POLARIZED-SURFACE-WAVE-SCATTERING SYSTEM (PSWSS)
FOR IN-SITU AND ON-LINE CHARACTERIZATION OF NANOSTRUCTURES
Mathieu Francoeur, Mustafa M. Aslan, Pradeep G. Venkata, and M. Pinar Mengüç
RADIATIVE TRANSFER LABORATORY
Department of Mechanical Engineering
www.engr.uky.edu/rtl
Radiative Transfer Laboratory, Department of Mechanical Engineering,
University of Kentucky, Lexington, KY 40506-0503
Results
Experimental System
Problem Statement
Ex-situ characterization of nanoparticles/nanostructures is possible via scanning
electron microscopy (SEM), tunnelling electron microscopy (TEM), or atomic force
microscopy (AFM). However, these techniques are intrusive and cannot provide realtime analyses. To be able to engineer “bottom-up” processes at nanoscale, new
approaches need to be developed for measurement and visualization of nanosize
particles and structures.
CPU
with a 20 nm Au thin film; λ = 514.5 nm ; θ0 = 23°. The influence of the level of
agglomeration is studied (a system is defined as a function of its composition of
unagglomerated nanoparticles [5]).
Measurement lock-in amplifier
(Stanford SR830 DSP)
Data acquisition card
(PCIM-DAS1602/16)
rotational
stage
1.0
PMT 2
1.0
0.8
OC
z
θ
Reference lock-in amplifier
(Stanford SR830 DSP)
0.2
x
sample
prism
translational
stage
PMT 1
NDF
OC
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.4
OC
θ0
PMT 3
θr = θ0
-1.0
0
OCh: optical chopper, NDF: neutral density filter, PMT: photomultiplier tube, BS: beam
splitter, FC: fiber collimator, OC: optical components (polarizer, retarder, iris, and /or lens)
Self assembly process of Au
nanoparticles [1].
-0.8
-1.0
FC
translational stage
scattering
measurement
rotational stage
20
40
60
80
θ
100
120
140
160
180
The Mueller matrix
S13
S22
S32
S 23
S33
S42
S 43
S14 ⎤⎛ I ⎞
⎜ ⎟
S24 ⎥⎜ Q ⎟
⎥
S34 ⎥⎜U ⎟
⎜ ⎟
S44 ⎥⎦⎜⎝ V ⎟⎠inc
elements Sij are functions of the scattering angles.
10
metallic film (optional)
-0.8
-1.0
0
20
40
60
80
100
θ
120
140
160
180
160
180
[M33]
-1
10
10 %
15 %
25 %
50 %
75 %
100 %
-2
10
-3
0
20
40
60
80
100
120
140
160
10
180
0
20
40
60
80
θ
100
120
140
with λ = 514.5 nm (150 mW Ar-Ion laser) and θ0 = 37°.
sapphire substrate
1.2
θr = θ0
1.1
semi-cylindrical
sapphire prism
1.0
incident radiation
-0.6
Measurements of the Mueller matrix elements: iron particles on quartz substrate
index matching
fluid
θ0 ( > θc)
180
0%
25 %
50 %
75 %
100 %
0.0
-0.4
θ
x
160
0.2
-0.2
norm,avg
norm,avg
10 %
15 %
25 %
50 %
75 %
100 %
-2
z
140
0.4
X%
[M12]
X%
-1
surface plasmon/surface wave
nanoparticles
to characterize
120
0
-3
scattered radiation
PMT
100
0.6
Normalized Mueller matrix elements Mij (Sij(θ)/S11(θ))
S12
10
0.9
totally reflected
radiation
The normalized Mueller matrix elements M11, M12, M22, M33, M34, and M44 are
measured experimentally via the PSWSS. Six independent sets of measurements
with specific orientations of polarizers/retarders are needed to measure these six
Mueller matrix elements. Size, size distribution, shape, and level of agglomeration
of the scatterers are then retrieve via an inverse algorithm [4].
M11 (S11(θ)/S11(25°))
The characterization procedure is based on the analysis of the change of intensity
and state of polarization after scattering. This information can be provided by the
Mueller matrix elements, relating the incident and scattered Stokes vectors:
air
rotating arm
10
80
10
air
reflectance
measurement
60
0.8
0
incident light
source
40
1.0
10
scattered radiation
Traditional
light
scattering
z
techniques cannot be used as surface wave/surface plasmon
the typical wavelengths of light nanostructures
x
metallic film (optional)
are large relative to the sizes of to characterize
high refractive
the scatterers (5-100 nm).
index medium
Nanostructures
to
be
totally reflected
radiation
incident radiation
characterized are consequently
illuminated by surface waves
created
by
total
internal
reflection (TIR). The evanescent
electromagnetic
field
thus
scattered by the nanostructures is then measured in the far-field to infer properties
such as size, size distribution, shape, and level of agglomeration.
20
θ
sensitivity of M11 is always low; the
information provided by the change of
state of polarization after scattering is
therefore crucial for characterization of
nanoparticles [4,5].
Theoretical Background
⎡ S11
⎛I⎞
⎜ ⎟
⎢
⎜ Q ⎟ = 1 ⎢ S 21
⎜U ⎟
k 2 r 2 ⎢ S31
⎜⎜ ⎟⎟
⎢S
⎝ V ⎠ sca
⎣ 41
0
Sensitivities of the Mueller matrix
elements to the level of agglomeration are
evaluated via the calculation of the
sensitivity coefficients X. In general, the
sample holder
and prism
0%
25 %
50 %
75 %
100 %
-0.6
-0.8
Laser
0.0
-0.2
-0.6
FC
OCh BS OC
0.4
M33
Motion control board
0.8
0%
25 %
50 %
75 %
100 %
0.6
M12
The objective of this project is the development of a
precise, accurate, robust, on-line, and non-intrusive
diagnostic
system
for
characterization
of
nanoparticles,
agglomerates
(colloids),
and
nanostructures
during
self-assembly
and/or
nanofabrication
approaches.
Our
integrated
characterization tool is called the “polarizedsurface-wave-scattering system” (PSWSS) and is
based on the measurements of scattered surface
waves. The PSWSS will allow us to characterize
structures as small as 5 to 100 nm.
Calculation of the Mueller matrix elements: Au nanoparticles (Gaussian
distribution of diameters from 38 to 42 nm) on Al2O3 (sapphire) substrate coated
M34
UNIVERSITY OF KENTUCKY
College of Engineering
www.uky.edu
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
20
30
40
50
60
70
80
90
100 110 120 130 140 150
Scattering angle θ
1.4
1.2
M22
1.0
0.8
0.6
M12
0.4
0.2
0.0
-0.2
M34
M44
-0.4
-0.6
-0.8
-1.0
10
M33
20 30
40
50 60
70
80
90 100 110 120 130 140 150 160
Scattering angle θ
Conclusions
Experimentally, we measured the normalized Mueller matrix elements Mij as a
function of the polar angle θ for a fixed azimuthal angle (φ = 0°). We have developed
a mathematical model to calculate the Mueller matrix elements for scattering by
spherical nanoparticles on a surface [2], and by 2D agglomerates of spherical
particles on a surface [3].
Numerical results have shown that it is possible to characterize nanostructures via surface wave scattering [5]. We are in the process of developing an inversion algorithm based on
the derivatives of scattering profiles to retrieve size, size distribution, shape, and level of agglomeration of the scatterers [4].
The experimental system needs to be calibrated with samples of known configuration. We are in the process of calibrating the PSWSS via 15 nm spherical Au particles deposited
uniformly on sapphire substrates. The Mueller matrix elements measured will then be compared with numerical predictions.
References: [1] T. Sato, D. Brown, and B.F.G. Johnson, Chemical Communications, 1007-1008 (1997).
[2] G. Videen, M.M. Aslan, and M.P. Mengüç, Journal of Quantitative Spectroscopy and Radiative Transfer 93, 195-206 (2005)
[3] P.G. Venkata, M.M. Aslan, M.P. Mengüç, and G. Videen, ASME Journal of Heat Transfer 129, 60-70 (2007)
[4] R. Charnigo, M. Francoeur, M.P. Mengüç, A. Brock, M. Leichter, and C. Srinivasan, Journal of the Optical Society of America A 24(9), 2578-2589 (2007)
[5] M. Francoeur, P.G. Venkata, M.P. Mengüç, Journal of Quantitative Spectroscopy and Radiative Transfer 106, 44-55 (2007)
Acknowledgments: This work has been sponsored by a National Science Foundation grant (NSF-NER DMI-0403703 2004-2006) and a Kentucky Sciences and
Engineering Foundation grant (KSEF-338-RDE-003 2004-2006). MF is grateful to the Natural Sciences and Engineering Research Council (NSERC) for their
financial support (ES D3 scholarship).
Contact Information: mfran0@engr.uky.edu (Mathieu Francoeur) and menguc@engr.uky.edu (M. Pinar Mengüç)