1 Introduction

Nanocomposite materials consisting of metal nanoparticles (NPs) embedded in bulk glasses are of great interest for a large variety of applications because of their linear and nonlinear optical properties with high potential for optical and optoelectronic devices [1]. The importance of surface excitations in nanometre-sized metallic particles leads to changes in their physical properties [2]. Their fundamental property used for optical applications is the excitation of surface plasmon resonances (SPRs) [1, 3] in the free-electron metallic grains (collective oscillations of the conduction electrons), which lead to enhanced optical absorption/scattering cross sections and near-field intensity. The SPR’s spectral features, such as the resonance wavelength and bandwidth, together with the topology of the enhanced near-field, depend on the NP size, shape and spatial arrangement in the glass matrix [4]. Controlling these structural parameters is required for achieving the desired applications. For instance, one can take advantage of the intense near-field or scattering at the SPR for enhancing the far-field luminescence intensity of rare-earth (RE) ions embedded in the glass, provided they are located at the close vicinity of Ag or Au NPs [5, 6] whose SPR must peak at the absorption or emission wavelength of the RE.

Several methods to obtain bulk glass with embedded metal NPs have been used [7–9]. Besides using the sol–gel methods in a few cases [7], most of the studied glasses (tellurites, germanates, silicates) have been obtained by the melting procedure. Ag or Au NPs are obtained either by Na–Ag ion exchange in the already produced glass samples [6, 9, 10] or by adding salts to the mixture of reagents to be melted, in both cases performing a further thermal annealing process in order to reduce the Ag+ or Au3+ ions for nucleation of silver or gold NPs [11]. The optical response in the near ultraviolet-to-near infrared range of noble metal-doped glasses has been extensively characterized by transmittance measurements, evidencing a SPR absorption band for the doped glass in the ion-exchanged glasses [6, 9, 10] and in many cases in glasses obtained by including Ag or Au salts to the reagent mixture [11–18]. However, there are many other cases concerning the latter glasses in which the SPR band is hardly or even not observed, although transmission electron microscopy shows the presence of metal NPs [19–29]. This has been explained as being due to the low metal NP concentration in the samples without any further checking. It is worth pointing out that the transmittance spectra of thick glass samples (thickness in the millimetre range) with a homogeneous volume distribution of NPs and a NP volume fraction as low as 1 % are expected to be heavily affected by the SPR absorption, unless strong SPR damping effects take place. Thus, assuming that damping effects are weak in the previously cited works [19–29], an infinitely low volume density of NPs would be required to explain the absence of SPR band. At this point, let us remark that the hypothesis of a homogeneous NP volume distribution may not be always correct, especially when the nanocomposite glasses are obtained by adding the metal dopant using the ion exchange technique. Indeed, in this case, the metal ions reach a depth of only several microns from the surface, and subsequent Ag migration towards the surfaces occurs during thermal annealing [30–34]. In contrast, in the glasses in which the dopant is added before melting, the NPs are therefore supposed to be uniformly distributed in the bulk since this is the case of the metal ions before aggregation. Some evidence about precipitation of silver metal NPs at the surface has nevertheless been found in a tellurite glass produced by melting [35], thus making further work desirable for understanding the metal NP formation in melted glasses. Let us note that the optical characterization of the glasses in the reported works remains limited to optical transmittance and is very basic, and is thus not able to provide fine information about the NP size, shape and localization, which must nevertheless be determined for a fundamental understanding of the glass formation mechanism as well as for applications involving the plasmonic properties of the NPs.

In this work, we present an original and accurate optical characterization of sodium–lead–germanate bulk glasses prepared by melting batches containing silver nitrate. The optical characterization of these glasses is performed in the near ultraviolet-to-near infrared range by combining transmittance and spectroscopic ellipsometry measurements, which give information about the volume and surface regions of the glass, respectively. From the simultaneous analysis of the transmittance and ellipsometry data, it is demonstrated that thermal annealing in air of samples induces the formation of the Ag NPs only in a thin layer near the sample surface. This result underlines the potential of combining transmittance and spectroscopic ellipsometry for determining the localization of the NPs in glasses of any nature. Mid-infrared spectroscopy characterization is also performed in order to address the processes involved in the sub-surface formation of the Ag NPs, which is a quite surprising result in such a way prepared glass samples.

2 Experimental

Germanates are good candidates for many optical applications (such as directly ultra-short-pulsed-laser-written optical waveguides with nonlinear optical properties and infrared transmitting windows) since they have high mechanical strength, chemical durability, thermal stability and excellent transmission in the infrared region. Moreover, they have maximum vibrational frequencies smaller than those of many other glasses, such as silicate, phosphate and borate glasses [36, 37], which makes them useful as hosts for RE ions for other optical applications as lasers and amplifiers. Among them, lead–germanate glasses are interesting because they can be easily obtained in fibre form [38, 39], their cut-off optical phonon energy being low (≤900 cm−1) [39]. A lead–germanate glass was thus used in this work, the composition of which (60 mol% GeO2–20 mol% PbO–20 mol % Na2O) was chosen from the glass forming region discussed elsewhere [40]. Glass batches were prepared from GeO2 (Aldrich 99.998 %), PbO (Aldrich 99.999 %) and Na2CO3 (Panreac 99.8 %) raw materials. A solution of AgNO3 (Alfa Aesar, 99.9 %) in water (15 g l−1) was used for Ag doping. Batches of 10 g with 0.15 wt% of Ag were melted in air for 1 h in a Pt crucible at 1,100 °C in an electrical vertical Thermostar furnace and stirred with a platinum bar to ensure homogenization. Only about 0.04 % weight loss upon melting was observed in thermogravimetric measurements, which is consistent with the results previously reported for similar glasses [40]. The melt was poured into a preheated brass mould followed by annealing at 350 °C and slow cooling down to room temperature. The glasses showed no visible sign of phase separation or bubbles. The glasses were cut into around 0.5-mm-thick slices and polished for optical measurements. Thermal annealing treatments of samples were made for 30 min at different temperatures between 325 and 380 °C in air atmosphere or in vacuum (10−3 mbar) in order to induce the formation of NPs. A differential thermal analyser from T. A. Instruments, Q600 model, was used to obtain the glass transition and crystallization temperatures as well as to perform the thermogravimetric measurements above mentioned. The glass transition temperature was determined by the usual onset intercept method, giving a value of 383 ± 1 °C, in good agreement with results in similar glasses [40]. The onset of crystallization occurs at 580 ± 2 °C.

Optical characterization in the near ultraviolet-to-near infrared range has been performed by spectroscopic ellipsometry and transmittance measurements. A VASE spectroscopic ellipsometer (Woollam Co. Inc.) was used to perform spectroscopic ellipsometry measurements in the 400–1,500 nm wavelength range at different incidence angles (30°, 40°, 50°, 60° and 70°). Transmission spectra at normal (0°) incidence were measured in the 190–1,500 nm wavelength range using a Varian Cary 5000 UV–VIS–NIR spectrophotometer. The analysis of the spectroscopic ellipsometry and transmittance data was performed using the WVASE32 software (Woollam Co. Inc.). Mid-infrared characterization has been performed by Fourier transform infrared (FTIR) spectroscopy and Raman spectroscopy. FTIR spectroscopy was carried out with a resolution of 4 cm−1 using a Bruker IFS 66 system and the KBr pellet technique. To obtain these pellets, about 1 mg of powdered samples, obtained by scraping samples from their surfaces on one hand and from the bulk on the other with a diamond tip, was mixed and pressed with 200 mg of KBr powder. Raman spectra were recorded with a Renishaw Raman Invia spectrometer under excitation at 532 nm with an unpolarized Nd:YAG laser. Spectra were obtained at 5 % of the maximum laser power (500 mW) for an exposure time of 10 s at 2 cm−1 resolution.

3 Results and discussion

3.1 Optical characterization in the near ultraviolet-to-near infrared range: qualitative interpretation

Samples cut from the as-prepared glass blocks are transparent. They become yellow upon annealing in air at temperatures above 300 °C. Figure 1 shows the transmittance spectra of an untreated and air-annealed Ag-doped samples. The untreated sample presents a high transmittance in the whole visible range, and the air-annealed samples present features characteristic of a resonant extinction around 460 nm, which is absent in the untreated one, due to a SPR mode evidencing the presence of Ag NPs. The amplitude (half width at half maximum) of the extinction band slightly increases as the annealing temperature increases, suggesting that the density of NPs increases and that their size does not vary strongly. As a first approximation, Mie calculations for spherical NPs [41] of 3–15 nm in diameter with the refractive index of the pure germanate glass [42] and the dielectric function of bulk silver [43] lead to SPR extinction bands peaking close to those of Fig. 1, this lending further evidence to the conclusion about the presence of silver NPs. From the spectral position of the SPR band, it can be inferred that the NPs are relatively small (diameter shorter than 30 nm), since bigger NPs would yield a red-shifted resonance due to retardation effects [44, 45]. In such a size regime, an estimation of the NP diameter can be made according to the expression \(D = 2v_{F} /\Updelta \omega_{1/2}\) [46] (where v F is the Fermi velocity of electrons, 1.39 × 108 cm s−1 for Ag, and Δω 1/2 the full width at half maximum of the SPR band) giving values of D from 2.8 to 3.9 nm.

Fig. 1
figure 1

Optical transmittance spectra of 60GeO2–20PbO–20Na2O samples doped with 0.15 wt% of Ag: untreated sample and samples thermally annealed for 30 min in air at different temperatures

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The spectra of the Ψ and Δ ellipsometric angles measured for the sample annealed at 380 °C in air are plotted in Fig. 2a, b for one of the used angles of incidence (50º). These spectra also show features characteristic of a resonant absorption around 460 nm, due to a SPR mode, their evolution with the annealing temperature being in agreement with that of the transmission spectra.

Fig. 2
figure 2

Ellipsometric angles ψ (a) and Δ (b) measured at an incidence angle of 50º for the untreated sample and for the samples thermally annealed for 30 min in air at different temperatures. c Simulated transmittance spectra of a sample having effective refractive index and effective extinction coefficient values determined from the first step of the fitting procedure of the ellipsometry data for the sample annealed in air at 380 °C, for two different thicknesses: 20 nm and 0.4 mm (real thickness of the sample)

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3.2 Sub-surface localization of the Ag NPs as inferred from spectroscopic ellipsometry and transmittance measurements

Each of the obtained glass samples presenting slightly non-parallel faces, the beams reflected by the top and bottom faces have been spatially separated during the ellipsometry measurements of this study. In these conditions, it has been possible to collect only the beam reflected by the top face, thus simplifying data analysis that is known to be tricky when backside reflection in thick samples cannot be rubbed out. As a first step, ellipsometry spectra were fitted considering each sample as a semi-infinite homogeneous effective material in order to extract the spectra of their effective refractive index \(n_{\text{eff}}^{{{\text{ellips}},\infty }}\) and effective extinction coefficient \(k_{\text{eff}}^{{{\text{ellips}},\infty }}\). This approximation is common in the case of thick samples containing NPs smaller than the wavelength of light and when no backside reflection is measured. Fitting was performed simultaneously on the spectra collected at the 5 incidence angles (multi-angle fitting). The dielectric function \(\varepsilon_{\text{eff}}^{{{\text{ellips}},\infty }} = \, \left( {n_{\text{eff}}^{{{\text{ellips}},\infty }} + {\text{i}}k_{\text{eff}}^{{{\text{ellips}},\infty }} } \right)^{ 2}\) of the effective material was described using a generalized oscillator model, consisting of the sum of a Cauchy law and a Lorentz oscillator. All the parameters of the Cauchy law and Lorentz oscillator remained free during the fit. An excellent fit quality was obtained (mean squared error <10).

In order to check the consistency of the semi-infinite effective medium model, the \(\varepsilon_{\text{eff}}^{{{\text{ellips}},\infty }}\) spectra extracted from the previous fits were used to simulate the corresponding transmittance spectra of the glass samples, assuming a thickness of 0.4 mm (typical of the glass slides considered in this paper). As shown in Fig. 2c for the sample annealed at 380 °C, a zero simulated transmittance is obtained in the whole wavelength range, in huge contrast with the experimental data shown in Fig. 1. This important discrepancy is likely due to the fact that the ellipsometry measurements on the thick samples give information about the first reflection only, that is, the optical response of the surface of the material, in contrast to transmittance measurements that give information integrated over the whole volume of the sample. The non-sense zero transmittance obtained from the simulation seems to indicate that the NPs are located only in a thin layer close to the surface of the glass, whose volume presents a high optical transparency in the whole range of analysis. Indeed, a simulation of the transmittance performed for a 20-nm-thick film with the same effective dielectric function \(\varepsilon_{\text{eff}}^{{{\text{ellips}},\infty }}\) yields a better agreement with experiment, as seen in Fig. 2c, which shows a well-defined and non-saturated SPR extinction band.

In an analogous way, fitting of the transmittance spectrum of each sample considering it as a thick homogeneous effective slab has been performed, and the obtained \(\varepsilon_{\text{eff}}^{T,\infty }\) dielectric function has been used for simulating the ψ and Δ spectra (not shown). No significant contribution of the SPR is observed in the simulations whatever the incidence angle, in contrast to experimental spectra that show clear SPR structures, as observed in Fig. 2a, b. In a similar way as in the previous paragraph, the strong discrepancy between simulated and measured spectra are very likely due to the fact that the NPs are not located in the whole volume of the slab, but in thin layers close to the surface. These results therefore suggest that a reliable analysis of the optical response of the glasses requires (1) simultaneous fitting of the ellipsometry and transmittance spectra, (2) using a more realistic model taking into account the layered structure of the material.

3.3 Determination of the optical response and thickness of the surface nanocomposite layer from simultaneous fitting of transmittance and ellipsometry spectra

In order to extract the \(n_{\text{eff}}^{{T + {\text{ellips}},{\text{surface}}}}\) and \(k_{\text{eff}}^{{T + {\text{ellips}},{\text{surface}}}}\) spectra of the thin surface layer containing the NPs and to get information about its thickness, simultaneous fitting of transmittance and ellipsometry spectra has been performed using a refined model. A “sandwich” structure was considered for fitting transmittance data, with a central transparent thick slab (“core”) described by a Cauchy law and two thin surface layers described by identical generalized oscillator models (Cauchy law and Lorentz oscillator). Since backside reflection was not detected during ellipsometry measurements, a simpler bilayered structure was considered for fitting ellipsometry spectra. The dielectric functions of the thin top layer and the thick bottom layer were coupled to those of the surface layers and “core” described above, respectively. The oscillator and Cauchy parameters remained free during the fits together with the (uncoupled) thicknesses of the surface layers. It can be appreciated in Fig. 3a–c that this fitting procedure gives good results. Figure 3d depicts the \(n_{\text{eff}}^{{T + {\text{ellips}},{\text{surface}}}}\) and \(k_{\text{eff}}^{{T + {\text{ellips}},{\text{surface}}}}\) spectra obtained for the three samples annealed respectively at 325, 350 and 380 °C. The absorption band attributed to the SPR of the NPs is observed, and the trends described in Sect. 3.1 still hold. Let us remark that the values of \(n_{\text{eff}}^{{T + {\text{ellips}},{\text{surface}}}}\) away from the absorption range (i.e., in the near infrared, values around or below 1.6) drop below those of the undoped glass (around 1.73). This result might indicate that the NPs are embedded in a medium of lower refractive index than the glass “core” or are in contact with the air. This second hypothesis has been discarded on one hand by immersion spectroscopy measurements using a high-refractive index (1.516) oil and on the other from failed attempts to remove the NPs by rubbing strongly the sample surfaces with an optical cleaning piece of paper soaked in ethanol. Therefore, these low infrared refractive index values might be due to changes in the glass composition and/or structure close to the surface because of the thermal annealing treatments.

Fig. 3
figure 3

Experimental values (full lines with symbols) and their fittings to the model explained in the text (dashed lines) for the ellipsometric angles ψ (a) and Δ (b) of the sample thermally annealed for 30 min in air at 380 °C at different incidence angles. c Experimental transmission spectrum of the sample annealed in air at 380 °C and its fitting to the model. d Effective refractive index n eff (\(n_{\text{eff}}^{{T + {\text{ellips,surface}}}}\) in text, upper curves) and extinction coefficient k eff (\(k_{\text{eff}}^{{T + {\text{ellips,surface}}}}\) in text, lower curves) obtained from the model for 60GeO2–20PbO–20Na2O samples doped with 0.15 wt% of Ag and thermally annealed for 30 min in air at 325, 350 and 380 °C

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Table 1 shows the thickness values obtained for the NP surface layers in the sandwich structure of the three samples. All of them present thicknesses around 50 nm. It has been found that the plasmon extinction is reduced to half its original value when removing material from one of the surfaces some microns in depth by using a polishing machine (Fig. 4). Polishing both sample surfaces makes the SPR band to disappear, as it was also observed by Ghiel et al. [35]. This lends support to the conclusion drawn before that the NPs are located in a thin layer underneath each surface. A new thermal annealing in the same conditions after polishing only recovers a minor part of the original SPR band, hence indicating that a large amount of Ag ions or atoms have migrated during the first annealing towards the surfaces where they aggregate. Loss of some amount of neutral silver through evaporation [30] cannot be disregarded. In this sense, it is noteworthy to point out that the formation of Ag NPs has been observed at the surface of Ag–Si3N4 films grown by a dual ion-beam co-sputtering process [47], in addition to the NPs formed in the dielectric matrix.

Table 1 Structural data of the annealed samples: thickness of the nanocomposite surface layer containing the Ag NPs as determined from ellipsometry fittings; half axis lengths of the NPs; NP volume fraction and density in the surface nanocomposite layer and corresponding mass of Ag in the NPs, as determined from Maxwell–Garnett fitting; calculated initial mass of Ag in the surface layer, that is, before annealing
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Fig. 4
figure 4

Optical transmittance spectrum of a 60GeO2–20PbO–20Na2O sample doped with 0.15 wt% of Ag thermally annealed in air at 380 °C before and after polishing about 4 μm of one of his faces, and of a sample thermally annealed in vacuum at 380 °C

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3.4 Estimation of the NP size, shape and density and Ag mass in the surface layer

Shape, size and density of NPs can be estimated by applying a generalized Maxwell–Garnett effective medium theory [47] to the \(k_{\text{eff}}^{{T + {\text{ellips}},{\text{surface}}}}\) spectra above obtained. This theory allows calculating the dielectric function ε eff of a dielectric medium containing randomly distributed ellipsoidal NPs, according to the expression:

$$\varepsilon_{\text{eff}} = \varepsilon_{\text{em}} \left[ {1 + f_{i} \frac{{\varepsilon_{i} - \varepsilon_{m} }}{{\varepsilon_{m} + L(1 - f_{i} )(\varepsilon_{i} - \varepsilon_{m} )}}} \right] $$
(1)

where ε m is the dielectric function of the matrix, f i is the volume fraction of NPs whose dielectric function is ε i , and L is the depolarization factor that takes into account the mean shape of the NPs and depends on the direction of the applied electromagnetic field. The expressions for L for spherical and spheroidal NPs can be found in [47]. From ε eff, the extinction coefficient of the dielectric medium containing NPs is obtained using the expression [48]:

$$k_{\text{eff}} = \sqrt {\frac{{ - \text{Re} (\varepsilon_{\text{eff}} ) + \sqrt {\text{Re} (\varepsilon_{\text{eff}} )^{2} + \text{Im} (\varepsilon_{\text{eff}} )^{2} } }}{2}} $$
(2)

The NPs are supposed to be far enough from one another to prevent mutual interaction and small enough to neglect electromagnetic wave retardation effects [45, 47]. A modified metal dielectric function to account for finite size effects of small particles of mean radius R is used [41, 45, 48]:

$$\varepsilon_{i} (\omega ) = \varepsilon (\omega ) + \frac{{\omega_{p}^{2} }}{{\omega (\omega + {\text{i}}\tau^{ - 1} )}} - \frac{{\omega_{p}^{2} }}{{\omega \left( {\omega + {\text{i}}\tau^{ - 1} + \frac{{{\text{i}}Av_{F} }}{R}} \right)}} $$
(3)

ω being the angular frequency, and using the bulk silver dielectric function ε(ω) given by Palik [43] and values for the plasma frequency ω p , Fermi velocity v F and damping rate τ: 1.33 × 1016 s−1, 1.39 × 1016 cm s−1, and 5.14 × 1012 s−1, respectively. The unknown value for the size parameter A [49], which is related to the finite size effect on the scattering of electrons, has been taken as 1. The glass dielectric constant has been obtained from the values of \(n_{\text{eff}}^{{T + {\text{ellips}},{\text{surface}}}}\) in the near infrared. The best fit of each \(k_{\text{eff}}^{{T + {\text{ellips}},{\text{surface}}}}\) spectrum is achieved for prolate spheroids (ellipsoids with half axes \(a > b = c,a\) being the axis perpendicular to the sample surface). The obtained values for their axes are shown in Table 1. The NP density is f i /V NP, where V NP is the volume of a single NP. As shown in Table 1, the NP size increases and the density of NPs decreases when increasing the annealing temperature. This suggests the occurrence of processes such as NP coalescence or Ostwald ripening.

From the glass density (ρ = 4.763 g cm−3 [42]) and from the initial glass Ag content (0.15 wt%), and assuming the initial Ag ions being homogeneously distributed in the untreated glass, the initial mass of Ag ions per cm2 in the layer is 0.0015 × ρ × d × 10−7 g (d in nm). On the other hand, from the total volume occupied by NPs in the layer the total mass of NPs per cm2 can be calculated taking the silver density (10.5 g cm−3) into account. As it can be seen in Table 1, this initial Ag mass in the layer is much less than the total mass of Ag NPs formed there after annealing, in agreement with the occurrence of migration of Ag atoms towards the sample surfaces.

3.5 Mechanisms involved in the NP formation investigated by mid-infrared spectroscopies

Ag NP formation by thermal processing in a variety of atmospheres (air, hydrogen, vacuum) has been widely studied in Ag–Na ion-exchanged silicate glasses. It has been found in many cases that Ag aggregation occurs below the sample surface within a depth that is significantly small compared to the depth (of several microns) to which silver diffuses during the ion exchange process [30–34]. There is then an outward diffusion of silver ions at high temperature before Ag0 aggregation. This process has been ascribed in vacuum-annealed samples to relaxation of surface tensile stress that was introduced by the size difference between Ag+ and Na+ ions [31, 33]. In hydrogen-annealed samples, diffusion is due to a complex process involving a charge balancing mechanism during hydrogen–sodium ion exchange [32]. In the case of heat treatment in air, NP formation is limited due to the mobility of silver and the concentration of reducing elements present in the glass. Moreover, there is a silver accumulation near the surface due to the interdiffusion induced by the ionic silver, which compensates the decreasing concentration during the reduction process [34].

Prior to thermal annealing to induce the formation of NPs, our bulk samples are cut from a glass block, in which Ag ions are supposed to be homogeneously distributed, on the contrary to ion-exchanged glasses in which silver is initially distributed along several microns beneath the surfaces. It is known that Ag+ ions are bound to non-bridging oxygen atoms (NBOs) that provide electrons to reduce those ions during thermal annealing [50] according to the polymerization reaction [33]:

$$2( \equiv\!\!\!{\text{Ge}}-{\text{O}}^{ - } ) \leftrightarrow\,\equiv {\text{Ge}}-{\text{O}}-{\text{Ge}} \equiv + {\text{ O}}^{ 2- } $$
(4)

the Ag+ ions being neutralized following:

$$2 {\text{O}}^{ 2- } + {\text{ 4Ag}}^{ + } \leftrightarrow 4 {\text{Ag}}^{0} + {\text{ O}}_{ 2} $$
(5)

The behaviour of FTIR spectra of air-annealed samples shown in Fig. 5 is consistent with this picture. With respect to the untreated sample, it can be seen that the absorption between 600 and 1,000 cm−1 increases because of annealing in air in both the surface and the bulk part of the sample, an increase in the 400–600 cm−1 region being also observed in the latter. In the 600–1,000 cm−1 region, different vibration modes of Ge–O–Ge bridges involving either [GeO4] tetrahedra and/or [GeO6] octahedra, with and without NBOs, occur, as well as other vibration bands related to Ge–O and Pb–O bonds, while the 400–600 cm−1 region includes other bands also ascribed to vibrations of Ge–O–Ge and Pb–O–Pb bridges and to Pb–O bonds [51–55]. Hence, these results imply that annealing in air increases the number of bridging oxygen atoms, thus indicating that polymerization [reaction (4)] takes place.

Fig. 5
figure 5

FTIR spectra of an untreated glass sample, the surface and the bulk part of a sample thermally annealed in air at 380 °C, and the surface and the bulk part of a sample thermally annealed in vacuum at 380 °C

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Raman spectroscopy leads to very similar results as FTIR spectroscopy. Figure 6 shows the spectra for an untreated sample and for samples thermally annealed at 380 °C, one in air and the other in vacuum. Although the excitation laser beam was focused on the sample surface, a penetration depth for the excitation beam of about 5 microns has to be taken into account; therefore, the obtained spectra mix the bulk part with the sub-surface region where the NPs are formed. Anyhow, the behaviour of the sample annealed in air agrees with FTIR spectra obtained for both the sample surface and the bulk, that is, an enhancement of the whole spectrum intensity is induced by this thermal treatment. All Raman spectra have been deconvoluted into 6 Gaussian components peaked at around 354, 431, 516, 585, 792 and 838 cm−1 (two very weak bands at around 320 and 643 cm−1 also appear in the spectrum of the air-annealed sample). These bands are related to different vibration modes of Ge–O–Ge bridges, some of them involving [GeO6] units and Ge–O bonds associated with NBOs [37, 54–56], which allows arriving to the same conclusion as that extracted from FTIR spectroscopy.

Fig. 6
figure 6

Raman spectra of an untreated sample, a sample thermally annealed in air at 380 °C and a sample thermally annealed in vacuum at 380 °C

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An Arrhenius plot (not shown) of the optical density peak values obtained from the data shown in Fig. 1 gives an activation energy for migration of Ag atoms or ions of 0.50 eV, which is close to the value obtained in silver–sodium exchanged soda lime glass [30]. So, a possible explanation to the sub-surface formation of Ag NPs could arise from oxygen in-diffusion [57] caused by the thermal annealing in air while Ag–O bond breaking is occurring. It is noteworthy that oxygen diffusion has been observed to take place in silicate glasses (whose glass transition temperatures are higher than those of the germanate glass here studied) at temperatures as low as 400 °C, the oxygen reaching penetration depths of the order of the NP layer thickness obtained in this work [58]. Since FTIR results indicate that, among others, the vibration bands related to [GeO6] groups grow by annealing in air, it is sensible to conclude that this extra oxygen induces the conversion of part of the four-coordinated Ge ions ([GeO4] tetrahedra) near surfaces to six-coordinated ones ([GeO6] octahedra), the extra charge leading to Ag+ migration to the surfaces for charge compensation, where Ag neutralization and aggregation take place together with oxygen release through the surfaces [33].

On the contrary, annealing in vacuum hardly causes Ag NP formation, as it can be seen in Fig. 4. This thermal treatment seems to induce oxygen loss from the glass, since an absorption decrease in the FTIR spectrum in the whole region between 400 and 1,100 cm−1 in the surface part of the sample is observed (Fig. 5). In the bulk part of the vacuum-annealed sample, only the absorption between 800 and 1,100 cm−1 is seen to decrease with respect to the untreated sample. Some of the Ge–O–Ge vibration bands involving [GeO4] units, Ge–O–Ge vibration bands perturbed by [GeO6] units and Ge–O and Pb–O bond-related vibrations occur in this region [51, 54]. Therefore, this decrease seems to be due to oxygen migration towards the surface, and this, combined with the subsequent oxygen loss from the sample, avoids Ag migration and aggregation. Annealing in vacuum makes the Raman spectrum intensity to slightly diminish (Fig. 6), resembling the behaviour of a combined surface-bulk FTIR spectrum, thus supporting the conclusions drawn from FTIR measurements.

4 Conclusions

From the simultaneous analysis of optical transmittance and spectroscopic ellipsometry in the near ultraviolet-to-near infrared range, it has been shown that thermal annealing in air of bulk silver-doped lead–germanate glass prepared by the melting method induces the formation of Ag NPs in a thin layer underneath the sample surfaces. From characterization in the mid-infrared, a mechanism to the sub-surface formation of the NPs has been proposed. Unveiling the localization of these NPs is an important achievement in view of SPR-mediated enhancement of the luminescence of Er3+ ions dispersed in the glass. The optical analysis performed in this paper could be applied to glasses of other nature, on which only basic characterization has been performed and not much about the NP size and localization is known. Indeed, the presence of NPs only in a thin surface layer and with a low density might explain why very small SPR bands, or even no band, have been detected in many cases by optical transmittance measurements in glasses containing NPs, as mentioned in the Introduction.