We prove criteria for the invertibility of the binomial functional operator
\[
A=aI-bW_\alpha
\]
in the Lebesgue spaces \(L^p(0,1)\), \( 1 < p < \infty\), where \(a\) and \(b\) are continuous functions on \((0,1)\), \(I\) is the identity operator, \(W_\alpha\) is the shift operator, \(W_\alpha f=f\circ\alpha\), generated by a non-Carleman shift \(\alpha:[0,1]\to[0,1]\) which has only two fixed points \(0\) and \(1\). We suppose that \(\log\alpha'\) is bounded and continuous on \((0,1)\) and that \(a,b,\alpha'\) slowly oscillate at \(0\) and \(1\). The main difficulty connected with slow oscillation is overcome by using the method of limit operators.

Gallium-doped zinc oxide films were prepared by rf magnetron sputtering at room temperature as a function of the substrate-target distance. The best results were obtained for a distance of 10 cm, where a resistivity as low as 2.7×10-4 Ωcm, a Hall mobility of 18 cm2/Vs and a carrier concentration of 1.3×1021 cm-3 were achieved. The films are polycrystalline presenting a strong crystallographic c-axis orientation (002) perpendicular to the substrate. The films present an overall transmittance in the visible part of the spectra of about 85 %, in average. The low resistivity, accomplished with a high growth rate deposited at RT, enables the deposition of these films onto polymeric substrates for flexible applications.

Amorphous undoped a-Si:H films have been produced by hot wire plasma assisted chemical vapour deposition (HWPA-CVD), which combines the hot wire chemical vapour deposition (HW-CVD) and plasma enhanced chemical vapour deposition techniques. In this work we analyse the dissociation mechanism of the gas during the film growth in both processes with a quadrupole mass spectrometer. Besides that, the energy delivered to the gas dissociation is determined and correlated with the films properties. Thus, based on the results of the dissociated species for each deposition condition and process, we explain why the growth rate is enhanced when the filament temperature rises in HW-CVD process and why it decreases as r.f. power is enhanced in HWPA-CVD process. © 2002 Elsevier Science B.V. All rights reserved.

Doped a/μc-Si:H films were produced in different starting deposition conditions by the hot wire chemical vapor deposition technique. In this paper, we show that by changing the initial onset deposition conditions of the process and maintaining the overall pressure, hydrogen dilution and filament temperature, it is possible to control the compactness of the films. As the films nucleation is the key parameter to produce compact films, we show that starting the process with hydrogen and progressively introducing the process gas enhances the compactness and improve the electrical properties of the films produced. © 2002 Elsevier Science B.V. All rights reserved.

Highly transparent and conductive ZnO:Ga thin films were produced by rf magnetron sputtering at room temperature on polyethylene naphthalate substrates. The films present a good electrical and optical stability, surface uniformity and a very good adhesion to the polymeric substrates. The lowest resistivity obtained was 5×10-4 Ωcm with a sheet resistance of 15 Ω/sqr and an average optical transmittance in the visible part of the spectra of 80%. It was also shown that by passivating the polymeric surface with a thin SiO2 layer, the electrical and structural properties of the films are improved nearly by a factor of 2.

In this paper, we present results concerning the thickness dependence (from 70 to 890 nm) of electrical, structural, morphological and optical properties presented by gallium-doped zinc oxide (GZO) deposited on polyethylene naphthalate (PEN) substrates by r.f. magnetron sputtering at room temperature. For thicknesses higher than 300 nm an independent correlation between the electrical, morphological, structural and optical properties are observed. The lowest resistivity obtained was 5 × 10-4 Ω cm with a sheet resistance of 15 Ω/□ and an average optical transmittance in the visible part of the spectra of 80%. It is also shown that by passivating the surface of the polymer by depositing a thin silicon dioxide layer the electrical and structural properties of the films are improved nearly by a factor of two. © 2003 Elsevier B.V. All rights reserved.