x-ray interaction with matter, scattering and diffractionattwood/sxr2009/... · univ. california,...

$: X-Ray Interaction with Matter, Scattering and Diffractionattwood/sxr2009/... · Univ. California, Berkeley X-Ray Interaction with Matter: Absorption, Scattering and Diffraction, EE213$
X-Ray Interaction with Matter:Absorption, Scattering

and Diffraction

David Attwood

University of California, Berkeley

(http://www.coe.berkeley.edu/AST/sxr2009)

X-Ray Interaction with Matter: Absorption, Scattering and Diffraction, EE213 and AST210, 22 Jan 2009

1 m 100 nm 10 nm 1 nm 0.1 nm = 1Å

10 keV

CuK

2a0

SiK OK CK SiL

1 keV

Photon energy

Wavelength

100 eV 10 eV 1 eV

IR VUV

Hard X-raysUV Extreme Ultraviolet

Soft X-rays

• See smaller features

• Write smaller patterns

• Elemental and chemical sensitivity

CuKα

The Short Wavelength Regionof the Electromagnetic Spectrum

Ch01_F01.aiProfessor David AttwoodUniv. California, Berkeley

Ch01_Eqs1.1_2.ai

Photon Energy, Wavelength, Power

Professor David AttwoodUniv. California, Berkeley

(1.1)

(1.2a)

(1.2b)

+Ze +Ze

+Ze +Ze

Primaryelectron

Photoelectron(E = ω – EB)

KLL Augerelectron

Photon

(ω)

Scatteredprimary electron (Ep)

Secondaryelectron (Es)

(Ep)

′

KL

M

KL

M

(a) Electron collision induced ionization

e–

e–

e–

e–

(b) Photoionization

(c) Fluorescent emission of characteristic radiation (d) Non-radiative Auger process

KL

M

KL

M

e–

ω

Basic Ionization and EmissionProcesses in Isolated Atoms

Ch01_F02.aiProfessor David AttwoodUniv. California, Berkeley X-Ray Interaction with Matter: Absorption, Scattering and Diffraction, EE213 and AST210, 22 Jan 2009

ApxB_1_47_Jan07_lec2.ai

Electron Binding Energies, in Electron Volts(eV), for the elements in their Natural Forms

www.cxro.LBL.gov

X-Ray Interaction with Matter: Absorption, Scattering and Diffraction, EE213 and AST210, 22 Jan 2009Professor David AttwoodUniv. California, Berkeley

K-shellAuger

L3-subshellfluorescence

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

00 20 40 60

Atomic number

Flu

ores

cenc

e an

d A

uger

yie

lds

80

(Courtesy of M. Krause, Oak Ridge)

100

Fluorescence and Auger Emission Yields

Ch01_F03_2005.ai

L3-subshellAuger

K-shellfluorescence

Professor David AttwoodUniv. California, Berkeley X-Ray Interaction with Matter: Absorption, Scattering and Diffraction, EE213 and AST210, 22 Jan 2009

1 10 100

Energy above Fermi level (eV)

1000

100

10

1

0.1

0

1

2

3

4

4

0

1

2

3

Al

Au

Mea

n fr

ee p

ath

(nm

)

100 101 102 103 104

(a)

(b)

(c)

Electron Mean Free Paths As a Function of Energy

Ch01_F05.ai

Courtesy of: Penn (a & b), Seah and Dench (c)


x

x

(a)

(c)

(b)

(d)

(e)

na

Ι0

Ι0

Ι0

Ι(x)

ω

ρ

ω

ωΙ(x)

II0

ω

Cu foil

Cu atom

3p

3s4s

3d

2p2s

10 100Photon energy (eV)

σabs

1000

10 100Photon energy (eV)

Distance, x

Inte

nsity1000

100

10

1

0.1

0.01

Mbatom

106

105

104

103

102

cm2

g

Exponentialdecay (e–ρµx)

= e–ρµx

Photoabsorption by Thin Foils and Isolated Atoms

Ch01_F08_Aug05.ai

II0

= e–naσabsx


Atomic Energy Levels and Allowed Transitions in the Bohr Atom

Ch01_Eqs4_5_6_9.ai

Equate Coulomb Force Ze2/4π0r2 to the centripetal force mv2/r:

En = (1.4)

(1.5)

(1.6)

(1.9)

mZ2e4

32π2220

1

n2

rn = · n24π02

me2Z

me4

32π202

rn = ; a0 = 0.529 Å

13.6 eV

a0n2

Z

1

nf

1

ni

ω = Ei – Ef = – Z2

2 2


Quantum Mechanics Basedon a Probabilistic Wave Function, Ψ(r, t)

Ch01_Eqs10_13_15.ai

– ∇2Ψ(r, t) + V(r, t)Ψ(r, t) = i

P(r, t)dr = Ψ∗(r, t) Ψ(r, t)dr

quantum numbers: n, , m, ms

selection rules for allowed transitions: ∆ = ± 1 ∆j = 0, ± 1

r = rP(r, t)dr = Ψ∗(r, t)rΨ(r, t)dr

(1.10)

(1.13)

(1.15)

2

2m∂Ψ(r, t)

∂t


Lower state

Upper state

1

0Time

Pro

babi

lity

Osc

illat

ion

ampl

itude

Time

Radiative Decay Involves An Atom Oscillating Between Two Stationary States at the Frequency if = (Ei – Ef) /


20

15

10

5

0 0.5 1.5

2s

3s

3p

1s

2pR

adia

l cha

rge

dens

ity d

istr

ibut

ion

1.0 2.0Normalized radius, r/a0

2.5 3.0 4.03.5

Probabilistic Radial Charge Distribution (e/Å)in the Argon Atom

Ch01_F12.ai

Courtesy of Eisberg and Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles.


n

N

M

L

K

44...4

NVII 4f7/2..NIV 4d3/2..NI 4s

MV 3d5/2MIV 3d3/2MIII 3p3/2MII 3p1/2MI 3s

LIII 2p3/2LII 2p1/2LI 2s

K 1s

33...0

7/25/2...1/2

33333

22110

5/23/23/21/21/2

222

110

3/21/21/2

1 0 1/2

j

Kα1

Cu Kα1 = 8,048 eV (1.541Å) Cu Lα1

= 930 eVCu Kα2

= 8,028 eV (1.544Å) Cu Lα2 = 930 eV

Cu Kβ1 = 8,905 eV Cu Lβ1

= 950 eV

Absorption edgesfor copper (Z = 29):

EN1, abs = 7.7 eV

.

.EM3, abs = 75 eV.EM1, abs = 123 eV

EL3, abs = 933 eVEL2, abs = 952 eVEL1, abs = 1,097 eV

EK, abs = 8,979 eV (1.381Å)

Kα2

Lα1

Mα1

Lβ2Lα2

Kβ1Kβ3

Kγ3

Energy Levels, Quantum Numbers, andAllowed Transitions for the Copper Atom

Ch01_F11_Jan07.aiProfessor David AttwoodUniv. California, Berkeley X-Ray Interaction with Matter: Absorption, Scattering and Diffraction, EE213 and AST210, 22 Jan 2009

λ

λλ

λ

λ

(a) Isotropic scattering from a point object (b) Non-isotropic scattering from a partially ordered system

(c) Diffraction by an ordered array of atoms, as in a crystal

(d) Diffraction from a well-defined geometric structure, such as a pinhole

D θnull

(e) Refraction at an interface

n = 1 n = 1–δ+iβ

(f) Total external reflection

1.22λd

n = 1–δ+iβ

θ<θc

λ

θ

mλ = 2d sinθ

θnull =

θ

d

Scattering, Diffraction, and Refraction


x-ray interaction with matter, scattering and diffractionattwood/sxr2009/... · univ. california,...

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