The photoelectric effect
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1 The photoelectric effect E K hν-e B E F hν E B
2 A photoemission experiment Lifetime broadening ΔE.Δτ~ħ ΔE~ħ/Δτ + Experimental resolution Hüfner, Photoelectron Spectroscopy (Springer)
3 A photoemission experiment UV-lamps : He-Lamp (21.2eV) X-ray tubes : Al-Kα (1486eV) Mg-Kα (1253.6eV) SR: From 5 to...ev Photons Electron analyzer
4 A photoemission experiment [Bi 2 Ba 2 O 4 ][CoO 2 ] hν=100 ev Kinetic Energy (ev) 95 Nicolaou et al.
5 The spectroscopist Bible φ Spectrometer 4.5 ev on CASSIOPEE
6 A photoemission experiment [Bi 2 Ba 2 O 4 ][CoO 2 ] Bi-5d 3/2 Bi-5d 5/2 hν=100 ev VB (O-2p+Co-3d) Ba-5p 1/2 Ba-5p 3/ Kinetic Energy (ev) 95
7 A photoemission experiment [Bi 2 Ba 2 O 4 ][CoO 2 ] Bi-5d 3/2 Bi-5d 5/2 VB (O-2p+Co-3d) Ba-5p 1/2 Ba-5p 3/2 E B = hν - E K - φ Spectrometer (φ Spectrometer 4.5 ev on CASSIOPEE)
8 CASSIOPEE Experiments Spin resolved photoemission Photons MBE Photons Surface preparation and Thin film deposition Angle resolved photoemission
9 Electron analyzer Simple energy analysis Outter hemisphere Inner hemisphere Entrance slits Entrance optics Exit slits Channeltron A potential is applied between the inner and the outter hemisphere. The electric field allows selecting a precise kinetic energy. Only the electrons with this kinetic energy can reach the detector. R. Belkhou, PhD thesis
10 Electron analyzer Multichannel energy analysis E K Max E K Min 2D detector A range of kinetic energies are simultaneously analyzed. The different kinetic energies are spatially sorted (vertically) by an electric field. Each horizontal line of the 2D detector corresponds to a kinetic energy.
11 Electron analyzer Multichannel energy and angular analysis «Scienta-type» analyzer Sample θ Kinetic energies are vertically sorted. Horizontally, the emission angle θ is conserved. Finally, the result of a measurement is an image (E K,θ).
12 Valence band Angle Resolved Photoelectron Spectroscopy
13 Reciprocal space-first Brillouin zone Wave vectors k corresponds to points in the reciprocal space. Band structures are calculated along high symmetry directions of the reciprocal space. U K First Brillouin zone Si band structure Can we measure a band structure E(k) with photoemission?
14 Principle An experiment k let's assume that, in addition to its kinetic energy, one also measures θ the angle between the photoelectron emission direction (direction of the photoelectron wave vector) and the surface normal. Angle Resolved Photoelectron Spectroscopy
15 Momentum conservation k f = k+k Photon k k Electron k Photon = 2mE Electron E Photon /c 103 ( E Electron =E Photon =1eV) The initial wave vector is conserved during the excitation process.
16 Binding energy and k // The analyzer measures E k E K = h ν E B ϕ S E B = h ν E K ϕ S (1) The wavevector of the photoelectron k out can be decomposed into two components parallel and perpendicular to the surface : n k out K out // θ k out k out(k out = 2mE K ħ k out // = 2mE K ħ cos θ sin θ) The component parallel to the surface is conserved. Hence, inside the solide : k // = 2mE K ħ sin θ (2)
17 Determination of k Free electron parabola Escape to vacuum through a surface potential barrier V 0 Transition to a free electron final state into the solid We assume that the photoelectron is excited to a free electron final state E f E B = h ν E f = E B +h ν = E K +Φ S E f = ħ2 k 2 2m E 0 E K +ϕ S = ħ2 k 2 2m E 0
18 Determination of k E K +ϕ S = ħ2 k 2 2m E 0 E K +ϕ S = ħ2 2m (k 2 // +k 2 ) E 0 Using and k // = 2mE K ħ V 0 = E 0 +ϕ S sin θ (Inner potential) k = 2m ħ (E kin cos 2 θ+v 0 ) 1 /2 (3)
19 The equations E B = h ν E K Φ S k = 2m ħ 2 (E K cos 2 θ + V 0 ) 1/2 k // = 2m ħ 2 1/ 2 E K sin θ determines E B and k One can choose k and travel in the reciprocal space by changing either hν or θ Changing hν ~ changing k Changing θ ~ changing k // By increasing hν, one shrinks the reciprocal space into a smaller θ range
20 Band structure by changing the angle Using 2D(E,θ) detector... Raw spectrum θ k (Å -1 ) Kinetic energy (ev) Kinetic energy (ev) θ( ) k (Å -1 ) W. Srour, A. Tejeda and A. Taleb-Ibrahimi
21 Band structure by changing the angle k x X U Γ K K k y First Brillouin zone We found the photon energy to be at k Z =0 We want to measure the band structure in the (k x,k y ) plane
22 Band structure by changing the angle Real space Reciprocal space X Analyzer slit Γ K X Γ K By rotating the sample in front of the analyzer, one can travel in the reciprocal space...
23 Band mapping and Fermi surface k x,k y,e band mapping Fermi surface Fermi surface Fermi surface k x (Å 1 ) Band structure (E,~k // ) along one direction
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