Diffusion of silver in silicate glass and clustering in hydrogen atmosphere

Transcription

1 Defect and Diffusion Forum Vols. 7-4 (5) pp online at 5 Trans Tech Publications, Switzerland Diffusion of silver in silicate glass and clustering in hydrogen atmosphere Yu. Kaganovskii 1, a, E. Mogilko 1, b, A. Ofir 1, c, A. A. Lipovskii, d, and M. Rosenbluh 1, e 1 The Jack and Pearl Resnick Institute for Advanced technology, Department of Physics, Bar-Ilan University, Ramat-Gan 59, Israel; Department of Solid State Physics, St.-Petersburg Polytechnical University, Russia. a kagany@mail.biu.ac.il; b mogilke@mail.biu.ac.il; c ph15@mail.biu.ac.il; d lipovskii@mail.ru; e rosenblu@mail.biu.ac.il Keywords: Diffusion, silver doped glass, hydrogen, clustering, surface plasmon resonance. Abstract. Annealing in a hydrogen atmosphere of silicate glass plates doped by + ions leads to the reduction of silver to a metallic state ( ) and to the formation of silver nanoclusters. The kinetics of clustering during hydrogen diffusion into the glass and diffusion of atoms in the glass matrix have been studied in a temperature ranging from 16 to o C by SEM, AFM and optical spectrometry. The absorption spectra have a peak near 41 nm corresponding to the surface plasmon resonance in clusters. The position of the peak moves as the clusters grow. A theoretical analysis of the absorption spectra allowed us to estimate the cluster size as a function of time, as well as the thickness of the layer filled by clusters, which also changes with time. From AFM data we could measure the kinetics of cluster growth on the surface. We have theoretically analyzed the kinetics of cluster growth during reactive hydrogen diffusion, the kinetics of bulk cluster growth, surface cluster growth, and thickening of the layer filled by clusters. 1. Introduction Glasses containing silver nanoclusters are of interest for multiple applications in optical recording [1], laser microfabrication [] and communication []. It is known that the replacement of sodium ions in a glass with silver ions increases the refractive index of the glass and thus the subsurface layer becomes a waveguide. Diffusion of silver ions in a glass during ion exchange was previously studied and the diffusion coefficients were estimated for various glasses [-5] If a glass contains + ions, annealing in a hydrogen atmosphere leads to the reduction of silver to a metallic state ( ) due to the following reaction [6] Si O + + ½ Si O + (1) As the solubility of metallic silver in glasses is negligible, the reduction of silver leads to the formation of nanoclusters. In this paper we study the kinetics of clustering during hydrogen diffusion into the glass and diffusion of atoms in the glass matrix.. Experimental Silicate glass plates were doped by + ions for various depths in an ion exchange process. The concentration distributions of + ions, which replaced Na + ions in a subsurface diffusion layer of the glass, were measured by electron beam microanalysis technique, as well as by waveguide mode spectroscopy [7]. In the later case, the diffusion width of the doped layer (the thickness of the waveguide) was determined by measuring the effective indices of the waveguide modes. Licensed to A.A. Lipovskii (lipovskii@mail.ru) - Russia All rights reserved. No part of the contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of the publisher: Trans Tech Publications Ltd, Switzerland, (ID: //5,9:51:55)

2 69 Diffusion in Materials - DIMAT4 The samples with various diffusion depths were annealed in a range of 16 - o C in a hydrogen atmosphere. The reduction of the silver during diffusion of hydrogen into the glass was accompanied by growth of silver clusters, both in the bulk and on the surface. At subsequent stages of the annealing, the optical absorption spectra as well as the cluster growth kinetics at the surface of the samples were measured (by AFM).. Results and discussion The diffusion layer doped by silver after ion exchange is clearly seen in back scattered electrons in SEM (Fig. 1). After annealing in the hydrogen atmosphere, silver clusters first appear at the surface 1. nm.75 1nm.5 nm.5 Fig. 1. SEM image of a cross section of a glass sample after ion exchange. The diffusion layer doped by silver is seen in back scattered electrons µm Fig.. AFM image of the glass surface after annealing in a hydrogen atmosphere. T = 16 o C, t = min. (Fig. ) and then in the subsurface layer of the glass (Fig. ). The average cluster size varies in the range 8 15 nm and grows with time. The typical absorption spectra after the successive stages of isothermal annealing are shown in Fig. 4. All of them have a peak near 41 nm corresponding to the surface plasmon resonance in clusters. The position of the peak moves with hydrogen annealing time to either longer or shorter wavelengths depending on the average cluster size. As the layer filled by the clusters penetrates into the glass, the optical density grows with the volume fraction of the clusters. To understand the kinetics of clustering, we have first analyzed the diffusion kinetics of hydrogen (responsible for the reduction of silver ions), and then the kinetics of surface and bulk clustering. Optical density Fig.. igh-resolution SEM image in back scattered electrons obtained from a cross section of the subsurface glass layer doped by silver after annealing in a hydrogen atmosphere. T = o C, min. Silver clusters of 1 nm in radius are clearly seen. The glass surface is located at about 5 nm from the top of the picture. Fig. 4. Optical absorption spectra of silver-doped glass after annealing in a hydrogen atmosphere. T = o C. 1 t =; min; 4 min; 4 6 min; 5 1 min. The peak near 41 nm is caused by the surface plasmon resonance in silver clusters.

3 Defect and Diffusion Forum Vols Diffusion penetration of hydrogen Diffusion penetration of hydrogen into glass doped by silver ions is accompanied by the capture of hydrogen atoms in traps in which they lose electrons and form O bonds (see Eq. 1). An analysis of diffusion with point traps [8] shows that there are two extreme situations that may arise depending on the relationship between the concentration of traps (equal to the concentration N + of + ions) and the solubility of hydrogen N. If N >> N +, the traps do not affect the hydrogen diffusion penetration, and it can be described by erfc-function. In the other extreme case of N << N +, the penetration of hydrogen occurs mainly by the filling of traps, leading to the thickening of the filled layer with diffusion time. To estimate the thickening kinetics, one can use the following mass balance equation: N dl dt + = D N l, () in which the right side represents the hydrogen flux through the layer l with the filled traps (the hydrogen concentration drops to zero at the boundary x = l of the filled layer), D is the diffusion coefficient of hydrogen atoms in the glass free from traps (or with the filled traps). After integrating Eq., we obtain a parabolic kinetic law l ( t) = D N N + t () in which the rate constant is much smaller than the hydrogen diffusion coefficient D (because N << N + )... Bulk clustering As the hydrogen flux is captured by traps near the boundary plane x = l, this plane becomes a source of neutral silver atoms ( ). The number of atoms, which appear at unit surface at x = l per unit time is defined by Eq.. The diffusion of neutral silver into the bulk glass is given by N ( x, t) N ( x, t) = D πr N j x t t 4 cl (, ) (4) x The last term describes the sink of silver due to clustering. ere N is the concentration of neutral silver atoms (in m - ), R is the average cluster radius, N cl is the cluster concentration, ( ) j ( x, t) = D N ( x, t) / r D N ( x, t) / R is the flux of silver to a solitary r = R cluster located at the distance x from the glass surface. It can be calculated in spherical coordinates with the origin in the center of cluster. We neglect equilibrium concentration compared to supersaturated value N (x,t). The generation of atoms at the plane x=l should be taken into account in the boundary condition: D N l N = J+ + J = D + D x N x x = l + x = l where J + and J - are the fluxes (at x = l) directed to the bulk (x>l) and to the surface (x<l) of the glass plate respectively. Using a steady state approximation ( N / t = ), Eq. 5 and the boundary conditions N ( ) N ( ) =, one can give the solution of Eq. 4 in the form (5)

4 69 Diffusion in Materials - DIMAT4 x L N x N l x l N x N l e L ( ) x l ( ) sinh( / ) sinh( l / L), < < ; ( ) ( ), > (6) D L sinh( l / L) 1/ where N ( l) = N, L = ( 4πRN ) D l cosh( l / L) + sinh( l / L) cl Eq 6 shows an exponential decrease of the silver concentration at a characteristic distance L from the plane x = l. Time dependence of N is defined by time dependence of l(t) and L(t). The kinetics of cluster growth at the distance x from the surface can be estimated from the equation dr N ( x, t) = j Ω D Ω (7) dt R( t) where Ω is the atomic volume of silver. At the beginning of the clustering process (when l << L) we have obtained from Eqs. 7 and R ( x, t) 8D N N Ω x t, < x < l; R ( x, t) D N Ω e L t, x > l (8) whereas at the final stages (l >>L) 5 x l 5 x l x l x l + cl R ( x, t) Ae L t, < x < l; R ( x, t) Ae L t, x > l; A = 5D Ω N N / π N (9) All kinetics are independent of the silver diffusion coefficient and the cluster growth is defined solely by the hydrogen diffusion characteristics... Optical properties of silver clusters It is known that the optical spectra of metal nanoparticles embedded in a dielectric matrix contain absorption peaks caused by the surface plasmon resonance, whose frequency depends on the size of the metal particles and the dielectric properties of both the metal and the surrounding medium [9]. When the particle radius R is small enough compared to the wavelength of light λ and the volume fraction of particles f << 1, an absorption peak appears due to excitation of a dipole plasma mode. In this case the optical extinction is given by 18πε α( ω) = ϕ( ω) f ; ϕ( ω) = λ ω p ε1( ω) = ε' 1 ( ω) + 1 ω + ω c 1/ m ε ( ω) [ m 1 ] ε + ε ( ω) + ε ( ω) p c + ωc (1) ω ω, ε ( ω) = ε' ( ω) +, (11) ω( ω ) where ε 1 and ε are the real and imaginary parts of the dielectric constant of the bulk metal, ω p is the plasma frequency, ω p = n e e /ε m e, n e is the electron density, e electron charge, ε = C /Nm is the permittivity of space, m e electron mass, ω c = v F /L e + v F /R is the damping frequency, v F is the Fermi velocity, and L e is the electron mean free path in bulk metal. According to Eq. 1, α(ω) shows the resonance behavior whenever the denominator takes its minimum. The position and shape of the resonance do not directly depend on the particle radius R, but only indirectly due to the size dependencies of ε 1 (ω)and ε (ω). To calculate the optical extinction α as a function of light wavelength with the given cluster radii, we used ε 1 and ε tabulated in Ref. [1], ω p = s -1, v F = m/s, L e = 57 nm [11], ε m =.5, the volume fraction f = 4πR N cl /, and N cl = 1 m - as follows from the SEM and AFM studies. Some results of our calculations are presented in Fig. 5. As can be seen, the peak position is extremely sensitive to the cluster radius, which allowed us to find the average cluster size from the optical absorption spectra.

5 Defect and Diffusion Forum Vols R=8 nm, f=.1 R=1 nm, f=.8 R=1 nm, f=.4 R=14 nm, f=.11 Fig. 5. Extinction coefficients calculated for various cluster sizes R and volume fractions f corresponding to the same cluster density N cl =1 m -. The peak position is rather sensitive to R. Optical density nm 45 nm 5 nm l (µm) nm 45 nm 5 nm t 1/ (min 1/ ) Fig. 6. Optical density vs t 1/ for various wavelengths t 1/ (min 1/ ) Fig. 7. Thickness of the layer filled by clusters vs t 1/ calculated from optical absorption spectra.. 4. Optical density As the optical extinction, α, is determined by light absorption inside the clusters, it depends on the distance x from the surface and time. This dependence can be described (see Eq. 1) as follows α( ω, x, t) = ϕ( ω) f ( x, t) = ( 4 / ) ϕ( ω) πn R ( x, t) (1) cl As the dependence α(x,t) is determined by the coordinate and time dependence of the cluster volume fraction, f(x,t),one can find the following expression for the optical density: S( ω, t) =. 4 α( ω, x, t) dx = 18. ϕ( ω) N R ( x, t) dx = 18. α( ω) l( t) cl where α( ω) is the average extinction coefficient inside the layer l(t) filled by clusters. We assume that the cluster concentration is independent of x, f(x) is defined only by dependence R(x), and the layer filled by clusters thickens with l(t) because the plane x = l(t) defines maximum (1)

6 694 Diffusion in Materials - DIMAT4 supersaturaturation by atoms. Accordingly the dependence of S on hydrogen annealing time, S(t), is defined by the dependence l(t). We have found from optical measurement (Fig. 4) that S(t) follows a parabolic law for various wavelengths (Fig. 6), similar to l(t) (see Eq. ). Using the calculated values of α(ω) (Fig. 4) and the measured values of the optical density S, we calculated the effective thickness l of the layer filled by clusters (Fig. 7) and estimated the hydrogen diffusion coefficients D. Setting in Eq. 5 N /N 1 we have found D = m /s for o C and m /s for 18 o C..5. Surface clustering Surface clustering occurs due to the diffusion flux of neutral silver atoms js = D N x D / x = N l( t) directed to the glass surface. If Ns is the surface cluster density and the average cluster radius R, one can write (assuming a hemispherical cluster shape) πr N dr = j Ω dt, and after integrating Eqs. 5 and 6, determine that the total volume of clusters per unit surface grows with time as N Ω 1/ Vs ( t) = D t = D D N d ( l) N Ω t l( t) Eq. 7 allows the estimation of D from the experimental data V s (t), if the dependence l(t) is known. We have obtained D = m /s for 16 o C. 4. Summary As it follows from experimental data on optical extinction and our analysis, the propagation rate of the layer filled by nanoclusters as well as the kinetics of cluster growth in the bulk of glass are independent of the silver diffusion coefficient D and defined by the hydrogen diffusion coefficient D. The coefficient D can be estimated from data on optical density of the glass as a function of annealing time, whereas the coefficient D from the kinetics of surface clustering. References [1] Yu. Kaganovskii, I. Antonov, D. Ianetz, M. Rosenbluh, J. Ihlemann, S. Mueller, G. Marowsky, A. Lipovskii: Solid State Phenomena Vol. 94 () p. 15 [] I. Antonov, F. Bass, Yu. Kaganovskii, M. Rosenbluh, A. Lipovskii: J. Appl. Phys. Vol. 9 () p. 4 [] J. Linares, A. A. Lipovskii, D. K. Tagantsev, J. Turunen: Opt. Mater., Vol. 14, () p. 115 [4] G. De Marchi, F. Caccavale, F. Gonella, G. Mattei, G. Battaglin< A. Quaranta: Appl. Phys. A, Vol. 6 (1996) p. 4 [5] A. Motello, G. De Marchi, G. Mattei, P. Mazzoldi: Appl. Phys. A, Vol. 67 (1998) p. 57 [6] M. Suszynska, L. Krajczyk, R. Capelletti, A. Baraldi, K. J. Berg: J. Non-Crystalline Solids, Vol. 15 () p. 114 [7] J. Linares, D. Sotelo, A.A. Lipovskii, V.V. Zhurihina, D.K. Tagantsev, J. Turunen: Optical Materials, Vol. 14 () p. 145 [8] Ya.E. Geguzin, Yu.S. Kaganovskii: Phys. Met. Metallogr., Vol. 49 (198) p. 18 [9] U. Kreibig and M. Vollmer: Optical Properties of Metal Clusters (Springer, Berlin, 1995) [1] American Institute of Physics andbook, Ed. D. E. Gray (McGraw-ill Inc. New York, 197) [11] S. K. Mandal, R. K. Roy and A. K. Pal: J. Phys. D, Vol. 5 () p. 198 s s (14) (15)