)/銅(100)多層膜，其晶格結構與磁性特性分別由 X 光繞射儀與磁光柯爾效應儀、鐵磁共振儀所確認及分析。. 藉由 X 光繞射頻譜可知，鈷能以面心立方結構穩定生長於銅(100)/矽(100)之表面，樣品中銅、鈷兩者的繞射峰值分別位於 50.34 度及 51.26 度。其橫向磁光科爾效應圖亦顯示此批樣品有著面心立方結構所特有的磁四重對稱性，樣品之磁易軸及磁難軸分別坐落於鈷[100]、鈷[110]方向。. 本次研究亦發現，於常溫下進行鈷(100)之磊晶則須提鍍膜能量密度至 4.25 焦耳每平方公分，與高溫沉積之鈷(100)相比(飽和磁場 1.5 千厄斯特、矯頑場 25 厄斯特)，室溫成長之薄膜整體有著較低的飽和磁場(250 厄斯特)及矯頑場(16 厄斯特)。. 關鍵字: 脈衝雷射沉積法、面心立方、氫氣鈍化矽、鈷(100)外延、四重對稱。. II.

(4) Abstract. We have successfully used Pulse Laser Deposition (PLD) method to produce high quality Cu(100)/Co(100) multilayer on hydrogen passivated Si(100) surface at room temperature and at 350 ℃. The crystalline structure was characterized by X-Ray diffraction, while its magnetic behaviors were examined by LMOKE and FMR.. As confirmed by X-Ray diffraction, that FCC Co(100) can be stable on Cu(100)/H-Si(100), the diffraction peak of Co(100) and Cu(100) are located at 51.26° and 50.34° , respectively. The FCC Co exhibs four fold symmetry with as revealed by LMOKE measurement. However, the RT growth lattice has coercivity and saturation field of 16 Oe and 250 Oe, respectively, which are less than that of the high temperature growth one (coercivity and saturation are 25 Oe, and 1.5 kOe, respectively).. Keywords: Pulse Laser Deposition, Face Centered Cubic, Hydrogen Passivation Si(100), Epitaxial Co(100), Four fold Symmetry.. III.

(5) Contents. Acknowledgements .......................................................................................................................... I 摘要................................................................................................................................................. II Abstract ......................................................................................................................................... III Contents ........................................................................................................................................ IV Figure ............................................................................................................................................ VI Table ............................................................................................................................................. XI Chapter 1. Introduction ............................................................................................................... 1. Chapter 2. Literature Reviews .................................................................................................... 3. 2.1 Pulse Laser Deposition ....................................................................................................... 3 2.1.1 Overview of Pulse Laser Deposition Method .............................................................. 3 2.2.2 Mechanism of Pulse Laser Deposition ........................................................................ 4 2.2.3 Pros and Cons of Pulse Laser Deposition .................................................................... 8 2.2.4 Methods to Further Reduce PLD splashing ............................................................... 10 2.2 Magnetic Materials ........................................................................................................... 12 2.2.1 Magnetism ................................................................................................................. 12 2.2.2 Different Types of Magnetic Materials ..................................................................... 15 2.2.3 Characteristics of Ferromagnetic Materials ............................................................... 18 2.3 Magnetism in Microscopic Scale ...................................................................................... 20 IV.

(6) 2.3.1 Magneto – Crystalline Anisotropy ............................................................................. 20 2.3.2 Shape Anisotropy ....................................................................................................... 21 2.3.3 Stress Anisotropy ....................................................................................................... 25 2.5 Magneto – Optical Kerr Effect ......................................................................................... 29 Chapter 3. Instrumentations and Experiment Methods ............................................................ 37. 3.1 Sample Fabrication ........................................................................................................... 37 3.2 Pulse Laser Deposition System......................................................................................... 38 3.4 Magneto – Optical Kerr effect Measurement ................................................................... 42 3.6 X-Ray Diffraction ............................................................................................................. 44 3.6 Experimental Procedure and Parameters .......................................................................... 46 Chapter 4. Results and discussions ........................................................................................... 51. 4.1 X-Ray Diffraction Data Analysis...................................................................................... 51 4.2 Magnetic Property Measurement ...................................................................................... 58 4.2.1 MOKE Data Analysis ................................................................................................ 58 Chapter 5. Conclusions ............................................................................................................. 73. Reference ...................................................................................................................................... 74. V.

(7) Figure. Figure 2-1 Schematic diagram of PLD system we use in our experiment. .......................... 4 Figure 2-2 The mechanism of pulse laser deposition .......................................................... 5 Figure 2-3 PLD absorption process ..................................................................................... 6 Figure 2-4 PLD non - absorption process ............................................................................ 7 Figure 2-5 Schematic diagram of high energy plasma induced surface roughness and stress, (a) high energy plasma travels toward sample surface. (b), (c) plasma particles strikes into substrate and causing surface roughness and stress in substrate............................................. 9 Figure 2-6. Threshold – ablation duration graph from 1053 nm ablation gold target. experiment from [19] p.109. ................................................................................................. 10 Figure 2-7 Schematic diagram of different PLD deposition setups (from [18]). ............... 11 Figure 2-8 Vane velocity particle filter setup Schematic diagram. (picture modify from [21]) ............................................................................................................................................... 11 Figure 2-9 The magnetic moment orientation of all kinds of magnetic materials ............. 17 Figure 2-10 Domain of magnetic materials. ...................................................................... 18 Figure 2-11 Hysteresis loop of ferromagnetic materials. ................................................... 19 Figure 2-12 Magnetic anisotropy schematic graph. ........................................................... 21 Figure 2-13 The magnetic field line distribution diagram. ................................................ 21 Figure 2-14 The induction magnetic field distribution diagram inside a bar shape magnetic bar. ........................................................................................................................................ 22 Figure 2-15 Ellipsoid shape magnet. ................................................................................. 23. VI.

(8) Figure 2-16 The magnetic domain wall movement under stress. ...................................... 28 Figure 2-17 MOKE polarizing diagram 2-13 .................................................................... 29 Figure 2-18 Three different types of MOKE, P-MOKE L-MOKE and S-MOKE ............ 32 Figure 2-19 MOKE P mode and S mode schematic diagram. ........................................... 34 Figure 3-1 Sample holder. .................................................................................................. 37 Figure 3-2 The picture of PLD system that we use in our experiment. ............................. 38 Figure 3-3 PLD system interior 3D diagram. .................................................................... 39 Figure 3-4 The sample holder assembly diagram. ............................................................. 39 Figure 3-5 Picture of the laser source we use for the PLD system. ................................... 40 Figure 3-6 The picture of our high vacuum annealing system (left). ................................ 41 Figure 3-7 High vacuum annealing system inner view 3D diagram (right). ..................... 41 Figure 3-8 The picture of MOKE setup. ............................................................................ 43 Figure 3-9 Crystal diffraction and Bragg’s Law schematic diagram. ................................ 44 Figure 3-10 XRD and GIXRD comparison schematic diagram. ....................................... 45 Figure 3-11 The schematic diagram of FME setup............................................................. 50 Figure 4-1 (a) XRD pattern of 30nm Cu(100) deposited by PLD at 250 ℃ epitaxy on HSi(100) surface. (b) The diffraction pattern of Cu(100) epitaxy on hydrogen terminated Si(100) substrate by sputtering deposition[32]. ................................................................................. 52 Figure 4-2 The XRD pattern of sample (𝐶𝑢 80 𝑛𝑚/𝐶𝑜 25 𝑛𝑚)1/𝐶𝑢/H-Si deposit at 350℃, shows that PLD deposited Cobalt can epitaxy on Cu(200). ................................................. 53 Figure 4-3 The XRD pattern of sample (𝐶𝑢 80 𝑛𝑚/𝐶𝑜 40 𝑛𝑚)1/𝐶𝑢/H-Si deposit at 350℃, shows that the counts of XRD pattern changes with its thickness. ....................................... 53. VII.

(9) Figure 4-4. XRD Phi-Scan pattern of PLD deposit Py(100)/Cu(100)/H-Si(100), which. Py[010]//Cu[010]//Si[110], phi scan pattern comes from [33]. ............................................ 54 Figure 4-5. Crystalline orientation schematic diagram of Cu(100)/H-Si(100) interface. (modify from [32]). ............................................................................................................... 54 Figure 4-6 The XRD pattern of sample (𝐶𝑢 80 𝑛𝑚/𝐶𝑜 40 𝑛𝑚)2/𝐶𝑢/H-Si deposit at 350℃, shows that cobalt and copper can epitaxy on each other and forming multilayer single crystal. ............................................................................................................................................... 55 Figure 4-7. The XRD pattern of sample (𝐶𝑢 80 𝑛𝑚/𝐶𝑜 40 𝑛𝑚)1/𝐶𝑢/H-Si deposit at RT,. which shows with higher laser power, we can successfully create FCC cobalt on FCC copper surface. .................................................................................................................................. 56 Figure 4-8 XRD of Cu/H-Si(100) grown at 400℃. ........................................................... 57 Figure 4-9 (a) Surface morphology of PLD Cu deposit on H-Si(100) at 400℃, measured by AFM. (b) AFM cross section, ℎ ≈ 550 𝑛𝑚 and 𝑤 ≈ 5 𝜇𝑚 refers to the height and width of cone shape structure. (c), (d) x300, x22,000 times magnification SEM picture of 400℃ PLD Cu/H-Si(100) surface. .................................................................................................. 57 Figure 4-10 Magnetization curves for single crystals of FCC Nickel, easy axis, hard axis located at <111> and <100> direction (modify from [26]). ................................................. 58 Figure 4-11 Comparison of surface morphology between (a), (c) 350℃ and (b), (d) room temperature fabricated Cu/Co/Cu/H-Si, observed by SEM. ................................................. 59 Figure 4-12. (a) Schematic MOKE curve of different kinds of domain wall motion. (b). Barkhausen jump can be observed from MOKE measurement (modified from[34]). (c) Real MOKE data of two periodic cobalt layer, the steps should causes by Barkhausen effect. (d). VIII.

(10) Real hysteresis loop of RT fabricated sample, the angled curve near zero field is caused by FCC un-balanced crystalline anisotropy. .............................................................................. 60 Figure 4-13 the hysteresis loop of MBE growth, 4ML FCC Co epitaxy on Cu(100)(a) easy axis, (b) hard axis (from [35]). Hysteresis loop of RT fabricated epitaxial Cu/Co/Cu/H-Si (c) easy axis, (d) hard axis.......................................................................................................... 61 Figure 4-14 surface morphology of room temperature fabricated samples, annealed at 350℃ for 3hours. (a), (d): Cu/Co(25 nm)/Cu/H-Si, (d), (b): [Cu/Co(25 nm)]2/Cu/H-Si, (c), (e): [Cu/Co(40 nm)]2/Cu/H-Si, revealed with SEM. ................................................................ 62 Figure 4-15 MOKE data of sample (𝐶𝑢 80𝑛𝑚/𝐶𝑜 25𝑛𝑚)1/Cu/H-Si at 350℃. .............. 63 Figure 4-16 Coercivity of (𝐶𝑢 80𝑛𝑚/𝐶𝑜 25𝑛𝑚)1/Cu/H-Si at 350℃. ............................. 63 Figure 4-17 MOKE data of sample (𝐶𝑢 80𝑛𝑚/𝐶𝑜 40𝑛𝑚)1/Cu/H-Si at 350℃. .............. 64 Figure 4-18 Coercivity of (𝐶𝑢 80𝑛𝑚/𝐶𝑜 40𝑛𝑚)1/Cu/H-Si at 350℃. ............................. 64 Figure 4-19 MOKE data of sample (𝐶𝑢 80𝑛𝑚/𝐶𝑜 25𝑛𝑚)2/Cu/H-Si at 350℃. .............. 65 Figure 4-20 Coercivity of sample (𝐶𝑢 80𝑛𝑚/𝐶𝑜 25𝑛𝑚)2/Cu/H-Si at 350℃. ................ 65 Figure 4-21 MOKE data of sample (𝐶𝑢 80𝑛𝑚/𝐶𝑜 40𝑛𝑚)2/Cu/H-Si at 350℃. .............. 66 Figure 4-22 Coercivity of (𝐶𝑢 80𝑛𝑚/𝐶𝑜 40𝑛𝑚)2/Cu/H-Si at 350℃. ............................. 66 Figure 4-23 MOKE data of sample (𝐶𝑢 80𝑛𝑚/𝐶𝑜 25𝑛𝑚)1/Cu/H-Si at RT. ................... 67 Figure 4-24 Coercivity of sample (𝐶𝑢 80𝑛𝑚/𝐶𝑜 25𝑛𝑚)1/Cu/H-Si at RT. ..................... 67 Figure 4-25 MOKE data of sample (𝐶𝑢 80𝑛𝑚/𝐶𝑜 40𝑛𝑚)1/Cu/H-Si at RT. ................... 68 Figure 4-26 of sample (𝐶𝑢 80𝑛𝑚/𝐶𝑜 40𝑛𝑚)1/Cu/H-Si at RT. ....................................... 68 Figure 4-27 MOKE data of sample (𝐶𝑢 80𝑛𝑚/𝐶𝑜 25𝑛𝑚)2/Cu/H-Si at RT. ................... 69 Figure 4-28 Coercivity of sample (𝐶𝑢 80𝑛𝑚/𝐶𝑜 25𝑛𝑚)2/Cu/H-Si at RT. ..................... 69 Figure 4-29 MOKE data of sample (𝐶𝑢 80𝑛𝑚/𝐶𝑜 40𝑛𝑚)2/Cu/H-Si at RT. ................... 70. IX.

(11) Figure 4-30 Coercivity of sample (𝐶𝑢 80𝑛𝑚/𝐶𝑜 40𝑛𝑚)2/Cu/H-Si at RT. ..................... 70 Figure 4-31 MOKE data of sample (𝐶𝑢 20𝑛𝑚/𝐶𝑜 8𝑛𝑚)10/Cu/H-Si at RT. ................... 71 Figure 4-32 Coercivity of sample (𝐶𝑢 20𝑛𝑚/𝐶𝑜 8𝑛𝑚)10/Cu/H-Si at RT. ..................... 71 Figure 4-33. Ferromagnetic resonance absorption graph of sample. (𝐶𝑢 80𝑛𝑚/. 𝐶𝑜 25𝑛𝑚)1/Cu/H-Si at 350℃, measured at 90°. ................................................................. 72. X.

(12) Table. Table 3-1 Spec of LOTIS TII LS – 2147 Nd − 3: YAG Laser. .......................................... 40. XI.

(13) Chapter 1. Introduction. For years, researchers have been searching for high quality / high performance thin film fabrication method to replace conventional PVDs such as MBE, thermal evaporation and sputtering, with the laser technology’s breakthrough at 1960s, pulse laser deposition (PLD) method becomes an ideal candidate for producing atomic scale high quality thin film[1], with the energetic plasma generated by focus high power laser beam, the whole deposition procedure can have lower substrate temperature and still retain well crystalline structure, but yet PLD method are mostly been used on fabricating semiconductor materials, metal oxides or organics, but rarely use for fabricating pure metal. Since 20 century, semiconductor materials such as silicon, gallium arsenide or glass are widely use as substrate of microcircuit, transistors or devices, especially for silicon, by doping or oxidation its surface, we can easily change it characteristic from conductor, semiconductor to insulator. Having well performance with cheap price, silicon becomes the most commonly use substrate material in thin film epitaxy researches [2, 3]. Also, because of the lattice mismatch and surface energy between silicon – copper interface is fairly small, and the lattice mismatch between copper and transitional metals are often less than 5% [4-9], thus instead of directly grow magnetic material on silicon surface, we usually deposit additional layer of copper thin film epitaxial on Si(100) or Si(111) served as seed layer to decrease it’s mismatch, to further improve the quality of Cu crystalline structure, we often use hydrogen fluoride to etch out SiO2 on its surface and produce an reconstructed[10-12] hydrogen-terminated. 1.

(14) Si(100)(H-2x2)[13] / Si(111)(H-7x7)[10] surface, with this kinds of treatment, we can lower down it’s deposition requirement from Ultra High Vacuum to High vacuum[14]. Thanks to the discovery of GMR effect (1988, 2007 NP) and the advancement in material science, the performance and the market demand of nano-scale magneto-electronics as hard drive GMR read head, MR sensors and MEMS also reach to its highs. Generally, the efficiency of Spintronics devices are related to its crystal structure as well as magnetic properties. Because of cobalt’s magneto – optical properties and can be transit its crystalline structure from HCP to FCC simply by increase its deposition temperature[15-17], with these interesting characteristics cobalt platinum, cobalt copper multilayer and their alloys have become a popular research topic for decades[9].. 2.

(15) Chapter 2. Literature Reviews. 2.1 Pulse Laser Deposition 2.1.1 Overview of Pulse Laser Deposition Method With laser technology breakthrough at 1960s, pulse laser deposition (PLD) method becomes an available thin film manufacture option. By focusing high energy pulse laser on target surface, it then simultaneously strikes out and vaporizes target ingredients, producing high energy plasma plume. By optimizing the number of laser shots and its power density, we can precisely control film quality and its thickness, this makes PLD method becomes an ideal candidate for producing atomic scale high quality thin film.. This kind of deposition can be simply achieved with vacuum environment, high power laser and optical sets, by adjusting the power and focus spot of laser beam, Pulse Laser Deposition / Evaporation (PLD/PLE) method can adapt to fabricate a wide variety of material, from ceramics, metal, high temperature superconducting materials to biological components such as protein (MAPLE method). The yield and efficiency of PLD method often related to targets’ thermal property and the wavelength of laser source, the deposition mechanism will be discuss in following chapters.. 3.

(16) 2.2.2 Mechanism of Pulse Laser Deposition. Figure 2-1 Schematic diagram of PLD system we use in our experiment.. When target absorbs electro - magnetic energy of laser, it then evaporate into plasma plume and travels through vacuum, finally it will ends up settling down on the substrate surface, this deposition process can roughly separate into four parts:. 4.

(17) Figure 2-2 The mechanism of pulse laser deposition. 1) At 0.1 to 20 ns, a high energy (0.1 – 10 J/cm2 ) laser pulse impinges on ablation target. 2) Laser induced plasma (atomic, diatomic, molecular, ionic) forms on target surface with ablation. 3) Highly forward direction plasma plume traverses away from target. 4) Ablation plume impinge on substrate, deposited plume species on the substrate surface.. For a more precise illustration and analyzing the process of producing plasma plume: PLD mechanism can classify into two major types: absorption process and non – absorption process. For an absorption process, the photon energy is greater than the bonding energy of the target, the laser may break down the chemical bonding or excite the material making it become ionic form. The electric field produced by high power laser is strong enough to ionize the electrons in the target, thus for a non – absorption process, even though the photon energy not high enough to reach the bound-breaking energy level, the electric field of the laser may still ionize and. 5.

(18) generate seed electrons, seed electrons will again affect by this field and accelerated toward the target striking out plasma.. Absorption process (figure 2-3): 1) Laser reaches target surface. 2) Surface temperature raises and starts to melt down. 3) Temperature is high enough to vaporize the Ingredients and become plasma. 4) The plasma starts to inter - collision and ends up thermal equilibrium. 5) Plasma began to travel and expand in the vacuum. 6) The collision with gas molecules cools down the plasma. 7) Plasma temperature drop and settle down on substrate surface.. Figure 2-3 PLD absorption process. 6.

(19) Non – absorption process (figure 2- 4): 1) Laser Strikes the target and generates a strong electric field. 2) The field ionized surface materials and generates seed electrons. 3) The temperature of the target gets higher and seed electrons are continuous blasting target surface due to the acceleration of electric field. 4) Seed electrons strikes target and form plasma. 5) Plasma began to travel and expand in the vacuum. 6) The collision with gas molecules cools down the plasma. 7) Plasma temperature drop and settle down on substrate surface.. Figure 2-4 PLD non - absorption process. 7.

(20) 2.2.3 Pros and Cons of Pulse Laser Deposition Pros: Conventional deposition process such as magnetron sputtering or thermal evaporation, the energy parameter is limited from several eV to about a dozen eV, but for PLD systems, by adjusting the focus of the input laser, the ion beam energy can be easily rose 3 ~ 4 orders or more. Unlike other deposition process needs to involve chemical or thermal equilibrium to accomplish the job, PLD does not need to be at a thermal equilibrium state while it reaches substrate surface, thus the ingredient of the film can remain almost the same as the chemically stoichiometry of the target, this feature makes PLD efficient at multi-deposit process. For some deposition we need to apply oxygen to produce oxidation films, but for conventional deposit process the energy of the plasma or molecules are often not strong enough to apply in a lower vacuum environment, this kind of process will have to take place in UHV surroundings, which will greatly decrease its yield and efficiency. Due to the highly adjustable input energy bandwidth, PLD can tolerate a lower vacuum environment, and the deposit material can have better chances to react with applied gases. We often tend to heat up the substrate in a deposition process, to give extra mobility to the molecules on substrate in order to produce thin film with a better crystal structure. Owing to its higher plasma energy of PLD, the deposit adatoms have higher mobility, this extra energy makes adatoms can move alone substrate surface to search a lowest energy spot to forming better crystalline structure.. 8.

(21) Cons: Due to the laser energy is way stronger than other deposition methods, it has greater possibility to strike out larger clusters, which will also deposit on the film, and if the deposition distance is too short, the higher energy plasma will not only deposit but also will consume the film or substrate, sometimes it will penetrate the substrate surface and embed in it, leaving plume-induced stress (Figure 2-5), these issues can be eliminated by several methods, such as off –axis deposition[18], cross-beam ablation and adding particle filter in front of the plasma[19].. The direction of PLD produced plasma is highly concentrate and normal to the target surface, thus is almost impossible to use PLD to produce large scale sample with high uniformity, making PLD hard to use on industrial or massive production.. Figure 2-5 Schematic diagram of high energy plasma induced surface roughness and stress, (a) high energy plasma travels toward sample surface. (b), (c) plasma particles strikes into substrate and causing surface roughness and stress in substrate.. 9.

(22) 2.2.4 Methods to Further Reduce PLD splashing. These are some solutions to reduce the splashing effect of PLD method, by lower down the laser energy or extend the deposition length may greatly decrease the amount of large particles. Here is an equation of laser power limit without having splashing[20]:. D𝑚𝑎𝑥𝑖𝑚𝑢𝑚 =. 252∙𝜌∙𝐻𝑒𝑣 √𝜎∙𝑓∙𝐾𝑚 ∙𝑡𝑟. 𝜎: electro conductivity. 𝑓: frequency of laser source. 𝐾𝑚 : permeability of target.. .. (2-1). 𝐻𝑒𝑣 : heat of evaporation. 𝜌: mass density of target material. 𝑡𝑟 : deposit materials’ relaxation time on substrate surface.. With the data from Fig. 2-6, we can predict the threshold energy of gold target of our system (266 nm / 10 Hz / 18 ns) should be somewhere around 3J/cm2 .. Figure 2-6 Threshold – ablation duration graph from 1053 nm ablation gold target experiment from [19] p.109.. 10.

(23) Another convenient way is using off-axis deposition instead of rotational-transitional and rastering mode, by offsetting the deposition from the substrate center to avoid larger clusters.. Figure 2-7 Schematic diagram of different PLD deposition setups (from [18]).. Larger particles created by PLD process travels slower in vacuum (20 m/s ~ 50 m/s), thus by applying circular rotation chopper in front the plasma serve as a velocity filter, we can further reduce larger particles and droplets.. Figure 2-8 Vane velocity particle filter setup Schematic diagram. (picture modify from [21]). 11.

(24) 2.2 Magnetic Materials Magnetic materials have been widely used in our life since ancient China, stones with magnet were used to navigate and distinguish north from other directions. In 21st century magnetic materials are commonly used in memory devices, such as hard drives, MRAM and MEMS, thus a lot of scientists still put a lot of effort into making magnetic electronics devices more powerful and inexpensive.. 2.2.1 Magnetism All materials were made up by atoms, an atom can be roughly separate into two parts, nuclei and electrons, nuclear are charged with positive charges and electrons are charged with negative charge which surrounds its nuclear and making a periodic rotation. As the electron ⃑⃑ at the same time. rotates, it generates magnetic moments 𝜇⃑ [22] and magnetic field 𝐻. ⃑⃑⃑ = ∑𝑛 𝜇⃑⃑ 𝑀 𝑉. (2-2). The definition of magnetization is the amount magnetic moments in unit volume. Occasionally, we also use magnetic flux density to represent induction magnetic field, the ⃑⃑ and induction magnetic field 𝐵 ⃑⃑ is: relation between magnetization⃑⃑⃑⃑⃑ 𝑀, magnetic field 𝐻. ⃑B⃑ = 𝜇0 (𝐻 ⃑⃑ + 𝑀 ⃑⃑⃑ ). 𝜒 =. ⃑⃑⃑ 𝑀 ⃑⃑ 𝐻. (2-3). (2-4) 12.

(25) The 𝜇0 in equation 2-5 is permeability of vacuum, and we define magnetic susceptibility 𝜒 ⃑⃑⃑ over⃑⃑⃑⃑ as 𝑀 𝐻 .The mechanism of magnetic moments is define under atomic scale, thus from a quantum mechanics point of view, μ can write in this form:. μ = − g 𝜇𝐵 𝐽⃑. 𝜇𝐵 =. ̅ 𝑒ℎ. (2-5). (2-6). 2𝑚𝑒. ⃑⃑ + 𝑆⃑ 𝐽⃑ = 𝐿. (2-7). e: Charge of an electron. ℎ̅: Planck constant. 𝑚𝑒 : Mass of an electron. g: Land g-factor.. 𝜇𝐵 is Bohr magnetron, the total momentum 𝐽⃑ can be written as electron spin moment 𝑆⃑ plus ⃑⃑, and Land g-factor is define as: orbital momentum 𝐿. g =1 +. 𝐽( 𝐽 +1 ) +𝑆 ( 𝑆 +1 ) −𝐿( 𝐿 +1 ) 2𝐽( 𝐽 +1 ). (2-8). J: Total angular momentum quantum number. S: Spin quantum number. 13.

(26) L: Orbital angular momentum.. The quantum number of transition metal are primary contribute by spin quantum number, so for transition metals J ≅ S, g ≅ 2.. 14.

(27) 2.2.2 Different Types of Magnetic Materials ⃑⃑ , the magnetization 𝑀 ⃑⃑⃑ of this When a magnetic material is placed in a magnetic field 𝐻 material will change. Using the material’s magnetic susceptibility 𝜒 , we can generally characterizing them into five types[23], (1) Diamagnetism, (2) Paramagnetism, (3) Ferromagnetism, (4) Ant-ferromagnetism and (5) Ferrimagnetism, the magnitude of 𝜒 also effected by the arrangement of its magnetic momentum.. (1) Diamagnetism Diamagnetic is an effect that can be found in all materials, in most cases the magnetic susceptibility 𝜒 of the material is around negative 10−5 , and almost immune to temperature. When there is no filed applied, electrons in the material must obey Pauli Exclusion Principle, all electron spins are coupled in pairs, and the net magnetic momentum μ will be zero. If we applied an external field to the material, due to the Lenz's law, the electron spins will re-orient and yield an induction magnetic field which have opposite direction with the external field.. (2) Paramagnetism The magnetic of paramagnetic materials is come from its electron spin momentum, this kind of material have a relatively small 𝜒. At higher temperature, the material’s susceptibility 𝜒 will inversely to temperature T, the relation of 𝜒 and T can be determine by Curie’s Law:. 𝐶. 𝜒 = 𝜇0 × (𝑇). (2-9). 15.

(28) C: Curie constant.. (3) Ferromagnetism Ferromagnetic materials have a relatively large 𝜒, the magnetic field generated by each electron magnetic moments will affect others nearby, leading all moments pointing at same direction and causing the phenomenon of hysteresis and magnetization. When it’s at a high temperature, ferromagnetic material will transform into paramagnetism due to the influence of thermal disturbance is greater than magnetic moments coupling, the relation between magnetization and temperature is ( 𝑇𝐶 is the Curie temperature):. 𝜒 =. μ0 C ( 𝑇− 𝑇𝑐 ). (2-10). (4) Antiferromagnetism Due to the stronger interaction between atoms, the magnetic moments coupled in antiparallel arrangement in antiferromagnetism, the magnetic behavior of antiferromagnetic substance will behave like paramagnetic material when it reaches Néel temperature. The temperature - magnetization relation can be written as (𝑇𝑁 is the Néel temperature):. 𝜒 =. μ0 C ( 𝑇− 𝑇𝑁 ). (2-11). 16.

(29) (5) Ferrite The arrangement of magnetic moments in ferrite is very similar to ferromagnetism, but the moments in ferrite are not perfectly antiparallel arranged, the moments that pointing to opposite direction will not be canceled out and causing remanent magnetization.. Figure 2-9 The magnetic moment orientation of all kinds of magnetic materials. 17.

(30) 2.2.3 Characteristics of Ferromagnetic Materials Having high permittivity μ, magnetization 𝜒 and can produce a strong magnetic field are the most significant features of ferromagnetic materials. The field that produced by a magnet is contributed by its magnetic domains, the size of the domain can range from few micro meters to one millimeter, and can contain 1015 ~ 1016 atoms. Domains are separated by domain walls, which is around 100 atoms wide. Even if there is no external field applied, the strong coupling between atoms’ magnetic dipole will still cause the electron spins in domains lines up at the same direction. From a macro perspective, because of the magnetization direction of each domains are all pointing in random directions, so we cannot observe any magnetic field, the net momentum of this material remains zero, as the figure 2-10 (modified from [24]) shows.. Figure 2-10 Domain of magnetic materials.. 18.

(31) When an external field applied (figure 2-11), the domain momentum start to rotate toward the direction of the external field (course 1), meanwhile the external field also changes the shape and size of domain and domain walls. If the field is strong enough, the material will transform from multi-domain into a single domain, the field that we measured at this point will be its saturation magnetization M𝑆 . Once it been magnetized, even we remove the external field (course 2), some of the domain will still line up in the same direction, causing the magnetic remanence M𝑟 . The opposite direction field (course 3) that requires to cancel out the remanent magnetization is called Coercivity, as the opposite field getting stronger (course 4), the material will again reaches its saturate, this whole process can be plot into an external field - magnetization graph, which we will get a hysteresis loop as figure 2-11 shows.. Figure 2-11 Hysteresis loop of ferromagnetic materials.. 19.

(32) 2.3 Magnetism in Microscopic Scale 2.3.1 Magneto – Crystalline Anisotropy Magneto – crystalline anisotropy is an anisotropy which its magnetic property is crystallographic axis related. For qualitative analysis this phenomenon, we have to consider the effect of these three types of electron coupling: 1) Spin – spin coupling. 2) Orbital – lattice coupling. 3) Spin – orbital coupling.. Spin – spin coupling is a spin exchange interact with another spin nearby, the exchange energy is significantly strong, but isotropic. Thus this term doesn’t have contribution to crystalline anisotropy. Orbital – lattice coupling is also a relatively strong exchange force. In high magnetic field, orbital – lattice coupling remain intact, therefore, in the process of magnetization, the effect of orbital magnetic momentum can be ignore, makes orbital – lattice coupling no contribution to crystalline anisotropy either. Spin - orbital coupling on the other hand is a relatively weak interaction, but is generally acknowledged as the main factor that causes anisotropy, the electron spin is restricted by the crystal structure, the bounding energy is different on each orientation due to the crystal axis. Because this effect is crystal structure related, so this phenomenon is named crystalline anisotropy. The magnetic anisotropy energy of crystalline anisotropy can express as equation 2-21:. 𝑐𝑢𝑏𝑖𝑐 𝐸𝑐𝑟𝑦𝑠𝑡𝑎𝑙 = 𝐾0 + 𝐾1 (𝛼12 𝛼22 + 𝛼12 𝛼32 + 𝛼22 𝛼32 ) + 𝐾2 𝛼12 𝛼22 𝛼32 + ⋯.. (2-12). 20.

(33) The magnetic anisotropy of different structure is shown as the graph below(form [25]):. Figure 2-12 Magnetic anisotropy schematic graph.. 2.3.2 Shape Anisotropy The demagnetization field of magnetic materials is the main reason of shape anisotropy[26], for instance, the external field line of a bar shape magnetic starts from N pole and ends at S pole, and pointing from S to N while it’s in the magnetic, forming a close loop. Thus the direction of induction magnetic field inside the magnetic bar have an opposite direction with ⃑⃑𝑑 . external field. We defined induction field inside the bar as demagnetization field 𝐻. Figure 2-13 The magnetic field line distribution diagram.. 21.

(34) It also means that the magnet will produces demagnetization field even if there is no external field applied, because the amplitude of demagnetization field is less than 4πM so, ⃑⃑ = −𝐻 ⃑⃑𝑑 + 4𝜋𝑀, which pointing the magnetic field inside the magnetic bar can represent as 𝐻 in the opposite direction of the field that applied as the figure 2-14 shown. The induction field has its maximum at the center of the bar, that is due to the demagnetization field is stronger at the magnetic pole, thus we now know the demagnetization field is weaker at the center of the bar, this makes the center easier to be magnetized.. Figure 2-14 The induction magnetic field distribution diagram inside a bar shape magnetic bar.. 22.

(35) ⃑⃑⃑ : The demagnetization of a magnetic material is proportional to its magnetization𝑀. ⃑⃑⃑⃑⃑⃑ ⃑⃑⃑ . 𝐻𝑑 = 𝑁𝑑 𝑀. (2-13). The 𝑁𝑑 term in equation 2-22 is the demagnetization coefficient, which is related to the shape of the magnet. By calculation we can get 𝑁𝑑 of a ball shape magnet equals to 4𝜋⁄3, and 𝑁𝑑 = 4𝜋 for thin film. Because 𝑁𝑑 is constant in any direction, thus there is no shape anisotropy in these cases. With the work that have been done by Maxwell, Stoner and the rest[27, 28], we have the demagnetization coefficient of an ellipsoid shape magnet, by adjusting three axis of ellipsoid sphere, we can simulate ball shape (a = b = c), rod shape (a = b ≠ c) or a prolate shape (a = b ≠ c) magnetic grain.. Figure 2-15 Ellipsoid shape magnet.. 23.

(36) For a prolate shape or rod shape magnetic grain, the corresponding demagnetization constant of its three axis, 2a 2b 2c is 𝑁𝑎 , 𝑁𝑏 and 𝑁𝑐 , and the relation between 𝑁𝑎 , 𝑁𝑏 and 𝑁𝑐 is:. 𝑁𝑎 + 𝑁𝑏 + 𝑁𝑐 = 4𝜋.. 𝑁𝑐 =. (2-14). 4𝜋 𝑟 [ 𝑙𝑛( 𝑟+ √𝑟 2 −1 ) −1] 𝑟2 − 1 √𝑟2 −1. .. 𝑁𝑎 = 𝑁𝑏 =. 4𝜋− 𝑁𝑐 2. .. (2-15). (2-16). in equation 2-24, when r is large (rod shape), equation 2-24 can be written as:. 𝑁𝑎 + 𝑁𝑏 ≅ 2𝜋.. 𝑁𝑐 ≅. 4𝜋 [ 𝑙𝑛2𝑟 𝑟2. (2-17). − 1 ].. (2-18). For an r >> 1 case, it’s obvious the demagnetization coefficient in this direction is smaller than a b axis, thus c axis is relatively easy to be magnetized and have shape anisotropy. The magneto statistic energy 𝐸𝑚𝑠 will be:. 𝐸𝑚𝑠 =. =. 1. 𝑁 𝑀2 = 2 𝑑. 1. 1. 1. 𝑀2 𝑁𝑐 + 2. 2. 2. [(𝑀𝑐𝑜𝑠𝜃)2 𝑁𝑐 + (𝑀𝑠𝑖𝑛𝜃)2 𝑁𝑎 ]. (𝑁𝑎 − 𝑁𝑐 )𝑀2 𝑠𝑖𝑛2 𝜃.. (2-19) 24.

(37) ⃑⃑⃑ and c axis, thus magnetic anisotropy constant 𝐾𝑠 can be written as: θ is the angle between 𝑀. 𝐾𝑠 =. 1 2. (𝑁𝑎 − 𝑁𝑐 )𝑀2 .. (2-20). When the length of c axis is longer than a axis, the magnetic anisotropy constant 𝐾𝑠 will be positive value. For instance, at room temperature, the saturation magnetization of a prolate shape Cobalt crystal is around 1422 emu⁄𝑐𝑚3 , and if the c/a ratio is equals to 3.5, with equation 2-29 we can calculate the magnetic anisotropy constant 𝐾𝑠 = 4.5 × 105 𝑒𝑟𝑔⁄𝑐𝑚3 ≅ 𝐾1 . By this, we now know the shape anisotropy have great contribution to its magnetic anisotropy in thin film system,. 2.3.3 Stress Anisotropy When a magnetic material is placed in a magnetic field, the size and shape may be slightly change by the external field, this phenomenon is known as magnetostriction effect. The deformation λ can be express as ∆𝑙⁄𝑙 , while we apply an external field to a λ > 0 material, it will stretch along the field direction, if we further apply an external tensile stress to it, the stretch caused by the tensile can increase its magnetization. The saturation magneto – striction of a simple cubic crystal structure is define as:. 3. 1. 𝜆𝑠𝑖 = 2 𝜆100 (𝛼12 𝛽12 + 𝛼22 𝛽22 + 𝛼32 𝛽32 − 3) + 3𝜆111 (𝛼1 𝛼2 𝛽1 𝛽2 + 𝛼2 𝛼3 𝛽2 𝛽3 + 𝛼3 𝛼1 𝛽3 𝛽1 ).. (2-21). 25.

(38) The two factor 𝜆100 , 𝜆111 in equation 2-30 is the saturation magneto – striction on crystal axis [100] and [111], and 𝛼1 , 𝛼2 , 𝛼3 are the cosine value of saturation magnetization and each crystal axis. In a situation of no stress or other magnetic anisotropy takes effect, the magneto – crystalline anisotropy will be the main factor that affects the orientation of magnetic moment, but if we applied an external stress on it, the orientation of saturation magnetization will be depend no its stress constant σ (dyns/cm3 ) and magneto – crystal constant 𝐾1 . For FCC and BCC crystals, the energy can express as:. 3. E = 𝐾1 (𝛼12 𝛼22 + 𝛼22 𝛼32 + 𝛼32 𝛼12 ) + 2 𝜆100 𝜎 (𝛼12 𝛾12 + 𝛼22 𝛾22 + 𝛼32 𝛾32 ) − 3𝜆111 𝜎(𝛼1 𝛼2 𝛾1 𝛾2 + 𝛼2 𝛼3 𝛾2 𝛾3 + 𝛼3 𝛼1 𝛾3 𝛾1 ). (2-22). 𝛾1 , 𝛾2 , 𝛾3 are the cosine value between stress σ and crystal axis.. Equation 2-31 is a combination between equation 2-21 and equation 2-30, the firs term comes from crystalline anisotropy, and the rest are from magneto – striction, thus the elastic energy that caused by magnetostriction is called magneto elastic energy 𝐸𝑚𝑒 . The orientation of saturation magnetization must pointing at a direction that making the whole system have its minimum free energy, the relation between magneto anisotropy energy and 𝐾1 , 𝜆100 , 𝜆111 are too complicated to calculate, but we still can analyze it qualitatively by comparing 𝐾1 to 𝜆100 𝜎 and 𝜆111 𝜎 .. For a non – orientation related case, the striction on each axis are the same, 𝜆100 = 𝜆111 = 𝜆𝑠𝑖 , by applying it to equation 2-31 we now get the magneto elastic energy 𝐸𝑚𝑒 : 26.

(39) 3. 𝐸𝑚𝑒 = − 2 𝜆𝑠𝑖 𝜎𝑐𝑜𝑠 2 𝜃.. (2-23). 𝜃: The angle between saturation magnetization and stress.. With the help of equation 2-32 we now know the striction only depends on the sign of 𝜆𝑠𝑖 and 𝜎. Thus, when a positive 𝜆𝑠𝑖 material suffered under an expansion will have the same behavior as a negative 𝜆𝑠𝑖 material being compress, and for most of the magnetic materials, the sign of 𝜆𝑠𝑖 are negative.. By replacing the cos2 𝜃 in equation 2-32 into (1 − 𝑠𝑖𝑛2 𝜃) and ignoring the constant term, we can rewrite it as equation 2-33:. 𝐸𝑚𝑒 =. 3. 𝜆 𝜎𝑠𝑖𝑛 2 𝑠𝑖. 2. 𝜃.. (2-24). For a case of crystalline anisotropy and shape anisotropy are weak enough to ignore, the saturation magnetization of the material will be fully dominated by its stress anisotropy. As figure 2-16 (𝐚𝟏 ) shows, a fully demagnetized 𝜆𝑠𝑖 > 0 sample is only effected by stress anisotropy. When this sample is suffered under a side expansion, its magnetic moment is perpendicular to external stress, this makes the system have greater elastic energy, which 𝜆𝑠𝑖 ∙ 𝜎 > 0, the sample will move its domain wall to lower down its free energy. If we add a strong enough external force to expand it, the domain wall move and shrink down perpendicular domains (𝐛𝟏 ) and arranged as (𝐜𝟏 ) shows. Simply by applying an external field, we can make 27.

(40) the domain rotate in 180° and reaches its saturate. After it saturates, the intersection angle between domain structure and external field will be 180° , thus it doesn’t have contribution to magneto – striction (𝐝𝟏 ).. Reversely if we apply a side pressure to the sample (𝐛𝟐 ), because its (𝜆𝑠𝑖 ∙ 𝜎) < 0, the domain will arranged as figure 2-16 ( 𝐜𝟐 ) shows, the direction of moment will align perpendicularly to external force. As the field applied, the domain will make a 90° rotation to meets its saturate and also make the sample stretch, this kind of domain rotation will have significant magneto – stretching effect.. Figure 2-16 The magnetic domain wall movement under stress.. 28.

(41) 2.5 Magneto – Optical Kerr Effect When a linear polarized MOKE (Magneto – Optical Kerr Effect) light source incident into a magnetized magnetic material, the linear polarized light will split into two beams due to the refraction index is different for its compositions, dextrorotation and levorotation light. Because of the phase difference between two light beams, they will merge into elliptically polarized light when it pass through the material, we define the angle between the major axis of elliptically polarized light and linear polarized light as Kerr angle θk , the ellipticity of elliptically polarized light as Kerr ellipticity εk , which θk and εk is far less than 1° and have positive relation between the magnetization of the material. Thus, by applying a polarizer in front of a photo detector, we can measure θk , εk as well as its hysteresis loop.. Figure 2-17 MOKE polarizing diagram 2-13. 29.

(42) When we apply a magnetic field to a magnetic material, it will add a non-diagonal term in its dielectric matrix, thus for different rotation of polarized light will have a different refraction index and travel speed ( nr : refraction index of dextrorotation light, nl : refraction index of levorotation light), the dielectric matrix of a magnetic material which is placed in magnetic field can be express as:. εMatrix. ε11 = [−Jε12 0. −jε12 ε11 0. 0 0 ]. ε11. (2-25). And now, because of the electromagnetic field always perpendicular to the light path, we have k z = 0 only Ex and Ey exist, with this condition we can discuss the relation between ε and n:. ⃑⃑ + ω2 μ ‖ε‖E ⃑⃑ = 0. −k 2 E. (2-26). ∵ −k 2 Ex + ω2 μ(ε11 Ex + jε12 Ey ) = 0.. (2-27). −k 2 Ex + ω2 μ (−jε12 Ex + ε11 Ey ) = 0.. (2-28). With three equations above, we can further derive:. |. −k 2 + ω2 με11 −jω2 με12. jω2 με12 | = 0. −k 2 + ω2 με11. (2-29). 30.

(43) yields. →. (k 2 − ω2 με11 )(k 2 − ω2 με11 ) = ω4 μ2 ε12 2 .. → k = ω√ με0 √ε11 ∓ ε12 .. ∴ nr =. ∴ nl =. kr ω√με0. kl ω√με0. (2-30). (2-31). = √ ε11 + ε12 .. (2-32). = √ ε11 − ε12 .. (2-33). By Fresnel equation, the reflection coefficient γ can be written in j form:. γr =. γl =. nr − 1 nr − 1. nl − 1 nl − 1. = |γr |ejr𝜙 .. (2-34). = |γl |ejl𝜙 .. (2-35). With the equation above, we can see that γr and γl are complex number, two beams interference will become elliptically polarized light, and its Kerr angle θk and ellipticity εk can be express as:. 1. n −n. θk = − 2 (𝜙r − 𝜙l ) ≅ −Im (n rn − 1l ). r l. |γ | − |γ |. n −n. εk = − |γr | + |γl | ≅ −Re (n rn − 1l ). r. l. r l. (2-36). (2-37). 31.

(44) Normally, the dielectric constant ε11 is much greater than ε12 , thus we replace the refraction index as dielectric constant in equations above, and we can get:. θk = −Im (. εk = −Re (. ε12. ε12. ) ≅ −Im( n( ε. 1 n[(ε11 2 − ε12 2 )2 ]. ε12. ε12. ) ≅ −Re( n( ε. 1 n[(ε11 2 − ε12 2 )2 ]. 11 − 1 ). 11 − 1 ). ).. (2-38). ).. (2-39). We also know that ε12 is proportional to the magnetization of the material, thus θk and εk are also proportional to⃑⃑⃑⃑⃑ M.. Figure 2-18 Three different types of MOKE, P-MOKE L-MOKE and S-MOKE. 32.

(45) J. Zak using universal approach method derive that the Kerr angle of polar MOKE θpol and longitudinal MOKE θlon are:. N2. 4π. θpol = − ( λ ) ∙ ( 1− N. 2. ) Qd .. 2. ) θQd .. sub. θlon =. 4π. N. ( λ ) ∙ ( 1− sub N. 2. sub. (2-40). (2-41). N: refraction index of the magnetic thin film. d: thickness of the film. θ: incident angle of MOKE light source. Q: Voigt constant of the sample, which is related to its magneto – optical coupling. It is easy to see from equation 2.51 and 2.52, the Kerr angle is proportional to the thickness of the film.. 33.

(46) Figure 2-19 MOKE P mode and S mode schematic diagram.. MOKE can separated into two modes, P mode and S mode, which is define by the polarization of the incident MOKE light source, as figure 2-19 shown, the electric field of P mode laser is parallel to the incident plane, and S mode is perpendicular to it. With Bader’s MOKE theory, we now know: Kerr angle θk and Kerr ellipticity εk is proportional to the magnetization of material, and the relation between electric field of P MOKE as well as S MOKE can be written as:. 𝐸𝑠 𝐸𝑝. = 𝜃𝑘 + 𝑖𝜀𝑥 .. (2-42). by measuring the ratio of E𝑠 and𝐸𝑝 we then can acquire MOKE signal.. 34.

(47) We first define zero degree as angel of the polarized which the photo detector can get its minimum signal, and the reflect laser intensity I𝑟 at a very small angle δ (which δ ≅ 0 ) is approximate to:. 2. I𝑟 = |𝐸𝑝 𝑠𝑖𝑛𝛿 + 𝐸𝑠 𝑐𝑜𝑠𝛿 | .. (2-43). owing to Kerr angle is small 𝜃𝑘 is ≪ 1° , the reflection light electro field component on S direction 𝐸𝑠 is way smaller than P direction 𝐸𝑝 , the equation above can be rewrite as:. I𝑟 ≅ 𝐸𝑝 2 |𝛿 + 𝜃𝑘 + 𝑖𝜀𝑥 | ≅ |𝐸𝑝 2 |(𝛿 + 2𝛿𝜃𝑘 ) .. (2-44). and the intensity of incident light I0 can also written in 𝐸𝑝 and 𝛿 form:. I0 = 𝐸𝑝 2 𝑠𝑖𝑛2 𝛿 = 𝐸𝑝 2 𝛿 2 .. (2-45). with equation 2.56, we now replace I𝑟 into I0 form:. I𝑟 = I0 ( 1 +. 2𝜃2 𝛿. ).. (2-46). so, the intensity difference of incident and reflection light ∆I:. 𝜃. ∆I = I0 ( 𝛿𝑘) .. (2-47). 35.

(48) finally, by arranging equation 2-59:. 𝜃𝑘 =. 𝛿 ∆𝐼 2. (𝐼 ) . 0. (2-48). With the equation above, it’s clear to see that Kerr angle is proportional to ∆I. Thus, with a constant incident light intensity the change of I𝑟 can be seen as the change of Kerr angle, by plotting out field - ∆I graph we can have the hysteresis graph of the sample material.. 36.

(49) Chapter 3. Instrumentations and Experiment Methods. 3.1 Sample Fabrication Before deposition, silicon (100) wafer will be cut to 12mm × 12mm by tungsten pen. The sample holder we choose in our deposition process is design with a round shape hold, this round shape design is meant to reduce shape induced magnetic anisotropy.. After cutting of the substrate from the wafer, we then clean the substrate with acetone, alcohol and deionized water, each process is vibrate with an ultrasonic vibrator for 10 minutes to degrease. After substrate surface be cleaned, we then soak it into 15% hydrogen – fluoride solution for 30 Sec to etch out silicon dioxide Figure 3-1 Sample holder.. on substrate and produce hydrogen – terminated surface.. There are several features of an H - passivated surface: 1) H - passivated surface can remain clean for a few minutes in the air and this passivation can least for weeks in vacuum or few days in air, the hydrogen on the surface can withstand up to 680K. 2) Because of the silicon dioxide as well as the dangling bonds has been removed from the surface and replaced with hydrogen, the surface will reconstruct and forming a 1 × 1 structure, thus with this kind of reconstruction, Cu can have greater chance epitaxy on it.. 37.

(50) 3.2 Pulse Laser Deposition System The High Vacuum Pulse Laser Deposition system that we used in our thin film preparation is shown as figure 3-2, the input laser source is a 266nm ultraviolet Nd+3 ∶ 𝑌𝐴𝐺 laser, model name: LS-2147, which is manufactured by LOTIS TII, the detail spec can refer to Table 3 – 3, the heating system in our PLD system is a thermoelectric heater, which can heating substrate up to 700 ℃. The pumping system of our PLD high vacuum system can be divided into two parts, low vacuum part, which is achieved by Pfeiffer DuoLine𝑇𝑀 Duo 10 rotary pump, with ultimate pressure 4.5 × 10−3 Torr and high vacuum chamber achieved by VARIAN Turbo-V 551 Navigator turbo pump with its ultimate pressure < 1.0 × 10−10 Torr, but because some of our access ports are using KF flanges and O-rings instead of CF flanges, so our system ultimate pressure can only reach to 10−8 Torr.. Figure 3-2 The picture of PLD system that we use in our experiment.. 38.

(51) Figure 3-3 PLD system interior 3D diagram.. Figure 3-4 The sample holder assembly diagram.. 39.

(52) Figure 3-5 Picture of the laser source we use for the PLD system.. Wavelength Energy(Maximum) Pulse duration Pulse repletion rate Beam divergence Beam diameter Energy stability. 266nm 120 mJ 16 ns ~18 ns 1 Hz ~ 10Hz ≤ 0.7mrad ≤ 0.8 mm ± 3.0 %. Table 3-1 Spec of LOTIS TII LS – 2147 Nd−3 : YAG Laser.. 40.

(53) The high vacuum annealing system that we use in our experiment can heating up samples up to 700 ℃, the heater of this this system is same as the one we build in PLD system, with K-type thermal couple and PID temperature controller, we can control our temperature accuracy up to ± 0.1 ℃. The pumping system of our high vacuum anneal system is using ULVAC GCD-136K rotary pump as our low vacuum pumping, which its ultimate pressure is about 5.0 × 10−3 Torr, and VARIAN Turbo-V 301 Navigator turbo pump as our high vacuum pump with ultimate pressure around 5.0 × 10−10 Torr, but because of the O-ring parts of the chambers’ access door, the ultimate pressure of this annealing system can only be stable at around 10−8 Torr.. Figure 3-6 The picture of our high vacuum annealing system (left). Figure 3-7 High vacuum annealing system inner view 3D diagram (right).. 41.

(54) 3.4 Magneto – Optical Kerr effect Measurement Back to mid-19th, when Faraday first discovered the polarization of a linear polarized light changes after it passes through a magnetic material, this phenomenon later then called Faraday effect, in late 19th, Kerr measured the light reflected from a magnetic material and discovered the incident linear polarized light will reflect as an elliptical polarized light, we define the ellipticity of reflected light as Kerr ellipticity and the angle between its major axis and the electric field of incident light as Kerr rotation angle, this kind of relation between magnetic field and light polarization we then called it as Magneto-Optical Kerr Effect, or MOKE in short.. For magnetic property reaches, MOKE measurement have great advantage over Faraday Effect, because Faraday effect measures the samples’ transition light, the sample substrate and the film both have to be polished and transparent. Thus, for convenience’s sake, we often choose MOKE measurement rather than Faraday Effect measurement.. MOKE is a relatively cheap magnetic property measurement approach while having decent accuracy and sensitivity, the Kerr rotation angle of ordinary ferromagnetic material is around 105 ~ 106 𝑟𝑎𝑑⁄𝑐𝑚 or 10−2 ~ 10−3 𝑟𝑎𝑑⁄Å , but because MOKE can only measure the rotation of momentum, thus we cannot acquire absolute momentum change from MOKE studies.. 42.

(55) Figure 3-8 The picture of MOKE setup.. 43.

(56) 3.6 X-Ray Diffraction. Figure 3-9 Crystal diffraction and Bragg’s Law schematic diagram.. The wavelength of X-ray is around 10−2 to 102 Å , which have the same order as crystal lattice, this diffraction may occur when a beam of X-Ray incident into crystalline material at certain angles. We can get a maximum intensity from X-Ray photo detector if the phase difference of two reflection X-Ray beam is 2π, we called this kind of constructive diffraction as Bragg diffraction, which its incident angle, X-Ray wavelength and crystal lattice will satisfy Bragg’s Law:. 2dsinθ = 2λ. (3-1). In general, we often use Symmetric Bragg Diffraction measurement, which the incident angle of X-Ray is the same as the photo detector, this kind of method is also called theta - 2 theta measurement. If we assume μ is the X-Ray absorption factor of material, ∅ is its incident angle, then sin∅⁄𝜇 will be its penetration depth, for most of the materials, 1⁄𝜇 is 44.

(57) about 10mm to 100 mm, which is way longer than the thickness of thin film. Thus, for symmetric Bragg diffraction measurements, thin film diffraction peaks are usually concealed by the strong diffraction signal of its substrate. If we attempt to acquire better diffraction signal from ultra-thin film, Grazing Incident X-Ray Diffraction (GIXRD) will be a better candidate, the geometrical schematic diagram of GIXRD is shown as below.. Figure 3-10 XRD and GIXRD comparison schematic diagram.. To further analyze the crystalline orientation between each layer as well as its rotational symmetry of epitaxial thin film, an X-Ray Phi-Scan measurement is required. With an additional azimuthal degreed of freedom - ∅ and θ angle that we chose from earlier theta 2theta experiment, we can not only determine the planner crystalline symmetric of each material exclusively, but also reveals their epitaxial relationship.. 45.

(58) 3.6 Experimental Procedure and Parameters. Deposition: After we done all the sample preparation process that we have mentioned in chapter 3.1, we then puts the samples into PLD chamber and turn on rotary pump and turbo pump in sequence. The sample fabrication process starts once the system base pressure reaches 2.0 × 10−7 Torr. First, we will turn on the heater and heat up the substrate to 250 ℃ at a rate slower than 10 ℃⁄𝑚𝑖𝑛 for Copper deposition, we then turn our PLD Nd3+ ∶ YAG laser source on at power 0.4 ~ 0.7 Watt to pre-deposition and cleaning up targets’ surface, which laser power that we choose for experiment is depends on the thickness or deposition rate that we attempt to achieve.. There are several reasons for choosing 250 ℃ as the deposition temperature for first layer of Copper, first of all, Copper and Silicon/ Hydrogen passivated Silicon surface will from Copper Silicon at higher temperature, which is about 350 ℃ degrees, since it is the very first layer, we don’t want to have strong interface diffusion during its deposition, the second reason is that, is some conduction, the granule size and surface roughness of Copper raises with its deposition temperature[29, 30]. Third, we tried to use higher deposition temperature for first layer, but it turns out with no X-Ray Cu (100) diffraction signal, and the last reason is Hydrogen passivation surface can only stand around 430 ℃, for those reasons above, we choose 250 ℃ as the growth temperature of first layer.. 46.

(59) The laser beam will pass through several motorized reflector automated by NI LabVIEW program and a focal length 40cm magnifier before it focus on the target, using this program we can make the laser focus spot scanning on the target to make the deposition happen and control the thickness as well as uniformly of the film. The focus laser spot has its radius approximately 0.5 mm, with the light spot and energy fixed, we now can estimate the laser energy per unit area is around 4.25 J⁄𝑐𝑚2 (the transition rate of PLD laser view port is about 50%) After 7 min pre-deposition, we then starts the Copper deposition process at 250 ℃ / deposition height 4 cm, the growth rate of Copper and Cobalt is verified by atomic force microscope, which are 0.3 nm⁄min and 0.25 nm⁄min, respectively. To produce face centered cubic (FCC) Cobalt (100) epitaxially on Copper (100), we need to heat up our sample to 350 ℃ to reach its phase transition temperature, Cobalt stable state transforms from hexagonal close pack to face centered cubic, and then we continue the process. After all the deposition work is done, we will keep the sample at 350 ℃ in high vacuum environment for another 1.5 hour, let it develop better crystal structure and leave it cool down overnight.. Annealing: For some samples that we fabricated at room temperature, we annealed them after they been measured with XRD. The post-annealing process take placed at the high vacuum annealing system that we build for post-annealing, the temperature parameter that we choose. 47.

(60) for annealing is same as the one we deposit cobalt (350 ℃, ∆T < 10 ℃⁄𝑚𝑖𝑛), and also leave the samples in high vacuum environment cool down overnight.. Usually, we anneal our substrate at 350 ℃ for three hours, this parameter is determined by X-Ray diffraction data. We have compared the XRD pattern of sample which annealed for one and three hours, the result shows the same, but to ensure better crystalline quality, we still choose three hours as our post-annealing parameter.. X-Ray Diffraction Measurement: The XRD experiments were done at Academia Sinica, the XRD machine that we use on our measurement is manufactured by Philips, model name PANalytical –X’Pert 3 Powder, the X-ray source of this machine is generated by Cu target, which its average Cu − k α and Cu − k β are 1.54184 Å and 1.39222 Å, respectively. The scanning speed that we chose for our research is 0.02deg⁄step with 1sec⁄step.. MOKE Measurement: First, we calibrate the levelness of MOKE magnetic coil before we done our MOKE measurement, after the calibration, we then adjust the laser level to make it reflect on the sample then pass through photo detector as S-mode, meanwhile, the incident plane should also be parallel to the horizontal plane.. 48.

(61) When all the calibrations were done, we rotate the polarizer in front of the photo detector to search the best angle for MOKE data acquisition, we chose the angle that is approximately 0.5 degree before digital multi-meter gets its minimum value.. The electromagnet of MOKE machine that we build is powered by programmable DC power supply: Sorensen DCS 20-150E, which can supply maximum voltage 150 V, maximum current 20 A, and with 16-bit resolution when it is controlled via IEEE488 interface (using code M130). With this setups, we can generate 50 Oe (no yoke) / 500 Oe (with yoke) magnetic field from 1 ampere, the theoretical field resolution this MOKE system is around 0.015 Oe (no yoke) / 0.152 Oe (with yoke).. Ferromagnetic Resonance Measurement: For FMR measurement, we first double-sided taped our sample to Teflon sample holder and put it in the resonance chamber, then we adjust the iris making the absorption Q-factor to be in range 3000 ~ 10000. Because of the microwave wave guide and cavity that our FMR using is X-band, that our resonance peak will appear around 9.6 GHz to 9.8 GHz. After we done with the adjustments, we then starts the program, it will rotate the sample and acquires data automatically. Our experiential setup of FMR measurement schematic diagram is shown as the figure below. For further details of FMR theories this [31] article can serve as reference.. 49.

(62) Figure 3-11 The schematic diagram of FME setup.. 50.

(63) Chapter 4. Results and discussions. 4.1 X-Ray Diffraction Data Analysis Single periodic (Co/Cu) thin film deposited at high temperature: The XRD pattern of figure 4-1 shows, Pulse Laser Deposited copper(100) can successfully epitaxy on hydrogen passivation silicon(100) surface from room temperature to 250 ℃, the X-Ray diffraction peak (theta – 2theta experiment) of Cu(200) can be found at 50.34° , and Si(200), Si(400) substrate signal can also be found at 32.91° and 61.65° , the 2θ - diffraction peak at 61.65° is caused by Cu-𝑘𝛽 . A high intensity Si(400) main peak which caused by Cu𝑘𝛼 can also be found at 69.10° , but due to its counts is too strong, we often avoid to measure it to extend the life time of X-Ray detector. The lattice constant of Si(100), Cu(100) are 5.427Å and 3.618Å, respectively. Although from its’ lattice constant, it seems like the lattice mismatch between Si(100) and Cu(100) are about 33.3%. But actually, the orientation of Cu[010] is 45° away from Si[100], this makes the mismatch can be lower down to 5.7%, which can be verified by XRD phi-scan. We also tried to deposit thin film by different laser power, 4.25 𝑤/𝑐𝑚2 and 3.07 𝑤/𝑐𝑚2 . XRD results suggests, both high / low laser energy can from epitaxial Co(100)/Cu(100) on H-Si(100) at 350℃, but 4.25 𝑤/𝑐𝑚2 deposit samples have sharper Co(100) XRD pattern (lower FWHM), better repeatability and most important is using 4.25 𝑤/𝑐𝑚2 can successfully epitaxy Co on Cu(100) at room temperature while using 3.07 𝑤/𝑐𝑚2 cannot.. 51.

(64) Figure 4-1 (a) XRD pattern of 30nm Cu(100) deposited by PLD at 250 ℃ epitaxy on H-Si(100) surface. (b) The diffraction pattern of Cu(100) epitaxy on hydrogen terminated Si(100) substrate by sputtering deposition[32]. XRD pattern of sample (𝐶𝑢 80 𝑛𝑚/𝐶𝑜 25 𝑛𝑚)1/ 𝐶𝑢/ H-Si at 350 ℃ is shown as figure 4-2, by comparing this XRD curve to the previous one we can found a new peak at 51.26° ,which belongs to cobalt(100), this indicated that with this kind of temperature parameter and deposition condition, we can successfully develop epitaxial FCC cobalt(100) on Cu(100). For this sample, cobalt with thickness 40 nm is sandwiched by two 80 nm thick copper, bottom one is served as a seed layer, top layer is for capping, to prevent cobalt from oxidation. An almost invisible peak which located at 47.72° should be the peak of CuSi component, and no matter how the deposition temperature or the thickness of changes, its intensity remain unchanged. 52.

(65) Because of the peak intensity of XRD pattern is usually proportional to the thickness of the material, thus by the XRD pattern of cobalt with different thickness (figure 4-3), we can further justify the epitaxy of cobalt.. Figure 4-2 The XRD pattern of sample (𝐶𝑢 80 𝑛𝑚/𝐶𝑜 25 𝑛𝑚)1 / 𝐶𝑢 /H-Si deposit at 350 ℃ , shows that PLD deposited Cobalt can epitaxy on Cu(200). The XRD pattern of sample (𝐶𝑢 80 𝑛𝑚/ 𝐶𝑜 40 𝑛𝑚)1/𝐶𝑢/H-Si deposit at 350℃ is shown as figure 4-3, except the thickness of cobalt, the rest parameters are same as the one of figure 42. By comparing this pattern to figure 4-2, it is obvious to see that the intensity of cobalt’s diffraction peak increase a lot, the reason that the diffraction counts of cobalt in figure 4-3 is not Figure 4-3 The XRD pattern of sample (𝐶𝑢 80 𝑛𝑚/𝐶𝑜 40 𝑛𝑚)1 / 𝐶𝑢 /H-Si deposit at 350 ℃ , shows that the counts of XRD pattern changes with its thickness.. exactly 1.6times of figure 4-2, this might caused by the inter diffusion between Cu and Co or laser energy fluctuation.. 53.

(66) Form the data above, we can only see the peak of Si, Cu(200), Co(200). Therefore, the thin film we fabricated by PLD should be single crystal Copper and Cobalt. With FCC(100) structure and similar lattice constant of Co(100) and Py(100), Co(100) on Cu(100) and Py(100) on Cu(100) Figure 4-4 XRD Phi-Scan pattern of PLD deposit Py(100)/Cu(100)/H-Si(100), which Py[010]//Cu[010]//Si[110], phi scan pattern comes from [33].. should share the same crystalline orientation.. From figure 4-4, 4-5 we can speculate the orientation between each single crystal thin films should be Co[100] // Cu[100] // Si[100], and Co[010] // Cu[010] // Si[110], the lattice constant of Si(100), Cu(100), Co(100) are 5.427 Å, 3.618 Å and 3.554 Å , respectively. The relative error between theoretical lattice constant of Cu (3.617 Å), Co (3.544 Å) and PLD fabricated Cu Figure 4-5 Crystalline orientation schematic diagram of Cu(100)/H-Si(100) interface (modify from [32]).. (3.618 Å), Co (3.554 Å) are 0.027 % and 0.282 %.. 54.

(67) Two periodic (Co/Cu) thin film deposited at high temperature: We also fabricate multilayer (Co/Cu) thin film to demonstrate the possibility of PLD deposited epitaxial (Co/Cu)n and to discuss the exchange effect of multilayer Co(100),. Figure 4-6 The XRD pattern of sample (𝐶𝑢 80 𝑛𝑚/𝐶𝑜 40 𝑛𝑚)2/𝐶𝑢/H-Si deposit at 350℃, shows that cobalt and copper can epitaxy on each other and forming multilayer single crystal.. 55.

(68) (Co/Cu) thin film deposited at Room Temperature: After some experiment we found that, using 0.45 Watt as the deposition laser energy is not powerful enough to fabricate epitaxial FCC cobalt at room temperature, we then later adjust the deposition laser power to 0.70 ~ 0.75 Watt. Having higher laser power also means higher deposition rate and higher kinetic energy, with such high energy. we finally can fabricate epitaxial Co(100) on Cu(100) at room temperature.. Figure 4-7 The XRD pattern of sample (𝐶𝑢 80 𝑛𝑚/𝐶𝑜 40 𝑛𝑚)1/𝐶𝑢/H-Si deposit at RT, which shows with higher laser power, we can successfully create FCC cobalt on FCC copper surface.. 56.

(69) Cu thin film deposit at 𝟒𝟓𝟎℃: on H-Si(100) surface:. Figure 4-8 XRD of Cu/H-Si(100) grown at 400℃.. We have discovered in this experimental condition (PLD, substrate Temp. 400℃ ), Cu has great chance instead of growing epitaxially on H-Si, it would rather chose to form Cu(111) phase (or amorphous). And sometimes it’ll form some interesting cone shape structure evenly distributed on samples’ surface.. Roughly estimating, the average cone. height and diameter is around 550 nm tall and 5 𝜇𝑚 wide, this should be caused by higher deposition temperature.. Figure 4-9 (a) Surface morphology of PLD Cu deposit on HSi(100) at 400℃, measured by AFM. (b) AFM cross section, ℎ ≈ 550 𝑛𝑚 and 𝑤 ≈ 5 𝜇𝑚 refers to the height and width of cone shape structure. (c), (d) x300, x22,000 times magnification SEM picture of 400℃ PLD Cu/H-Si(100) surface.. 57.

(70) 4.2 Magnetic Property Measurement. 4.2.1 MOKE Data Analysis From MOKE measurement we discovered some of the samples that fabricated with PLD method are with magnetic four-fold rotational symmetry (figure 4-13, 17, 21, 23, 25, 27, 29), the easy axis can be found at 45° away from Si<100> axis, and because of the orientation between Co<100> and Si<100> is also 45° , the MOKE result also matches the fact that cobalt has grown epitaxilly on Cu(100) as FCC structure. In principle, FCC cobalt has structural four fold rotational symmetry, it has its easy axis, hard axis on Co<111>, Co<100>, respectively. But because our samples were measured with LMOKE setup, the easy axis will be the projection of Co<111> on the surface, which should be observed in Co<110>, Si<100> direction.. Figure 4-10. Magnetization curves for. single crystals of FCC Nickel, easy axis, hard axis located at <111> and <100> direction (modify from [26]).. 58.

(71) High temperature deposit samples: Form MOKE study of high temperature fabricated samples, we found out samples with 25 nm cobalt layer preforms stronger four fold magnetic anisotropy, its easy axis and hard axis can be measured at Si<100> and Si<110> direction. With the thickness of cobalt raise up to 40 nm, it doubles its coercivity as well as saturation field, and starts to behave isotropically. It’s worth mentioning, for the samples with thicker cobalt layer although the shape of its hysteresis loop almost identical from 0° ~ 1800 , but we still can observe slightly difference in their coercivity, the maximum coercivity (easy axis) shifts about 15° away from Si<110> axis.. Room temperature deposit samples: Room temperature deposit samples shows significant four fold anisotropy, the coercivity H𝑐 have been greatly reduce from several hundred Oe to around 30 Oe. From MOKE pattern studies we discovered, the MOKE curve measured at easy axis directions have an asymmetric bump( Figure 4-13 (c) ), which should caused by the unbalancing between samples’ two easy axis, this phenomenon can be observed in lots of cubic systems. RT growth samples have. Figure 4-11 Comparison of surface morphology between (a), (c) 350℃ and (b), (d) room temperature fabricated Cu/Co/Cu/H-Si, observed by SEM.. 59.

(72) better domain wall movement as the deposition temperature drops[34] ( figure 4-12 (a) ), such difference should cause by its change in surface morphology, the surface roughness and pinning effect of high temperature deposit sample should stronger than RT ones, this not only makes the squareness drops, but may also suppress and balance out the effect of Barkhausen jump which can be observed at some of the RT fabricated samples.. We also compared our MOKE with MBE fabricated 4ML FCC cobalt epitaxial growth on Cu(100) sample (figure 4-13 (a), (b) from [35]), we found our results are similar, but not. Figure 4-12 (a) Schematic MOKE curve of different kinds of domain wall motion. (b) Barkhausen jump can be observed from MOKE measurement (modified from[34]). (c) Real MOKE data of two periodic cobalt layer, the steps should causes by Barkhausen effect. (d) Real hysteresis loop of RT fabricated sample, the angled curve near zero field is caused by FCC un-balanced crystalline anisotropy.. 60.