X-Ray Interaction with Matter: Absorption, Scattering and Refraction

Transcription

1 X-Ray Interaction with Matter: Absorption, Scattering and Refraction David Attwood University of California, Berkeley 1

2 The short wavelength region of the electromagnetic spectrum n = 1 δ + iβ δ, β << 1 2

3 Photon energy, wavelength, power 3

4 Characteristic absorption edges for almost all elements in this spectral region 4

5 Energy levels, quantum numbers, and allowed transitions for the copper atom 5

6 Electron binding energies, in electron volts (ev), for the elements in their natural forms 6

7 Refractive index from the IR to the x-ray region of the electromagnetic spectrum 7

8 Refractive index at nanometer wavelengths 8

9 Available optical techniques for soft x-rays and EUV 9

10 The Equations of Light Michael Faraday André-Marie Ampère Maxwell s Equations James Clerk Maxwell Charles- Augustin de Coulomb Carl Friedrich Gauss Heinrich Hertz Courtesy of Andrew Aquila (AS&T, UC Berkeley) 10

11 Scattering, refraction, and reflection 11

12 Scattering cross-sections 12

13 Scattering by a bound electron 13

14 Example: complex atomic scattering factor for carbon 14

15 Wave propagation and refractive index at x-ray wavelengths 15

16 Refractive index in the x-ray spectral region 16

17 Refractive index for x-rays 17

18 Quantum mechanical model of refractive index 18

19 Phase variation and absorption of propagating waves 19

20 Phase shift relative to vacuum propagation 20

21 Spatial continuity along the interface 21

22 Normal incidence reflection at an interface (both polarizations) 22

23 Glancing Incidence Optics 23

24 Total external reflection of soft x-ray and EUV radiation 24

25 Total external reflection with finite β 25

26 X-Rays and Extreme Ultraviolet (EUV) Radiation Optics behave differently at these very short wavelengths (nanometers rather than 520 nm green light) The refractive index is less than unity, n = 1 δ + iβ Waves bend away form the normal at an interface Absorption is significant in all materials and at all wavelength. Because of absorption, refractive lenses do not work, except at high photon energies 20 kev. Because light is bent away from the surface normal, it is possible to have total external reflection at glancing incidence a commonly used technique. 26

27 Buried, trace amounts of iron in a defective silicon solar cell 27

28 X-ray microprobe at SPring-8 98m f1: 252mm 45m f2: 150mm PIN photodiode Optical microscope Now focused to 7 nm Undulator DCM TC1Slit SDD Mirror manipulator Beam monitor Ion chamber Sample & Scanner Incident Slit Experimental hutch S. Matsuyama et al., Rev. Sci. Instrum. 77, (2006) Front end Courtesy of K. Yamauchi and H. Mimura, Osaka University. 28

29 Scattering by density variations within a multilayer coating 29

30 Multilayer mirrors can provide high reflectivity at the Bragg condition 30

31 Atomic scattering factors for silicon (Z = 14) 31

32 Atomic scattering factors for molybdenum (Z = 42) 32

33 A High Quality Mo/Si Multilayer Mirror Small reflections at many interfaces add in phase at the Bragg angle N = 40 d = 6.7 Courtesy of Sasa ˇ Bajt (DESY) 33

34 High reflectivity, thermally and environmentally robust multilayer coatings for high throughput EUV lithography 34

35 Multilayer mirrors have achieved 70% reflectivity Courtesy of Sasa Bajt, LLNL 35

36 The Cassegrain Telescope with multilayer coatings for EUV imaging of the solar corona 36