Luận án Nghiên cứu áp dụng một số phương pháp hạt nhân nguyên tử trong phân tích vật liệu TiO₂/SiO₂ sử dụng chùm ion từ máy gia tốc

ctromagnetic waves are aligned or have a certain recurring pattern known as polarized light as shown in Fig. 2.7. The light that results when two orthogonal light waves are in phase is linearly polarized. The resulting light is circularly polarized if the orthogonal waves are 900 out of phase and equal in amplitude. The most typical polarization is called "elliptical", and it consists of orthogonal waves with any amplitude and phase. This is the origin of the name ellipsometry. Fig. 2.7. Schematic of non-polarized light (a) and different polarized light forms: linear (b), circular (c), and elliptical (d) polarized light [89]. 48 The process by which incident light changes direction on the interface of two optically different media is known as refraction. This phenomenon is linked to the differences in propagation velocity between media. The only exception to this process occurs when light arrives at an angle perpendicular to the surface. The degree of refraction is determined by the refractive index n, defined by 𝑛 = 𝑐/𝑠, where, 𝑠 defines the phase velocity of light in a medium and 𝑐 the speed of light in vacuum. The absorption of light in materials is characterized by the extinction coefficient (𝑘). In transparent mediums, no absorption of light occurs and 𝑘 corresponds to 0. In absorbing medium, 𝑘 > 0. The amount of wave energy lost to the material is indicated by the extinction coefficient, related to the absorption coefficient 𝛼 as follows 𝛼 = 4𝜋𝑘 λ . (2.3) Light that propagates in a medium can be characterized using the complex refractive index 𝑁 defined by: 𝑁 = 𝑛 – 𝑖𝑘, with 𝑛 is the refractive index, and 𝑘 is the extinction coefficient. An electromagnetic wave influences the material by generating polarization within the material. This is described by the dielectric constant 𝜀 and is closely related to the complex refractive index 𝑁. From Maxwell’s equations for conductors, 𝑁 ≡ 𝑛 − 𝑖𝑘 is defined as 𝑁² ≡ 𝜀. 2.5.2. Interaction of Light and Materials When light hits a surface separating two materials with different refractive indexes, or oblique incidence, different phenomena occur. The direction of the propagation of light may change due to either refraction or reflection. The most important phenomena for ellipsometry are transmission (refracted wave) and reflection (reflected wave). Snell’s law proves that the angle of the refracted light is dependent of the refractive index of both media. Snell’s law is described by the following equation: 𝑁𝑖𝑠𝑖𝑛𝜃𝑖 = 𝑁𝑡𝑠𝑖𝑛𝜃𝑡, where, 𝑁𝑖 and 𝑁𝑡 represent the complex refractive indices of the two 49 media i and t, and 𝜃𝑖 and 𝜃𝑡 the angle of incidence and angle of transmitted light respectively (Fig. 2.8a). (a) (b) Fig. 2.8. Reflection and refraction of light according to Snell’s law (a), and the plane of incidence (b) [93]. In ellipsometry, the electric field vector is expressed in the (s, p, z) coordinate system, rather than the three dimensional Cartesian (x, y, z) coordinate system. This coordinate system simplifies the notation used to describe incident light. The z-axis describes the direction of the incident wave, while s-polarized light has the electric field vector perpendicular to the plane of incidence, p-polarized light parallel to the plane of incidence. (German: s = senkrecht = perpendicular; p = parallel). This is illustrated in Figure 2.8.b. When light reflects off or refracts on a sample surface at oblique incidence, the p- and s- polarized light behave differently upon interacting with the sample. The electric field vector is split into a p- and s- electric field vectors for incident, reflected and refracted light, respectively notated as: Eip, Eis, Etp, Ets, Erp and Ers. The amplitude coefficients for p- and s-polarized light is defined by Fresnel equations consist of rp, rs, rp, rs. Where rp(s) is the reflection coefficient and tp(s) the transmission coefficient for p(s) polarized light. These values are utilized to characterize light reflection and transmission in terms of amplitude and phase variations. 50 2.5.3. Ellipsometry Measurements Ellipsometry measures the change of polarization of light for each wavelength by thin films and determine the ψ and Δ values. Through a proper optical dispersion model, these angles are modeled to obtain the optical constants and thickness of thin films. In ellipsometry, Δ is considered as the difference in phase difference between the phase difference of p and s incoming waves and of the outgoing wave, and Ψ is the relative amplitude ratio. The fundamental equation of ellipsometry was given by tan(ψ) 𝑒𝑖Δ = 𝑅𝑝 𝑅𝑠 . (2.4) In a real situation, multiple mediums should be considered and multiple interfaces influence the reflected light measured by ellipsometry. As a result, ellipsometry offers information on all media. The ratio of the resultant reflected wave to the amplitude of the incident wave can be calculated by the total reflection coefficient for p-parallel polarized light (𝑅𝑝) and (𝑅𝑠) 𝑅𝑝 = 𝑟𝑝 12+𝑟𝑝 23.𝑒−𝑖2𝛽 1+𝑟𝑝 12.𝑟𝑝 23.𝑒−𝑖2𝛽 , 𝑅𝑠 = 𝑟𝑠 12+𝑟𝑠 23.𝑒−𝑖2𝛽 1+𝑟𝑠 12.𝑟𝑠 23.𝑒−𝑖2𝛽 , (2.5) where 𝑟𝑥 (𝑥 + 1) is the Fresnel coefficient for media 𝑥 and 𝑥 + 1, calculated from the Fresnel equations, and 𝛽 is the thickness factor describing the influence of the thickness on the polarization state of the electromagnetic wave. 𝛽 is calculated using: 𝛽 = 2𝜋𝑁2𝑐𝑜𝑠𝜃𝑟/𝜆, (2.6) where d is the thickness of the medium, with λ the considered wavelength, 𝑁 the complex refractive index and 𝜃𝑟 the angle of the refracted wave. 51 Fig.2.9. Reflection and refraction of light at each interface leading to multiple beams in a thin film [93]. It should be notice that Eq. 2.4 describes the sample homogeneous isotropic environment, flat layer with two opposite parallel walls and homogeneous isotropic substrate. In a real situation, multiple mediums should be considered and multiple interfaces influence the reflected light measured by ellipsometry. As a result, ellipsometry offers information on all media. The following are the main equipment needed to gather ellipsometry data: light source, polarization generator, sample, polarization analyzer, and detector. Common ellipsometer configurations include rotating analyzer (RAE), rotating polarizer (RPE), rotating compensator (RCE), and phase modulation (PME) [92]. In the present study, the RAE configuration was used. Fig. 2.10 is an overview of an RAE operation. 52 Fig. 2.10. The rotating analyzer ellipsometer (RAE) configuration [93]. Light from the source is polarized in the PSG by a linear polarizer oriented to provide both p- and s-electric fields. The light reflects from the sample, changing the polarization to generally an elliptical state. The elliptically polarized light travels through the rotating analyzer to the detector. Detector transforms light into an electronic signal to ascertain the polarization of the reflected light. To determine the polarization change caused by the sample reflection, this data is compared to the known input polarization. This is how Psi (Ψ) and Delta (Δ) are measured in ellipsometry. In the present study, the ES experiments were conducted at the Institute of Electron Technology in Warsaw, Poland using the RAE configurations. The ellipse of the angles Ψ(λ) and Δ(λ) was measured with the light wavelength from 250 nm to 1100 nm, with the step of 1 nm at six different incident angles (i.e., the angle between direction of incident light beam and the normal of the sample surface), namely 70.00, 72.00, 74.00, 76.00 78.00, and 80.00. Once all these SE experiments had done, all the measured angles Ψ(λ) and Δ(λ) were used as input to calculate the spectra of Ψ(λ) and Δ(λ) using the Multiple-angle-of-incidence Ellipsometry (MAIE) method [90]. In order to analyze the optical parameters of the irradiated TiO2/SiO2/Si systems, a four-layer optical model was constructed. It consists of a Si substrate, a SiO2 layer, TiO2 layer, and an interface layer 53 between SiO2 and TiO2. It was assumed that all layers are homogeneous, and the boundaries between the materials are sharp. The thickness, and concentration of the compounds of the material layers are free parameters, whose values were determined by fitting to the experimental Ψ(λ) and Δ(λ) spectra. Knowing the values of all the parameter models, the refractive index 𝑛, and extinction coefficient 𝑘, of the investigated samples were deduced using the effective medium approximation (EMA) method [91]. 2.6. X-ray Photoelectron Spectroscopy (XPS) method. X-ray photoelectron spectroscopy (XPS) is a surface-sensitive analytical method that bombards a material's surface with X-rays and measures the kinetic energy of the released electrons [92]. The surface sensitivity of this technique and its capacity to extract chemical state information from the elements in the sample are two of its key qualities that make it effective as an analytical method. Soft X-rays are used in the XPS method to excite the core and valence electrons of surface atoms. If the X-ray energy is high enough, photoelectrons are released from the substance, and the instrument measures their kinetic energies (𝐾𝐸). The photoelectric effect, which represents this excitation process, is shown in Figure 2.11. Based on binding energy (𝐵𝐸), which is calculated in relation to the Fermi level (EFermi) of the individual atoms, differences between chemical elements in the near surface region are found. The key equation of the photoeffect mechanism that combines the 𝐾𝐸 and 𝐵𝐸 of the photoelectron is given by: 𝐾𝐸 = ℎ𝜗 − 𝐵𝐸 − ∅𝑠𝑝𝑒𝑐𝑡𝑟𝑜𝑚𝑒𝑡𝑒𝑟, (2.7) where ℎ𝜗 represents the energy of the absorbed photon, and ∅𝑠𝑝𝑒𝑐𝑡𝑟𝑜𝑚𝑒𝑡𝑒𝑟 is the work function of the spectrometer. Even when the Fermi levels of the spectrometer and the sample are lined up in electrical contact, their associated work functions are not the same. The work functions difference, which is really the contact potential between the sample and the spectrometer, accelerates or decelerates an electron as it travels to the analyzer. 54 Fig. 2.11. Schematic of the electron's energy indicating the absorption of a photon and emission of a photoelectron 2p level [93]. The element and orbital from which the photoelectron was emitted are noted on photoelectron peaks. For instance, "O 1s" refers to electrons that leave an oxygen atom's 1s orbital. Any electrons emitted from the sample with binding energies smaller than the energy of the x-ray source can be seen using the XPS technique. An electron's binding energy is a property of the material and is unaffected by the X-ray source that ejected it. The binding energy of photoelectrons will not change when experiments are run with various X-ray sources, but the kinetic energy of the photoelectrons that are released will vary, as shown by Eq. 2.7. This general equation makes it obvious that the binding energies of the released electrons affect the kinetic energies that are measured by the spectrometer. A depiction of the number of electrons detected versus their kinetic energy characterizes a typical XPS spectrum. This spectrum tells us how the energy of electrons is distributed throughout a material. The Fermi energy is used as the "natural" zero reference point for solids in actual data accumulation. Each element that exists in or on 55 the surface of the material creates a characteristic set of XPS peaks at distinctive binding energy values that directly identify each element. These characteristic peaks are related to the atom's electron configuration, such as 1s, 2s, 2p, 3s, etc. XPS has been used to analyze the surface of practically any substance from plastics to fabrics, dirt and semiconductors. All elements with order numbers 3 and higher can be measured, however hydrogen and helium cannot be found because their orbitals' diameters are so small that their electrons' photoemission cross sections are nearly zero. It turns out that the inner electrons are most susceptible to being knocked out by X-ray energies. It is crucial to remember that XPS only detects electrons that have really escaped into the instrument's vacuum. The photo-emitted electrons that have escaped into the instrument's vacuum are those that came from the material's top few nanometers. All of the deeper photo-emitted electrons, produced as the X-rays pierced the material by 1 to 5 micrometers, are inelastically lost before escaping. The probabilities of an electron interacting with a substance is higher than that of a photon. The electron's path length is on the scale of tens of Ångströms, but the photon's path length is on the order of micrometers. Consider a volume element of the sample with thickness 𝑑𝑧 at a depth 𝑧 under the sample surface. The photoelectrons that are emitted at an angle θ to the sample surface's normal enter the detector and add to the spectrum. The probability that a photoelectron will escape from the sample and enter semi-infinite space without losing energy is: 𝑃(𝑧) = exp (− 𝑧 𝜆sin𝜃 ), (2.8) where 𝜆 is the photoelectron inelastic mean free path. Suppose that one layer of thickness 𝑑𝑧, by photoionization produces the intensity of photoectrons 𝑑𝐼 and assuming that the thickness of the sample is much larger than few Ångströms then we can calculate the intensity of the electrons emitted from the depth 𝑑 by following integral: ∫ 𝑑𝐼 𝑑 0 = ∫ 𝛼exp(− 𝑧 𝜆sin𝜃 )𝑑𝑧 𝑑 0 , (2.9) 56 where 𝛼 is a coefficient depending on photoemission crosssection incident X-ray flux, angle between photoelectron path and analyzer sample axis and others. The Beer- Lambert relationship is then used to determine the intensity of electrons 𝐼𝑑 emitted from all depths greater than 𝑑 in a direction normal to the surface. The electrons that can leave the surface without losing energy and contribute to the peaks in the spectra are those that originate within tens of Ångströms below the solid surfaces. The remaining electrons that undergo inelastic processes, suffer energy loss, and either contribute to secondary emission or enhance the spectral background. This is the primary cause of the XPS method's high surface sensitivity. Fig.2.12: The electron mean free path versus their kinetic energy for variety of metals [94]. As indicated in Fig. 2.13a and 2.13b, XPS measurements were taken for the present dissertation using the UHV (ultra-high vacuum) equipment at the Faculty of Chemistry, MCSU in Lublin, Poland. Firstly, the sample is introduced through a prechamber that is in contact with the outside environment. This prechamber is closed and pumped to low vacuum. The sample is then placed into the main chamber, which has an ultra-high vacuum environment. Ultra-high vacuum (10−9 mbar) was maintained throughout the analytical process to ensure the photoelectrons traveled the farthest 57 distance feasible along their mean path and to prevent contamination of the sample surface. Fluids and other outgassing materials cannot be examined under low pressure in ultra-high vacuum, making them unsuitable for XPS characterization. An X-ray beam is used to irradiate the sample's surface. By reflecting from a bent quartz crystal, X-rays can be efficiently monochromatized to create so-called monochromatic X-ray sources. Monochromatic X-rays have the advantage of having a narrower natural beam width than the unfiltered X-ray line, which enhances the resolution of the photoelectric peaks in the XPS spectra. Electrostatic transfer lens transport the photoelectrons from the X-ray-excited material to the electrostatic hemispherical mirror analyzer. An electron detector, a hemispherical deflector with entrance and exit slits, and a multi-element electrostatic input lens make up a traditional hemispherical analyzer. The deflector, which has two concentric hemispheres (of radius 𝑅1 and 𝑅2), is the analyzer's main component. These hemispheres are maintained at a potential difference of 𝛥𝑉 when the constant analyzer energy mode is used. The functions of the electrostatic lens is deceleration and focusing the photoelectrons onto the entrance slit. Electrons entering the analyzer with an energy 𝐸0 and a radius 𝑅0 = (𝑅1 + 𝑅2)/2 , follow a circular path with constant radius. This energy 𝐸0 is defined as the pass energy. The chosen pass energy and the analyzer's size determine the potentials applied to the inner and outer hemispheres. On the end of the analyzer the electrons hit the electron detector, and their energy is measured. We can efficiently record the photoemission intensity versus the photoelectron kinetic energy by scanning the lens retarding potential. In this work, XPS method was used to study experimentally influence of changes in chemical composition induced by ion irradiation on mixing amount of TiO2/SiO2 systems as function of ion energy. XPS spectra were recorded in the energy range of 450 eV - 462 eV, this energy range represents the binding energy of the electrons Ti 2p. 58 Fig. 2.13. UHV ultra-high vacuum system in Faculty of Chemistry, MCSU in Lublin, Poland (a), and the simplified schematic (b) [96]. The Thermo Scientific equipped with a monochromatic Al K radiation source (E = 1486.6 eV). Al anodes was used because of a dominant, strong resonance in the X- ray spectrum. For the Al X-ray, a doublet arises from the 2p1/2, 2p3/2 → 1s electronic relaxation. These are so called Kα1,2 lines. The analyser was operated in the CAE mode with a pass energy of 20 eV. This method provides detection limits to ~ 0.1% atomic, is very surface sensitive (top <10 nm) and gives chemical bonding information. a) b) 59 CHAPTER 3 RESULTS AND DISCUSSION 3.1. Influence of ion energy and mass on mixing of TiO2/SiO2 structures with different thickness In this section, variation in structural properties TiO2/SiO2/Si systems induced by noble gas ion irradiation will be investigated using RBS method. The mixing process at the TiO2/SiO2 interface is described by shifting of borders associated to elements in RBS spectra. Mixing amount and direction are determined by changes in thickness of TiO2 and TiO2/SiO2 transition layers. The mixing behavior will be investigated as a function of energy and mass of the incident ions for different thicknesses of TiO2 and SiO2 thin films. 3.1.1. Characterization of samples and the mixing process. Regarding modification of the irradiated TiO2/SiO2/Si structures, the RBS spectra of the thinner-layer samples (group 1) irradiated with Kr+ ions of 100, 150, 200, and 250 keV as well as that of the virgin one are shown in Fig. 3.1 as an example. The distribution of elemental concentrations inside a sample can be seen in the RBS spectrum, which expresses the yield of backscattered ions as a function of their energy. In a brief, the peaks whose position and width in corresponding RBS spectrum correlate to the element species and location (in depth profile) inside the sample are used to represent the presence of elements. In Fig. 3.1, vertical arrows pointing to the high-energy edges of the corresponding peaks (also known as kinetic borders) at 530 and 1100 keV, respectively, denote the presence of O and Ti at the near surface layer of the examined TiO2/SiO2/Si samples. The high-energy edge positions of O and Ti are not significantly affected by the angle between the incident ion beam and the samples since the scattering interactions take place at the near surface layers. Actually, the detector-limited resolution is the only factor contributing to the expansion of these high-energy edges. These edges are shifted in accordance with the change in incidence ion angle when incident ions 60 interact with atoms in subsurface layers. Meanwhile, the shape of the corresponding low- energy edges depends strongly on energy straggling and film thickness. In Fig. 3.1, inclined arrows at the energy boundaries of 770 and 830 keV, respectively, indicate the presence of Si in the substrate and SiO2 layers. He+ ions backscattered from O in both the TiO2 and SiO2 layers are shown by the band having an energy between 370 and 530 keV. Whereas, a vertical arrow pointing to the high-energy edges of the corresponding peaks at about 1225 keV indicates the presence of Kr atoms in the irradiated samples. O and Si concentrations dropped as a result of the implantation of Kr+ ions, and this was associated by a significant decline in the yields of backscattered He+ ions with energies roughly equal to 485 and 800 keV for O and Si, respectively. Clearly, the RBS spectrum of non-irradiated TiO2/SiO2 sample lacked a Kr peak. In the meantime, the Kr peaks of the irradiated samples shifted as the ion energy increased. This shift can be partially attributable to variations in the Kr distribution, which also affect TiO2 and SiO2 layer thicknesses and the degree of mixing between these materials. 300 400 500 600 700 800 900 1000 1100 1200 1300 0.0 5.0x103 1.0x104 1.5x104 Kr+ => TiO2/SiO2/Si E He+ = 1500 keV 600 1700 Ti Y ie ld [ c o u n ts ] Channel number Virgin 100 keV 150 keV 200 keV 250 keV Kr Si SiO2 layer Si Si substrate O 400 600 800 1000 1200 Energy [keV] Fig.3.1. The RBS spectra that were collected from the thinner-layer samples (group 1) un-implanted and implanted with Kr+ ions at different energies. 61 For better understanding in structure of the TiO2/SiO2/Si irradiated material, the elemental depth profiles (also called the RBS profiles) from the experimental RBS spectra were determined using the SIMNRA code. Fig. 3.2 provides an illustration of the most instructive portion of the RBS profile for the sample implanted with 250-keV Kr+. With the 1.5-MeV He+ ion beam, all the RBS profiles were produced with an accessible depth of up to about 609 nm and an accuracy of 0.1% for the Ti. It should be emphasized that the SIMNRA calculations made use of the assumption that material layers were homogeneous. The structure of the sample material can thus be inferred from the RBS profiles, which show the relative atomic concentrations throughout the depth of the sample. In the case of 250-keV Kr+ implantation, the sample structure is formed by Si substrate; SiO2, TiO2 layers and a transition area between them (the latter is highlighted by gray in Fig. 3.2). Based on the 1:2 ratios between Ti-O and Si-O concentrations, the individual TiO2 and SiO2 layers are identified. Si and O concentrations reduced in the deep region from 205 to 410 atoms/cm2, but the Si:O ratio remained constant at 1:2. This fact is interpreted by the presence of Kr atoms (green triangles) in the irradiated material. 0 200 400 600 800 0.0 0.2 0.4 0.6 0.8 1.0 Si A to m ic c o n c e n tr a ti o n [ a t. % ] Depth [*1015*atoms/cm2] O Si Ti Kr TiO2 T ra n s it io n l a y e r SiO2 1 5 n m Fig.3.2. The most informative part of the RBS depth profiles for 250-Kr+ implanted TiO2/SiO2/Si sample. In standard international units, the thickness of the transition layer determined from the RBS depth profile is 15 nm. 62 The transition layer is recognized due to the fact that, in this region, the concentration of Ti (blue triangles) decreases and that of Si (red circle) increases with depth. High concentration of Si was found for both un-irradiated and irradiated samples. This refers to diffusion of the Si from SiO2 layer towards sample surface during fabrication process. Means that the transition layer was form even before ion irradiation. Using an atomic density 5.13x1022 predicted by SRIM code, thickness of the transition layer for the virgin sample equal 9.7 nm, it broadens to 15.0 nm after implanted by 250- keV Kr+ ions. This fact, together with variation in TiO2 layer thickness, dedicates the approaches for mixing characterization that will be discussed in the next sections. Based on SRIM simulation, the element displacement distribution showing in Fig. 3.3 confirms the variations in the TiO2/SiO2 transition layer found by RBS, in which the transition layer is likewise indicated in gray. Since Kr+ ions have low energy (250 keV), the mixing process, which refers to the migration of displaced Ti or Si atoms across the SiO2 or TiO2 layers, is solely caused by ballistic effects. The latter implies