Positron Annihilation Spectroscopy Measurements for ...
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Positron Annihilation Spectroscopy Measurements for Porosimetry
R. Krause-Rehberg, Dept. of Physics, University Halle
2015 Frontiers of Characterization and Metrology for Nanoelectronics
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Positron Annihilation Lifetime Spectroscopy - PALS
When trapped in vacancies: Lifetime increases
due to smaller electrondensity in open volume
γ
γ
positrons: thermalize (reach thermal
energies) diffuse being trapped and annihilate
1.274 MeV
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Digital lifetime measurement
simple setup timing very accurate each detector for start & stop (double statistics)
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Screenshot of two digitized anode pulses
time difference = 2.65471 samples = 663.67 ps
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Principles of PALS: ortho-Positronium
In materials without free electrons Positronium may be formed (Polymers, glass, liquids, gases).
25% 75%
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Principles of PALS: pick-off Annihilation
pick-off annihilation:
o-Ps is converted to p-Ps by capturing an electron with anti-parallel spin
happens during collisions at walls of pore
lifetime decreases rapidly
lifetime is function of pore size 0.5 ns ... 142 ns
lifetime can be extracted from spectra
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Principles of PALS: typical spectrumtypical lifetime spectrum for porous glass:
4 exponential decay components
p-Ps -> 0.125 ns
free positrons ~ 0.5 ns
o-Ps in amorphous region of glass ~ 1.5 ns
o-Ps in pores
0 200 400 600 80010
100
1000
10000
100000
1000000
5 nm 26 nm
N
time (ns)
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PALS: detection limits lower detection limit: open
volume of 2Å diameter e.g. open volume between
polymer chains
upper limit: ≈ 60 nm diameter
physical limit: vacuum lifetime of o-Ps = 142 ns
upper limit depends also on corresponding intensity
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New Analysis Technique: MELT
MELT1 = Maximum Entropy for Lifetime Analysis
number of components must not be known
output is intensity versus lifetime
pore size distribution can be determined
disadvantage: very high statistics necessary (> 107
counts)
1A. Shukla et al., 1997, Materials Science Forum, 255-257, 233
porous polymer
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The TE model
Pore size < 1 nm -> neglected, only pick off annihilation
102
02
03
02
32
243
)()1()(
1
−
−−
≈=+
=
≅−+=
+=
=
ns
PPP
ATS
PsoPso
λλλλ
λλλ
λλ
λτ
γ
γγγ
γγ
∆++
∆+−=
RRR
RRRR ATE
ππ
λλ 2sin211)(
γλ3
Tao, S. J. J. Chem. Phys. 1972, 56, 5499-5510. / Eldrup, M.; Lightbody, D.; Sherwood, J. N. Chem. Phys. 1981, 63, 51-58.
Annihilation rate:
= 0.166 nm determined by Eldrup and Jean Pore size > 1 nm -> cannot be neglected, temperature dependence of o-Ps
lifetime (excited states)
R∆
γλ3
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The TE model (valid until 1 nm radius)
Tao, S. J. J. Chem. Phys. 1972, 56, 5499-5510. / Eldrup, M.; Lightbody, D.; Sherwood, J. N. Chem. Phys. 1981, 63, 51-58.
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The TE model
Tao, S. J. J. Chem. Phys. 1972, 56, 5499-5510. / Eldrup, M.; Lightbody, D.; Sherwood, J. N. Chem. Phys. 1981, 63, 51-58.
TE model valid for r > 2nm very successful for open-volume
characterization in polymers
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Polymer research
G. Dlubek et al., Macromol. Chem. Phys. 2008, 209, 1920–1930 and e-Polymers 2007, no. 108
PALS study of different polymers under CO2 gas exposure and pressure densified (200 MPa)
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Polymer research
G. Dlubek et al., Macromol. Chem. Phys. 2008, 209, 1920–1930 and e-Polymers 2007, no. 108
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Mesopores - Controlled pore glasses
IUPAC (International Union of Pure and Applied Chemistry)
• Micropores ( < 2 nm)
• Mesopores ( 2 - 50 nm)
• Macropores ( > 50 nm)
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Controlled pore glasses - CPGVYCOR-Process
alkali borosilicateExtractionT
HCl/NaOH530 – 71 0° Cglass
dP 1 to 1 1 0 nm
F. Janowski, D. Enke in F. Schüth, K.S.W. Sing, J. Weitkamp (Eds.), Handbook of Porous Solids, WILEY-VCH, Weinheim, 2002, 1432-1542.
spinodal phase separation decomposition is initiated by heat treatment alkali rich borate phase <-> pure silica alkali phase soluable in acid -> silica network pore size depends on basic material shape depends on duration and T of heat treatment
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Model for R > 1 nm – RTE
D. W. Gidley, T. L. Dull, W. E. Frieze, J. N. Sun, A. F. Yee, J. Phys. Chem. B 2001, 105, 4657.
3
1
13
2
2
2
2
2sin121
4),(
+−−
−=
∑
∑∞
=
−
∞
=
−
i
kTDi
i
kTDi
SARTE
e
eDi
iD
TDβ
β
γ
πδπδλλ
λλ
Rectangular TE model = RTE model (for 3D cubic pores):
1 10 1000
20
40
60
80
100
120
140
500 K300 K
50 K
RTE model
τ 4 (n
s)
Pore Size D (nm)
Boltzmann statistics ascribes explicit temperature dependence to the lifetime
Rectangular geometry -> prevention of complicated Bessel functions
= 0.18 nm analogous to TE modelδ
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The experiments at room temperature
we measured porous glass in a broad pore size range
pore size obtained by N2-adsorption method
for T=300 K general agreement to the RTE model
calibration curve for the correlation of o-Ps lifetime and pore size
1 10 1000
20
40
60
80
100
120
140
T = 300 K
RTE Model Exp. Data
τ 4 (ns
)
Pore Size D (nm) from LN2 absorption
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The RTE model
D.W. Gidley et al., Annu. Rev. Mater. Res. 2006. 36:49–79
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Small pores in the wall of larger pores
LN2 adsorption
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amount of solvent
data analysis by MELT
15 nm pores4 nm pores
solvent (MCM) was added into a larger pore system
large pores: 15 nm
small pores are formed in the walls: 4 nm
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The Slow-Positron Beam Technique
- broad positron emission spectrum from beta sources
- deep implantation into solids
- no use for study of defects in thin layers
- moderation necessary
Mean implantation depth of un-moderated positrons (1/e): Si: 50µm
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Moderation of Positrons
moderation efficiency: ≈10-4
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HZDR Dresden-Rossendorf: Ground map of the ELBE hall
Martin-Luther-Universität Halle
GiPS MePS
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Martin-Luther-Universität Halle
MePS scheme
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MePS system @ ELBE, 26. November 2013
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modern ultra-large scale microprocessors suffers from long relaxation times
information transport is limited by product R × C
R has been decreased: Copper technology (instead of Al)
C is relatively high when SiO2 is used as isolation layer; εr=4
low-k (small εr = 2…2.5) layers may help
these are layers with micropores with pore size of d≈1 nm with high porosity
problem for characterization: closed porosity
Low-K dielectric layers
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Low-K dielectric layers
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Low-K dielectric layers
Positrons are ideal tool for closed porosity in low-k layers
Lifetime spectra of differently treated low-K layers
Treatment:− untreated porous
layer
− plasma treatment for compactation
− TiN cap layer
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Low-K dielectric layers
dispersion of lifetime gives the size distribution of the pore system
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Low-K dielectric layers
monoenergetic positrons can be used to depth scan the layer
monoenergetic positrons are obtained by moderation
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Summary
PALS is a useful porosimetry tool very sensitive method for small pores (0.3 to 10 nm) upper sensitive limit ≈ 60 nm non-destructive method Works in open and closed pore systems applicable also for thin layers (50 … 2000 nm)
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http://positron.physik.uni-halle.de
Uni Halle
Stefan ThränertDirk EnkeMarco JungmannMaik ButterlingSteve ZiegerThomas CudrigMohamed Elsayed
HZDR
Andreas WagnerMaik ButterlingWolfgang Anwand
….and more
Acknowledgement