Combinatorial Thin-Film Research Laboratory (CTRL) http://web.mse.ncku.edu.tw/~ctrl/ Course Handouts 1 Week Mon. Tue. 1. 9/12 (RBS) 9/13 (RBS) 2. 9/19 (SIMS) 9/20 (SIMS) 3. 9/26 (IR) 9/27 (IR) 4. 10/3(IR) 10/4 (IR/Raman) 5. 10/10 (holiday) 10/11 (Raman) 6. 10/17 (Raman) 10/18 (exam) Note 1. Microstructural Characterization of Materials, David Brandon and Wayne D. Kaplan, 2nd edition. 2. Principles of Instrumental Analysis, Douglas A. Skoog, F. James Holler, Stanley R. Grouch, 6th edition. 3. Semiconductor Material and Device Characterization, Dieter K. Schroder, 2nd edition. 2 Spectroscopy • Spectroscopy is the study of the interaction between matter and radiated energy. • Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a prism. ⇒ Later the concept was expanded greatly to comprise any interaction with radiant energy as a function of its wavelength or frequency. http://jtgnew.sjrdesign.net/exploration_obs erve_spectroscopy.html • Spectroscopic data is often represented by a spectrum, a plot of 3 the response of interest as a function of wavelength or frequency. Types of radiant energy A. Electromagnetic radiation was the first source of energy used for spectroscopic studies. ⇒ typically classified by the wavelength region of the spectrum, including radio, microwave, terahertz, infrared, near infrared, visible, and ultraviolet, x-ray and gamma spectroscopy. http://mail.colonial.net/~hkaiter/electromagspectrum.html B. Particles, due to their de Broglie wavelength, can also be a source of radiant energy and both electrons and neutrons are commonly (de Broglie wavelength λ = h/p) used. ⇒ For a particle, its kinetic energy determines its wavelength. 4 λ = c/ν In quantum mechanics: photons ⇒ de Broglie waves (matter wave) reflects the wave–particle duality of matter. ⇒ The theory was proposed by Louis de Broglie in 1924 in his PhD thesis. 1. De Broglie first used Einstein's famous equation relating matter and energy: E = mc2 (Particle properties) E= energy, m = mass, c = speed of light 2. Using Planck's theory which states every quantum of a wave has a discrete amount of energy given by Planck's equation: E = hν (wave properties) E = energy, h = Plank's constant (6.62607 x 10-34 J s), ν = frequency http://chemwiki.ucdavis.edu/Physical_Chemistry/Quantum_Mechanics/Qua ntum_Theory/De_Broglie_Wavelength 5 3. Since de Broglie believes particles and wave have the same traits, the two energies would be the same: mc2 = hν 4. Because real particles do not travel at the speed of light, De Broglie substituted v, velocity, for c, the speed of light. mv2 = hν 5. Through the equation λ , de Broglie substituted v/λ for ν and arrived at the final expression that relates wavelength and particle with speed. mv2 = hv/λ λ = hv/mv2 = h/mv = h/p ⇒ The de Broglie relations show that the wavelength is inversely proportional to the momentum of a particle and is also called de Broglie wavelength. 6 C. Acoustic spectroscopy involves radiated pressure waves. • How acoustic energy loss changes as a function of frequency. • The loss is dependent on the microstructure of the material. • To estimate the concentration and particle size distribution. 7 Nature of the interaction • Types of spectroscopy can also be distinguished by the nature of the interaction between the energy and the material. 1. Absorption: when energy from the radiant source is absorbed by the material. It is a process. ⇒ Absorption is often determined by measuring the fraction of energy transmitted through the material; absorption will decrease the transmitted portion. • Absorbance is a quantitative measure expressed as a logarithmic ratio between the radiation falling upon a material and the radiation transmitted through a material. A = log P0 P P %T = x 100 % P0 P0: incident beam power P: transmitted or reflected beam power T: transmittance 8 Photon absorptance: ⇒ The fraction of electron–hole (e-/h+) pairs generated per incident photon flux (ηe-/h+ ) ⇒ The assumption is that the number of e-/h+ pairs generated equals the number of photons absorbed. photons absorbed p P0 - p = 1 - 10-A ηe-/h+ = = 1P0 P0 εt∂ P0 Absorbance A = log P P0: incident beam P: transmitted or reflected beam Transmittance %T = P x 100 % P0 9 2. Emission indicates that radiant energy is released by the material. ⇒ A material's blackbody spectrum is a spontaneous emission spectrum determined by its temperature. • The emissivity of a material (ε): the relative ability of its surface to emit energy by radiation. ⇒ It is the ratio of energy radiated by a particular material to energy radiated by a black body at the same temperature. ⇒ A true black body would have an ε = 1 while any real object would have ε < 1. • Emissivity is a dimensionless quantity. Kirchhoff's law states: For an arbitrary body emitting and absorbing thermal radiation in thermodynamic equilibrium, the emissivity is equal to the absorptivity (A = αbc). 3. Elastic scattering and reflection spectroscopy determine how incident radiation is reflected or scattered by a material. ⇒ Crystallography employs the scattering of high energy radiation, such as x-rays and electrons, to examine the arrangement of 10 atoms in proteins and solid crystals. 4. Inelastic scattering phenomena involve an exchange of energy between the radiation and the matter that shifts the wavelength Atoms/molecules of the scattered radiation. ⇒ These include Raman and Compton scattering. • Compton scattering is an inelastic scattering of an incident photon by a free charged particle, usually an electron. ⇒ Result in a decrease in energy of the photon. 5. Impedance spectroscopy studies the ability of a medium to impede or slow the transmittance of energy. ⇒ For optical applications, this is characterized by the index of refraction (n) and extinction coefficient (k). 6. Coherent or resonance spectroscopy are techniques where the radiant energy couples two quantum states of the material in a coherent interaction that is sustained by the radiating field. ⇒ Nuclear magnetic resonance (NMR) spectroscopy is a widely used resonance method and ultrafast laser methods are also now possible in the infrared and visible spectral regions. 11 Advanced Characterization Tools (TEM, SEM, …) (RBS, SIMS, …) Beam Typical x-y resolution capabilities 12 Electron Beam Techniques 13 Ion Beam Techniques 14 Optical Characterization Techniques 15 ION BEAM TECHNIQUES 1. Rutherford Backscattering Spectrometry (RBS) • Institute of Physics Academia Sinica • Nuclear Science & Tech. Development Center/NTHU F. Ernst • Institute of Nuclear Energy Research (INER), Atomic Energy Council (AEC), Taiwan. (行政院原子能委員會核能所) 16 • Ernest Rutherford (1871 – 1937) was a New Zealand-born British chemist and physicist who became known as the father of nuclear physics. • Experiments by Rutherford and his students in the early 1900s proved the existence of nuclei and scattering from these nuclei. • Rutherford backscattering spectrometry is based on backscattering of ions incident on a sample. It is quantitative without recourse to calibrated standards. • RBS can provide absolute quantitative analysis of elemental composition with an accuracy of about 5%. • RBS is based on bombarding a sample with energetic ions—typically He ions of 1 to 3 MeV energy—and measuring the energy of the backscattered He ions. ⇒ allows determination of the masses of the elements in a sample, their depth distribution over distances from 10 nm to a few microns from the surface, their areal density, and the crystalline 17 structure. • With RBS, it is possible to determine atomic masses and elemental concentrations as a function of depth below the surface. • RBS can provide depth-profile information from surface layers. ⇒ The penetration depth of 2 MeV He ions is about 10 μm in silicon and 3 μm in gold. (μm range) ⇒ Beam diameters are commonly around 1 to 2 mm but microbeam backscattering with beam diameters as small as 1 μm is possible. • However, the high-energy beam can damage the surface. This is particularly a problem with insulating materials, such as polymers, alkali halides, and oxides. 18 • The use of ion backscattering as a quantitative materials analysis tool depends on an accurate knowledge of well known nuclear and the atomic scattering processes. • Ions of mass M1, atomic number Z1, energy E0, and velocity v0 are incident on a solid sample or target composed of atoms of mass M2 and atomic number Z2. Z2 Z1 (He2+) 19 Mechanism • Most of the incident ions come to rest within the solid, losing their energy through interactions with valence electrons. ⇒ The incident ions lose energy traversing the sample until they experience a scattering event and then lose energy again as they travel back to the surface, leaving the sample with reduced energy. ⇒ A small fraction—around 10−6 of the number of incident ions— undergoes elastic collisions and is backscattered from the sample at various angles. • After scattering, atom M2 has energy E2 and velocity v2 and ion M1 has energy E1 and velocity v1. (He2+) Z2 ⇒ Conservation of energy gives Z1 20 • Conservation of momentum in the directions parallel and perpendicular to the incidence direction gives // ⊥ 1. Eliminating φ and v2 2. Taking the ratio E1/E0 = (M1v12/2)/(M1v02/2) ⇒ gives the kinematic factor K • The key RBS equation. 21 R = M1/M2; θ: the scattering angle. • The approximation holds for R << 1 and θ close to 180°. sinθ ≈ 0 cos2θ ≈ 1 1+2Rcosθ+R2+(2R-2R) (1+Rcosθ)2 1+2Rcosθ+R2cos2θ = = 2 2 (1+R) (1+R)2 (1+R) (1+R)2-2R(1-cosθ) = (1+R)2 2R(1-cosθ) = 1(1+R)2 22 • The scattering angle should be as large as possible and angles around 170° are commonly used. • The unknown mass M2 is calculated from the measured energy E1 through the kinematic factor. measured R = M1/M2; θ: the scattering angle. M2: can then be calculated • The kinematic factor is a measure of the primary ion energy loss. 23 Instrumentation • An RBS system consists of an evacuated chamber containing the He ion generator, the accelerator, the sample, and the detector. • Negative He (He-) ions are generated in the ion accelerator at close to ground potential. In a tandem accelerator, these ions are http://www.mrsec.harvard.edu/cams/RBS.html accelerated to 1 MeV, traversing a gas-filled tube or “stripper canal,” where either two or three electrons are stripped from the He− to form He+ or He2+, respectively. ⇒ These ions with energies of around 1 MeV are accelerated a second time to ground potential at which point the He+ ions have 24 2+ 2 MeV and the He ions have 3 MeV energy. He ion generators (1) 1. A single ended accelerator (more efficient => more popular) 25 http://www.eaglabs.com/mc/rbs-focusing-elements.html#next 2. Tandem accelerator He ion generators (2) N2 Stripper (+ terminal) He20~30 keV Rubidium Tandem • Negative helium ions • Helium: inert, must overcome • The charge exchange process is this natural tendency of helium inefficient; 1 mA of He+ leads to form negative ions. to 1 µA of He-. • Two stages: • Injected into the tandem (1) positive ions are produced as accelerator at 20 to 30 keV. described earlier. • A magnetic field separates any He-, (2) An hot alkali metal vapor He, or He+ from the He2+ beam. (Rubidium (Rb)) channel 26 converts He+ into He-. The sample position • The sample is mounted on a goniometer for precise sample-beam alignment or channeling measurements. Detector • The pulse height, proportional to the incident energy, is detected by a pulse height or multichannel analyzer that stores pulses of a given magnitude in a given voltage bin or channel. • The spectrum is displayed as yield or counts versus channel number, with channel number proportional to energy. • The energy resolution of Si detectors, set by statistical fluctuations, is around 10 to 20 keV for typical RBS energies. • RBS runs take 15–30 min. 27 Channel • A multi channel analyser • The signal height is proportional to the energy • Converted into 512 channels ranging from 0 to 2 MeV. Backscattering yield (counts/channel) • In each channel those events are collected which have a specific energy of the recoiled He+ ions. 28 http://www.nat.vu.nl/CondMat/rector/rbs_analysis1.htm Si Examples RBS Spectrum X-axis: Mass and depth • Fig. 11.26(a) consists of a silicon substrate with a very thin film of nitrogen, silver, and gold. • Since N, Ag, and Au are only at the surface in this example, RBS signals from these elements have narrow spectral distributions confirmed by experimental data. • The thick Si substrate has a characteristic slope with the yield 29 increasing at lower energies due to scattering within the target. • Two important properties of RBS plots N7 Si14 Ag47 Au79 The RBS yield increases with element atomic number and the RBS signal of elements lighter than the substrate rides on the matrix background while heavier elements are displayed by themselves. ⇒ This makes the nitrogen signal more difficult to detect because it rides on the Si signal. • The Si background count represents the “noise” and the signal-to -noise ratio is degraded compared to heavy elements on a light matrix. • Plural scattering results in an yield increase at low energies. 30 substrate Si Dr. Matej Mayer Max-Planck-Institut Fuer Palsmaphysik EURATOM Association Garching, Germany 31 0.01% 0.14% • The yield increases with increasing atomic number leading to 2+ He higher RBS sensitivity for high-Z elements. R = M1/M2 ⇒ However, due to the kinematics of scattering, high-mass elements are more difficult to distinguish from one another 32 than low-mass elements. ⇒ The atomic weight and calculated R, K, and E1 in Table 11.2 are for θ = 170° and incident helium ions (M1 = 4) with E0 = 2.5 MeV. ⇒ Helium ions have energies of 0.78, 1.41, 2.16 and 2.31 MeV after scattering from the N, Si, Ag, and Au atoms at the sample surface. measured (m1/m2) (E1/E0) unknown measured 33 2.31 MeV (Very thin layer of Au) 2.31 MeV (some thicknesses of Au) Schematic spectrum for a Au film on Si. “A” is the area under the curve • RBS plots are more complicated for layers of finite thicknesses. • In Fig. 11.26(b), we consider a gold film of thickness d on a silicon substrate. ⇒ The He ions are backscattered from surface gold atoms with E1,Au = 2.31 MeV as in Fig. 11.26(a). 34 2.31 MeV 2.31 MeV Schematic spectrum for a Au film on Si. “A” is the area under the curve ⇒ However, those ions backscattered from deeper within the Au film emerge with lower energies, due to additional losses within the film. ⇒ These losses come from Coulombic interactions between helium ions and electrons. 35 ∆Ein (E0 − ∆Ein) (1-KAu) 2.31 MeV ∆Eout Si Au 2.31 MeV Thickness Measurement theory • Consider a scattering event from those Au atoms at the Si-Au interface at x = t . The He ion loses energy ∆Ein traveling through the Au film before the scattering event at the back gold surface. • Upon scattering, it loses additional energy (E0 − ∆Ein) (1-KAu). - (E0 − ∆Ein) KAu Coming in energy Going out energy (E0 − ∆Ein) = (E0 − ∆Ein) (1-KAu) 36 ∴ Another interpretation E0 = E1 + ∆E 1 - K = 1- E1/E0 = (E0- E1)/E0 = ∆E/E0 Energy loss due to scattering = (E0 − ∆Ein) (1-KAu) 37 ∆Ein (E0 − ∆Ein) (1-KAu) 2.31 MeV ∆Eout Si Au 2.31 MeV • To reach the detector it must traverse the film a second time, losing energy ∆Eout. • The total energy loss is the sum of these three losses. ∆E = ∆Ein + (E0 − ∆Ein) (1-KAu) + ∆Eout 38 ∆Ein (E0 − ∆Ein) (1-KAu) • The energy of He ions scattered from the sample at depth d is ∆E = ∆Ein + (E0 − ∆Ein) (1-KAu) + E1(d) = E0 - [ ∆Ein ∆Eout ∆Eout 2.31 MeV + (E0 − ∆Ein) (1-KAu) + ∆Eout ] • The energy difference of the ions backscattered from the surface and from the interface E can be related to the film thickness d ∆E = E0KAu - [ (E0 − ∆Ein) KAu surface ∆Eout ] depth d [S0](eV/Å): the backscattering energy loss factor [S0] = 133.6 eV/Å for gold films with a 2 MeV beam energy. 39 The backscattering yield A • The backscattering yield A, also designated as the total number of detected ions or counts. (density) Q σ σ = average scattering cross-section in cm2/steradian (sr) N scatterers blocking area A = Ω(sr) Q(#ions) (σ(cm /sr) NS(atoms/cm )) 2 sr #ions cm2/sr atoms/cm2 2 40 • The backscattering yield A, also designated as the total number of detected ions or counts N scatterers σ blocking area A = Ω Q (σ NS) Q (atoms/sr) • A: the area under the experimental yield-energy curve or the total number of detected He ions backscattered from the element of interest or the sum of the counts in each channel. σ = average scattering cross-section in cm2/steradian (sr), Ω = detector solid angle in steradians , Q = total number of ions incident on the sample, • Q is determined by the time integration of the current of charged particles incident on the target. Ns = sample atoms/cm2. = N * d for a thin film A steradian "cuts out" an area 41 of 3 (d: thickness, N is atoms/cm ). a sphere equal to (radius)2. Scattering Cross Section F. Ernst 42 • Piece of area dσ offered by the scatterer for scattering into a particular increment dΩ in solid angle σ Q • dσ varies with the location of dΩ, characterized by the scattering angle θ dσ(θ) A = QΩ (σNS) Differential scattering cross section dΩ • The differential scattering cross section, dσ/dΩ, of a target atom for scattering an incident particle through an angle θ into a differential solid angle dΩ centered about θ is given by A = Q dΩ dσ(θ) Ns dΩ ⇒ number of particles detected by the detector positioned at scattering angle θ. • dσ/dΩ needs to be known and are tabulated for all elements for He probe ions. 43 • Typical values of the differential scattering cross-section are (1 to 10) × 10−24 cm2/sr. • RBS: the detector solid angle ΩD is small: typically < 10−2 steradian. ⇒ an average differential cross section is used. • The average differential scattering cross-section (or scattering cross section) is Differential scattering cross section A = Ω Q (σ NS) 44 Average cross section • Derived by the conserved angular momentum under a central force. • High-energy particles penetrate up to the core of the target atom, so this force mainly corresponds to an unscreened Coulomb repulsion between the two positively charged nuclei. ⇒ Cross section (or average cross section) originally derived by Rutherford • The experiments by Geiger and Marsden in 1911–1913 verified the predictions that the amount of scattering was proportional to (sin4 θ/2)−1 and E−2. 45 • The RBS sensitivity can be enhanced by changing the differential scattering cross section by increasing the atomic number Z1 of the incident ion from He to C, for example, and/or decreasing the energy E of the incident ion from several MeV to hundreds of keV, known as heavy ion backscattering spectroscopy (HIBS). ⇒ Replacing 3 MeV 4He with 400 keV 12C increases the backscattering yield by a factor of 1000. ⇒ In contrast to conventional RBS with a sensitivity of around 1013 cm−2, HIBS can reduce that to the 109–1010 cm−2 range. 46 ⇒ In addition, the cross-section can be enhanced by using ion beams for which the elastic scattering is resonant. ⇒ ex. the resonance at 3.08 MeV for oxygen enhances the cross-section 25 times compared to its corresponding Rutherford cross-section. • The lower energy, heavier ions, however, have the potential of inducing surface sputter damage. 47 • In addition, they found that the number of elementary charges in the center of the atom is equal to roughly half the atomic weight. ⇒ This observation introduced the concept of the atomic number of an element, which describes the positive charge carried by the nucleus of the atom. • The very experiments that gave rise to the picture of an atom as a positively charged nucleus surrounded by orbiting electrons has now evolved into an important materials analysis technique. 48 Applications: How to measure an unknown impurity on a known substrate? 1. It may be difficult to determine Q accurately. 2. The detector solid angle (Ω) may change if the detector develops “dead” spots after prolonged exposure to energetic projectiles. Thin Solid Films 17, 1 (1973). A = Ω(sr) Q(#ions) (σ(cm /sr) NS(atoms/cm )) 2 2 An example: impurity Au on Si • A convenient feature of RBS analysis is that the number of impurity per cm2 can be determined without precise knowledge of Q and Ω. ⇒ This number is found by comparing the area Aimp of the impurity spectrum to the plateau height Hsi of the silicon spectrum. (impurity Au on Si) 49 atoms/cm2 AAu = σAuΩQ(Ns)Au HSi = σSiΩQNSi∆X = σSiΩQNSiδE/[S]Si atoms/cm3 N * d for a thin film (d: thickness, N is atoms/cm3). (dE = [S]dX) [S](eV/Å): the backscattering energy loss factor A: the total count (area) H: the plateau height (count/channel) of the spectrum ⇒ The plateau height HSi given in counts per channel is determined by the number of scattering events in an incremental target thickness ∆X. 50 AAu = σAuΩQ(Ns)Au HSi = σSiΩQNSiδE/[S]Si = σSiΩQNSi∆X AAu σx(Ns)Au AAuσSiNSiδE/[S]Si ⇒ (Ns)Au = = HSi σSiNSiδE/[S]Si σ H 2 Au Si (atoms/cm ) AAu σSiδE AAu σSiδE = = σAuHSi [S]Si σAuHSi [ε]Si NSi The backscattering stopping cross-section (ε) (atoms/cm3) • An incident ion loses most of its energy through interactions with electrons (i.e. due to electronic stopping), mainly by ionization and excitation of target electrons. • The energy loss per depth (dE/dx [eV/nm]) is given by the stopping cross section (ε): [ε] = [S]/N (dE = [S]dX) energy loss51factor N (atoms/cm3): 3-D density of the film = (dE/dx)/N ⇒ Typical values for the stopping cross-section (ε) lie in the 10 to 100 eV/(1015 atoms/cm2) range with [ε]Si = 49.3 eV/(1015 atoms/cm2) and [ε]Au = 115.5 eV/(1015 atoms/cm2) for 2 MeV He ions. (Ns)Au = AAu σSiδE HSi σAu [ε]Si • δE is determined by the detector and the electronic system: typically 2 to 5 keV. • To find the unknown density ((Ns)Au): Determine 1. RBS spectrum area (area of the peak Au) or counts 2. the plateau height of the Si spectrum ( HSi) 3. the two cross-sections ( σSi σAu ). 4. the Si stopping cross-section ([ε]Si). 52 Other Applications • Typical semiconductor applications include measurements of thickness, thickness uniformity, stoichiometry, nature, amount and distribution of impurities in thin films, such as silicides and Si- and Cu-doped Al. • The technique is also very useful to investigate the crystallinity of a sample. ⇒ Backscattering is strongly affected by the alignment of atoms in a single crystal sample with the incident He ion beam. If the atoms are well aligned with the beam, those He ions falling between atoms in the channels penetrate deeply into the sample and have a low probability of being backscattered. ⇒ Those He ions that encounter sample atoms “head-on” are scattered. 53 • The yield from a well-aligned single crystal sample can be two orders of magnitude less than that from a randomly aligned sample. ⇒ Channeling been extensively used to study ion implantation damage in semiconductors with the yield decreasing as the single crystal nature of an implanted sample is restored by annealing. Channeling http://teacher.blsh.tp.edu.tw/0412/RBS/RBS&channel.htm • RBS is particularly suited for heavy elements on light substrates, e.g., contacts to semiconductors. ⇒ extensively used in the study of such contacts. 54 Pt Si • Fig. 11.27 shows RBS spectra for platinum and platinum silicide on silicon. ⇒ Initially a Pt film is deposited on a Si substrate. The “no anneal” RBS spectrum clearly shows the Pt film. The Si signal is consistent with E1 taking into account the loss into and out of the Pt film. ⇒ As the film is heated, PtSi forms. ⇒ Note the formation from the Pt-Si interface indicated by the Pt yield decrease for that part of the film near the Si substrate. 55 • At the same time, the Si signal moves to higher energies, indicative of Si moving into the Pt film. • When stoichiometry is attained, the Pt signal is uniform, but reduced and the Si signal has risen. 56 Conclusions • A particular difficulty is the ambiguity of RBS spectra, because the horizontal axis is simultaneously a depth and a mass scale. • Through the use of tabulated constants, experimental techniques such as beam tilting, detector angle changes, and incident energy variations as well as good analytical reasoning, sample analysis is usually successful, but additional information may have to be provided to resolve ambiguities. • Computer programs are extensively used in spectrum analysis. • As with other physical and chemical characterization techniques, the more is known about the sample before the analysis, the less ambiguous are the results. • A comparison of RBS with SIMS is given by Magee. C.W. Magee, “Secondary Ion Mass Spectrometry and Its Relation to High-Energy Ion 57 Beam Analysis Techniques,” Nucl. Instrum. and Meth. 191, 297–307, Dec. 1981. What RBS can do? • Thickness • Crystallinity (Channeling) • Compositions • Impurities in Si • Heavier elements in Si • Heavier ion source and less energy: enhance sensitivity 58
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