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Optical properties and Interaction of radiation with matter S.Nannarone TASC INFM-CNR & University of Modena Outline •Elements of Classical description of E.M. field propagation in absorbing/ polarizable media Dielectric function •Quantum mechanics microscopic treatment of absorption and emission and connection with dielectric function Physics related to a wide class of Photon-in Photon-out experiments including Absorption, Reflectivity, Diffuse scattering, Luminescence and Fluorescence or radiation-matter interaction [some experimental arrangements and results, mainly in connection with the BEAR beamline at Elettra http://new.tasc.infm.it/research/bear/] Systems •bulk materials the whole space is occupied by matter •Surfaces matter occupies a semi-space, properties of the vacuum matter interface on top of a semi-infinite bulk •Interfaces transition region between two different semiinfinite materials Information [see mainly following lectures] •Electronic properties full and empty states, valence and core states, localized and delocalized states •Local atomic geometry /Morphology electronic states – atomic geometry different faces of the same coin Energy range Visible, Vacuum Ultraviolet, Soft X-rays) Synchrotron and laboratory sources/LAB Conceptually Shining light on a system, detecting the products and measuring effects of this interaction This can be done by Laboratory sources They cover in principle the whole energy range nowadays covered by synchrotrons (J.A.R.Samson Techniques of vacuum ultraviolet spectroscopy) •Incandescent sources •Gas discharge •X-ray e- bombardment line emission •Bremsstrahlung continuous emission sources •Higher harmonic source Synchrotron and laboratory sources / Synchrotron Some well known features •Collimation •Intrinsic linear and circular polarization •Time structure (typically 01-1 ns length, 1 MHz-05GHz repetition rate) •Continuous spectrum, high energy access to core levels • Reliable calculability of absolute intensity •Emission in clean vacuum, no gas or sputtered materials •High brilliance unprecedented energy resolution • High brilliance small spot Spectromicroscopy “The one important complication of synchrotron source is, however, that while laboratory sources are small appendices to the monochromators, in a synchrotron radiation set-up the measuring devices becomes a small appendices to the light source. It is therefore recommendable to make use of synchrotron radiation only when its advantages are really needed.” C.Kunz, In Optical properties of solids New developments, Ed.B.O.Seraphin, North Holland, 1976 Radiation-Matter Interaction Polarization and current induction in E.M. field Matter polarizes in presence of an electric field Result is the establishment in the medium of an electric field function of both external and polarization charges Matter polarizes in presence of a magnetic field Result is the establishment in the medium of a magnetic field function of both external and polarization currents The presence of fields induce currents •Mechanisms and peculiarities of polarization and currents induction in presence of an E.M. field •Scheme to calculate the E.M. field established and propagating in the material •Basis to understand how this knowledge can be exploited to get information on the microscopic properties of matter Basic expressions - Charge polarization and induced currents P p i i Polarization vectors V M m i i V pol P J pol P t J mag c M J cond transport Escalar potential optical Eem wave J transport J optical Charge and Magnetic/current polarization – closer look P p i M i V m i i V m E -Ze- B +Ze pi e P0 J mag Induced currents J cond transport Escalar potential optical Eem wave J transport J optical E ( ) V Ze+ e+ _ J transport qNv transport E transport (V ) transport Ne 2 2m B ( ) optical ( ) E ( ) Motion of charge under the effect of the electric field of the E.M. field but in an environment where it is present an E.M. field Expansion of polarisation Pi ij E j ij E j Ek higher order terms j ij Linear and isotropic media P e E D E 4 P Physical meaning Elastic limit the potential is not deformed by the field M m B E 4e E E H B 4 M B 4m B B(1 4 m ) 1 4 e Dielectric function 1 1 4 m Permeability function Linear versus non linear optics Formally linear optics implies neglecting terms corresponding to powers of the electric field Physically it means E.M. forces negligible with respect to electronnuclei coulomb attraction E 109 V / cm breakdown fields 108 V / cm Nuclear atomic potential is deformed not harmonic (out of the elastic limit) response distortion higher harmonic generation Dielectric function and response In very general way D( r , t ) All space External stimulus t dr ' dt ' (r , r ' , t , t ' ) E (r ' , t ' ) (r , t ) E (r , t ) D 4ext Responce function Note is defined as a real quantity -1 Summary material properties within linear approximation 1 4 e 1 1 4 m And optical Conduction in an e.m. field J EE.M . transport Conduction under a scalar potential – Usual ohmic conduction J Estatic Maxwell equations in matter for the linear case E 4ext H 0 1 1 E H H E 4 optical E 4 J ext c t c t Corresponding equations for vacuum case E 4ext B E t B 0 1 4 B E J ext c t c Wave equation - Vacuum 2 1 2 E 2 2E c t E E0 exp i(q r t ) 2 2 q c 2 q c Vacuum supports the propagation of plane E.M. waves with dispersion / wave vector energy dependence Wave equation - Matter 4 optical E 2 2 E E 2 c t c t 2 2 q2 2 c 2 ( i 4 ) 2 c 2 n2 Matter supports the propagation of E.M. waves with this dispersion Formally q is a complex wavevector Wave vector eigenvalue/dispersion depends on the properties of matter through (all real quantities) Complex refraction index q2 2 c2 ( i 4 ) 2 c2 n2 E E0 exp ksˆ r exp i( nsˆ r t ) c c Absorption Phase velocity 1 i 2 n 2 1 n 2 k 2 / Real and imaginary parts not independent 2 2nk / 4 / Absorption coefficient IE 2 c v n dI Idr Lambert’s law 2 k c I (d , ) I 0 ( )e 4 k ( ) d Complex dielectric constant – Complex wave vector q 2 2 c2 ( i 4 ) n n ik 1 n 2 k 2 / 1 i 2 n 2 / 2 2nk / 4 / E (r , t ) E0 exp ( kqˆ r ) exp i ( nqˆ r t ) c c I E dI Idr 2 k 4 k c 2 Supported/propagating E.M. modes depend on the properties of matter through The study of modes of the e.m. field supported/propagating in a medium and the related spectroscopical information is the essence of the optical properties of matter Relation between (r,t), (r,t) (r,t) or (q,) (q, ) (r ) and the properties of matter 1st part Classical scheme / macroscopic picture 2nd part Quantum mechanics / microscopic picture Spatial dispersion q 2 qˆ extension on which the average is made a (q , ) (q q 2 qˆ 0 0, ) (0, ) Note 0 wavevector does not mean lost of dependence on direction anisotropic materials excited close to origin q 2 qˆ 0 Unknowns and equations (real quantities) are the unknowns related with the material properties (r,t) is close to unity at optical frequencies magnetic effects are small J mag c M (not to be confused with magneto-optic effects: i.e. optics in presence of an external magnetic field) Generally a single spectrum – f.i. absorption – is available from experiment (An ellipsometric measurement provides real and imaginary parts at the same time. It is based on the use of polarizers not easily available in an extended energy range) Real and imaginary parts are related through Kramers – Kronig relations Sum rules Kramers – Kronig dispersion relations Under very general hypothesis including causality and linearity ' 2 ( ' ) ' 1 1 P ' 2 d 0 ( ) 2 2 ' ( ) 1 ' 2 1 2 ( ) P d ' 2 2 0 ( ) Models for the dielectric constant / Lorentz oscillator Mechanical dumped oscillator forced by a local e.m. field ev BLocal / c Neglecting the magnetic term e- ELocal ( ) d2 d m 2 r m r m02 r eELoc dt dt 2 Induced dipole e ELoc 1 p ( ) ELoc 2 2 m (0 ) i Out of phase – complex/dissipation – polarizability (Lorentzian line shape) e2 ELoc 1 ( ) m (02 2 ) i Complex dielectric function From P N E D E 4 P E 4e E E ( ) 1 4 ( ) 1 ( ) i 2 ( ) 4 Ne2 1 1 m (o2 2 ) i (o2 2 ) 4 Ne2 1 1 m (o2 2 )2 2 2 4 Ne2 2 m (o2 2 )2 2 2 Lorentz oscillator Dielectric function Lorentz oscillator Refraction index Lorentz oscillator Absorption Reflectivity Loss function Physics Difference between transverse and longitudinal excitation EEL spectroscopy Optical spectroscopy Non linear Lorentz oscillator Anarmonic potential d2 d e 2 2 r 2 r 0 r r ELoc 2 dt dt m r r1 r2 .... r1 1E r2 2 E 2 d2 d e 2 r 2 r1 0 r1 E 2 1 dt dt m i n t E ( ) e n e r1 m ( 0 n ) 2 2i n d2 d 2 2 r 2 r r r 2 2 0 2 1 dt 2 dt • induced dipole at frequency and 2 • the system is excited by a frequency oscillates also at frequency 2 • re-emitting both and 2 2 ( n ) e 1 m 2 2 2i 2 2 2 2 2i 2 n n n n 0 0 but Lorentz oscillator in a magnetic field 1/2 d2 d dr 2 m 2 r m r m0 r e( ELoc BExt ) BExt (0, 0, B) dt dt dt m 2 x im x m02 x eEx eBy (i ) m 2 y im y m02 y eE y eBx(i ) x and y motions are coupled m 2 z im z m02 z 0 Px Nex ; Py Ney Solving for x and y 2 2 e 2 0 i Ex 2i L E y Px n 2 m 02 2 i 4 L 2 2 2 e 2 0 i E y 2i L E x Py n 2 m 02 2 i 4 L 2 L eB 2m Larmor frequency Lorentz oscillator in a magnetic field 2/2 xx 1 xy xz Ex Px P 1 yy yz E y y 0 yx P zx 0 1 zy zz z P 0 ( 1) E Px ( xx 1) Ex xy E y xz Ez i e ( xx 1) ( yy 1) n m 0 2 2 i 2 4 2 0 L 2 2 0 2 2i L e2 xy n m 0 2 2 i 2 4 2 0 L 2i L e2 xy yx n m 0 2 2 i 2 4 2 0 L zz 1 ij ( B) Lorentz oscillator in a magnetic field 1/3 P 0 ( 1) E 02 2 i ne2 xx 1 yy 1 m 0 2 2 i 2 4 2 2 0 L 2i L ne2 xy m 0 2 2 i 2 4 2 2 0 L 2i L ne2 yx xy m 0 2 2 i 2 4 2 2 0 L The dielectric function is a tensor [ Physically lost of symmetry for time reversal ] xx xy 0 xy yy 0 0 0 ; zz B (0, 0, B) Propagation in a magnetised medium 1/2 Note ≠ 0 in anisotropic media 2 ( E ) E 0 2 D t 2 2 2 D E Ej i 0 ij j 0 ij 2 2 t t j j Wave equation 2 ki k j E j k 2 Ei 0 0 2 ij E j Eigenvalue equation j n 2 n 2 k x2 / k 2 xx n 2 k k / k 2 y x yx n 2 k k / k 2 z x zx with i 1, 2 ,3 n 2 k y k x / k 2 xy n 2 n 2 k y2 / k 2 yy n 2 k z k y / k 2 zy k n k0 j n 2 k z k x / k 2 xz n 2 k y k z / k 2 yz 0 n 2 n 2 k z2 / k 2 zz Propagation in a magnetised medium 2/2 Considering the medium with B||z n 2 xx yx 0 xy n 2 yy 0 0 yz 0 zz n2 xx i zy Magneto-optics effects Dichroism N+ Right circular polarized wave N- Left circular polarized wave Two waves propagating with two different velocities and different absorption Magneto-optic effects e.g. Faraday and Kerr effects/geometries Longitudinal geometry M M Linear polarized Elliptically polarized Rotation according to n+-n- Dielectric tensor (q, ), (q, ), (q, ), e (q, ), m (q, ) are in general tensorial quantities D E 4 P E 4e E E xx Dx Ex Dy E y 4 yx D E zx z z xy yy zy xz Px yz Py zz Pz Dielectric tensor xx yx zx xx xy xz xy xz xx xy xz 4 yy yz yx yy yz yy yz yx zx zy zz zy zz zx zy zz Scalar medium xx yy zz Magnetized medium xx yx zx xy yy zy xz yz 0 zz 0 xx xy 0 0 0 0 0 xy 0 yy yz 0 zz Longitudinal and transverse dielectric constant 1/2 Any vector field F can be decomposed into two vector fields one of which is irrotational and the other divergenceless FL 0 FL F If a field is expanded in plane waves FT is perpendicular to the direction of propagation. FT 0 FT F D E D 0 D k BE 0 k B Longitudinal and transverse dielectric constant 2/2 J T (q , ) i (1 T ) ET (q , ) 4 i J L (q , ) (1 L ) EL 4 2 1 2 4 q (1 ) (1 ) E ( q , ) i JT (q, ) T T 2 2 c c 1 2 2 q (1 ) 2 c (T L ) Optics EELS/e- scattering The description in terms of longitudinal and transverse dielectric function is equivalent to the description in terms of the usual (longitudinal) dielectric function and magnetic permeability. They are both/all real quantities together with conductivity. They combine together to forming the complex dielectric constant defined here. Transverse and longitudinal modes 1/3 Propagating waves and excitation modes of matter are two different manifestation of the same physical situation Plasmon is a charge oscillation at a frequency defined by the normal modes oscillation produces a field only a field of this kind is able to excite this mode + E ( ) _ q Modes can be transverse or longitudinal in the same meaning of transverse and longitudinal E.M. field searching for transverse waves is equivalent to searching for transverse modes q Transverse and longitudinal modes 2/3 Searching for modes eigenvectors of ij Transverse modes Polaritons sˆ D(q , ) 0 E sˆ E (q , ) 0 N k c The quantum particles are coupled modes of radiation field and of the elementary excitations of the system, called Polaritons including transverse (opical) phonons, excitons,…. Longitudinal modes E Esˆ E 0 Di ( , k ) ij ( , k ) E j ( , k ) 0 ij ( , k ) 0 the quantum particles are coupled modes of radiation field and of the elementary excitations of the system: Plasmons, longitudinal opical phonons, longitudinal excitons,…. Transverse and longitudinal modes 3/3 Polarization waves D0 D P 4 E ( , k ) 0 0 Ei ( , k ) ij Dij ( , k ) 0 ( , k ) 1 ij ( , k ) 1 ij 1 Sum rules for the dielectric constant Examples of sum rules 1 2 0 Im ( )d 2 p ' ' ' ' 1d ' 2 2 (0) Re 0 Of use in experimental spectra interpretation Quantum theory of the optical constants Macroscopic optical response Microscopic structure Transition probability Ground state HRADIATION + HMATTER perturbed by radiation-matter interaction Two approaches • fully quantum mechanics • semi classical Three processes • Absorption • Stimulated emission • Spontaneous emission Microscopic description of the absorption and emission process H HR HM HI System O ° O ° O O ° ° O Radiation mi,ei 1 H R ( Pk2 k2Qk2 ) k 2 E (nk , k 1 ) k 2 ....nk .... Matter HM 1 i 2mi ei p i c Aj (ri ) ei j (ri ) H spin j i j i 2 Term neglected for non relativistic particles mj,ej •Interaction Hamiltonian HI •Effect of the interaction on the states of the unperturbed HR + HI Hamiltonian of a charged particle in E.M. field H A 1 E A c t A 0 1 e e e HR p A p A p Az x x y y z 2m c c c 2 px i 1 F e E v H c 2 2 e x 1 2 2 e e e2 2 HR i A 2i A 2 A e 2m c c c 1 2 2 e e2 2 HR 2i A 2 A 2m c c 2 e 2 A p mc 2m 1 2 2 e 2 i A 2m c Particle radiation interaction 2 ei e 2 2 H i 2i AR (ri ) 2 AR ei j (ri ) H spin c c i 2mi i j i 2 ei 2 j (ri ) H spin 2i AR (ri ) i 2m i i ei c j i i Matter Hamiltonian Problem to be solved + perturbation Hamiltonian H E Eigenstate and eigenvector of the matter radiation system in interaction Important notes The solution is found by a perturbative method • it is assumed here – formally - that the problem in absence of interactions has been solved. • In practice this can be done with more or less severe approximations. • The calculation of the electronic properties of the ground state is a special and important topic of the physics of matter n n (ri , si ...nk ... n (ri , si ) n H M H R n En n Many particles state Generally obtained by approximate methods Transition between states of ground state due to the perturbation term The effect of perturbation HI on the eigenstates of H0 n .....nk .... n n (ri , si ) Obtained by time dependent perturbation theory t 0 n (t ) cn (t ) n (t ) ' ' n' dcm (t ) i m H I n dt m Matrix elements 1/3 cn (0) 1 m (0) n The evolution of the state m is obtained calculating the matrix element m (t ) cn (0) m (0) H I n (0) System states under perturbation due to A A0 exp i(k r ik t ) n ...nk .... n (ri , si ) Changes of photon occupation and matter (f.i. electronic) state Matrix elements 2/3 It is found that for photon mode k, only nk nk 1 ' contribute linear terms to matrix elements +1 photon emission -1 photon absorption Probability of transition of the system from state n n' Matrix element 3/3 1 sin 2 n'n k t 2 2 8 (nk ) 2 (E E ) cn' (t ) M n' n ( k , ) n 2 n' V n' n k Absorption 1 sin 2 n'n k t 2 2 8 (nk 1) 2 ( E E ) Emission cn' (t ) M n' n ( k , ) n 2 n' V n' n k M n' n n' ei i m exp(ik r )(i i n i Transition probabilities Integrating in time from 0 to infinity for the transition probabilities per unit time Stimulated emission Spontaneous emission 2 4 2 (nk 1) M n'n (k , ) ( En En' ) Emission V k 2 4 2 (nk ) M n'n (k , ) ( En' En ) V k Absorption Spontaneous emission present only in quantum mechanics treatment Dielectric function and microscopic properties Dissipated power T ( ) 1 4 ( ) i 4 4 2 nk 2 8 nk V 4 V V M nn ' n ' f ( n) E 2 nk 8 V 1 P( ) J E dt E 2 T0 M nn' 2 4 ( En En ) f (n) f (n ') 2 nn' ' ei i m exp(ik ri ) pia n i probability of finding the state in a state n, at thermodynamic equilibrium f (n) f (n ') for En En ' Microscopic expression of the dielectric function 4 2 1 2 Im ( ) 2 M n ' n ( En ' En k ) f (n) f (n ') V nn' Physical meaning Sum of all the absorbing channels at that photon energy Note dissipation originates from non radiative de-excitation channels Intuitive meaning of the expression for absorption coefficient 4 2 1 2 Im ( ) 2 M n ' n ( En ' En k ) f (n) f (n ') V nn' En’ N ( En ' ) N(E) density of states (Number of states/eV) En Im ( ) N ( En ) Joint Density Of States N(E) N(E’) N ( En' ) N ( En ) M nn' ( En ' En k ) f (n) f (n ') Dipole approximation 2 M n' n ( k , ) 8 (nk ) n' V k ei i m exp(ik ri ) pi n i 2 exp ik r 1 ei M n'n ( ) n' pi n i mi i n'n n' e r i i i n Matrix elements of position operator Semi classical approach Note that the same result can be obtained by considering the transition probability between quantized states of the matter system under the effect of classical external perturbation of the E.M. field with given by the same expression of AR ei A0 exp i (k r i k t ) 2i AR (ri ) c This semi classical approach gives identical results for absorption and stimulated emission probabilities, but does not account for spontaneous emission Selection rules for Hydrogen atom n' e r i i ˆ (sin cos ,sin sin , cos ) n i Generic light polarization n 'l ' m ' n'l 'm' er nlm ˆ ' ' ' er sin cos nlm ie nl m ˆje ' ' ' er sin sin nlm nl m nlm ˆ ' ' ' er cos ke nlm nl m nlm R(r ) Pl (cos )eim m Selection rules/2 m' i ( m m ) drd d cos sin sin r R ( ) P ( ) e ' Rn P ' l n l 2 m' ' m drr Rn' Rn d cos ( ) Pl ' ( ) Pl ( ) dei ( m m ) 2 ' m n' l ' l 1m' For radiation polarized along z n'l 'm' er nlm kˆ n'l 'm' er cos nlm m m' l' l 1 nlm [linear polarized light ] Expressions valid in any central field Hydrogen - Selection rules Circular polarization r sin ( x iy ) E or l 1 2 r sin ( x iy ) e i 2 i m 1 Calculation of matrix elements - Optical properties of matter ei n' pi n mi M n'n ( ) The basic step in calculation involves i many particles wavefunctions i n'n n' e r i i n i Born - Oppenheimer approximation Nuclear motions separated from electronic motions One electron description n (r , R) n (r , R) n ( R) M m'k ,mk ( ) One electron WF Solution of motion in an average potential generated by all other electrons e * dr ( k , r )( i ) m (k , r ) m r Dielectric function in one electron approximation Case of crystals K reduced vector within the Brillouin zone Crystal states E(k) Im ( ) 4 2 m' m 2 dk M 2 3 2 m' k , mk ( ) ( Em' ( k ) Em ( k ) BZ f F ( Em (k )) f F ( Em' (k )) M m'k ,mk ( ) 2 dk ( E m' 2 (k ) Em (k ) M m'k ,mk ( ) JDOS BZ e * M m'k ,mk ( ) dr (k , r )(i ) m (k , r ) m r Joint Density of States - JDOS Phenomenology of absorption •Interband transitions -direct/indirect -Intraband absorption -Phonon contribution •Core/localized (e.g. molecular) level absorption Local field effects - Local (Lorentz) field corrections P EL E 3 0 Decay and relaxation of excited states Probability of relaxation/decay of excited state as integral on all the spontaneous emission channels of field and matter states 1 R n , k , ' 4 2 (nk 1) V k 2 M n'n (k , ) ( Em En' k ) As a consequence the dependence of Im () has to be modified •Lorentzian broadening • function substituted for by Lorentzian curve (e.g. see Lorentz oscillator) ( 1 1 1 R e ph ee ) Lorentzian broadening ( Em En' k ) 1 (02 2 ) i Exploitation of emission / radiative decay Total/Partial yield measurement of absorption through electron (Secondary, Auger,..) and photon (fluorescence, luminescence,…) yields De-excitation spectroscopies •Fluorescence •Luminescence XEOL •Auger electron and photon induced – Selection rules and surface sensitivity 3 2 I c ( ) 3 dk ( En (k ) Ec ) dr n* (k , r ) er c (r ) f F ( En (k )) n 1 matrix element ~ constant I Density of states and 3 Boundaries reflectivity From material filling the whole space to material with boundaries and matter-vacuum interfaces Reflectivity - Measure of the reflected intensity as a function of incident intensity Fresnels relations based on boundary conditions of fields link reflected intensity with dielectric function Reflectivity from a semi-infinite homogeneous material Surface plane Normal to surface Modellisation of surfaces and interfaces Multiple boundaries S and p reflectivity Diffuse scattering 1/2 Small and/or rough objects Scattered wave scattering medium Incident field 2 E (r , ) k 2 (r , ) E (r , ) E (r , ) ln (r , ) 0 2 E (r , ) k 2 n 2 (r , ) E (r , ) 0 Term neglected if dimensions Inhomogeneous filling of space Scalar theory of scattering (single Cartesian component) 1 2 2 F (r , ) k n (r , ) 1 4 Defining: Scattering potential U (r , ) k U (r , ) 4 F (r , )U (r , ) 2 2 ŝ Diffuse scattering 2/2 ŝ0 Born approximation U (rsˆ) f1 (sˆ, sˆ0 ) F (r )e ' e ik ( sˆ0 r ) ik ( sˆ sˆ0 )r ' f1 ( sˆ, sˆ0 ) d r F (r )e 3 ' ' e iksˆr r iqr ' d 3r ' The scattering amplitude is the Fourier transform of the scattering potential Inverting F(r) n(r) q q ksˆ ks0 Conclusions Classical scheme Introduction of the dielectric function Microscopic (quantum mechanics) treatment of emission and absorption Relation between macroscopic dielectric function (measured quantity) and microscopic properties http://www.gfms.unimore.it/ Calculation of ij elements Source Source: 3.3 m of arc, 3.1 m x 3.3 m vertical x horizontal two fields – vertical and horizontal – out of phase of ±/2 according to the sign of take off angle (J.Schwinger PR 75(1949)1912) Electric fields E0 z ( ) i e 3 23 3 23 ( ) Ai [( ) (1 2 2 )] 4 c 2 0 cr 4 c e 3 13 ' 3 23 E0 y ( ) ( ) A i [( ) (1 2 2 )] 4 c 2 0 cr 4 c ≈ 103 photons/bunch - bunch duration ≈ 20 ps 4.5 320eV r=1m 0.1% BW 3.5 2.5 3 2 Eoz N/C Eoy N/C 4 3 x 1012 T x 10125 // 2 1 0 320eV -1 1.5 r=1m 0.1% BW 1 -2 0.5 0-2 -1.5 -1 -0.5 0 0.5 (mrad) 1 1.5 2 -3 -2 -1.5 -1 -0.5 0 0.5 (mrad) 1 1.5 2 Polarimetry 100 eV ellipse 0 -0.4 -100 Vertical I(A*e-12) -50 Electric field at E= 100 eV +0.4 E = 100 eV Exit slits 900um * 30 um -150 -200 -250 15 20 25 30 Zc 35 40 45 -0.4 -1 Horizontal +1 Electric field at E = 100eV Erepresentation +0.4 0 Selector fully open: Zc= 45 mm, Zg = 1 mm S1=-0.9 S2=0.011 S3=0.068 Ey=0.95 Ez=0.04 =-1.4 Ellipticity, =0.04 Vertical I , A*e-12 -50 -100 -150 -200 0 Zc = 34 Zg = 41 100 eV -250 20 30 Zc, mm 40 -0.4 -1 0 +0.4 -50 Horizontal +1 =-1.44 Ellipticity, =0.33 -100 -150 -200 Ey=0.98 Ez=0.04 Electric field at E = 100 eV Vertical I , A*e-12 Polarization selector position: Zc = 34 mm, Zg = 41 mm (aperture 4 mm) S1=-0.97 S2=0.011 S3=0.082 Zc = 31 Zg = 31 100 eV -250 20 30 Zc, mm 40 -0.4 -1 Horizontal +1 Polarization selector position: Zc = 31 mm, Zg = 31 mm (aperture 14 mm) S1=-0.77 S2=0.08 S3=-0.57 Ey=0.93 Ez=0.31 =1.43 Transport and conditioning optics Source 4 m HxV Mirrors in sagittal focusing reduction of slope errors effects in the dispersion plane GAS CELL Helicity selector P2 BPM Intensity monitor P1 EXIT SLITS MONO Light spot plane-grating-plane mirror monochromator based on the Naletto-Tondello configuration Energy range 3- 1600 eV Energy resolution E/E ≈ 3000 (peak 5000) at vertical slit (typically 30 μm) x 400 μm (variable) Variable divergence (maximum, variable) 20 m vert x hor ellipticity variable horizontal/vertical (typically in the range 1.5 – 3.5, Stokes parameters (normalized to the beam intensity) S1 0.5 - 0.6, S2 0 - 0.1, S3 0.75 -0.85 ) helicity variable (typical value for rate of circular polarization P or S3 0.75 – 0.95) Examples and experimental arrangements at BEAR (Bending magnet for Absorption Emission and Reflectivity) Bulk materials Absorption Surfaces Reflectivity Interfaces Fluorescence Luminescence – XEOL Diffuse scattering Experimental arrangements BEAR (Bending magnet for Emission Absorption Reflectivity) beamline at Elettra Experimental/scattering chamber Detection e- analyser / photodiodes (2 solid angle) VIS Luminescence monochromator Goniometers , 0.001° M A A 0.01° (Positive S 0.05° Differentially 0.1° pumped joints) C Sample manipulator 6 degree of freedom Rotation around beam axis any position of E in the sample frame Optical constants of rare hearths See f.i. Mónica Fernández-Perea, Juan I. Larruquert, José A. Aznárez1, José A. Méndez Luca Poletto, Denis Garoli, A. Marco Malvezzi, Angelo Giglia, Stefano Nannarone, JOSA to be published 2 10 1 10 0 10 -1 10 -2 10 -3 10 -4 10 -5 10 k -6 10 -7 10 -8 10 -9 10 -10 10 -11 10 -12 10 -13 10 Endriz Drude O2,3 Larruquert N4,5 Current M4,5 L1,2,3 Henke K Chantler Extrapolation 10 -2 10 -1 10 0 10 1 10 2 10 3 10 photon energy (eV) 4 10 5 10 6 Interfaces & surface physics in periodic structures (multilayer optics) See also poster P III 26 ML : Artificial periodic stack of materials (Optical technology Band pass mirrors) Z At Bragg Z dependent standing e.m. field establishes both inside the structure and at the vacuum-surface interface modulated in amplitude and position •Devices of use in spectroscopy BRAGG ultra-thin deposited films buried interface spectroscopy Standing waves & excitation Scanning through Bragg peak In energy or angle Si Mo Si Local modulation of excitation Spectroscopy of interfaces Physics of mirror/Reflection Photoemission, Auger, fluorescence, luminescence etc.. Cr/Sc Cr-Oxide interface 573 eV X 60 (6 Å) Cr O 2 3 Cr Sc (15 Å) (25 Å) Qualitative analysis -Opposite behavior of Cr and Sc -Different chemical states of the buried Sc -Two signals from oxygen: one bound to Cr at the surface, the second coming from the interface - Carbon segregation at the interface (As received ) Ru (Clean) -Si buried interface Angular scan through the Bragg peak st 1 component nd 2 Ru (15 Å) Si (41.2 Å) Ru 3d 838 eV Peak area (arb. units) at component Mo (39.6 Å) X 40 Ru 3d st Intensity (arb. units) 1 component nd 2 component background 5.0 5.5 6.0 6.5 Grazing angle (°) 7.0 7.5 h = 838 eV silicide Intensity (arb. units) Mo 3d Ru 3d Si 2p 278 280 282 284 286 Binding energy (eV) 288 290 560 580 600 620 Kinetic energy (eV) 728 732 736 740 Model – Ru-Si interface • Interface morphology • Calculation of e.m. field inside Ml •Photoemission was calculated, (Ek= h - EB) Minimum position and lineshape depend critically on Ru Ru-Si the morphology profile Mo-Si ML & i.f. roughness Motivation role of ion kinetic energy and flux during ML growth ML (P 8 nm, 0.44) Performance- R (10°) Ion assistance Mo/Si 61.2 % 58.4 % Wavelength [nm] Ions EK: 5 eV (1st nm), 74 eV > 1nm Controlled activation of surface mobility Performance & diffuse scattering Performance differences are to be related to interface quality Diffuse scattering around the specular beam was measured KS= Ki + qZ + q// diffuse scattering - MLs I.f.roughnes produces diffuse scattering around the specular beam I.f.roughnes can/can not be coherently correleted through the ML Description on a statistical base, ….fractal properties Single interface – Autocorrelation function R 2 H ( x x' , y y ' ) H ( R ) 2 1 e 2 2 1 qz 1 qz2 2 S (q // ) 2 e d R e qz H ( R) 2 e iq// R In plane Fourier transform on q// of potential f.i. Stearns jAP 84,1003 MLs : S(q) two terms See f.i. Stearns JAP, 84, 1003, 1998 KS= Ki + qZ + q// • incoherent scattering by single interfaces • correlated/coherent scattering among i.f. (interlayer replica of roughness) Diffuse scattering Detector qdetector 0.003 nm-1 - scan At 0.48 nm (13.1 eV) Rocking scan Incident beam Divergence qdiv 0.0005 nm-1/m At 0.48 nm (13.1 eV) Mo-Si ML diffuse scattering See also poster Borgatti et al. P III 17 Mo/Si Ion assistance ξ= 300 Å ξ=400 Å ξ=120 Å ξ=200 Å In plane correlation function - absence of interface correlation Correlation function 2h 2 C ( R ) exp R / ξ , correlation length h, fractal dimension/jaggedness Pentacene on Ag(111) See also poster Pedio et al. P II 33 Chemisorption morphology - tilt angle & electronic structure ( Concentrating on 1 Mono layer ) Premise about C22H14/substrates •He scattering on pentacene deposited by hyperthermal beams 1ML planar •Morphology and electronic properties ( delocalization of the electrons) transport properties highly anisotropic; •on Metals: nearly planar orientation a condition hindering the formation of an ordered overlayer; on semiconductors/oxides: SiO2 standing GeS lying. Surface Cell ( By He scattering ) Danışman et al. Phys. Rev. B 72, 085404 (2005) C3 symmetry Oblique cell Periodicity (6 x 3) , 1 monolayer XAS C K-edge resonances (At magic angle 54.7°) LUMO+1 Gas phase XAS LUMO 2 (Alagia et al.JChemPhys 122(05)124305) 6 4 4 3 13 5 6 5 1 gas phase 2 Multilayer 3 ML 2 ML 10° 1 ML 27° 0.5 ML 25° 0.3 ML 284 286 288 290 292 Photon Energy (eV) Redistribution of the oscillator strength in the C1s – LUMO excitation region (1-3 of gas phase) 294 296 298 Tilt angle VB photoemission LDA calculations C22H14/Al(100) Simeoni et al. S.Science 562,43 (2004) Photoemission EV h=30 eV 0 6.6 eV 7.4 8.3 3b3g 3b2g 2au 3b3g EF 2au 3b2g 3 ML 2 ML 1 ML 0.5 ML 0.3 ML clean Redistribution of states upon chemisorption -4 -3 -2 -1 Kinetic Energy (eV) 0 1 HOMO-LUMO gap increasing XAS 1 ML - precession scan Dichroism/Bond directionality & Tilt angle of the molecule resonances 1 Ml C22H14/Ag(111) ε= EV/EH = 0.29 Nex_185_int Nex_186_6_int Nex_187_6_int Nex_188_6_int Nex_189_int absorption coefficient a. u. C=90° i= 10° resonances beam zM yM C=0° xM 280 285 290 295 300 Photon Energy (eV) 305 310 XAS – 1 ML - deconvolution 0.5 1 Ml C22H14/Ag(111) absorption coefficient a.u. 0.4 data fit 0.3 i iCi Step A C=54.7° C E B D 0.2 F ACA BCB 0.1 CCC 0.0 284 286 288 Photon Energy (eV) 290 292 294 0.5 absorption coefficient a.u. Precession scan - Formulae 1 Ml C22H14/Ag(111) 0.4 data fit i iCi Step 0.3 A C=54.7° C E B D 0.2 F ACA BCB 0.1 CCC 0.0 Fit function for Single domain 284 286 288 Photon Energy (eV) P 2 E p p 2 EH2 2 cos 2 C sin 2 C 2 cos C sin C cos sin M sin cos cos M cos 2 cos 2 C 2 sin 2 C 2 cos C sin C cos sin 2 sin 2 2 cos C sin C 2 1 cos cos 2 C sin 2 C sin M sin cos cos M cos sin sin Fit parameter: θ (polar angle of dinamic dipole ) 290 292 294 Tilt angle - Fit Coverage Tilt angle precession scan Tilt angle Polar scan 0.3 25° +/- 5° 0.6 27° +/- 5° 28° +/- 4° 1.0 10° +/- 4° 8° +/- 4°