Quadratic estimates and functional calculi of perturbed Dirac operators

We prove quadratic estimates for complex perturbations of Dirac-type operators, and thereby show that such operators have a bounded functional calculus. As an application we show that spectral projections of the Hodge--Dirac operator on compact manifolds depend analytically on $L_\infty$ changes in the metric. We also recover a unified proof of many results in the Calder\'on program, including the Kato square root problem and the boundedness of the Cauchy operator on Lipschitz curves and surfaces.Comment: To appear in Inventiones Mathematicae. Minor final changes added 4/7 200

Characterisation and optimisation of PECVD SiNx as an antireflection coating and passivation layer for silicon solar cells

In this work, we investigate how the film properties of silicon nitride (SiNx) depend on its deposition conditions when formed by plasma enhanced chemical vapour deposition (PECVD). The examination is conducted with a Roth & Rau AK400 PECVD reactor, where the varied parameters are deposition temperature, pressure, gas flow ratio, total gas flow, microwave plasma power and radio-frequency bias voltage. The films are evaluated by Fourier transform infrared spectroscopy to determine structural properties, by spectrophotometry to determine optical properties, and by capacitance–voltage and photoconductance measurements to determine electronic properties. After reporting on the dependence of SiNx properties on deposition parameters, we determine the optimized deposition conditions that attain low absorption and low recombination. On the basis of SiNx growth models proposed in the literature and of our experimental results, we discuss how each process parameter affects the deposition rate and chemical bond density. We then focus on the effective surface recombination velocity S eff, which is of primary importance to solar cells. We find that for the SiNx prepared in this work, 1) S eff does not correlate universally with the bulk structural and optical properties such as chemical bond densities and refractive index, and 2) S eff depends primarily on the defect density at the SiNx-Si interface rather than the insulator charge. Finally, employing the optimized deposition condition, we achieve a relatively constant and low S eff,UL on low-resistivity (≤1.1 Ωcm) p- and n-type c-Si substrates over a broad range of n = 1.85–4.07. The results of this study demonstrate that the trade-off between optical transmission and surface passivation can be circumvented. Although we focus on photovoltaic applications, this study may be useful for any device for which it is desirable to maximize light transmission and surface passivation.This work was supported by an Australian Research Council Linkage between The Australian National University and Braggone Oy under Grant LP0989593

Femtosecond laser ablation-ICP-mass spectrometry analysis of a heavy metallic matrix : determination of platinum group metals and gold in lead fire-assay buttons as a case study

Owing to the shorter time interval during which energy is delivered to the sample material, femtosecond (fs) laser ablation is preferable over nanosecond laser ablation for metallic samples. In this project, the influence of various laser parameters-beam diameter, repetition rate and laser fluence-on the ablation of Pb as a heavy metallic matrix using an infrared (lambda = 795 nm) fs-LA system (150 fs pulse duration) was studied. The merits of Ar and He as carrier gases were compared and as He did not provide a substantial improvement in the limits of detection, while deposition of sample material on the window of the ablation chamber was more pronounced, Ar was selected for all further measurements. The effect on the ICP caused by the introduction of various amounts of sample aerosol was studied by monitoring the signal intensity for Ar-38(+). It was shown that maximizing the amount of sample ablated and thus, the amount of sample aerosol introduced into the ICP, did not result in maximum sensitivity, which was rather obtained under 'compromise' conditions. Subsequently, femtosecond LA-quadrupole-based ICP-mass spectrometry (ICP-MS) was used for the determination of traces of the platinum group metals (PGMs) Rh, Pd, Ru, Ir and Pt and of Au in Pb buttons obtained by fire assay of platiniferous ore reference materials. The signal of Pb-204(+) was used as an internal reference, correcting for variations in the laser ablation and transport efficiencies and in the instrument's sensitivity. The spectral interferences established for some of the target nuclides due to the occurrence of Pb2+ ions were successfully overcome by pressurizing the reaction cell with NH3. Quantification versus a calibration curve constructed on the basis of the results obtained for matrix-matched standards (>99% Pb) provided excellent accuracy, superior to those obtained using nanosecond LA-ICP-MS. Also the limits of detection were improved by a factor ranging between 3 and 10 and are <0.010 mu g g(-1) for the most important PGMs (Rh, Pd, Pt) and Au. Several measures, such as the use of a large ablation cell and housing up to 10 Pb buttons, were taken to increase the sample throughput. In the same context, day-to-day reproducibility of the calibration curve was also examined. When recording a 'fresh' calibration curve every day, the average bias between the experimental results and the corresponding reference values was established to be <2.5% for every target element. When using one calibration curve during three consecutive days, the bias still remains <10%, while the sample throughput is increased and analysis of several tens of buttons per day is feasible (10-15 min total analysis time per sample)

Temperature dependent carrier lifetime studies of Mo in crystalline silicon

The capture cross sections of both electronsσn and holes σp were determined for interstitialmolybdenum in crystalline silicon over the temperature range of −110 to 150 °C. Carrier lifetimemeasurements were performed on molybdenum-contaminated silicon using a temperature controlled photoconductance instrument. Injection dependent lifetime spectroscopy was applied at each temperature to calculate σp and σn. This analysis involved a novel approach that independently determined the capture cross sections at each temperature assuming a known defect density and thermal velocity. Since the energy state is in the lower half of the bandgap, the determination of σp is unaffected by the defect energy at all temperatures, and σp is found to decrease with temperature in a fashion consistent with excitonic Auger capture. At temperatures below 0 °C, the determination of σn is also unaffected by the defect energy due to the suppression of thermal emission, and σn decreases with temperature as well. It is shown that a projection of σn to higher temperature suggests the defect has an energy of 0.375 eV above the valance band edge of silicon.D.M. likes to thank the Australian Research Council for fellowship and G.C. likes to thank “CrystalClear Integrated Project” Contract No. SES6-CT_2003-502583 funded by the European Commission

The Contribution of Planes, Vertices, and Edges to Recombination at Pyramidally Textured Surfaces

We present a methodology by which one may distinguish three key contributors to enhanced recombination at pyramidally textured silicon surfaces. First, the impact of increased surface area is trivial and equates to a √3-fold increase in Seff,UL•. Sec

Surface passivation of c-Si by atmospheric pressure chemical vapor deposition of Al2O3

Atmospheric pressure chemical vapor deposition of Al₂O₃ is shown to provide excellent passivation of crystalline silicon surfaces.Surface passivation,permittivity, and refractive index are investigated before and after annealing for deposition temperatures between 330 and 520 °C. Deposition temperatures >440 °C result in the best passivation, due to both a large negative fixed charge density (∼2 × 10¹² cm⁻²) and a relatively low interface defect density (∼1 × 10¹¹ eV⁻¹ cm⁻²), with or without an anneal. The influence of deposition temperature on film properties is found to persist after subsequent heat treatment. Correlations between surface passivation properties and the permittivity are discussed

Recombination at textured silicon surfaces passivated with silicon dioxide

The surfaces of solar cells are often textured to increase their capacity to absorb light. This optical benefit is partially offset, however, by an increase in carrier recombination at or near the textured surface. A review of past work shows that the additional recombination invoked by a textured surface varies greatly from one experiment to another. For example, in the most commonly investigated structure—pyramidal textured silicon diffused with phosphorus and passivated with a hydrogenated oxide—recombination ranges from being 1–12 times more than in an equivalently prepared planar {100} surface. Examination of these experiments reveals consistent trends: small increases in recombination occur when the surface is very heavily diffused and dominated by Auger recombination, while larger increases in recombination occur when the surface is lightly diffused and dominated by Shockley–Read–Hall recombination at the surface, making the latter depend critically on surface area and the density of surface states. Comparisons of pyramidal and planar {100} surfaces indicate that when lightly diffused, the difference in recombination is substantially greater than the difference in surface area (1.73) and it is regularly attributed to the pyramid facets having {111} orientations—well known for their higher density of dangling bonds than {100} orientations. This high dangling-bond density makes recombination at pyramidal facets strongly dependent on the passivation scheme, and it is variations in these schemes that led to the wide range of results observed in experimental studies. In addition to surface area and crystal orientation, some experiments suggest a third mechanism that enhances recombination on oxide-passivated pyramids. With capacitance-voltage and photoconductance measurements, we confirm this speculation, showing that oxide-passivated pyramidal textured silicon has a higher density of interface states than can be accounted for by surface area and orientation, and that the additional defects are predominantly acceptorlike when above, or donorlike when below, an energy of 0.3 eV higher than the valence band.This work was funded by an Australian Research Council Linkage Grant between the Australian National University, SierraTherm Production Furnaces, and SunPower Corporation

A roadmap for PERC cell efficiency towards 22%, focused on technology-related constraints

Presently, the crystalline silicon (c-Si) photovoltaic (PV) industry is switching from standard cells to PERC cells to increase cell efficiency from about 18% to about 20%. This paper gives a roadmap for increasing PERC cell efficiency further towards 22%. Which equipment and which process conditions are feasible to go beyond 20% efficiency? To help answer this as generally as possible, we conduct state-of-the-art modelling in which we sweep the inputs that represent major technology-related constraints, such as diffusion depth, metal finger width and height, alignment tolerances, etc. (these are assigned to the x- And y-axes of our graphs). We then predict the optimum device parameters resulting from these restrictions (shown as contour lines). There are many different ways to achieve 22%. Our modelling predicts, for example, that 60 μm wide screen-printed metal fingers are sufficiently narrow if the alignment tolerance (width of the n++ region) is below 90 μm. The rear may be contacted with 30 μm wide openings of the Al2O3/SiNx stack and with local J0,BSF values as high as 900 fA/cm2. If these requirements cannot be met, they may be compensated by improvements in other device parts. Regardless of this, the wafer material requires a SRH lifetime of at least 1 ms at excess carrier densities near 10(14) cm(-3)

On effective surface recombination parameters

This paper examines two effective surface recombination parameters: the effective surface recombination velocity Seff and the surface saturation current density J0 s . The dependence of Seff and J0 s on surface charge Q, surface dopant concentration Ns , and interface parameters is derived. It is shown that for crystalline silicon at 300 K in low-injection, Seff is independent of Ns only when Q²/Ns   1.5 × 10⁷ cm for accumulation and Q¹˙⁸⁵ /Ns  > 1.5 × 10⁶ cm for inversion. These conditions are commonly satisfied in undiffused wafers but rarely in diffused wafers. We conclude that for undiffused silicon, J0 s is superior to the conventional Seff as a metric for quantifying the surface passivation, whereas for diffused silicon, the merit in using J0 s or Seff (or neither) depends on the sample. Experimental examples are given that illustrate the merits and flaws of J0 s and Seff