Modelling the nanosecond laser ablation of a silicon target

Der Laser ist zweifellos eine der außergewöhnlichsten Erfindungen des letzten Jahrhunderts. Dank der einzigartigen Eigenschaften des Laserlichts, wie Kohärenz, Monochromie und Kollimation, hat diese Energiequelle unzählige Anwendungen in verschiedensten Bereichen gefunden. In der Halbleiterindustrie sind Laser ideale Werkzeuge, um die immer kleineren Bauteile herzustellen, die heutzutage in der mikroelektronischen Industrie entwickelt und kommerzialisiert werden. Insbesondere wird sich Laserlicht höchstwahrscheinlich als Referenztechnologie etablieren, um den Dicingprozess- das Zersägen - von ultradünnen Siliziumwafern mittels Materialablation durchzuführen. Beim Dicing von Chips, die dünner als 100 µm sind, zeigt die herkömmliche mechanische Vorgehensweise starke Einschränkungen, da die induzierten Vibrationen zur vollständigen Zerstörung des Chips führen können. Trotz der Popularität des Lasers bleiben viele Aspekte noch unklar, insbesondere bezüglich der zugrunde liegenden Wechselwirkung intensiver Lichtpulse mit Materie. Deshalb werden industrielle Laserbearbeitungsprozesse immer noch hauptsächlich in kostspieligen und ineffektiven Versuchs- und Irrtumsverfahren optimiert. Eine wertvolle Strategie zur Analyse der Laserablation ist daher die numerische Modellierung: Ergänzend zu experimentellen Untersuchungen erlaubt sie, die Grundlagen der relevanten physikalischen Prozesse zu studieren; gleichzeitig bietet sie eine preiswerte Lösung für die Prozessoptimierung. Ziel der vorliegenden Arbeit ist es, die wichtigsten, der Nanosekunden-Laserablation zugrunde liegenden Mechanismen in einem verallgemeinerten numerischen Rahmen zu implementieren. Dazu wurde eine Modellierungsstrategie entwickelt, die es erlaubt, diesen komplexen Prozess mit annehmbarer Genauigkeit und physikalischer Stringenz zu simulieren. Laserablation bei hoher Intensität ist ein multiphysikalisches und multidisziplinäres Problem, da alle Phasen der Materie - von Feststoff bis zu hoch ionisiertem Plasma - beteiligt sind. Die vielen eng miteinander verzahnten physikalischen Mechanismen haben unterschiedliche Zeitskalen und werden von einem komplexen Satz gewöhnlicher und partieller Differentialgleichungen beschrieben. Trotz der Näherungen und Annahmen, die im Rahmen dieser Arbeit eingeführt werden, um der mathematischen und physikalischen Komplexität Herr zu werden, trägt diese Arbeit hoffnungsweise dazu bei, den Modellierungsansatz zur Simulation der Laserablation zu verbessern. Insbesondere wird die Umsetzung einiger Aspekte hervorgehoben, die in der Literatur oft übermäßig angenähert oder sogar vernachlässigt werden, obwohl sie in der Physik des Problems eine dominante Rolle spielen. Bei den hohen Intensitäten, die in der industriellen Laserbearbeitung verwendet werden, entsteht oberhalb der bestrahlten Oberfläche ein induziertes Plasma. Diese expandierende Plasmawolke schirmt den einfallenden Laserstrahl ab und beeinflusst damit die gesamte thermodynamische Reaktion des Systems Target- Plasma und den anschließenden Verlauf des Ablationsprozesses. Im Gegensatz zu einigen anderen wissenschaftlichen Ansätzen macht die vorliegende Arbeit keine a priori-Annahme zum thermodynamischen Gleichgewichtszustand des Plasmas. Folglich werden Bildung und Entwicklung des Plasmas durch einen Satz von Ratengleichungen beschrieben, die die wichtigsten Stoß- und Strahlungsprozesse zwischen den verschiedenen Plasmabestandteilen darstellen. Die Fluiddynamik der Plasmawolke wird durch einen Satz von Euler-Gleichungen beschrieben. Erst wenn ein lokales thermodynamisches Gleichgewicht erreicht ist, wird die Plasmazusammensetzung entsprechend der Boltzmann-Saha-Verteilung bestimmt. Die Arbeit beinhaltet auch Vorschläge zur korrekten Beschreibung der festen und flüssigen Phasen. Da die Materialeigenschaften im Bereich zwischen Raumtemperatur und kritischer Temperatur stark variieren, erfolgt die Modellierung der kondensierten Phase anhand einer Enthalpie-Formulierung kombiniert mit einer realen Zustandsgleichung. Berücksichtigt werden Verdampfung und Kondensation, volumetrische Massenentfernung und Flüssigkeitsausstoß. Verdampfung und Kondensation erfolgen nach den Kopplungsbedingungen der Knudsen-Schicht an der Grenzfläche zwischen Flüssigkeit und Dampf. Zusätzlich wird bei der kritischen Temperatur die Zustandsgleichung der kondensierten Phase mit der Zustandsgleichung des Plasmas verschmolzen, die derjenigen für ein ideales Gas entspricht. Auf diese Weise wird der superkritische Flüssigkeitsanteil auf konsistente Weise vom Target- in den Plasmabereich verschoben. Damit wird der Übergang von Verdampfung zu volumetrischer Materialentfernung erfasst. Alle oben genannten Aspekte wurden in einem maßgeschneiderten eindimensionalen hydrodynamische Modell implementiert, das an ein dreidimensionales Finite-ElementeModell gekoppelt ist. In diesem lassen sich reale Laserdicing-Prozesse einfacher simulieren. Zudem werden zwei experimentelle Validierungsverfahren vorgeschlagen: der herkömmliche Vergleich von gemessener und vorhergesagter Kratertiefe sowie ein interessantes, aber weniger beliebtes Transmissivitäts-Experiment, das die Laserintensität bestimmt, die nach der Plasmaabsorption effektiv an das Target koppelt.The laser is undoubtedly one of the most extraordinary inventions of the last century. Thanks to its unique properties, such as coherence, monochromaticity and collimation, this energy source has found countless applications in the most disparate areas. In the semiconductor industry, lasers are ideal tools for processing the ever smaller electronic devices designed and commercialized nowadays. Laser dicing, in particular, will likely become the reference technology for the cutting of ultrathin silicon wafers through the ablation of material. Conventional mechanical dicing shows strong limitations when separating substrates thinner than 100 µm, as the cutting vibrations may cause severe damage to the processed chips. Despite the laser`s popularity, much remains unknown about the mechanisms underlying the interaction of an intense light pulse with matter. As a result, industrial laser machining is still mainly optimized through costly and ineffective trial-and-error approaches. Numerical modelling is therefore a valuable strategy for studying laser ablation: as a complementary tool to experiments, it enables the fundamental physics involved to be investigated and, at the same time, constitutes a cost-saving solution for process optimization. The aim of this work is to implement the most relevant mechanisms underlying nanosecond laser ablation in a generalized numerical framework. As a result, a modelling strategy has been developed that allows such a complex process to be simulated with reasonable accuracy and physical rigor. Laser ablation at high intensity is a multiphysics and multidisciplinary problem, involving all phases of matter from solid to highly ionized plasma. Several tightly interconnected physics phenomena are involved, which have different characteristic time scales and need to be described by an intricate set of ordinary and partial differential equations. Despite the approximations and assumptions introduced in order to relax the mathematical and physical complexities, the hope is that this work may contribute to improving the modelling approach for the simulation of nanosecond laser ablation. In particular, emphasis is placed on the implementation of some aspects that are often over-approximated or even neglected in the literature, despite playing a dominant role in the evolution of the ablation process. At the high intensities employed in industrial laser machining, an induced plasma is produced above the irradiated surface. This expanding plasma plume shields the target from the incoming laser beam, influencing the whole thermodynamic response of the target¿plume system and the subsequent evolution of the ablation process. In contrast to what is generally done in several works, no a priori assumption is made on the thermodynamic equilibrium state of the plasma. Consequently, the initial plasma formation and evolution are described by a set of rate equations governing the main collisional and radiative processes among the various constituent species, while the plume fluid dynamics is described by a set of Euler equations. Only when local thermodynamic equilibrium conditions are reached is the plasma composition determined according to the Boltzmann-Saha distribution. Suggestions are also given on how to correctly describe the solid and liquid phases. Because the material properties vary strongly in the interval from room temperature to critical temperature, an enthalpy formulation is used to model the condensed phase, together with a real equation of state. Evaporation and condensation, volumetric mass removal and liquid ejection are considered. Evaporation and condensation proceed according to the Knudsen Layer coupling conditions across the liquid-vapor interface. Additionally, in the vicinity of the critical point, the equation of state of the condensed phase is merged with the ideal-gas-like equation of state used for the plasma. This allows the supercritical liquid fraction to be shifted in a consistent manner from the target into the plasma domain. In this way, the transition of the material removal mechanism from evaporative to volumetric is captured. All these aspects have been implemented in a custom-made one-dimensional hydrodynamic code, which is coupled to a three-dimensional finite element model, in which a real process of laser dicing can be simulated more conveniently. Two experimental validation methods are also proposed: the classic comparison of measured and predicted single-pulse-induced crater depths as well as a more interesting, although less popular transmissivity experiment, meant to determine the amount of laser intensity effectively coupling to the target after plasma absorption.11

Prognostic Impact of Mitral Regurgitation Before and After Transcatheter Aortic Valve Replacement in Patients With Severe Low‐Flow, Low‐Gradient Aortic Stenosis

Background There is little evidence about the prognostic role of mitral regurgitation (MR) in patients with low‐flow, low‐gradient aortic stenosis undergoing transcatheter aortic valve replacement (TAVR). The aim of this study was to assess the prevalence and outcome implications of MR severity in patients with low‐flow, low‐gradient aortic stenosis undergoing TAVR, and to evaluate whether MR improvement after TAVR could influence clinical outcome. Methods and Results This study included consecutive patients with low‐flow, low‐gradient aortic stenosis undergoing TAVR at 2 Italian high‐volume centers. The study population was categorized according to the baseline MR severity and to the presence of MR improvement at discharge. The primary outcome was the composite of all‐cause death and hospitalization for worsening heart failure up to 1 year. The study included 268 patients; 57 (21%) patients showed MR >2+. Patients with MR >2+ showed a lower 1‐year survival free from the primary outcome (P2+ was an independent predictor of the primary outcome (P2+, MR improvement was reported in 24 (44%) cases after TAVR. The persistence of MR was associated with a significantly reduced survival free from the primary outcome, all‐cause death, and heart failure hospitalization up to 1 year. Conclusions In this study, the presence of moderately severe to severe MR in patients with low‐flow, low‐gradient aortic stenosis undergoing TAVR portends a worse clinical outcome at 1 year. TAVR may improve MR severity in nearly half of the patients, resulting in a potential outcome benefit after discharge

Post-COVID-19 Syndrome: Involvement and Interactions between Respiratory, Cardiovascular and Nervous Systems

Though the acute effects of SARS-CoV-2 infection have been extensively reported, the long-term effects are less well described. Specifically, while clinicians endure to battle COVID-19, we also need to develop broad strategies to manage post-COVID-19 symptoms and encourage those affected to seek suitable care. This review addresses the possible involvement of the lung, heart and brain in post-viral syndromes and describes suggested management of post-COVID-19 syndrome. Post-COVID-19 respiratory manifestations comprise coughing and shortness of breath. Furthermore, arrhythmias, palpitations, hypotension, increased heart rate, venous thromboembolic diseases, myocarditis and acute heart failure are usual cardiovascular events. Among neurological manifestations, headache, peripheral neuropathy symptoms, memory issues, lack of concentration and sleep disorders are most commonly observed with varying frequencies. Finally, mental health issues affecting mental abilities and mood fluctuations, namely anxiety and depression, are frequently seen. Finally, long COVID is a complex syndrome with protracted heterogeneous symptoms, and patients who experience post-COVID-19 sequelae require personalized treatment as well as ongoing support

Soft x-ray free-electron laser induced damage to inorganic scintillators

An irreversible response of inorganic scintillators to intense soft x-ray laser radiation was investigated at the FLASH (Free-electron LASer in Hamburg) facility. Three ionic crystals, namely, Ce:YAG (cerium-doped yttrium aluminum garnet), PbWO4 (lead tungstate), and ZnO (zinc oxide), were exposed to single 4.6 nm ultra-short laser pulses of variable pulse energy (up to 12 μJ) under normal incidence conditions with tight focus. Damaged areas produced with various levels of pulse fluences, were analyzed on the surface of irradiated samples using differential interference contrast (DIC) and atomic force microscopy (AFM). The effective beam area of 22.2 ± 2.2 μm2 was determined by means of the ablation imprints method with the use of poly(methyl methacrylate) - PMMA. Applied to the three inorganic materials, this procedure gave almost the same values of an effective area. The single-shot damage threshold fluence was determined for each of these inorganic materials. The Ce:YAG sample seems to be the most radiation resistant under the given irradiation conditions, its damage threshold was determined to be as high as 660.8 ± 71.2 mJ/cm2. Contrary to that, the PbWO4 sample exhibited the lowest radiation resistance with a threshold fluence of 62.6 ± 11.9 mJ/cm2. The threshold for ZnO was found to be 167.8 ± 30.8 mJ/cm2. Both interaction and material characteristics responsible for the damage threshold difference are discussed in the article

Investigating the interaction of x-ray free electron laser radiation with grating structure

The interaction of free electron laser pulses with grating structure is investigated using 4.6±0.1 nm radiation at the FLASH facility in Hamburg. For fluences above 63.7±8.7 mJ/cm2, the interaction triggers a damage process starting at the edge of the grating structure as evidenced by optical and atomic force microscopy. Simulations based on solution of the Helmholtz equation demonstrate an enhancement of the electric field intensity distribution at the edge of the grating structure. A procedure is finally deduced to evaluate damage threshold

Notulae to the Italian alien vascular flora: 13

In this contribution, new data concerning the distribution of vascular flora alien to Italy are presented. It includes new records, confirmations, exclusions, and status changes for Italy or for Italian administrative regions. Nomenclatural and distribution updates published elsewhere are provided as Suppl. material 1

Notulae to the Italian alien vascular flora: 13

In this contribution, new data concerning the distribution of vascular flora alien to Italy are presented. It includes new records, confirmations, exclusions, and status changes for Italy or for Italian administrative regions. Nomenclatural and distribution updates published elsewhere are provided as Suppl. materia