A hybrid model of laser energy deposition for multi-dimensional simulations of plasmas and metals

Basko, M. M.; Tsygvintsev, I. P.

doi:10.1016/j.cpc.2017.01.010

Cited by 30 publications

(7 citation statements)

References 19 publications

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“…Although the self-focusing instability has a clear physical origin, the amplitude of the ensuing fluctuations tends to be overestimated in the present RALEF simulations (especially on length scales comparable to, or smaller than the laser wavelength λ) due to the absence of diffraction effects in the laser propagation model 30 . However, when averaged over space and time, the impact of this "noise" on the calculated U values turns out to be negligible, i.e.…”

Section: Plasma Characterization In the Fully Ablative Regimementioning

confidence: 71%

“…Fig. 5 also demonstrates that the ablation flow is subject to hydrodynamic instabilities, the most salient of which appears to be the self-focusing instability due to laser refraction in the underdense plasma, inherent in the laser deposition model 30 . The resulting irregular fluctuations of the plasma parameters in space and time manifest themselves as "spotty" temperature distributions and "wavy" n e isocontours in Fig.…”

Section: Plasma Characterization In the Fully Ablative Regimementioning

confidence: 92%

“…The spatial laser profile is also Gaussian, with two values of the focal spot diameter (FWHM): d f oc = 115 µm (series A) and d f oc = 50 µm (series B). Propagation and absorption of the laser light is calculated within a hybrid model 30 , which accounts for refraction in the tenuous corona. In addition, it ensures a physically correct description of reflection from the critical surface, including the Fresnel reflection from the metal-vacuum interface.…”

Section: Simulation a Ralef-2d Codementioning

confidence: 99%

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Power-law scaling of plasma pressure on laser-ablated tin microdroplets

et al. 2018

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The measurement of the propulsion of metallic microdroplets exposed to nanosecond laser pulses provides an elegant method for probing the ablation pressure in dense laser-produced plasma. We present the measurements of the propulsion velocity over three decades in the driving Nd:YAG laser pulse energy, and observe a near-perfect power law dependence. Simulations performed with the RALEF-2D radiation-hydrodynamic code are shown to be in good agreement with the power law above a specific threshold energy. The simulations highlight the importance of radiative losses which significantly modify the power of the pressure scaling. Having found a good agreement between the experiment and the simulations, we investigate the analytic origins of the obtained power law and conclude that none of the available analytic theories is directly applicable for explaining our power exponent.

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Section: Plasma Characterization In the Fully Ablative Regimementioning

confidence: 71%

Section: Plasma Characterization In the Fully Ablative Regimementioning

confidence: 92%

Section: Simulation a Ralef-2d Codementioning

confidence: 99%

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Power-law scaling of plasma pressure on laser-ablated tin microdroplets

et al. 2018

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“…Laser light absorption and reflection are treated using a hybrid model combining a geometrical-optics ray-tracing approach in low-density plasma regions and a wave-optics approach in regions near and beyond the critical electron density. 19 Laser absorption coefficients are derived from the complex dielectric permittivity of the plasma as per the Drude model.…”

Section: Simulations With Ralef-2dmentioning

confidence: 99%

Tin fluid dynamics driven by laser-produced plasmas relevant to EUV nanolithography

Hemminga

Poirier

Hernández-Rueda

et al. 2023

Optical and EUV Nanolithography XXXVI

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State-of-the-art nanolithography machines employ extreme ultraviolet (EUV) light to pattern nanometer-scale features on silicon wafers for the production of integrated circuits. This radiation is generated in a laserproduced plasma formed on tin microdroplet targets. In this contribution, we give an overview of our recent experimental and theoretical studies on the properties of tin plasmas driven by short-wavelength lasers and the subsequent tin fluid dynamics. First, we will present a comprehensive characterization of the properties of laserproduced tin plasmas driven by lasers with wavelengths in the 1–10 µm range. Second, we present absolutely calibrated, charge-state-resolved measurements of the ion kinetic energy distribution recorded under multiple detection angles. Through extensive radiation-hydrodynamic simulations of the plasma formation, growth and expansion, we demonstrate that a single-fluid approach accurately reproduces the angular dependence of the ion energy distribution. Moreover, we identify the origin of a high-energy peak in the distribution as a high-speed shell generated at early times in the expansion. Finally, we show that the time evolution of the droplet target morphology is entirely determined by the early-time plasma-driven pressure impulse on the droplet.

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“…Аналитическим схемам посвящено относительно мало работ (см. [7]- [21] и цитируемую литературу). В первых публикациях [8]- [10] схема называлась «точной».…”

Section: Introductionunclassified

On the solution of elliptic equations by the ray variable method

Shilkov

2017

KIAM Prepr.

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Решение эллиптических уравнений методом лучевых переменныхНайдены неизвестные ранее решения внутренних краевых задач для неоднородных линейных эллиптических уравнений второго порядка при достаточно слабых ограничениях на поведение коэффициентов, источников и форму области. Решения ищутся в виде суперпозиции вкладов объемных и граничных источников, размещенных на лучах, приходящих в данную точку области от границ. Источники задаются с помощью лучевых переменных: направления луча, соединяющего две точки, и расстояния, отсчитываемого вдоль луча.Построена конечно-аналитическая схема для численного решения задач с разрывными коэффициентами и источниками. Область разбивается на ячейки, в пределах которых коэффициенты и источники непрерывны, а конечные разрывы (если они есть) приходятся на границы ячеек. Далее выполняется сшивка решений на границах. В схеме отсутствует жесткая зависимость точности аппроксимации от размеров и формы ячеек, присущая конечно-разностным схемам.Ключевые слова: эллиптические уравнения, краевые задачи, метод лучевых переменных, конечно-аналитические схемы. Alexander Victorovich ShilkovOn the solution of elliptic equations by the ray variable methodPreviously unknown solutions of the inner boundary value problems for inhomogeneous linear second-order elliptic equations with sufficiently weak restrictions on the coefficients, sources, and the region shape are found. Solutions are sought in the form of a superposition of the contributions of volume and boundary sources placed on the rays arriving at the reference point from the boundaries of the region. Sources are given by means of ray variables: the direction of the ray connecting two points and the distance, measured along the ray.The finite-analytic discretization scheme is constructed for the numerical solution of problems with discontinuous coefficients and sources. The region is divided into cells, within which the coefficients and sources are continuous, and the finite discontinuities (if any) occur at the cell boundaries. Next, the solutions are cross-linked at the boundaries. In the scheme, there is no strong dependence of the accuracy of approximation from the size and shape of the cells that inherent in finite-difference schemes.

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A hybrid model of laser energy deposition for multi-dimensional simulations of plasmas and metals

Cited by 30 publications

References 19 publications

Power-law scaling of plasma pressure on laser-ablated tin microdroplets

Power-law scaling of plasma pressure on laser-ablated tin microdroplets

Tin fluid dynamics driven by laser-produced plasmas relevant to EUV nanolithography

On the solution of elliptic equations by the ray variable method

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