Plasmonic properties and sizing of core-shell Cu ...

Plasmonic properties and sizing of core-shell Cu-Cu2O nanoparticles fabricated by femtosecond laser ablation in liquids 1

J. M. J. Santillán1, F. A. Videla1,2, D. C. Schinca1,2 and L. B. Scaffardi1,2 Centro de Investigaciones Ópticas (CIOp), (CONICET La Plata - CIC), Argentina 2 Departamento de Ciencias Básicas, Facultad de Ingeniería, UNLP, Argentina

ABSTRACT The synthesis and study of optical properties of copper nanoparticles are of great interest since they are applicable to different areas such as catalysis, lubrication, conductive thin films and nanofluids. Their optical properties are governed by the characteristics of the dielectric function of the metal, its size and environment. The study of the dielectric function with radius is carried out through the contribution of free and bound electrons. The first one is corrected for size using the modification of the damping constant. The second one takes into consideration the contribution of the interband transitions from the d-band to the conduction band, considering the larger spacing between electronic energy levels as the particle decreases in size below 2 nm. Taking into account these specific modifications, it was possible to fit the bulk complex dielectric function, and consequently, determine optical parameters and band energy values such as the coefficient for bound electron contribution Qbulk = 2 x 1024, gap energy Eg = 1.95 eV, Fermi energy EF = 2.15 eV and damping constant for bound electrons γb = 1.15 x 1014 Hz. The fit of the experimental extinction spectra of the colloidal suspensions obtained by 500 µJ ultrashort pulse laser ablation of solid target in water and acetone, reveals that the nanometric and subnanometric particles have a CuCu2O structure due to an oxidation reaction during the fabrication. The results were compared with those obtained by AFM, observing a very good agreement between the two techniques, showing that Optical Extinction Spectroscopy (OES) is a good complementary technique to standard electron microscopy. Keywords: Cu-Cu2O nanoparticles, copper dielectric function, subnanometric size, optical extinction spectroscopy, ultrashort pulse laser ablation.

1. THEORETICAL BACKGROUND In general, the complex dielectric function for bulk metals can be decomposed in two terms, a free-electron term and an interband (or bound-electron) term as:

ε size (ω , R ) = ε bound −electrons (ω , R ) + ε free −electrons (ω , R )

(1)

For bound electrons, the complex dielectric function arising due to transitions from the copper d-band to the conduction sp-band, can be calculated using the expression given by Scaffardi et al. [1]:

ε bound−electrons (ω, R) = Qbulk (1 − exp (− R R0 )) ∫

∞

ωg

x − ωg x

[1 − F ( x, T )] (x − ω + γ + i 2 ω γ ) dx (x − ω + γ ) + 4ω γ 2

2

2

b

2

2 2

2

b

b

2

2

(2)

b

where ħ ωg is the copper gap energy (Eg), F (x, T) is the Fermi energy distribution function of conduction electrons of energy ħx at the temperature T with Fermi energy EF ; γb represents the damping constant of the interband transition,

Qsize = Qbulk (1 − exp (− R R0 )) is a radius dependent proportionality factor [1], R is the particle radius, R0 = 0.35 nm is a

scale factor and Qbulk is the coefficient for bound electron contribution. For free electrons, the complex dielectric function can be written as: Plasmonics: Metallic Nanostructures and Their Optical Properties X, edited by Mark I. Stockman, Proc. of SPIE Vol. 8457, 84572U · © 2012 SPIE · CCC code: 0277-786/12/$18 · doi: 10.1117/12.928670

Proc. of SPIE Vol. 8457 84572U-1

ε free−electrons (ω , R ) = 1 −

ωp

2

v  ω + i  γ bulk + C F R  2

(3)

 ω 

where ωp = 13.4 x 1015 Hz [2] is the bulk plasma frequency and the term in parenthesis in the denominator is the size modification of the free-electron damping constant. The value of γbulk = 1.45 x 1014 Hz, was taken from Johnson and Christy [3] and vF = 15.7 × 1014 nm/s is the Fermi velocity for copper [4]. C = 0.8 is a constant that depends on the electron scattering processes inside the nanoparticle. The Qbulk, Eg, EF and γb parameters that appear in eq. (2) influence independent features in the experimental dielectric function, especially in the imaginary part. For example, theoretical calculation of the imaginary part of the full dielectric function for different Eg values changes the curve in the wavelength region between 350 and 530 nm while small variations in EF values influence the imaginary part in the region between 530 and 700 nm. When eq. (2), (3) are introduced in eq. (1) to fit the bulk dielectric function considering R = 100 nm (R>>R0), it is possible to determine the following parameters for copper: Qbulk = 2 x 1024, Eg = 1.95 eV, EF = 2.15 eV and γb = 1.15 x 1014 Hz. Figure 1 (a) and (b) shows the real and imaginary components of bound (eq. 2) and free electron (eq. 3) contributions calculated separately, while its sum (full line) is the best fit to experimental bulk values derived from complex refractive index data taken from Johnson and Christy [3], represented by full triangles. 20

10

(a)

10

bound electrons

(b)

calculated values

8

experimental values

0

6 experimental values

calculated values

ε''

ε'

-10 4

-20 2

free electrons

-30

bound electrons 0

-40 -50

free electrons

-2

300

400

500

600

700

800

900

1000

300

400

λ [nm]

500

600

700

800

900

1000

λ [nm]

Figure 1. Comparison between experimental bulk values (full triangles) and theoretical calculation for the real and imaginary part of copper dielectric function. Experimental values were derived from Johnson and Christy [3] while theoretical free and bound electron contributions to the complex dielectric function were carried out using eq. (1) to (3). (a) Real component ε’ and (b) imaginary component ε’’.

Figure 2 shows the behaviour of the real and the imaginary parts of the total dielectric function (eq. 1) as a function of wavelength for different nanometric and subnanometric particles radii, using the optimum parameters obtained after fitting the experimental bulk dielectric function. It can be seen that the real part of the dielectric function (fig. 2 (a)) is very sensitive to size for R < 2 nm. However, this sensitivity decreases for the range 2 - 10 nm and it is almost coincident with the bulk curve for R = 10 nm. On the other hand, the imaginary part (fig. 2 (b)) shows a similar limit behaviour for R > 15 nm, but there seems to be also a limiting behaviour for R = 0.6 nm.


0

(a)

24 20 16

ε'' (R)

ε' (R)

-10

0.6 nm 0.8 nm 1 nm 1.2 nm 2 nm 10 nm bulk

-20

-30

(b)


12 8 4 0

-40 300

400

500

600

700

800

300

900

400

500

600

700

800

900

λ [nm]

λ [nm]

Figure 2. Real (a) and imaginary (b) parts of the copper complex dielectric function considering free and bound electron contributions for different values of nanometric and subnanometric particles radii.

To study the influence of the subnanometric correction (1 − exp (− R R0 )) in eq. 2, the real and the imaginary part were calculated without it. Figure 3 (a) and (b) shows these calculations for the same radii as in fig. 2 (a) and (b). It can be seen that the influence of this correction affects particles under 2 nm radii approximately, especially in the wavelength region under 600 nm. The curves for ε’ (fig. 3 (a)) without the (1 − exp (− R R0 )) correction show a larger splitting for radii under 2 nm, while for radii over this value, the correction is negligible. 0

24

(a)

20

-10

-20

-30

ε''

ε'

16 0.6 nm 0.8 nm 1 nm 1.2 nm 2 nm 10 nm bulk

(b)


12 8 4 0

-40 300

400

500

600

700

800

900

300

400

500

600

700

800

900

λ [nm]

λ [nm]

(

(

Figure 3: theoretical calculation for full dielectric function using eq. (2) without the 1 − exp − R R0

)) subnanometric

correction. (a) Real part and (b) imaginary part. Lack of inclusion of the subnanometric correction overestimates the dielectric function below 600 nm wavelength.

A similar behaviour is observed in fig. 3 (b) for the imaginary part. These results show that the dielectric function for small particles is overestimated if the correction for the larger spacing between energy levels for small radii is not taken into account in eq. (2). The apparently small influence of the subnanometric correction on the dielectric function is more noticeable when the optical extinction spectrum is calculated. Since the size of the copper particles considered in this paper is very small compared with the incident wavelength, the response to optical extinction can be described using the electrostatic approximation. In this approach, the expression for the extinction cross section is


Cext = k ′ Im(α )

(4)

where α is the polarizability, k ' = 2 π nm is the wavenumber in the medium surrounding the particle, nm is the refractive λ index of the medium and λ is the wavelength of the incident light in vacuum. Since during ablation there are conditions of high temperature and high pressure in the plasma plume, oxidation processes proceed very fast over the formed copper particles and there is a large probability that copper-copper oxide particles may be generated. In view of this, it is important to take into account the expression of the polarizability for capped particles. So, for spherical particles with core-shell structure, the polarizability can be written as [5]: α = 4 π R ′3

(ε

(ε

2

2

− ε m )(ε1 + 2 ε 2 ) + f (ε1 − ε 2 )(ε m + 2 ε 2 )

(5)

+ 2 ε m )(ε1 + 2 ε 2 ) + f (2 ε 2 − 2 ε m )(ε1 − ε 2 )

3

where f =  R  is the ratio between inner and outer radius volumes, R = rcore is the metal central core (copper),  R' 

R’ = r (core + coating) is the outer radius (copper core + copper- oxide coat thickness), ε1 = ε1 (λ, R), ε2 = ε2 (λ) and εm = εm (λ) are the dielectric functions of the core, coating (shell) and surrounding medium, respectively. Another parameter related with the extinction cross section is the extinction coefficient defined as Qext = C ext π R ' . 2

Figure 4 shows the extinction coefficient for a subnanometric copper bare core particle with and without correction. The differences between the spectra are more evident for wavelengths shorter than 600 nm. This difference in the shape of the spectra in the short wavelength region is readily measurable with a moderate resolution spectrophotometer. In turn, this behaviour is important when the composition of copper colloidal solution has to be determined by optical extinction spectroscopy. 0.06 Bare core Cu particles R = 0.7 nm

Extinction

0.05 0.04

with bound electron size correction without bound electron size correction

0.03 0.02 0.01 0.00 300

400

500

600

700

800

900

1000

λ [nm] Figure 4. Extinction coefficient for subnanometric bare core Cu particle, with and without bound electron size correction. The difference in the spectra is more noticeable for wavelengths smaller that the plasmon peak, where the influence of the bound electron is more important.

If a particle is surrounded by a shell of oxide (due, for example, to the fabrication process), the extinction spectrum is modified. Figure 5 shows the spectrum for a bare core (zero shell thickness) subnanometric particle of 0.7 nm radius compared with that corresponding to the same subnanometric particle capped with 0.35 nm (50% of core radius) thickness of Cu2O. It can be seen that there is a considerable redshift of the peak position (about 70 nm in this


case) and an increase of the slope for wavelengths below 600 nm in the extinction spectrum when an oxide shell thickness is considered. The inset shows the complex dielectric function corresponding to the Cu2O shell according to the data given by [6] used in the calculations. 12

ε' ε''

10

4 ε

8 6

Extinction

4

3

2 0 300

400

500

600

700

800

900

1000

λ [nm]

2

R = 0.7 nm R = 0.7 nm; shell 50% R 1

0 300

400

500

600

700

800

900

1000

λ [nm] Figure 5. Theoretical optical extinction spectra of subnanometric copper bare core particle compared with a subnanometric Cu-Cu2O particle with the same core and 50% of shell thickness for a 0.7 nm particle radius. The shell produces a measurable redshift of the plasmon peak. Inset shows the dielectric function of Cu2O taken from Johnson and Christy [3].

2. EXPERIMENTAL Subnanometric and nanometric copper particles were fabricated by ultrafast pulse laser ablation in liquids. A high purity grade 1 mm thick copper circular disk was used to carry out these experiments. Laser ablation was performed using a Ti:Sapphire chirped pulsed amplification (CPA) system from Spectra Physics, emitting pulses of 100 fs width at 1 kHz repetition rate centered at 800 nm wavelength. The maximum output energy was 1 mJ per pulse. A 5 cm focal length was used to focus the laser beam on the target disk surface, which was immersed in water or acetone. The energy per pulse used in this experiment was 500 µJ. The fabrication process was done during 20 minutes, after which the solution shows a typical greenish colour in water or reddish in acetone, which is attributed to the presence of a large number of subnanometric and nanometric particles in the solution. Optical extinction spectroscopy was conducted by means of a Shimadzu spectrophotometer from 300 to 1000 nm. Measurements were performed on highly diluted and sonicated colloidal suspensions immediately after laser ablation. Since many other authors work with laser ablation in pure liquids, no surfactants were added to the sample to make the analysis in pure water or acetone without extra additives. To compare our results with standard sizing technique, samples were also analyzed using AFM imaging.

3. RESULTS We have applied the above calculations to fit the experimental extinction spectra of the obtained suspension. Figure 6 shows the best fit of the experimental extinction spectrum corresponding to a colloidal suspension fabricated by fs laser ablation in water. The fit was attained considering a linear combination of two types of subnanometric core-shell particles: one with 0.9 nm core radius and shell thickness of 40% R and the other of the same core radius and a 150% R shell thickness. The coefficients of this combination, 0.45 and 0.55 respectively, give the optimum relative abundance of the specie. No combination of bare core particles could fit the whole spectrum.


Relative abundance

7

Extinction

6 5 4

100

40 % R 150 % R

80 60 40 20 0 0.6

0.7

0.8

0.9

1.0

1.1

1.2

R [nm]

3

Experimental Theorical fit

2 1 0 300

400

500

600

700

800

900

1000

λ [nm] Figure 6. Experimental spectra and theoretical fit of colloidal suspension in water with pulse energy E = 500 µJ. The fit is based on a combination of Cu-Cu2O structures with the same core size and different shell thicknesses.

Figure 7 shows the experimental curves (red full line) and the theoretical fit (hollow diamond and dashed line) corresponding to subnanometric and nanometric copper particles in acetone fabricated with 500 µJ. The optimum size distribution has a dominant size of Cu bare core 2 nm radius and includes a 7% abundance of 4 nm radius and a 14% abundance of 10 nm radius of Cu-Cu2O nanoparticles. There is also an important subnanometric contribution of 0.8 nm core radius of the same configuration whose abundance is 32%. It is important to remark the fact that core radii and shell thicknesses that appear in the histogram depicted in the inset indicate a bimodal distribution composed by small radii in the range 1 to 4 nm and a larger one centered at 10 nm.

Relative abundance

2.0

Extinction

1.5

1.0

50 0%R 5%R 100 % R 150 % R 200 % R

40 30 20 10 0 0

2

4

6

8

10

R [nm]

Experimental Theorical fit

0.5

0.0 400

500

600

700

800

900

1000

λ [nm] Figure 7. Experimental spectra and theoretical fit of colloidal suspension in acetone with pulse energy E = 500 µJ. The fit is based on a combination of Cu bare core and Cu-Cu2O structures.

Figure 8 (a) shows an AFM picture of the colloidal sample generated in water using 500 µJ pulse energy laser ablation. Individual particles are clearly resolved by AFM imaging of the scanned 1.2 µm x 1.2 µm area under the low


concentration condition used. The height profiles of line 1 and line 2 in figure 8 (a) are shown in figure 8 (b). The scan of the first line in the range 0.9 µm < x < 1.1µm includes a single nanoparticle of 4.5 nm height (diameter). This size agrees with the results obtained by extinction spectroscopy of the same sample considering a core-shell Cu-Cu2O particle with a core radius of 0.9 nm and a shell thickness of 1.35 nm. On the other hand, line 2 scans over a 2.2 nm height nanoparticle, which agrees with the other size present in the core-shell Cu-Cu2O colloidal suspension. 1,2 1.2

(a) 1,0 1.0

line 1

Y [µm]

0,8 0.8

line 2

0,6 0.6

0,4 0.4

0,2 0.2

0,0 0.0

h [nm]

0.0

66 5 44 3 22 1 00

0 .0

0.2

0.4

0.6

0 .2

1.0

1.2

X X [µm]

line 1

line 2

(b) (b)

0.8

0 .4

0 .6

0 .8

1 .0

1 .2

[µ m ] X [Xµm]

Figure 8. (a) AFM image of the diluted colloidal suspension in water obtained by laser ablation with 500 µJ pulse energy; (b) height (diameter) of the nanoparticles vs X position for line 1 and line 2 marked on AFM image. Notice the single peak in line 1 and two single nanoparticle peaks in line 2.

4. CONCLUSIONS This work was focused on two aspects of subnanometric and nanometric copper particles characterization. The first one dealt with the analysis of the behaviour of free and bound electron contribution to the wavelength dependent dielectric function of copper. The free electron contribution was modified as usual including a term inversely proportional to the particle radius in the expression of the bulk damping constant. With this modification, both real and imaginary parts of the free electron dielectric function show a noticeable dependence with size from 1 nm to 10 nm, with a limiting behaviour to bulk for a radius R ≈10 nm. The bound electron contribution of transitions from the d-band to the conduction band was modelled using an expression that takes into account all the possible interband transitions. The parameters involved in the expression for the bulk bound electron dielectric function, such as Qbulk, Eg, γb and EF, were adjusted to fit simultaneously the real and imaginary experimental values for bulk copper complex dielectric function. For subnanometric particles, a size dependence factor that accounts for the larger energy level spacing was included in the former expression for the bound electron dielectric function. This correction is important from subnanometric size to a radius of about 2 nm, above which the correction is negligible. The second part of the work was devoted to the application of this technique to retrieve the size distribution of colloidal copper suspensions generated by fs laser ablation in water and acetone, as well as the possible appearance of


core-shell copper-copper oxide structure. The expressions of the obtained dielectric function were used in the calculation of the polarizability of subnanometric and nanometric particles within Mie’s theory, showing particularly the influence of bound electron size correction on the shape of the extinction spectrum of subnanometric particles. We have successfully fitted the experimental optical extinction spectra of subnanometric and nanometric coreshell Cu-Cu2O particles fabricated by ultrashort pulse laser ablation of solid target in water and acetone with 500 µJ pulse energy. In the former, the optimum fitting using Mie’s theory yielded a dominant core radius R = 0.9 nm with a shell thickness distribution of 40% R and 150% R, while in the latter there is a larger size dispersion with a dominant size of Cu bare core 2 nm radius together with a small abundance of Cu-Cu2O 10 nm particles as well as an important subnanometric contribution of 0.8 nm core radius of the same configuration. We also showed that the method of spectral fitting is extremely sensitive to small variations in core radius (± 0.1 nm) or shell thickness (± 20% R). These small changes modify the shape of the curves and depart from the experimental spectrum. For comparison purposes the colloidal suspensions generated by fs laser ablation were analyzed with standard microscopy technique such as AFM. The results show very good agreement with those obtained from the fitting of the experimental extinction spectra using the Drude-interband model.

ACKNOWLEDGMENTS The authors wish to thank Dr Marcela Fernández van Raap from the Instituto de Físca La Plata (IFLP) for the AFM pictures. This work was performed by grants PIP (CONICET) 0394, PME 2006-00018 (ANPCyT), 11/I151 (Facultad de Ingeniería, Universidad Nacional de La Plata) and funds from IFLP-CONICET, Argentina. Daniel C. Schinca and Fabián A. Videla are members of CIC, Comisión de Investigaciones Científicas de la Provincia de Buenos Aires. L. B. Scaffardi and Marcela B. Fernández van Raap are researchers of CONICET and Jesica M. J. Santillán is fellow of CONICET, Argentina.

REFERENCES [1] Scaffardi, L. B. and Tocho J. O., “Size dependence of refractive index of gold nanoparticles”, Nanotechnology 17(5), 1309-1315 (2006). [2] Cai, W. and Shalaev, V., Optical metamaterials. Fundamentals and Applications, Springer. Berlin, (2010). [3] Johnson, P. B. and Christy, R. W., “Optical constants of the noble metals”, Phys. Rev. B 6(12), 4370-4379 (1972). [4] Kaye, G. W. C. and Laby, T. H., Tables of Physical and Chemical Constants and Some Mathematical Functions, Longman Scientific and Technical, London, (1995). [5] Bohren, C. F. and Huffman, D. R., Absorption and Scattering of Light by Small Particles, Wiley, New York, (1998). [6] Palik, E. D., Handbook of Optical Constants of Solids vol 1, Academic, New York, (1998).
