How to explore a system?

1. How to explore a system? Electrons Electrons Photons Photons Atoms Atoms

2. How to explore a system? Electrons Electrons Photons With different kinetic energies

3. Electron Energy Analyzers Detect the charged particles for a given energy range with good energy (and space) resolution Retarding Field Analyzer (RFA) Cylindrical Mirror Analyzer (CMA) Hemispherical Analyzer (HA)

4. N(E) E0 + ΔE E0 Electron Energy (eV) Electron Energy Analyzers Energy distribution curve: response of the system Separate the electrons with a defined energy band

5. V0 Retarding Field Analyzer (RFA)

6. V0 Retarding Field Analyzer (RFA) N(E) V0 = Retarding potential E0 = eV0 = Pass energy Current to screen N(E) E0 + ΔE E0 To obtain N(E) one has to differentiate Electron Energy (eV)

7. Retarding Field Analyzer (RFA) Modulation

8. First harmonic N(E) Second harmonic dN(E)/dE RFA: poor sensitivity and energy resolution No angular resolution

9. Electrostatic deflection analyzers Cylindrical Mirror Analyzer (CMA) Hemispherical Analyzer (HA) Dispersing field Deflection is function of electron energy Concept Energy band pass - v1 Electrons have angular spread around the entrance direction v2 v1 + Electrons with same v will be deflected by different amounts Degradation of energy resolution

10. Cylindrical Mirror Analyzer (CMA) e- cross the inner cylinder through a slit experience the field –V of the outer cylinder go to second slit and and arrive in F V=deflecting voltage between cylinders consider an e- arriving at an angle 0 with e- energy work of the e.m. field on e- e- energy inside cylinder

11. Cylindrical Mirror Analyzer (CMA) The trajectory for which the e- is focussed is a solution of the equation of motion (cyl. coord.) The maximum deflection depends on the entrance angle, and shows that K0 depends also on  Electrons with same E will be deflected by different amounts depending on the entrance angle focussing condition

12. Cylindrical Mirror Analyzer (CMA) The numerical solution shows that for a single K0 there are two values of entrance angle This means that in general there are two focussing distances For K0 = 1.31 the two focal distances merge into one A single focussing length L correspond to different acceptance angles (see curve (c)) L = 6.130 r1 High sensitivity with one pass energy

13. Cylindrical Mirror Analyzer (CMA) L The emission angle determines three main factors (a) source-image distance on the common cylinders axis (L) (b) the deflecting voltage for particles with energy E (c) the required ratio between the cylinders radii For 0= 42°18.5' the first spherical aberration term = 0

14. Cylindrical Mirror Analyzer (CMA) For small  and small E, the shift in the axis crossing point is (Taylor series) r1 = inner cylinder One looks for L  0 Neglecting the product Base resolution

15. Cylindrical Mirror Analyzer (CMA) Transmission = fraction of space in front of the sample intercepted by the analyser analyser transmission For a fixed slit, T does not depend on energy

16. Cylindrical Mirror Analyzer (CMA) The image of the source can be reduced by inserting a slit before the focus that reduces the coefficients of 3 by a factor of 4 Finite source + ring slit of width W and radius r1 For a given slit, T does not depend on energy while EB  E So the energy resolution is not constant with E peak area  (T x EB) N(E) but (T x EB)  E E0 + ΔEB E0 Peak area  N(E)xE The spectrum contains the intensity-energy response function of the analyser Electron Energy (eV)

17. Concentric Hemispherical Analyzer (CHA) Two spherical electrodes 1/r electrostatic potential Electrons are injected with energy eV0 at slit S in the point corresponding to radius R0 The condition to allow e- to describe the central orbit is (point source) Focussing condition in F For R1=115 R2=185 mm K = 1.013

18. Concentric Hemispherical Analyzer (CHA) e- forming angle  with tangential direction e- with energy E with respect to E0 Shift in the radial position Considering two slits of width W1 and W2 Base resolution R0=150 mm W1 = W2 = 3 mm R0=150 mm W1 = W2 = 1 mm The resolution is mainly determined by the central hemispherical radius

19. Concentric Hemispherical Analyzer (CHA) Transmission If the sample is at the position of the slit W1, we assume W1 = 0 and neglect  so the angular acceptance in the plane depends on the slit W2 We also have to consider the angular acceptance in the plane perpendicular to the screen () Transmission of the analyser In analogy to the CMA Worse than CMA (lower transmission and resolution)???

20. Concentric Hemispherical Analyzer (CHA) Problem: sample cannot be at position of slit 1 solutions Use lenses to focus beam at slit 1 Reduce the analyzer angle to 150° • r = source radius • = cone semiangle of source E = e- energy at the source rp = source image at entrance slit W1 • = cone seminagle of image Ep = e- energy at the image Helmoltz-Lagrange equation Lens magnification Retarding ratio  = cone semiangle of source defined by the lens

21. Concentric Hemispherical Analyzer (CHA) What is defining the transmission of the analyser? Consider the cone with semiangle  • The lens defines the transmission • The lens defines the transmission in and the spectrometer in  • The spectrometer defines the transmission The CHA is designed to accept  of about 4-5° (similar to  = 5)

22. Electrostatic lenses Optical ray refraction Electron refraction e speed Refraction index electrostatic potential Snell’s law: n1 sin1 = n2 sin2 The potential changes abruptly at the interface: only the perpendicular component of the momentum changes

23. Electrostatic lenses For real lenses there are no abrupt changes in the potential, as shown in the figure e path Equipotential lines But one can assume the asymptotic behavior of the electron trajectories to make use of the lens equations Transverse magnification Angular magnification Helmoltz-Lagrange equation Conservation of brightness

24. Electrostatic lenses Lenses has the effect to change the kinetic energy of the beam Focussing Defocussing Focussing Electron lenses formed using metallic apertures.

25. Electrostatic deflection analyzers CMA Energy resolution E0 = pass energy ΔEB = Emin-Emax transmitted s = slit width , angular apertures CHA

26. Electrostatic deflection analyzers Geometry of the acceptance slit is very different CHA 5° CMA 6° 42.3° Small signal Compatible with simple electrostatic aperture and tube lenses Long focal distance Radius 100 - 150 mm Res. Power about 1000-5000 Working distance about 25-50 mm Large signal Non compatible with simple electrostatic aperture and tube lenses Short focal distance Cyl diam 100 - 150 mm Res. Power about 200 Working distance about 5 mm

27. Electrostatic deflection analyzers Detection mode Single Multi Scan over voltages acquiring the position and therefore the energy of the electrons with different trajectories Scan over voltages acquiring counts at each energy E(V) E1 E2 E3

28. Electrostatic deflection analyzers Detection mode Multi Channeltron Channelplates + ccd camera Scan over voltages acquiring the position and therefore the energy of the e- with different trajectories

29. Electrostatic deflection analyzers Mode of operation No pre-retarding potential Pre-retarding potential Vary the pre-retarding potential and not E0 Vary E0 with Vscan EB is constant EB is increasing with energy

30. Hemispherical Analyzer of Electron Kinetic Energy

31. Lay-out of an Electron Spectroscopy Experiment Based onto a Double-Pass Cylindrical Mirror Analyzer

32. Hemispherical Analyzer of Electron Kinetic Energy with Entrance Optics Designed for Lateral Resolution

33. Electron Source and Energy Monochromator and Electron Kinetic Energy Analyzer HREELS Apparatus

34. Electron Multiplier Detection efficiency 80 % Gain 108

35. Microchannel plates Thin Si-Pb oxide glass wafers Channel density  105 cm-1 Channel walls act as electron multipliers Detection efficiency 80 % Gain 105 - 108