Lecture 13. Surfaces

Transcription

1 Lecture 3 Surfaces 3. Thermodynamics 3. Surface Electronics Structures 3.3 Local Electronic Probes: Scanning Tunneling Microscopy (STM) 3.4 Photoemission Spectroscopy (XPS, UPS) - Principles; Interpretation; Instrumentation; Applications References: ) A. Zangwill, Physics at Surfaces, 988; Chapter -3 ) Kurt W. Kolasinski, Surface Science: Foundations of Catalysis and Nanoscience nd ed, 8; 3) John C. Vickerman, Surface Analysis - The Principal Techniques, 997; 4) D.P. Woodruff, T.A. Delchar, Modern Techniques of Surface Science. nd ed.; 994 D. Briggs, M.P. Seah, Practical Surface Analysis. 99; Vol.. 5) 6) Lecture 3 Surface Properties Structure Bonding properties Dynamics of surface processes Applications Semiconductor devices Catalysis Friction and lubrication (tribology) Sensors Electrochemistry Aspects of Solid Surfaces Chemical composition Kinetics (adsorption, diffusion, desorption) Probing Surface Properties atoms, molecules E-field atoms, molecules e - ions heat ions hν e - hν IR X-rays Course will primarily focus on: atomic structure and electronic properties, chemical composition and adsorption properties of surfaces But Many important aspects of surface properties can be understood from the point of view of macroscopic thermodynamics; the surface under equilibrium conditions (e.g., faceting, wetting, island growth) Lecture 3

2 3. Surface Thermodynamic Functions Similarly: Total Entropy Now, suppose a crystalline solid bounded by surfaces Total Energy # of atoms in solid Gibbs free energy (per unit area) Total free energy: S S = NS O + AS S U = NU O + AU surface area S S G = H + o G = NG + AG S TS S excess energy due to unit area for surface Surface thermodynamic values defined as excesses over the bulk values N.B.: Importance of Gibbs free energy: at equilibrium surface reactions, phase changes occur at constant T, P, where G = const dg = Lecture 3 3 In 3D system to create a volume: Similarly, to create a surface: Surface Energy δ W = P dv δ W S T,P = γ da γ is D analog of pressure: surface tension e.g., for D liquid film, infinite work done to create additional surface area da: Units of γ : ev/surface atom erg/cm Joules/m δ W =F dx=γ ldx dynes/cm Newtons /m Note: work of crystal cleavage proportional to γ da Lecture 3 4

3 U du = S V, N, A = TdS PdV + µ dn + A Thermodynamics of Surfaces U ds + V S, N, A i, j U dv + N σ dε i, j γ is independent of small strains only for liquids More generally we must consider the expression (cf. Zangwill, p.): j i dγ σ ij = γδij + dε For liquid or solid under small strain: σ = γ S r W In solids it is convenient to denote γ as γ i, or γ ( n) = lim ( A ) A Note: γ = G S specific free surface energy of one component system i, j ij (.) T S, V, A γ is always positive! dn + A i, j U V S, V, N dε i, j σ i,j and ε i,j surf. stress and strain tensors Lecture 3 5 = Order of magnitude estimates of γ For metals: γ E coh Z Z S N Consider Cu() one surface atom: Z = (bulk), Z S = 3 (surface) S Broken surface bonds # atoms/cm nearest neighbor bonds Surface tension of selected solids and liquids ev 3 5 atom 5 ev γ = = atom cm cm 5 ev erg ergs.55.6 = 48 cm ev cm Lecture 3 6 3

4 Order of magnitude estimates of γ Covalent bonded system: diamond the simplest case of bond breaking C C bond strength ~ 3.9 ev/bond (bond strength in C H 6 ) From crystallography:.85 x 5 bonds/cm for () surface γ = ½ total bond energy γ = 565 ergs/cm ~ 5.65 J/m Lecture 3 7 Curves Surfaces For a bubble, surface tension counteracts internal pressure γ Pint Pext = r For curved surface of a solid, vapor pressure P r, depends on r Flat surface: Curved surface: Kelvin equation: r =, P = P O P γ V ln = P O RT r in( specific) Applied to important surface problems: melting point, nucleation and growth (e.g., ripening : r P int Pr γ = exp K important for r << Å P r O γ P ext t = t = For distribution of particles on surface, little ones disappear, large one grow Lecture 3 8 4

5 Contact Angle Measurements of γ for liquid: shape of drop determined by combination of γ and g (gravity) d max Contact angle γ L, γ S surface free energy of liquid (solid) γ SL interface energy or tension Surface tension exerts force along surface at line of intersection At equilibrium: γ L cos α = γ S γ SL (Young s eq.) γ S γ cosα = γ L Complete wetting Wetting No wetting SL γ S > (γ L + γ SL ) γ L < (γ S + γ SL ) < γ L γ SL > (γ L + γ S ) Lecture 3 9 Need to include structural information The surface energy or the surface tension of a planar solid surface depends on the crystallographic orientation of the sample Bulk energy < surface energy < step energy < kink or adatom energy from G.A Somorjai Chemistry in two dimensions: surfaces Lecture 3 5

6 Equilibrium Crystal Shape (ECS) In equilibrium, shape of a given amount of crystal minimizes the total surface energy For Liquids: spherical shape For Solids: Equilibrium Crystal Shape (ECS) has facets Dependence of ECS on degree of anisotropy: γ/γ < % nearly spherical ~ % - %: flats connected by curves ~ % - %: polyhedra with rounded > 3% polyhedra flats only Lecture 3 Terrace Ledge - Kink (TLK) Model also Solid on Solid (SOS) Model Typical surface sites and defects on a simple cubic () surface (6 N.N. in bulk) From Somorjai To form vacancy in terrace and move atom to kink, break 5 bonds, remake 3 G = W W N N surf V K T G = exp kt At high T, get surface roughening as vacancies interact V V Lecture 3 6

7 3. Surface Electronic Structure Often surface termination is not bulk-like There are atom shifts or to surface These surface region extends several atom layer deep Rationale for metals: Smoluchowski smoothing of surface electron charge; dipole formation Lecture 3 3 Bulk Truncated Structures Lecture 3 4 7

8 3.3 Scanning Tunneling Microscopy (STM) STM used for direct determination of images of surface, with atomic resolution. Method is based on electron tunneling between tip and surface Was developed by G.Binnig and H. Rohrer (IBM) in early 98 Nobel prize in Physics (986) Scanning Tunneling Spectroscopy (W. Ho, Cornell) STM tip made from Pt-Ir alloy chemical etching) Get structural information by scanning tip across surface in constant height or constant current modes Tersoff and Hamann developed a simple theory of STM: the tunneling current I I ~ V ρ tip ρ sample, where V - voltage applied, Lecture 3 ρtip andρ sample are the density states of the tip and sample 5 Piezoelectric Scanners PZT (PbxZr-xTiO4) lead zirconate titanate Scanners are made from a piezoelectric material that expands and contracts proportionally to an applied voltage V No applied voltage +V -V Extended Lecture 3 Contracted 6 8

9 Tunneling current between biased tip-sample Negative sample bias: e s below E f tunnel to tip Probability of finding e s on the other side of the barrier: ψ () exp m( U E) w h Tunneling current scales exponentially with barrier width e s in the sample with energy within E sf -ev to E sf tunnel into the tip above its E tf to E tf +ev. This tunneling of e s will be measured by the circuit connecting the tip and sample Lecture 3 and used as the feedback parameter 7 STM image Si() (7x7) Probing atoms in real space Phys.Rev. B 7, 733 (4) Advantages: atomic resolution on the surface, spectroscopic studies for a single atom are possible Disadvantages: conductive samples, often need UHV, good vibration isolation is critical Lecture 3 8 9

10 3.4 Photoemission Spectroscopy: Principles Electrons absorb X-ray photon and are ejected from atom Energy balance: Photon energy Kinetic Energy = Binding Energy hν KE = BE Photoemission Auger Decay Spectrum Kinetic energy distribution of photoemitted electrons Different orbitals give different peaks in spectrum Peak intensities depend on photoionization cross section (largest for C s) Extra peak: Auger emission Lecture 3 9 Photoemission Spectroscopy: Basics Electrons from the sample surface: d x I( d) = K exp dx λ cosθ Fraction of signal from various depth in term of λ Depth Λ λ 3λ I ( λ) = I ( ) Equation λ I (λ) = I ( ) I (3λ) = I ( ) x exp dx λ cosθ x exp dx λ cosθ λ λ x exp dx λ cosθ x exp dx λ cosθ x exp dx λ cosθ x exp dx λ cosθ Fraction of signal ( θ= ) C. J. Powell, A. Jablonski, S. Tanuma, et al. J. Electron Spectrosc. Relat. Phenom, 68, P. 65 (994). D. F. Mitchell, K. B. Clark, W. N. Lennard, et al. Lecture, Surf. 3 Interface Anal., P. 44 (994).

11 Photoemission Spectroscopy: Instrumentation X-ray source X-ray lines Line Energy, ev Width, ev Ti L α Cu L α Mg K α Al K α Ti K α 45.. How to choose the material for a soft X-ray source:. The line width must not limit the energy resolution. The characteristic X-ray energy is enough to eject core electrons for an unambiguous analysis 3. The photoionization cross sections Lecture 3 Instrumentation Essential components: Sample: usually cm X-ray source: Al ev;mg 56.6 ev Electron Energy Analyzer: mm radius concentric hemispherical analyzer; vary voltages to vary pass energy. Detector: electron multiplier (channeltron) Electronics, Computer Note: All in ultrahigh vacuum (< -8 Torr) (< - atm) State-of-the-art small spot ESCA: 5 µm spot size Lecture 3

12 Typical XPS spectrum BE= hν- KE Lecture 3 3 X-ray and spectroscopic notations Principle quantum number: n =,, 3, Orbital quantum number: l =,,,, (n-) Spin quantum number: s = ± ½ Total angular momentum: j = l +s = /, 3 /, 5 / Spin-orbit split doublets Subshell s p d f j values / ½; 3/ 3/; 5/ 5/; 7/ Area ratio - : : 3 3: 4 Quantum numbers n l Etc. j / / / 3/ / / 3/ 3/ 5/ X-ray suffix Etc. X-ray level 3p / Lecture 3 4 K L L L 3 M M M 3 M 4 M 5 Etc. Spectroscopic Level s / s / p / p 3/ 3s / 3p 3/ 3d 3/ 3d 5/ Etc.

13 Binding energy reference in XPS Energy level diagram for an electrically conductive sample grounded to the spectrometer common to calibrate the spectrometer by the photoelectron peaks of Au 4f 7/, Ag 3d 5/ or Cu p 3/ the Fermi levels of the sample and the spectrometer are aligned; KE of the photoelectrons is measured from the E F of the spectrometer. Lecture 3 5 Typical spectral features Associate binding energies with orbital energies, BUT USE CAUTION! Energy conservation: E i (N) + h ν = E f (N-) + KE h ν KE = E f (N-, k) E i (N) = E B Binding energy is more properly associated with ionization energy. In HF approach, Koopmans Theorem: E B = E k (orbital energy of k th level) Formally correct within HF. Wrong when correlation effects are included. ALSO: Photoexcitation is rapid event sudden approximation Gives rise to chemical shifts and plasmon peaks Lecture 3 6 3

14 Qualitative results A: Identify element B: Chemical shifts of core levels: Consider core levels of the same element in different chemical states: E B = E B () E B () = E K () E K () Often correct to associate E B with change in local electrostatic potential due to change in electron density associated with chemical bonding ( initial state effects ). Peak Width: Lecture Peak Identification: Core level binding energies Lecture 3 8 4

15 Quantification of XPS Primary assumption for quantitative analysis: ionization probability (photoemission cross section) of a core level is nearly independent of valence state for a given element intensity number of atoms in detection volume π π I A = σ A(hω) D( EA) LA( γ ) J ( x, y) T ( x, y, γ, ϕ, EA) N γ = ϕ= x, y where: σ A = photoionization cross section D(E A ) = detection efficiency of spectrometer at E A L A (γ) = angular asymmetry of photoemission intensity γ = angle between incident X-rays and detector J (x,y) = flux of primary photons into surface at point (x,y) T = analyzer transmission φ = azimuthal angle N A (x,y,z) = density of A atoms at (x,y,z) λ M = electron attenuation length of e s with energy E A in matrix M θ = detection angle (between sample normal and spectrometer) x A z ( x, y, z)exp dxdydzdγdθ λ cosθ Lecture 3 9 Quantitative analysis For small entrance aperture (fixed φ, γ) and uniform illuminated sample: I A = σ A( hω) D( EA) LA( γ i ) J N AλM ( EA)cosθiG( EA) Angles γ i and θ i are fixed by the sample geometry and G( E ) G(E A )=product of area analyzed and analyzer transmission function A = x, y T ( x, y, E ) dxdy A D(E A )=const for spectrometers Operating at fixed pass energy σ A : well described by Scofield Calculation of cross-section Lecture 3 3 5

16 Comparison XPS and UPS XPS: photon energy hν=- ev to probe core-levels (to identify elements and their chemical states). UPS: photon energy hν=-45 ev to probe filled electron states in valence band or adsorbed molecules on metal. Angle resolved UPS can be used to map band structure. UPS source of irradiation: He discharging lamp (two strong lines at. ev and 4.4 ev, termed He I and He II) with narrow line width and high flux A synchrotron radiation source. Introduction to Photoemission Spectroscopy Lecture in solids, 3 by F. Boscherini 3 Surface Science Western - XPS Kratos Axis Ultra (left) Axis Nova (right) Contact: Mark Biesinger biesingr@uwo.ca Lecture 3 3 6