Moderní experimentální metody Rentgenová a elektronová spektroskopie III Fotoelektronová spektroskopie • Fotoelektronová spektroskopie (XPS) a spektroskopie Augerových elektronů (AES) • Experimentální aspekty • Zdroje: ARPES, ARUPS • Detektory • Příprava vzorků • Úhlově rozlišená fotoelektronová spektroskopie (ARPES) Fotoemise a Augerův jev Fotoelektrony - přímo vyražené fotonem Augerovy elektrony - sekundární emise - alternativní proces ke vzniku charakteristického rtg záření. photoemission Auger Elektronová spektroskopie měří kinetickou energii elektronů. Fotoemise a Augerův jev Fotoelektrony - přímo vyražené fotonem Augerovy elektrony - sekundární emise - alternativní proces ke vzniku charakteristického rtg záření. K fi TlO) vac «TB(PE) kin kin(sp) photoemission Auger vzorek spektrometr XPS - ESCA Electron spectroscopy for chemical analysis • All elements above Z>=3, Li • Sensitivity - 1 permile • Surface sensitivity - surface contamination • Chemical state of surface • Profiles along surface • Depth profiling with ion beam Fotoelektronovä Spektroskopie Experiment: Photon energy: 6eV to 2000eV Laboratory sources: • He discharge 21 eV • Mg x-ray tube 1254 eV •Al x-ray tube 1486 eV • Laser 6eV (4x1.5eV) Synchrotron - variable source Ultra high vacuum (maximal pressure 106 Pa) High quality surfaces needed Optical elements - only in reflection geometry - mirrors, diffraction gratings, no windows! Penetration depth 10°- 101 nm XPS Sample preparation Atomically clean and smooth surface • Cleaving in vaccum • Depozition chamber connected to XPS chamber • Vacuum suitcase • Protecting layers • Ion sputtering • heating XPS ARPES Hemisférický analyzátor + CCD Hemisférický analyzátor V(r) = - (R2 - At) (R1R2) + const \E(r)\ = - (Vi - Vi) {R2 - R1) (R1R2) V(r) = ^r°^°^ const. R0=(R1+R2)/2 ARPES Hemisfericky analyzator VG Scienta R4000 Scienta R4000 Spectrornicroscopy Performance Optics: Enecgy resolution: Theoretical resolving power using 0.2 mm entrance slit: Kinetic energy range: Spatial resolution: Magnification: Imaging Mode Transmission Mode Ultimate angular resolution: Widest angular range for multiplexed angle recordings: < 2 meV 1 Ox, 20x, 40x 5x 0.1 degrees 10 degcees R4000 Spectrometer XPS Detekce: CCD Channeltron XPS h—r i t t i IM I— Alftl 50 CL 10 At* Theory \ I l M i-1—r 1 1 T T T i J_I_I L ' Hi* Ai* J_I_I J 1 I n . Of* 4ua ....... -i- 10 50 100 500 Electron energy ( eV ) 1000 2000 Electron escape depth * -* V ......1_I_I_■ i ■ i i « I_I_I_I_I ■ ' I' I_I_I_......'_I_I_I_l_L 10 UK) 1000 Kinetic I energy (eV) XPS Rentgenová fotoelektronová spektroskopie X-ray Photoelectron Spectroscopy-XPS, PES Kinetická energie elektronu dopovídá rozdílu energie fotonu a ionizační energie slupky. in Tilu- [eB(PE)+s p J Umožňuje detekovat změny vazebné energie chemickým stavem atomu. XPS na germaniu s velmi tenkou oxidovou vrstvou. c OJ •il—i—i—i—i—i—i—i—i—r Ge 2p 2.3 eV 3/2 Ge3d GeO j_i_ j—i—i—i—y—i—i—i—i—i—i—i 1224 1220 1216 34 30 Binding energy (eV) 26 XPS Příklad: BL(Se,Te), excitace 125 eV. 15 x 10 Sample series, Bi2(Se,Te)3,Exc energy=125.0eV 10 i— CD 5ľ Se 3d °60 BLSe, BLTe. ___/V- Bi5d Jli JU M JUl Al Jli JO aA 0% 8% ■9% 10% 27 % 30% 34 % ■38% 38% 39% 100 % 70 80 90 Kinetic energy (eV) 100 110 Fotoemise a Augerův jev Fotoelektrony - přímo vyražené fotonem Augerovy elektrony - sekundární emise - alternativní proces ke vzniku charakteristického rtg záření. K fi TlO) vac «TB(PE) kin kin(sp) photoemission Auger vzorek spektrometr AES Spektroskopie Augerových elektronů Auger Electron Spectroscopy - AES Energie elektronu při přechodu na uvolněnou hladinu se může předat Augerovu elektronu. ug efi - [eB(A) + <Ž>S pJ Charakteristické energie se značí FIB. Přechod I—>F, ionizuje se B. Pravděpodobnost emise Augerova elektronu a rtg záření závisí na protonovém čísle. Augerova spektroskopie je nejcitlivější na lehké prvky. Často se měří v kombinaci s XPS, používá se v elektronové mikroskopii. 1.0 0.9 0.8 £ 0.7 5 0.6 0.5 - hky = v2mĚ sin 0 sin (j> Tik? = v2mE cos 0 • energie ound — hbJi -Ekin, elektron (sin (0)x + cos (0) sin (0)y) 2meEk in Dispersive plane High \Pi Non dispersive plana SamplQ Measurement is > Electrons live in bands Interactions (electron-electron, electron-phonon, etc) can change band dispersions and quasiparticle lifetimes Single particle spectral function captures these interactions Single particle A(ko)) spectral function: Bare band: Self Energy: Z(k,tf>) 1 Z" (k, co) 7T [co-£k-T (k,oj)f + [Z (k,a?)J Z (k,&0 + zZ'(k, o)) Band position Linewidth or lifetime Band structure + Interactions Band structure: simple metal (Cu 111 surface) > ba 5(E? - E? - hv) N -N mc p=electron momentum A=vector potential of photon (points in direction of polarization) Express as antisymmetric product of 1-electron state and N-1 electron state e.g.: Wf = JlýfWf 1. Optical excitation of electron in bulk (continued) A/-l|iiJiV-l > Af *j = 'ARPES matrix elements' m=index given to N-l-electron excited state Total photoemission intensity originating from this step: Kk,Ekin) = Xf^Wfj f,i m Consequences of step 1: Observed band intensity is a function of experimental geometry, photon energy, photon polarization "Matrix element effects" Photoemission spectra: Matrix elements effect Binding Energy (eV) PRB 8, 2786 (1973) By varying hw we can put emphasis on one element or another. 3. Escape of photoelectrons into vacuum • Electron loses work function (<£>) worth of energy • Transmission probability through surface depends on energy of excited electron and Recovering e£ and k (1) Conservation of energy: E^n = huj — 0 — (£F - Recovering e£ and k (2) Momentum: Parallel component kjj is conserved up to a reciprocal lattice vector: k|| = Kout,|| - G|| . Recovering ejj and k (3) k,+ G Perpendicular component can be recovered if assumptions about the bulk final state (in the solid) are made. Assuming the free-electron-1 ike character of the final state, one gets (in the extended zone scheme): E0 = h2k2 h2 2m 2m (k± + G1_)2 + (k|,+G,|) Recovering ejj and k (4) k,+ G Energy balance: Ef — Eq — Ekin + (Ev - E0) Free-electron approx.: Ef E0 = r9_ 2m {k± + G±)2 + (k|, + G Recovering £JJ and k (5) 2m {k± + G±)2 + (k„ + G,,)2] = Ekin + (Ev - E0) k± + G± = 2m [Ekin + (Ev - E0)] - Kl out, 2m ^2" fkin + (£V - £b) - £km sin2 0 2m [Ekincos20 + (Ev E0)] ^ [Ekin cos2 e + Vo] Few more notes The inner potential Vq has to be determined by an educated quess (by fitting it so that experiment matches the theory or by imposing symmetry requirements — to make the bands have the symmetry of the solid). Weak point: Nearly-free electron approximation for the final bulk states will work well only for "nice" materials (such as alkali or simple metals) and/or for high energies. Surface states vers, bulk states ► Surface states have no dispertion along k±. ► Energies and momenta of surface and bulk states cannot overlap (otherwise, it would be a bulk state...) ► Surface state have sharper linewidths (DOS in surface layers in more atomic-like). I OP Publishing Semiconductor Science and Technology Semicond. Sei. Techno]. 27 (.2012") 12.4O01 C14pp> doi: 10.1088/0268-1242/27/12/1 24001 INVITED PAPER The electronic structure of clean and adsorbate-covered Bi2Se3: an angle-resolved photoemission study Marco Etiaiitlii1, Richard C Hatch1, Damian Giian1, Tilo Planke1 , Jianli Mi2, Bo Brummerstedt Iverseii2 and Philip Hofmann1 ARPES Příklad: pásová struktura Bi2Se3 Y-Scale [d eg] V-Scale [degj (A1) K (A1) (A1) Figure 5. ARPES spectra for the pristine surface of Bi2Se^ High photoemission intensity is displayed in bright, (a) Energy dispersion in the KTK direction of the SBZ and (b) Fermi surface for the stoichiometric Bi^Sei sample, (c) and ( critical value Topological transition can be tuned by temperature and Sn content p-type carrier concentration decreases with increasing of Pb content —I-1-1---1—— O OTA present aa la ( heating) *> data o , & ant- ond two - phasf samples ----a---- OTA d*t*r™iinfltL^fi of 2fwl ärdör Sn„SB x » O O O O Band inversijänih PbSnTe^Se) . -1-1 I ■"■ o.e o.4 Mole Fracrit 0.2 Si»ö_ S«„ Stoichiometric FbTe liquidus ^_ 1q23 1022 tq23 Electron Brillouin zone projections onto (001), (111), and (110) planes^ Pb^SnJe L\u et-al.,-88,241303(R) (2013) Angle Resolved Photoemission Spectroscopy Photo-excitation hv > 10eV/ E t Spectrum Photoemission ta N(EPE)~D(EBE) ^ = hv-EB-0A hv= const Angle resolved photoemission (ARPES) hv = const, zt Ekm = hv -(§)-«>, analyzer detector We need: binding energy - Eb initial momentum - k' a or b E - hv + W sample O E(k )-dispersion ® ^ Wn=kfn =7 2mE/fi 3D E(k) dispersion obtained by hemispherical electron analyzer and 2D detector array > Resolution: AE ~10meV, AG -0.1° Angular Resolved Photoemission: Examples Examples: Bi2Se3 ARPES experiment EF En Q BUTe (1/Ä) 0.2-0.2 ,y k\ (1/Ä) (1/A) 0.2 -0.2 (1/A) analyzer hv -(EB)-0A detector We need: binding energy - Eb initial momentum - k' ~aor b sample ■=> E(k)-dispersion EbY E- hv + w k\,=kfn =7 2mE/fv(sine) k^kV^y 2mE/f»2 cosG-G ■=> Measurement of angular dependent energy spectrum N(E) of photoexcited electrons 100 'S 50 T I? lu lu a: LL 10 6- -1 j I J i e I j lAjuaAu ( I I I 11JI--1—r ......J-1- Electron mean free path in solids I I I I ; IJ J__I_i I l i I i 11_ ....... 2 5 10 50 100 500 1000 2000 ELECTRON ENERGY (eV) Zoom-in around the r- Point: PbSnSe (111) Epilayers (a) PbSnSe with xSn = 10%: Normal band structure 84meV J1J HE 123 1 ?f -0.05 0 0.05 K.{A-1) -0.05 0 0.05 MA"1! -0.05 0 0.05 K,(A r::. j ■Mb 0 U.Ub -0.05 0 0.0b K|(A") K„{A1) K||(A ] 0£g(x,T) = 125 - 1021x + (480 + 0.256 J2)12 300 Ml I I I I I j I I I I I I I I I j I I I I I I I I I j I I I I j I I I I > ^ 200 150 CL CO 100 CD -o 50 00 -50 CD CO -100 c CO -150 -Q CL -200 -250 -300 250 |E (x,T) of PbSnSe xsn = 10% xsn = 20% 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 Temperature (K) 2D Structures: TCI Surface Quantum Wells ■=> MBE of asymmetric quantum wells (vacuum barrier): discreet 2D QW states ■=> Opening of a gap due to coupling between top & bottom topological surface state (a) PbSe QW dQW=100A xsn = 0% (M2969a) PbEuSe o CD > PbSe > m LU -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 LI = 305K; X^=0% I- E 11 ~60me\ L ~300meV i- LL= 2_30Ki X^=0% LL= 1J6K; ^=0% Ei_L 1 1 LI E a5K^X6„_=Q% -11 ~180meV 0.05 0 0.05 -0.05 0 .0.05 -0.05 0 0.05 -0.05 0 0.05 MA") Km (A"1) MA") MA") NanoESCA- kombinace mikroskopie a spektroskopie PEEM - photoelectron microscopy Imaging ESCA- zobrazení jen určité energie elektronů XPS -■ ■ - -1 ■ -11 ^ 5|fitem MCP Sawi I"um nt Jjiilik Rozlišení 50nm Clean Surface Preparation by Capping / Decapping ■=> Surface needs to be protected against oxidation during transfer from MBE to ARPES in air: Use of an easily desorbable capping layer I. Selenide Compounds: Amorphous Se cap layer (~ 100 nm ) deposited at RT: Volatile surface oxide I. PbSnSe growth II. Se capping After growth/350°C 1100 nm Se cap 50°C Se-cap PbSnSe substrate ■=> Clean surface recovered at Tdes < Tgrowth II. Tellurides: ^More difficult I. Decapping: Heating RT - 300C (P=const.) Tellurium oxide is too stable for desorption * Te 'Se double caP & Se strongly intermixes with tellurides layer structure used