Dynamic in situ spectroscopic ellipsometry is used to probe post-deposition nano-structural changes in silver films at room temperature in the pre- and post-coalescence stages of Volmer-Weber growth. In the island growth phase the Maxwell-Garnett theory is used to determine structural changes in the island film. Changes in the plasmon resonance frequency indicate an increased distance between islands which explain pre-coalescence resistivity changes. Post-coalescence changes in the resistivity are determined to be due to grain growth. A reduction in film thickness of 0.2–0.3 nm is also observed. The results are used to evaluate recent competing theories based on in situ stress measurements.
© 2007 Optical Society of America
Discontinuous and semi-continuous silver films have been extensively studied over the last half century due to their unique optical and electronic properties that differ markedly from the bulk material [eg. 1–3]. Far from being comprehensively categorised, the properties of these materials are of increasing interest as new applications and phenomena stemming from their inherent surface plasmon resonances are reported [4,5]. It was reported in a number of early studies that the post-deposition electrical conductivity of such films is not stable at room temperature, in both the discontinuous (island) and semicontinuous regimes (see for example  and references therein). Various theories attributed this to room temperature migration of islands , island shape changes  and temperature changes influencing the conduction mechanisms . Transmission electron microscopy performed shortly after the deposition supported the model of changes in the film nanostructure in the post-coalescence regime . Unfortunately, due to access limitations, routine electron microscopy studies during the deposition of metallic films by physical vapour deposition have not been feasible. Similarly, scanning probe microscopy  and synchrotron-based small angle X-ray scattering , whilst providing detailed information on film nanostructure during growth, are hindered by time resolution and access issues, respectively.
Over the last 20 years, in situ stress measurements have become the method of choice for investigating dynamic changes in metallic (especially silver) film nanostructure during growth due to their ability to non-invasively record real-time dynamics (see for example  and references therein). Significant insights have been reported into the morphological development during Volmer-Weber film growth which is characterised by nucleation, island growth, island coalescence, percolation and filling of channels, and finally continuous film growth. In the pre-coalescence phase a compressive stress develops, followed by a tensile stress increase during the coalescence phase and finally a compressive stress develops once more after percolation. It is generally agreed that the tensile stress during the coalescence phase stems from impinging islands stretching toward one another to create a grain boundary, thereby decreasing the surface free energy at the expense of an associated strain energy . The origin of the post-coalescence compressive stress is less clear. It is proposed that it originates from a relaxation of compressive strain which is locked-in during the pre-coalescence phase due to the reduced lattice spacing of small islands .
The work presented here investigates a new approach to study morphological changes in silver films during pauses in the deposition using dynamic in situ spectroscopic ellipsometry (SE). In recent years advances in hardware and software have improved the speed of SE to the point where real-time processes can now be measured which, when combined with the high sensitivity of SE to sub-monolayer changes in thin films, makes it a powerful method for non-invasive investigations of thin film dynamics. We use in situ spectroscopic ellipsometry to probe the nature of post-deposition changes in pre- and post-coalescence silver films. We use the Drude free-electron theory in the continuous film regime to model the electronic properties of the film. In the pre-coalescence regime an effective medium approximation is used to infer morphological changes in the film. The ellipsometric results provide new results with which to evaluate conclusions of stress measurement studies and resolve the origin of observed resistance changes.
Depositions were performed in a high-current pulsed filtered cathodic vacuum arc (FCVA) built in-house . This novel deposition system is designed to give precise control over the film growth rate due to the high reproducibility of the pulse parameters. Macroparticles were removed by a toroidal 90 degree filter resulting in a 100% ionized plasma with a density of the order of 1x1018 m-3. The background pressure was lower than 10-6 mbar before the pulsed plasma generation began and never rose above 5×10-6 mbar during the deposition. A silver cathode (99.99%) was ablated at 3 Hz producing plasma pulses 1.2 ms in duration. The average arc current was 1kA during the pulses and the deposition rate was 0.0325 nm/pulse, determined by measuring a comparatively thick continuous film using ellipsometry and profilometry and dividing by the number of arc pulses. This corresponds to an instantaneous deposition rate of 27.1nm/s during the pulses. At 3 Hz this produces a time averaged growth rate of 0.0975nm/s. To investigate the relaxation dynamics a series of ten pulses was deposited and the film was allowed to relax for 30 seconds before the next 10 pulses were deposited.
The deposition and relaxation was monitored in situ using a J. A. Woollam M2000 spectroscopic ellipsometer. The instrument operates in a rotating compensator configuration, with a white light source, refracting prism and CCD detector providing fast data acquisition capabilities. Data was acquired every 2 seconds at 400 wavelengths in the range 370–1000nm at an angle of incidence of 75 degrees from the normal. The data was analysed using the WVASE32 software in which a slab model of the thickness and dielectric function of the substrate and film is defined. By performing an iterative fit to reduce the mean squared error (MSE) between the measured and generated data the film thickness and/or optical constants are determined. Checks for parameter correlation and uniqueness are performed. Since the dielectric functions of very thin and discontinuous films vary significantly from the bulk values in the literature we model the film dielectric functions using the Drude and Maxwell-Garnett theories.
Silicon substrates with a 500nm thermal silicon oxide were prepared for both in situ ellipsometry and resistivity measurements. Prior to silver deposition, aluminium contacts were evaporated onto the substrate defining a 12mm square area to be used for sheet resistance measurement. Conductive probes were attached to the aluminium contacts and resistance was measured in situ with a HP34401A multimeter with a range up to 100MΩ. The temperature of the rear surface of the sample was measured in situ using a Luxtron thermometer which operates by measuring the optical emission from a fluorescent paint on the rear surface of the substrate.
3. Results and discussion
3.1 Resistivity and temperature observations
The resistance and temperature measurements, during the deposition and subsequent relaxation periods between 500 and 700 seconds from the start of the deposition, are shown in Fig. 1. For times before 500s the resistance value is outside the range of the measurement system. During the deposition periods the resistance decreases markedly. During the first two relaxation periods the resistance is clearly observed to increase before switching to a resistance decrease during subsequent relaxation periods. The percolation threshold of the film coincides with this switch . The effective thickness (accounting for voids and roughness) at which the percolation occurs for this deposition was determined by ellipsometry to be 7.6–8.0 nm, corresponding to a nominal thickness (number of pulses x deposition rate) of 5.2–5.5 nm.
Conduction in discontinuous films is generally agreed to be mediated by tunneling processes  which is highly sensitive to inter-particle distance and temperature. We consider first the temperature effects. It is well documented that discontinuous metal films exhibit a negative temperature coefficient of resistance (TCR), opposite in sign and many times greater in magnitude than for bulk films . Therefore, even a slight cooling of the substrate surface after the deposition may explain the resistance changes observed in the pre-coalescence phase. Surface cooling may also account for the resistance change after percolation since the TCR is positive, as for bulk metals.
We estimate the magnitude of the temperature effect using measured TCRs, α, from the literature. For films with initial resistance, Ro=1×106 Ω/▫, TCRs of the order of α=-0.1 and -0.25 K-1 have been reported for platinum  and gold films , respectively. The temperature change on the back surface of the substrate was approximately ΔT=0.4 °C during each pulse, falling quickly back to close to its pre-pulse temperature by the end of the relaxation period. Over the entire deposition the net temperature rise was approximately 2 °C. The change in resistance ΔR=Ro.ΔT.α, is then estimated to be between 0.4-1×105 Ω/▫, which is almost three orders of magnitude smaller than the observed increase in Fig. 1 for a film of initial resistance 3×106 Ω/▫. Although we may expect the substrate surface to be subjected to a much greater temperature variation than the rear surface we note that the temperature is comparatively stable toward the end of the relaxation periods while the resistance continues to increase markedly. We therefore conclude that the observed resistance changes are only weakly influenced by temperature.
The effect of gas adsorption on the substrate surface during the pauses should also be considered. The pressure during the pauses was below 1×10-6 mbar suggesting that a monolayer of adsorbed gas will form on the surface in around one second and reach an adsorption-desorption equilibrium within a few seconds. Since the resistance changes that we observe continue over many tens of minutes we rule out the adsorption of gas as being responsible for the changes. Additionally the possibility of oxidation of the silver may be ruled out since we would expect oxidation to increase the resistance, and yet a post-percolation decrease is observed.
Increasing average inter-island spacing during the pauses due to island shape changes  and/or agglomeration effects  have also been proposed to explain the resistance changes. Initially the average inter-island distance would increase due to Ostwald ripening. Similarly, during the coalescence phase, impinging islands stretch toward one another to create a grain boundary and subsequently reshape to reduce their surface energy thereby increasing the inter-island distance. The increase in inter-island spacing results in a reduction in electron tunnelling observable as an increased resistance. After percolation the conductivity is mediated by classical processes. The formation of larger grain boundaries resulting in larger conductive pathways in the percolated film is then observable as a decrease in the resistance.
3.2 Ellipsometric data and modeling
The raw ellipsometric parameters, Ψ and Δ, at 3 representative frequencies are shown in Fig. 2. The data is from the same deposition in Fig. 1. Changes in the film optical properties during the relaxation periods are evident. Modeling the optical properties of random media near the percolation threshold is extremely difficult due to complex interactions of the microscopic electric fields in the particles. However we can model the film in the very early stages where the interactions are limited and in the latter stages of deposition where the film becomes continuous.
3.2.1 Continuous film regime
In the continuous film regime silver is well described by the Drude theory 
where ωp is the bulk plasma frequency, Γ is the free electron relaxation frequency and ε∞ is the contribution from high energy transitions outside the measurement range. ħωp is proportional to the electron density and is assumed constant at 8.77 eV, determined by fitting (1) to literature data for bulk silver . Similarly, for the experimental energy range (1.25–3.3 eV) we assume that the contributions from inter-band transitions are contained within ε∞ which is determined to be equal to 4.1 from the bulk data.
Γ is inversely proportional to the mean free path of the electrons in the metal and arises from electron scattering from defects, phonons, surfaces and grain boundaries. In discontinuous and ultra-thin films at room temperature the latter two processes dominate . In the pre-coalescence phase, Γ is dominated by surface scattering and is an indicator of the island size. When the film thickness approaches the mean free path in the bulk (~40nm for silver), scattering from surfaces contributes a minor role. In the coalescence phase Γ is increasingly influenced by grain boundary scattering and is therefore increasingly an indicator of the grain size. Using (1) we fit the film thickness and Γ well past the percolation threshold near the point where the film becomes continuous. Effective medium modeling (discussed below) showed that the surface plasmon resonance of the film at this point has red-shifted close to or equal to zero and the Drude model is therefore an appropriate choice. Representative fits for time, t=950 s are shown in Fig. 3, showing excellent agreement between the data and the fit.
The film resistivity is related to the relaxation frequency via
where m* is the effective electron mass (0.96 times the electron rest mass ), N is the electron density and e is the electronic charge. The optical resistance was subsequently calculated from the product of the thickness and the resistivity, determined from (2), and compared to the measured DC resistance. The results are shown in Fig. 4 along with the film thickness.
The optical resistance closely follows the trend of the measured DC resistance, showing a reduction during the relaxation periods. The resistance changes are therefore attributed to changes in the electron scattering rate caused by increasing grain size. The two curves are offset by approximately 10Ω, which may be partly explained by enhanced resistance at the interface of the film and aluminium contacts . We should also note that resistance is frequency dependant due to the skin effect; however for the extremely small dimensions considered here we expect that the field will completely penetrate the film. In addition AC resistance is generally greater than DC resistance, which is the opposite of what we observe, so we rule out this effect as contributing to the observed discrepancy. It is feasible that the electron density in the film is overestimated since the value used is for crystalline silver . We expect here that some voids and channels to remain in the film and that the film is polycrystalline. This would result in a reduced electron density compared to the bulk and therefore underestimated resistance, thus explaining the observed discrepancy.
The film thickness reduces significantly during the pauses, showing a reduction of between 0.2 and 0.3 nm over 30 seconds, corresponding to approximately 1 monolayer. This result highlights the sensitivity and capabilities of spectroscopic ellipsometry to perform in situ film thickness measurements with temporal and spatial resolution comparable or better than that of Synchrotron-based X-ray scattering experiments [12, 24]. Electron diffraction measurements with comparable temporal resolution have been recently reported to qualitatively demonstrate surface roughness changes after the cessation of film growth  however quantitative results were not possible.
The changes in Γ correspond to an increase in the electron mean free path of the order of 2nm per relaxation period. This is an order of magnitude larger than the reduction in film thickness in the corresponding period. The thickness reduction counters the action of the grain growth by increasing the electron surface scattering however grain growth dominates resulting in a decreased resistance.
3.2.2 Island film regime
In the pre-coalescence phase an effective medium model is used. The Maxwell-Garnett Theory (MGT)  determines the dielectric function, , of a composite consisting of non-interacting spherical particles in the quasi-static limit in a host medium to be
where m and p are the bulk host and particle dielectric functions, respectively, and F is the fill factor of the particles. If F is too large then the non-interacting assumption is violated. Since the MGT assumes a three-dimensional dispersion of particles in a matrix, the applicability of this formalism to thin island films is questionable. Doremus  presents a theoretical argument of the application of the MGT to the thin film case. He showed that the theory can be used to relate the plasmon absorption maximum to the surface area coverage, Q, of gold and silver films, and presents an extensive survey of experimental evidence confirming the predictions in the range 0.19<Q<0.63. By comparing the MGT results with those determined using a model-independent inversion method we have recently shown that in the very early stages of film growth the qualitative predictions of the MGT remain sound .
Figure 5 shows the three variable parameters, F, Γ and d, as a function of time for the first 4 deposition bursts and pauses, determined by fitting the MGT to the ellipsometric data with p modeled using (1) and m equal to unity. The experimental and fitted data are shown in Fig. 3 for t=95s. The real, ε1, and imaginary, ε2, parts of the dielectric function of the film are also plotted. There is a significant reduction in Γ during the pauses implying an increase in the electron mean free path, also observable as a reduction in the broadening in ε2. This arises from an increase in the island size, driven by adatom diffusion and Ostwald ripening, which results in an increase in the inter-island spacing. Since conduction in the pre-coalescence phase is facilitated by tunneling processes which is highly dependent on the inter-island spacing, the reduction in Γ implies an increase in resistivity, contrasting the post-coalescence results above and supporting the observations in Fig. 1.
A reduction in the thickness increase with successive deposition bursts from 1nm for the first deposition to ca. 0.5nm for the fourth deposition is consistent with Volmer-Weber growth. There is no detectable increase in the film thickness during the relaxation periods. The observed reduction in F during the pauses without a concomitant increase in the thickness is unexpected. In fact, since adatoms do not contribute to the free electron absorption, we would expect F to increase as adatoms incorporate into the crystallites (analogous to the difference in absorption between a solution of silver ions and a suspension of silver nanoparticles).
The inconsistency can be explained by noting that the MGT does not include the effects of dipole-dipole interactions between the particles. This effect, which acts to red-shift the plasmon resonance energy, is dependent on the interparticle distance. As more material is deposited the increase in F red-shifts the centre energy of the plasmon resonance as expected [Figs. 5(b) and 5(d)]. However, during the pauses, the islands grow in size and the interparticle distance increases, thereby reducing the dipole-dipole interactions and blue-shifting the resonance energy. This shift is easily observed in the plot of the resonance energy, shown as an alternative axis in Fig. 5(b). The observed reduction in F is therefore an artefact of applying the MGT outside of the low-F limit, or conversely, the omission of the dipole-dipole interactions from the model.
4. Comparison with stress measurements
Recently there has been renewed debate on the physical mechanisms responsible for post-deposition tensile stress increases observed in both the pre-coalescence and post-coalescence regimes [27–33]. Using ex-situ transmission electron microscopy, Koch et al concluded that this arises from recrystallisation increasing the average grain size in the film . The observation of a reversible change in the stress when the deposition was recommenced is still not clarified. Three models have been proposed to explain the observations. (i) Friesen and Thompson attribute it to changes in a compressive stress arising from changes in the adatom population during deposition . In their model a compressive stress develops on the surface arising from an elastic displacement field exerted by the adatoms. When the deposition stops there is a reduction in the adatom population as they incorporate into islands and crystallites, resulting in a reversal of the compressive stress. (ii) Chason, et al. attributed the reversible stress change observed in the post-coalescence phase to a compressive stress arising from a flow of excess adatoms into the grain boundaries during deposition. The flow is driven by an increased surface chemical potential during deposition and reverses when the deposition stops . (iii) Koch counters both these theories by arguing that the seemingly reversible process is actually a result of two symmetric but irreversible processes; recrystallisation and post-growth surface flattening .
Our results show that grain growth occurs in the post-coalescence phase, supporting the original theory of Koch which claims that the stress changes are due to recrystallisation processes increasing the grain size. We also observe a reduction in film thickness which may arise from changes in the adatom population or post-growth surface flattening, supporting both models (i) and (iii), respectively. The results contradict model (ii): the movement of adatoms out of the grain boundaries when the deposition is stopped implies an increase in the average film thickness as opposed to the decrease observed here.
The ellipsometric results support the theory that the post-deposition resistance changes are caused by nanostructural changes in the film. Temperature changes do not contribute significantly to the resistance changes. In the post-coalescence phase a grain size increase causes a reduction in the resistance with a magnitude equal to the resistance changes observed in conductivity measurements. In the pre-coalescence phase, surface-energy driven island growth results in an increased inter-island distance thereby decreasing the tunneling probability. The absence of a change in the film thickness implies that the growth direction is parallel to the substrate for island heights less than 3nm.
With respect to the debated models for stress generation we propose that both the stress and resistivity changes stem from the same process. The ellipsometric results support the view that the seemingly reversible stress changes are a result of two symmetric but irreversible processes; recrystallisation and post-growth surface flattening. A change in the adatom population is neither confirmed nor denied by the results presented here and remains a plausible hypothesis; however the observed time-scale of both the resistance and stress changes (in excess of hundreds of seconds) appears excessive for the changes to originate from adatom population fluctuations. If dipole-dipole interactions are qualitatively included in the modeling then it may be possible to actually observe the changes in adatom population by monitoring the amplitude of the free electron absorption using dynamic in situ spectroscopic ellipsometry.
Financial support from the Australian Research Council is gratefully acknowledged.
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