Nano-Scale Characterization: M. Pinar Mengüç

RADIATIVE TRANSFER LABORATORYMechanical Engineering Department

UNIVERSITY OF KENTUCKYCollege of Engineering

Experimental Methods: (a) Ellipsometry; (b) Surface Plasmon reflectance; (c) Surface Plasmon scattering.

2

3

x

z

i s

Metal thin film

Solution with metalnanoparticles

Incident radiationReflectedradiation

t2

t1

Light sourceDetector

PolarizerAnalyzer

RetarderRetarder

2

3

1

Metalic thin film

Medium 3;nano-particles

Medium 1;Quartz substrate

x

z

Incident radiation Reflected radiation

i

t2

SPW

x

z

i

t

Metalthin film

Solution withnanoparticles

Light source

Polarizer

Scattered lightfrom particles

DetectorAnalyzer

Retarder

s

0

Einc

0

h

d

z'

x'

a

1

2

0

Esca

z2

x2z1

x1

d

Nano-Scale Characterization: M. Pinar Mengüç

RADIATIVE TRANSFER LABORATORYMechanical Engineering Department

UNIVERSITY OF KENTUCKYCollege of Engineering

PMT

Scattered light optics

Incident light optics

Translation stage to control incident angle

Rotational stage

Light source

Motor Control Unit

x

z

i

t

Metalthin film

Solution withnanoparticles

Light source

Polarizer

Scattered lightfrom particles

DetectorAnalyzer

Retarder

RADIATIVE TRANSFER LABORATORYMechanical Engineering Department

UNIVERSITY OF KENTUCKYCollege of Engineering

Sensitivity AnalysisA a sensitivity analysis is performed to determine the optimum conditions for characterization of gold nanoparticles and 2D-agglomerates via evanescent wave/surface plasmons. This analysis is of primary importance in order to determine the conditions for which a particular parameter can be estimated, and is a necessary step for the development of inversion techniques and optimal experiments.

Sensitivities of M11, M12, M33, and M34 are calculated via the normalized sensitivity coefficients:

kk

ijij

normM

MXk

),(),]([

The normalized sensitivity coefficients provide the variation of the output/measurement (normalized scattering matrix elements, Mij) associated to a relative variation of one parameter of the system (ψk), when all other parameters (known η or to be estimated ψl,l≠k) are fixed. In a general way, the estimation of a

parameter is considered to be conceivable when the normalized sensitivity coefficients are greater than 0.1, difficult but feasible between 0.01 and 0.1, and

very difficult or even impossible below the threshold 0.01.

It is assumed that the system is composed of single nanoparticles, as well as agglomerates (triangle, square, and linear chains). A given system is defined as a function of its composition in single spherical nanoparticles.

1- Sensitivity to composition

For this case, all particles have a diameter dm of 40 nm, and are all located on a thin gold film (h = 0). Results for M12 and M33 are reported in Fig. 1.

Figure 1: Averaged normalized sensitivity coefficient to the percentage of single nanoparticles % (dm = 40 nm, h = 0). (a) Sensitivity of M12. (b) Sensitivity of M33.

(a) (b)

(a) (b)Figure 2: Averaged normalized sensitivity coefficient to dm (h = 0). (a) Sensitivity of M12. (b) Sensitivity of M33.

2- Sensitivity to diameter

It is assumed that there is a non-uniform distribution of diameters from 38 to 42 nm (h = 0); the averaged normalized sensitivity coefficients of M12 and M33 are presented in Fig. 2.

Conclusions

The averaged normalized sensitivity coefficients of M11 (not shown) are always very low, which imply that the characterization should be done by using the polarization information. Moreover, in all cases performed in this work, the scattering matrix element M33 in the range of observation angles from 110 to 150º is found to have quite high sensitivity to all the pertinent parameters of interest. This window can therefore be used as a starting point for an experimental investigation and the development of an inversion technique.

0 20 40 60 80 100 120 140 160 18010

-3

10-2

10-1

100

0 % 25 % 50 % 75 % 100 %

X dm

norm,avg

[M12

]

0 20 40 60 80 100 120 140 160 18010

-3

10-2

10-1

100

10 % 15 % 25 % 50 % 75 % 100 %

X %norm,avg

[M12

]

0 20 40 60 80 100 120 140 160 180

10-3

10-2

10-1

100

10 % 15 % 25 % 50 % 75 % 100 %

X %norm,avg

[M33

]

0 20 40 60 80 100 120 140 160 18010

-3

10-2

10-1

100

0 % 25 % 50 % 75 % 100 %

X dm

norm,avg

[M33

]

Nano-Scale Characterization: M. Pinar Mengüç

(w/ Mathieu Francoeur)