Multilayer Interference Coating, Scattering, Diffraction ......

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  • 100 nm

    10 eV 100 eV Photon energy

    (D . W

    in dt

    , D . S

    te ar

    ns , J

    . K or

    tri gh

    t)

    Wavelength

    N or

    m al

    in ci

    de nc

    e re

    fle ct

    iv ity

    Natural crystals

    MgF2/Al

    Si C

    Pt, Au

    1 KeV 10 KeV

    10 nm 1 nm 0.1 nm

    Multilayer mirrors ( )

    1.0

    0.5

    0

    mλ = 2d sin θ

    Ch4_F00_Feb2007.ai

    (W/C, T. Nguyen)

    Multilayer Interference Coating, Scattering, Diffraction, Reflectivity

    Professor David Attwood Univ. California, Berkeley Multilayer Interference Coating, Scattering, Diffraction, Reflectivity, EE290F, 6 Feb. 2007

  • Scattering by Density Variations Within a Multilayer Coating

    Ch04_F01_Feb2007.ai

    (T. Nguyen, CXRO/LBNL)

    Mo/Si

    Professor David Attwood Univ. California, Berkeley Multilayer Interference Coating, Scattering, Diffraction, Reflectivity, EE290F, 6 Feb. 2007

  • Scattering of Radiation by a Sinusoidal Density Distribution (Atoms or Electrons)

    Ch04_F02VG.ai

    na(z)

    ki

    ks

    kd = zo2πd2θ

    d

    A

    B

    A

    B

    A

    B

    A

    ki ks z

    θ

    Professor David Attwood Univ. California, Berkeley Multilayer Interference Coating, Scattering, Diffraction, Reflectivity, EE290F, 6 Feb. 2007

  • ki

    ks

    kd = zo2πd2θ

    Scattering from Density Variations

    (4.1)

    (4.2)

    (4.3)

    (4.4a)

    (4.4b)

    (4.5a)

    (4.6a) or

    (4.6b)

    (4.5b)

    Ch04_Eqs1_6VG.ai

    In the long wavelength limit (λ >> a0)

    Professor David Attwood Univ. California, Berkeley Multilayer Interference Coating, Scattering, Diffraction, Reflectivity, EE290F, 6 Feb. 2007

  • Ch04_MltlyrMirBragg1.ai

    d

    ne Mo Si Mo Si Mo

    Mo Si

    Si

    λ

    θ

    mλ = 2d sinθ

    For normal incidence, θ = π/2, first order (m = 1) reflection λ = 2d d = λ/2 if the two layers are approximately equal ∆t  λ/4 a quarter-wave plate coating.

    Multilayer Mirrors Satisfy the Bragg Condition

    Professor David Attwood Univ. California, Berkeley Multilayer Interference Coating, Scattering, Diffraction, Reflectivity, EE290F, 6 Feb. 2007

  • Ch04_MltlyrMirBragg2.ai

    Multilayer Mirrors Satisfy the Bragg Condition

    d

    ne Mo Si Mo Si Mo

    Mo Si

    Si

    λ

    θ

    mλ = 2d sinθ (1 – )

    For normal incidence, θ = π/2, first order (m = 1) reflection λ = 2d d = λ/2 if the two layers are approximately equal ∆t  λ/4 a quarter-wave plate coating.

    4δd2 m2 λ2

    Professor David Attwood Univ. California, Berkeley Multilayer Interference Coating, Scattering, Diffraction, Reflectivity, EE290F, 6 Feb. 2007

  • Professor David Attwood Univ. California Berkeley Multilayer Interference Coating, Scattering, Diffraction, Reflectivity, EE290F, 6 Feb. 2007 Ch04_HiReflecMult.ppt

    High Reflectivity Multilayer Coatings Require:

    • Refractive index contrast at the interfaces • Minimal absorption in the low-Z material • Thin high-Z layer where possible (Γ ; ΔτH /ΔτH + ΔτL) • Interfaces which are chemically stable with time • Minimal interdiffusion at the interfaces • Minimal interfacial roughness (no crystallite formation

    within the layers, no shadowing in the coating process, surface mobility)

    • Thermal stability during illumination • Chemically stable vacuum interface

    (e.g., Si02 or capping layer) • Uniform coating thickness

  • Ch04_HiOrdrReflc.ai

    High Order Reflections from a Multilayer Coating

    4

    3

    2

    1

    0

    Distance from surface (in periods) 10d

    E2

    100

    10–1

    10–2

    10–3

    10–4

    10–5

    10–7 10–6

    0 2.5

    (Courtesy of Y. Wu and J. Underwood.)

    5

    R ef

    le ct

    iv ity

    Scattering angle 2θ (°) 7.5 10 12.5

    m = 1

    2 3

    4 5

    W/C multilayer 22 layer-pairs d = 36.1 Å λ = 1.54 Å

    Measured Calculated internal interference of incoming and outgoing waves

    Professor David Attwood Univ. California, Berkeley Multilayer Interference Coating, Scattering, Diffraction, Reflectivity, EE290F, 6 Feb. 2007

  • Ch04_SpillerBook.ai

    SOFT X-RAY OPTICS Eberhard Spiller

    SPIE (1994) Professor David Attwood Univ. California, Berkeley Multilayer Interference Coating, Scattering, Diffraction, Reflectivity, EE290F, 6 Feb. 2007

  • Professor David Attwood Univ. California Berkeley Multilayer Interference Coating, Scattering, Diffraction, Reflectivity, EE290F, 6 Feb. 2007 Ch04_AngulrScan.ppt

    An Angular Scan of a Multilayer Mirror Performs a Fourier-Transform of the Density Profile

  • Ch04_MultlyrIntrfMir.ai

    Multilayer Interface Mirrors Computational Model

    With refractive index n:

    www.cxro.LBL.gov

    (Courtesy of J. Underwood)

    1(Vacuum) E1

    z x

    θ ∆tA ∆tB

    Ej–1

    Ej

    En

    E2

    RE1

    RE2

    REj–1 REj

    Layer pair N

    Layer pair l

    2 (Material A)

    3 (Material B)

    j – i

    j

    j + 1

    n – 2 (A)

    n – 1 (B) n substrate

    n = 1 – δ + iβ = 1 – (f1 – if2) na re λ2

    2π 0 0

    Professor David Attwood Univ. California, Berkeley Multilayer Interference Coating, Scattering, Diffraction, Reflectivity, EE290F, 6 Feb. 2007

  • Atomic Scattering Factors for Silicon (Z = 14)

    (Henke and Gullikson; www-cxro.LBL.gov)

    Ch02ApC_Tb1F07_Sept05.ai

    Energy (eV) f1 f2 µ(cm 2/g)

    30 3.799 3.734E–01 1.865E+04 70 2.448 5.701E–01 1.220E+04 100 –5.657 4.580E+00 6.862E+04 300 12.00 6.439E+00 3.216E+04 700 13.31 1.951E+00 4.175E+03 1000 13.00 1.070E+00 1.602E+03 3000 14.23 1.961E+00 9.792E+02 7000 14.33 4.240E–01 9.075E+01 10000 14.28 2.135E–01 3.199E+01 30000 14.02 2.285E–02 1.141E+00

    15

    10

    5

    0

    –5

    –10

    101

    100

    10–1

    10–2

    f1

    f2

    µ( cm

    2 /g )

    10 100 1000 E (eV)

    10000

    10 100 1000 10000

    10 100 1000 E (eV)

    10000

    107

    105

    103

    101

    10–1

    σa(barns/atom) = µ(cm2/g) × 46.64 E(keV)µ(cm2/g) = f2 × 1498.220

    0 0

    0

    0

    Silicon (Si) Z = 14

    Atomic weight = 28.086

    K 1838.9 eV L1 149.7 eV L2 99.8 eV L3 99.2 eV

    Edge Energies:

    Professor David Attwood Univ. California, Berkeley Multilayer Interference Coating, Scattering, Diffraction, Reflectivity, EE290F, 6 Feb. 2007

  • Atomic Scattering Factors for Molybdenum (Z = 42)

    (Henke and Gullikson; www-cxro.LBL.gov)

    Ch02ApC_Tb1F12_Sept05.ai

    Energy (eV) f1 f2 µ(cm 2/g)

    30 1.071 5.292E+00 7.736E+04 70 19.38 4.732E+00 2.965E+04 100 14.02 1.124E+00 4.931E+03 300 4.609 1.568E+01 2.292E+04 700 31.41 1.819E+01 1.140E+04 1000 35.15 1.188E+01 5.210E+03 3000 35.88 1.366E+01 1.997E+03 7000 42.11 3.493E+00 2.189E+02 10000 41.67 1.881E+00 8.248E+01 30000 42.04 1.894E+00 2.769E+01

    µ( cm

    2 /g )

    10 100 1000 E (eV)

    10000

    10 100 1000 10000

    10 100 1000 E (eV)

    10000

    σa(barns/atom) = µ(cm2/g) × 159.31 E(keV)µ(cm2/g) = f2 × 438.590

    0 0

    Edge Energies:

    40 50 60 70

    20 30

    10 0

    101

    100

    f1

    f2

    106

    104 105

    102

    100 101

    103

    0

    0

    K 19999.5 eV L1 2865.5 eV M1 506.3 eV N1 63.2 eV L2 2625.1 eV M2 411.6 eV N2 37.6 eV L3 2520.2 eV M3 394.0 eV N3 35.5 eV M4 231.1 eV M5 227.9 eV

    Molybdenum (Mo) Z = 42

    Atomic weight = 95.940

    Professor David Attwood Univ. California, Berkeley Multilayer Interference Coating, Scattering, Diffraction, Reflectivity, EE290F, 6 Feb. 2007

  • Ch04_OptomizReflcty.ai

    Optimized Reflectivity with Thin “High-Z” Layers

    • Sharp interfaces needed for scattering • Thin high-Z layer to minimize absorption • Low-Z layer best as a “spacer”

    (Vinogradov and Zeldovich, 1977) (also see Borrmann, 1941)

    (4.7)

    (4.8)

    high-Z low-Z

    high-Z low-Z

    high-Z

    high-Z low-Z

    Professor David Attwood Univ. California, Berkeley Multilayer Interference Coating, Scattering, Diffraction, Reflectivity, EE290F, 6 Feb. 2007

  • Ch04_ComputdReflec.ai

    Computed Reflectivity of a W/C X-Ray Multilayer Mirror

    1.0

    0.8

    0.6

    0.4

    0.2

    0 0

    (Courtesy of J. Underwood and D. Solina)

    2

    λ = 8.34 Å d = 22.5 Å N = 100 Γ = 1/3

    4 6 Glancing angle (°)

    R ef

    le ct

    iv ity

    8 10 12

    W/C

    Professor David Attwood Univ. California, Berkeley Multilayer Interference Coating, Scattering, Diffraction, Reflectivity, EE290F, 6 Feb. 2007

  • Professor David Attwood Univ. California Berkeley Multilayer Interference Coating, Scattering, Diffraction, Reflectivity, EE290F, 6 Feb. 2007 Ch04_MultilyrIntrCtg.ppt

    Molybde