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Micro and Nanostructures in Thin Films Maria Cecilia Salvadori Thin Films Laboratory, Institute of Physics, University of São Paulo, Brazil
Synthesis and characterization of nanostructured thin films: (I) Electrical resistivity of metal thin films, with thickness between fraction of nanometer and 10 nm: measurements and development of a new quantum model; (II) Thermoelectric power of thin films, with thickness smaller than the mean free path of conducting electrons, showing considerable different behavior, when compared with thicker films; (III) Elastic Modulus of nanostructured thin films, with thickness between 20 nm and 80 nm, observing a decrease, when compared with the bulk material; (IV) Hydrophobic or hydrophilic character of surfaces with periodic microstructures fabricated on it.
I – Electrical resitivity of nanostructured thin films • Quantum effects are expected in electrical resistivity () of thin films when: • The film thickness (d) is smaller than the electronic mean free path (l0) • The energy-level quantization is enhanced in the direction along the film thickness d, that can be estimated by the • number of Fermi subbands, which must • be small.
In the case of Pt and Au films, that we have studied, these 2 conditions were satisfied:
In the quantum model the calculation of the conductivity ( = 1/) as function of the film thickness d is done considering the energy quantization of the conducting electrons in the direction along the film thickness d and using the Boltzmann transport equation.
In this way, the conductivity generated by the surface is given by: where are the wave numbers associated to the quantization in the direction along the film thickness d and Fs is a parameter that depends of the interaction between the conducting electrons and the rough film surface.
To calculate Fs, we take into account the height fluctuations of the film surface, which generate a scattering potential Then, the electrons scattering due to U is calculated by the transition probability given by:
In the Fishman and Calecki works, the scattering depends of the correlation distance () of the surface. But to fit this model with experimental data, it is necessary to have ~ nm. These parameter values have no physical meaning. Indeed, we have measured the correlation distance for the Pt and Au films, obtaining: ξPt(d) ≈ 200 nm e ξAu(d) ≈ 40 nm.
In our model we calculated the electron scattering by the surface taking into account an effective interaction range: where, , , and Therefore
In our model: • h(x,y) = n hnsen(2r/n), where r is the position vector modulus in the (x,y) plane • The wavelengths nDn, where Dn are the film grains sizes • n are given by n = n F • In this way, Fs is given by: Fs(g,ls) = g(d) ls(d) • Where the grain form factor g(d) is given by:
In the case of metals, where N >> 1, the total film resistivity ρ(d) = ρbulk + ρs(d) is given by where C is a constant that depends of the material, in this case: CPt = 6.261x103 nm-2 e CAu = 28.072x103 nm-2, Δ(d) is the roughness measured, g(d) was obtained through the grain sizes measurement ls(d) was calculated as previously described.
With this model, the Pt and Au resitivities were calculated, for films thickness between 1 e 10 nm, showing excellent agreement with the experimental data. • - M.C. Salvadori, A.R. Vaz, R.J.C. Farias, M. Cattani, Surface Review and Letters 11, 223 – 227 (2004). • - M.C. Salvadori, A. R.Vaz, R. J. C. Farias, M. Cattani, Journal of Metastable and Nanocrystalline Materials 20-21, 775 (2004). • - M. Cattani, M.C. Salvadori, Surface Review and Letters 11, 463-467 (2004). • - M. Cattani, M.C. Salvadori, Surface Review and Letters 11, 283 - 290 (2004). • - M. Cattani, M.C. Salvadori, J.M. Filardo Bassalo, Surface Review and Letters 12, 221-226 (2005). • M. Cattani, A.R. Vaz, R.S. Wiederkehr, F.S. Teixeira, M.C. Salvadori, I.G. Brown, Surface Review and Letters 14, 87 - 91 (2007). • - M. Cattani, M.C. Salvadori, F.S. Teixeira, R.S. Wiederkehr, I.G. Brown, Surface Review and Letters 14, 345 – 356 (2007).
Based on these results, we proposed that a surface morphological anisotropy could induce anisotropy in the film resistivity. In order to estimate the metric scale necessary to observe this effect, we have calculated the film resistivity considering a surface h(x,y) with different morphologies along de directions x and y.
The geometry used for this estimate was: That is a surface defined by a sinusoidal profile in the x-direction: , where h is the amplitude of the sinusoidal profile and L the morphological wavelength. A granular profile was assumed in the y-direction instead of a flat profile, as nanostructured thin films usually are when formed by filtered vacuum arc plasma deposition.
In this calculation gold was taken as the film material and the average thickness was 5 nm. The anisotropic factor ρx/ρy can be as high as 30, but for L < 6 nm.
We have investigated an alternative approach for creating an anisotropic surface morphology. The substrate was a glass microscope slide scratched in one direction with ¼ μm diamond powder dispersed in water. AFM image
The results show that resistivity anisotropy ratio ρx(d)/ρy(d) is greater than unity and varies with thickness. These results indicate a significant resistivity anisotropy that is a consequence of the film morphological anisotropy M.C. Salvadori, M. Cattani, F.S. Teixeira, R.S. Wiederkehr, I.G. Brown. Journal of Vacuum Science & Technology A 25, 330-333 (2007).
(II) - Thermoelectric power in very thin film When the film thickness becomes comparable to the mean free path of the charge carriers all transport processes are expected to exhibit size effects.
For thin films of pure metal, with thickness d >> l, it is known that where ΦF and ΦB are the thermopowers of a thin-film and a thick-film of the metal with respect to a thick standard film, respectively, T the temperature, ξ the Fermi energy, E = electron energy, p the scattering coefficient. The linear behavior of ΔSF as a function of 1/d have been experimentally observed for d >> l.
In our work we measured Pt thermopowers for d ≤ l. We have measured ΔSF for Pt using thermocouple Pt/Au, with very thin Pt films 2.2 < d < 24.5 nm (note that lPt ~ 10 nm ) and thick Au film (140 nm) as reference. Our experimental results showed that , for thickness less than about 20 nm, the thermopower ΔSFdoes not vary linearly with 1/d .
Experimental procedure: • A number of thick Au films were deposited on ordinary glass microscope slides; • Thin Pt films of different thicknesses were deposited on each sample; • The voltage, generated on the hot junction, were measured as function of the temperature, obtaining a linear graphic; • The thermopowers (ΦF) were defined by the slope of these linear graphics; • The bulk thermopower (ΦB) was obtained using a thick Pt film (~160 nm >> l ~ 10 nm), with the same procedure.
Our experimental results showed that , for d ≤ l ~ 10 nm (2.2 < d < 24.5 nm), the thermopower ΔSF = (ΦB - ΦF) X 1/d is not linear. The doted curve shows the linear behavior, typical for d >> l, extrapolated to the region d << l. M.C. Salvadori, A.R. Vaz, F.S. Teixeira, M. Cattani and I. G. Brown – “Thermoelectric effect in very thin film Pt/Au thermocouples”. Applied Physics Letters 88, 133106-1 - 3 (2006).
To explain this nonlinearity, we have used our previous results of resistivity for thin Pt films (d < 10 nm): ρ(d)/ρB = 1+ 6.5/d + 140/d 9 where semiclassical effects are present in the term 6.5/d and the quantum effects are present in the term 140/d 9. The nonlinear curve was calculated using the relation ρ(d)/ρB, given above, with a quantum formalism and the Boltzmann transport equations. M. Cattani, M.C. Salvadori, A.R. Vaz, F.S. Teixeira, I.G. Brown – “Thermoelectric power in very thin films Pt/Au thermocouples: quantum size effects”. Journal of Applied Physics 100, 114905-1 - 4 (2006).
(III) – Elastic modulus of nanostructured thin films In this work we obtained the elastic modulus of thin films, deposited on vibrating beams, measuring the resonance frequencies.
The resonance frequencies for vibrating beamsis given by: where t is the beam thickness ℓ the beam length E1 the elastic modulus of the material ρ1 the material density
When we coat the beam with a thin film with thickness , we modify its resonance frequency (νc): where w is the beam width E1 the beam elastic modulus 1 the beam density E2 the film elastic modulus 2 the film density Measuring the resonance frequency shift, allows us to determine the elastic modulus of the film (E2).
AFM probes were used as vibrating beams Monocrystaline Si AFM cantilever Typical dimensions: - length (ℓ): ~ 130 m - width (w): ~ 40 m - thickness (t): ~ 5 m
The thin films were deposited by Filtered Vacuum Arc. A rotating holder has been used to uniformly coat the cantilever.
Experimental procedure: - Determination of the resonance frequency of the original cantilever - Consecutive coatings of the cantilever, with thin films, increase gradually the thickness - Resonance frequencies are measured for each step of the film deposition
The elastic modulus E2 of the film was calculated through a best fit of the theoretical frequencies ratio (νc/ νu) with the experimental results Typical graphic
Results • - M.C. Salvadori, I.G. Brown, A.R. Vaz, L.L. Melo, M. Cattani. Physical Review B 67, 153404-1 - 4 (2003). • - M.C. Salvadori, A.R. Vaz, L.L. Melo, M. Cattani. Surface Review and Letters 10, 571 - 575 (2003). • M.C. Salvadori, M.C. Fritz, C. Carraro, R. Maboudian, O.R. Monteiro, I.G. Brown. Diamond and Related Materials 10, 2190-2194 (2001). • - A.R. Vaz, M.C. Salvadori, M. Cattani. Journal of Metastable and Nanocrystalline Materials 20-21, 758 – 762 (2004).
Results Interpretation - Grains with crystalline structure (D) and with bulk elastic modulus - Grain boundaries composed by disordered structures (d) and with elastic modulus lower than the bulk For nanocrystalline material, the grain boundaries contribute significantly for the film proprieties, decreasing the elastic modulus of the film.
(IV) - Hydrophobic character of surfaces with periodic microstructures fabricated on it Introducing micro or nanostructures on a surface, the wettability of the surface can be considerable changed. In this work we have fabricated periodic microstructures on surfaces. The originality of the work is related to the metric scale.
Experimental procedure: - Periodic microstructures were fabricated on SU-8 epoxy deposited on silicon surfaces. - The technique used was electron beam lithography. - The pattern was the same for all samples and consisted in squares regularly spaced. - Three samples were prepared with different structure periodicities:200 μm , 20 μm and 2 μm. - A reference sample was prepared with a continuous surface of SU-8 (without structures).
The contact angle measurements were: 85º for the sample with periodicity of 200 μm, 90º for the sample with periodicity of 20 μm, 105º for the sample with periodicity of 2 μm and 90º for the reference sample With this result, we can observe that, decreasing the structure dimensions, the contact angle increased.
Summary Experimental results were presented on synthesis and characterization of nanostructured thin films. Emphasis was done in: resistivity, thermoelectric power, elastic modulus and hydrophobic properties.
Acknowledgements: This work was supported by the Brazilian sponsors: FAPESP and by the CNPq.