X-Ray Interaction with Matter, Scattering and Diffractionattwood/sxr2009/... · Univ. California,...
Transcript of X-Ray Interaction with Matter, Scattering and Diffractionattwood/sxr2009/... · Univ. California,...
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)
Professor David AttwoodUniv. California, Berkeley X-Ray Interaction with Matter: Absorption, Scattering and Diffraction, EE213 and AST210, 22 Jan 2009
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
Professor David AttwoodUniv. California, Berkeley X-Ray Interaction with Matter: Absorption, Scattering and Diffraction, EE213 and AST210, 22 Jan 2009
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
Professor David AttwoodUniv. California, Berkeley X-Ray Interaction with Matter: Absorption, Scattering and Diffraction, EE213 and AST210, 22 Jan 2009
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
Professor David AttwoodUniv. California, Berkeley X-Ray Interaction with Matter: Absorption, Scattering and Diffraction, EE213 and AST210, 22 Jan 2009
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) /
Ch01_F09.aiProfessor David AttwoodUniv. California, Berkeley X-Ray Interaction with Matter: Absorption, Scattering and Diffraction, EE213 and AST210, 22 Jan 2009
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.
Professor David AttwoodUniv. California, Berkeley X-Ray Interaction with Matter: Absorption, Scattering and Diffraction, EE213 and AST210, 22 Jan 2009
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
Ch01_F13.aiProfessor David AttwoodUniv. California, Berkeley X-Ray Interaction with Matter: Absorption, Scattering and Diffraction, EE213 and AST210, 22 Jan 2009