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Let $f:(\mathbb C^n,S)\to (\mathbb C^{n+1},0)$ be a germ whose image is given by $g=0$. We define an $\mathcal O_{n+1}$-module $M(g)$ with the property that $\mathscr A_e$-$\operatorname{codim}(f)\le \dim_\mathbb C M(g)$, with equality if $f$ is weighted homogeneous. We also define a relative version $M_y(G)$ for unfoldings $F$, in such a way that $M_y(G)$ specialises to $M(g)$ when $G$ specialises to $g$. The main result is that if $(n,n+1)$ are nice dimensions, then $\dim_\mathbb C M(g)\ge \mu_I(f)$, with equality if and only if $M_y(G)$ is Cohen-Macaulay, for some stable unfolding $F$. Here, $\mu_I(f)$ denotes the image Milnor number of $f$, so that if $M_y(G)$ is Cohen-Macaulay, then Mond's conjecture holds for $f$; furthermore, if $f$ is weighted homogeneous, Mond's conjecture for $f$ is equivalent to the fact that $M_y(G)$ is Cohen-Macaulay. Finally, we observe that to prove Mond's conjecture, it is enough to prove it in a suitable family of examples., Bolsa Pesquisador Visitante Especial (PVE) - Ciˆencias sem Fronteiras/CNPq Project number: 401947/2013-0 DGICYT Grant MTM2015–64013–P CNPq Project number 401947/2013-0

25th European Photovoltaic Solar Energy Conference and Exhibition / 5th World Conference on Photovoltaic Energy Conversion, 6-10 September 2010, Valencia, Spain; 3026-3031, A method for the evaluation of electrical losses in the manufacturing of optoelectronic devices, with diode pumped solid-state lasers with temporal width of nanoseconds and wavelength in the visible spectrum (532 nm) in backscribing geometry is presented. By synchronizing laser micromachining systems and ultrafast electronics systems, the interconnection process can be controlled very precisely. This helps avoiding failures caused by mechanical and kinetics effects of the positioning systems, which play a decisive role in the interconnection and isolation of thin film photovoltaic cells of hydrogenated amorphous silicon a-Si:H in superstrate configuration. This work focuses on the back contact patterning process, commonly known as P3. The success in the P3 scribes depends in several process parameters. Film removal thresholds, number of scribes, groove-width, pulse repetition or scanning speed clearly influence the quality of the scribe. An incorrect set of parameters for the P3 scribe can lead to important electrical losses in the scribe and even result in a completely unworkable module. In this work, in addition to the previously mentioned parameters, back metallic contacts of different thickness are investigated. As will be shown, gradually increasing the contact layer thickness can lead to the worsening in the quality of an otherwise perfect P3 scribe. The investigation is primarily carried out in single solar cells. Several optical imaging techniques are used to assess the quality of the P3 scribes. In addition, by monitoring the electrical characteristics of the patterned solar cells the effect of the contact thickness can be evaluated. Finally, a-Si:H modules are fabricated using the optimum combination of back contact thickness and P3 process parameters with efficiencies 7.2 %.

25th European Photovoltaic Solar Energy Conference and Exhibition / 5th World Conference on Photovoltaic Energy Conversion, 6-10 September 2010, Valencia, Spain; 3042-3045, The matter of this study is UV-laser ablation of transparent conductive oxides for solar modules. Commercial transparent conductive oxide Asahi U-type® has been irradiated with 355 nm laser light at different irradiation conditions. The influence of different work parameters has been studied and the most relevant of them have been identified. A parametric window for good-quality scribing has been found. High-quality scribing processes have been obtained. Clean scribes have been produced with full ablation of transparent conductive oxide film without damage to the substrate or thermal affection. The electrical isolation obtained between strips has been found to be remarkably good (>MΩ). Ablation thresholds at different repetition frequencies have also been determined. The morphology of the ablated surfaces has been characterised by confocal microscopy and scanning electron microscopy. Finally laser-material interaction and the ablation process of fluorine-doped tin oxide (SnO2:F) thin films using a 355-nm laser is discussed.

23rd European Photovoltaic Solar Energy Conference and Exhibition, 1-5 September 2008, Valencia, Spain; 2438-2442, In this paper we present recent results in laser ablation of photovoltaic materials using excimer and UV wavelengths of Diode-Pumped Solid-State Laser Sources (DPSS). We discuss results concerning UV ablation of different TCO and thin-film silicon (a-Si:H and nc-Si:H), focussing our study on ablation threshold measurements and process-quality assessment using advanced optical microscopy techniques. Additionally we present preliminary results for Heat affected zone estimation using refractive index measurements. We include a comparison of ablation thresholds for different materials of interest as well. In that way we show the advantages of using UV wavelengths for minimizing the characteristic material thermal affection of laser irradiation in the ns regime at higher wavelengths. Additionally we include preliminary results of selective ablation of film on film structures irradiating from the film side (direct writing configuration) including the problem of selective ablation of ZnO films on a-Si;H layers. In that way we demonstrate the potential use of UV wavelengths of fully commercial lasers sources as an alternative to standard backscribing process in device fabrication.

Let f:U⊂R2→R3 be a representative of a finitely determined map germ f:(R2,0)→(R3,0). Consider the curve obtained as the intersection of the image of the mapping f with a sufficiently small sphere Sϵ2 centered at the origin in R3, call this curve the associated doodle of the map germ f. For a large class of map germs the associated doodle has many transversal self-intersections. The topological classification of such map germs is considered from the point of view of the associated doodles.

We characterize finite determinacy of map germs f:(C2,0)→(C3,0) in terms of the Milnor number μ(D(f)) of the double point curve D(f) in (C2,0) and we provide an explicit description of the double point scheme in terms of elementary symmetric functions. Also we prove that the Whitney equisingularity of 1-parameter families of map germs ft:(C2,0)→(C3,0) is equivalent to the constancy of both μ(D(ft)) and μ(ft(C2)∩H) with respect to t, where H⊂C3 is a generic plane.