X-Ray Interaction with Matter: Absorption, Scattering and …ilsf.ipm.ac.ir › News › 2014-03-03BeamlineOpWrkshp › ILSF_Attwood_… · X-Ray Interaction with Matter: Absorption,

Professor David Attwood / UC Berkeley / Iranian Light Source Workshop / March 3-4, 2014 ILSW_Attwood_Lec4_March2014.pptx

X-Ray Interaction with Matter: Absorption, Scattering and

Refraction

David Attwood University of California, Berkeley

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The short wavelength region of the electromagnetic spectrum

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n = 1 – δ + iβ δ, β << 1


Photon energy, wavelength, power

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Characteristic absorption edges for almost all elements in this spectral region

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

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

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www.cxro.LBL.gov

Professor David Attwood / UC Berkeley / Iranian Light Source Workshop / March 3-4, 2014 ILSW_Attwood_Lec4_March2014.pptx 7

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


Refractive index at nanometer wavelengths

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Available optical techniques for soft x-rays and EUV

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Charles-Augustin de

Coulomb

Carl Friedrich Gauss

Michael Faraday

André-Marie Ampère James Clerk

Maxwell

Heinrich Hertz

Maxwell’s Equations

Courtesy of Andrew Aquila (AS&T, UC Berkeley)

The Equations of Light


Scattering, refraction, and reflection

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Scattering cross-sections

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Scattering by a bound electron

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Example: complex atomic scattering factor for carbon

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Wave propagation and refractive index at x-ray wavelengths

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Refractive index in the x-ray spectral region

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Refractive index for x-rays

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Quantum mechanical model of refractive index

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Phase variation and absorption of propagating waves


Phase shift relative to vacuum propagation


Spatial continuity along the interface


Normal incidence reflection at an interface (both polarizations)


Glancing Incidence Optics

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Total external reflection of soft x-ray and EUV radiation


Total external reflection with finite β


X-Rays and Extreme Ultraviolet (EUV) Radiation

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• 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.


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

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X-ray microprobe at SPring-8

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Undulator DCM

TC1Slit Incident Slit

Ion chamber Mirror manipulator

SDD

Sample & Scanner

PIN photodiode

Beam monitor

Optical microscope

Front end

Experimental hutch

98m f1: 252mm

f2: 150mm

45m

Courtesy of K. Yamauchi and H. Mimura, Osaka University.

S. Matsuyama et al., Rev. Sci. Instrum. 77, 103102 (2006)

Now focused to 7 nm


Scattering by density variations within a multilayer coating

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Multilayer mirrors can provide high reflectivity at the Bragg condition

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Atomic scattering factors for silicon (Z = 14)

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Atomic scattering factors for molybdenum (Z = 42)

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A High Quality Mo/Si Multilayer Mirror

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N = 40 d = 6.7

Courtesy of Sasa Bajt (DESY) ˇ

Small reflections at many interfaces add in phase at the Bragg angle


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

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Multilayer mirrors have achieved 70% reflectivity

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Courtesy of Sasa Bajt, LLNL


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

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X-Ray Interaction with Matter: Absorption, Scattering and …ilsf.ipm.ac.ir › News › 2014-03-03BeamlineOpWrkshp › ILSF_Attwood_… · X-Ray Interaction with Matter: Absorption,