Plasmas induced by EUV radiation are unique since they are created without the need of any discharge. Moreover, it is essential to characterize these plasmas to understand and predict their long term impact on highly delicate optics in EUV lithography tools. In this paper we study plasmas induced by 13.5 nm EUV radiation in hydrogen gas. The electron density is measured temporally resolved using a non-invasive technique known as microwave cavity resonance spectroscopy. The influence of the EUV pulse energy and gas pressure on the temporal evolution of the electron density has been explored over a parameter range relevant for industry.

Our experimental results show that the maximum electron density is in the order of 1014 m−3 and depends linearly on the EUV pulse energy. Furthermore, the maximum electron density depends quadratically on the pressure; the linear term is caused by photoionization and the quadratic term by subsequent electron impact ionization. The decay of the plasma is governed by ambipolar diffusion and, hence, becomes slower at elevated pressures. Similarities and differences of the same processes in argon are highlighted in this paper.

/pdf/exploring-the-electron-density-in-plasma-induced-by-euv-2cj5x5hd4c.pdf

Exploring the electron density in plasma induced by EUV radiation:I. Experimental study in hydrogen

We used numerical modeling to study the evolution of EUV-induced plasmas in argon and hydrogen. The results of simulations were compared to the electron densities measured by microwave cavity resonance spectroscopy. It was found that the measured electron densities can be used to derive the integral amount of plasma in the cavity. However, in some regimes, the impact of the setup geometry, EUV spectrum, and EUV induced secondary emission should be taken into account. The influence of these parameters on the generated plasma and the measured electron density is discussed.

https://iopscience.iop.org/article/10.1088/0022-3727/49/29/295204/pdf

Exploring the electron density in plasma induced by EUV radiation: II. Numerical studies in argon and hydrogen

We studied the temporal evolution of the electron density distribution in a low pressure pulsed plasma induced by high energy extreme ultraviolet (EUV) photons using microwave cavity resonance spectroscopy (MCRS). In principle, MCRS only provides space averaged information about the electron density. However, we demonstrate here the possibility to obtain spatial information by combining multiple resonant modes. It is shown that EUV-induced plasmas, albeit being a rather exotic plasma, can be explained by known plasma physical laws and processes. Two stages of plasma behaviour are observed: first the electron density distribution contracts, after which it expands. It is shown that the contraction is due to cooling of the electrons. The moment when the density distribution starts to expand is related to the inertia of the ions. After tens of microseconds, the electrons reached the wall of the cavity. The speed of this expansion is dependent on the gas pressure and can be divided into two regimes. It is shown that the acoustic dominated regime the expansion speed is independent of the gas pressure and that in the diffusion dominated regime the expansion depends reciprocal on the gas pressure.

http://iopscience.iop.org/article/10.1088/0022-3727/48/43/432001/pdf

Dynamics of the spatial electron density distribution of EUV-induced plasmas

In order to continue the development of electronics, computer chips need to become cheaper, they need to have more functions and they need to use less power. To achieve this, industries are taking a next step in the production process of computer chips: EUV lithography. The radiation used in these lithography tools ionizes the background gas in the tool, which results in an EUV-induced plasma. Characterizing this plasma experimentally is the focus of this work. This chapter provides a general introduction on EUV lithography and EUV-induced plasmas. Finally, the goal and structure of this work are described. 1. General introduction 1.1 A typical day in 2025 Imagine a typical day in . It is time to wake up. Your bed measures the stage of your sleep and sends a signal to your alarm clock to wake you on the right moment. When you walk to the living room, your coffee machine already made you a fresh cup of coffee, the stereo is playing music based on your mood and your tablet made a selection of the news and messages you need to read at the start of your day. When you get into your car to go to work, the navigation system calculates the best route depending on the current traffic information. At the end of themorning you get an e-mail from your doctor to make an appointment because some body vitals are too far off. In the afternoon your refrigerator sends a message listing the products which are about to expire and some suggested recipes which comply with daily values. After you have chosen the recipe, the missing ingredients are collected at the supermarket in order for you to pick them up after work. When you are almost at home, your phone sends a signal to your house to switch on the central heating. If you decide youwant to go out in the evening, your phone lets you know which friends are available or, when you want to watch television, your tv suggests series and films you may want to watch. When you go to bed, all devices will go to standby. Although this may seem far away, we aremoving towards this point. Our smartphone has already taken an important place in our lives; 75% checks their phone first thing in the morning and we launch 106 apps per day per user []. Google tracks your way to work and suggests different routes based on traffic information [] and 60% of new cars are connected bymobile technology []. There are apps which measure your sleep stages [] and smart thermostats are controlled by your phone []. It seems that the only thing we need to do, is just connecting all these devices. Current predictions indicate that in  more than  billion devices (phones, cars, televisions, etc.) will be connected to the internet and can communicate with each other [], using your phone as a hub. Your smart phone will become a limb of your body. To build this future, we need computer chips which are cheaper, have more functionality and use less power. To achieve this, industries are taking a next step in the production process of computer chips: EUV lithography. In the remaining of this chapter, the basic principles of (EUV) lithography are discussed (section .) and the concept of plasma is introduced (section .). In section . and section ., the scope and outline of this dissertation are discussed respectively.

Electron dynamics in EUV-induced plasmas

Plasmas induced by EUV radiation are scarcely investigated, although they are unique since they are created without any discharge. These plasmas are also of interest from an applicational point of view, since they are related to the lifetime of optics in EUV lithography tools. In order to assess this impact, it is essential to characterize and understand EUV-induced plasma. In this contribution the influence of the background gas (argon and hydrogen) in the lithography tool and the spectrum of the illumination source on the electron density of EUV-induced plasma is investigated using microwave cavity resonance spectroscopy. The experimental results showed that out-of-band radiation (>20 nm) is the main contributor to EUV-induced plasma in both argon and hydrogen. In hydrogen, this contribution is relatively more important than in argon due to the stronger wavelength dependence of the photoionization cross section of hydrogen than of argon. Furthermore, the production of electrons by out-of-band radiation lasts longer than the production by in-band radiation (10–20 nm) due to the longer temporal width of out-of-band radiation. Finally, the obtained results correspond reasonably well with estimates from a simplified absorption model.

https://iopscience.iop.org/article/10.1088/0963-0252/25/1/015012/pdf

The influence of the EUV spectrum on plasma induced by EUV radiation in argon and hydrogen gas

The electron density in the positive column of DC glow discharges has been determined by means of an improved method of the microwave diagnostics. This method is based on the measurement of both the resonance frequency shift of the resonator cavity and the change of the inverse resonator quality. It makes explicit use of the associated phase delay between the microwave field and the induced HF electric current. To evaluate the applicability of the method and of a simplified version of it to complex molecular mixture plasmas, the electron density in CO 2 /CO/O 2 mixture plasmas has been measured for larger ranges of gas pressure and discharge current. The applicability check is made by a comparison between measured and calculated results for the phase delay. The good agreement between experimental and theoretical results supplies evidence for a far-reaching applicability of the simplified version of the improved microwave diagnostics method that allows the determination of the electron density without detailed information about the plasma composition and the electron energy distribution. The theoretical determination of the phase delay has been done by solving the time-dependent electron Boltzmann equation. Two different techniques have been employed to solve this kinetic equation. In particular, the conventional two-term treatment has been analysed with respect to its suitability to molecular gas mixtures and has been found to be sufficient for the determination of the phase delay.

Microwave Diagnostics of the Electron Density in Molecular Mixture Plasmas

Based upon former studies concerning the nonstationary electron kinetics in collision dominated, weakly ionized plasmas the phase delay between the ac electric field component and the resultant ac electron current density has been analysed, theoretically and experimentally, under the specific conditions of a microwave field superimposed to a dc discharge plasma column. The complex plasma conductivity and thus the phase delay has been calculated by solving an appropriate electron kinetic equation. The same quantities have been experimentally determined by using the microwave cavity which operates with different resonator modes. A comprehensive comparison between calculated and measured quantities for different neon discharge plasmas leads to a complete confirmation of the theoretical expectations.

The Nonstationary Behaviour of the Electron Current Density in the Weakly Inonized Plasma at High Field Frequencies

Diese Arbeit behandelt die Berechnung und Messung der Rauschtemperatur fur ein stationares und axial homogenes Saulenplasma einer Stickstoff-Entladung. Die Berechnungen basieren auf einer Energieverteilungsfunktion der Elektronen, welche durch Losung der Boltzmann-Gleichung fur ein Stickstoffplasma erhalten wurde. Die Rauschtemperatur in der Schwachstromsaule dieses Plasmas wurde mit einem Dicke-Radiometer gemessen. Der Vergleich der berechneten und gemessenen Werte der Rauschtemperatur zeigt eine gute Ubereinstimmung im betrachteten Parameter-bereich. Zusatzlich wurde die Rauschtemperatur theoretisch naherungsweise unter Verwendung einer uber die Energiebilanz der Elektronen angepasten Maxwell-Verteilung bestimmt und der kinetisch begrundeten Rauschtemperatur gegenubergestellt.



This paper covers the calculation and measurement of the noise temperature for a stationary and axial homogeneous column plasma of a nitrogen discharge. The calculations are based on an electron energy distribution function which was obtained by the solution of the Boltzmann equation for a nitrogen plasma. In the low current column of this plasma the noise temperature was measured, using a Dicke-radiometer. The comparison between the calculated and measured values of the noise temperature shows a good agreement in the considered parameter region. Using a Maxwellian distribution, which was fitted to the real nitrogen plasma by the aid of the formulation of an energy balance for the electrons, the noise temperature was additionally determined in a approximate way and compared to the first calculations.

Mikrowellendiagnostik der Rauschtemperatur im Stickstoffplasma der Schwachstromsäule

Es wird uber die Elektronendichtemessung in der Freifallsaule einer Neonentladung berichtet. Die experimentelle Bestimmung erfolgte mit Hilfe der Resonanzfrequenzanderung eines Mikrowellenresonators. Die auf diesem Wege ermittelten Werte der Tragerdichte werden zur Berechnung der Existenzgrenze von Ionenschallwellen verwendet.

Zur Mikrowellendiagnostik der Elektronendichte im Neonplasma der Freifallsäule

Zur Eindeutigkeit eines neuen Differenzmeßverfahrens für die sehr genaue Bestimmung der Resonatorgüte und der Resonanzfrequenz von Mikrowellenresonatoren

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