Consequences of high-frequency operation on EUV source efficiency

The success and the cost of the next generation computer chips will depend on the performance of extreme ultraviolet (EUV) sources and on the duration of the efficient operation and lifetime of these nanolithography devices. While the efficiency of the sources is continuously being improved, their operational cycle is still highly restricted due to the degradation of the optical mirrors as well as the necessity of maintaining a clean operating chamber environment and components.

Current investigations of EUV source production in the semiconductor industry are focused on the use of dual-pulse laser produced plasma (LPP) on droplets of liquid tin targets. The main objectives and the challenges in the enhancement of these light sources are related to maximizing the conversion efficiency (CE) of the source as well as to increase component lifetime of the collector optical system. Optimum conditions satisfying both requirements depend on the first laser for target preparation, second laser for EUV photon production, and on the initial droplet target size. The interaction of the pre-pulse laser beam with solid/liquid tin droplets results in the production of vapor, plasma, and a mist of nano-/micro-fragments. The prevailing concentration of neutrals or ions and size of dust particle agglomeration in the developed mix depend on laser characteristics, mainly pulse duration, intensity, and wavelength.

Various experiments showed that picosecond or nanosecond lasers with high intensity can deform or fragment small liquid droplets and expand them to a relatively larger volume of mix mist and matter.^1,2 Nanosecond lasers with lower intensity can transform small liquid droplets to disk-like targets that allows efficient usage of the larger spot size of a second follow up laser.³ The difference in the developed mixed composition affects the rate of tin accumulation in the chamber and determine requirement for the mitigating system. While most of the plasma species and neutrals from preceding iteration can escape the area of the next laser/droplet interactions, the remaining fragmented parts of previous droplets, having much lower velocities,⁴ can be heated by incoming laser of next iteration and/or absorb fraction of the emitted EUV. For example, spectroscopic, laser-induced-fluorescence analysis showed such a possibility of neutrals/fragments remaining after splitting even small, 20 μm droplets.⁵ 

Various approaches were proposed for the damage mitigation and protection from contamination of the mirror optical collection system by the atomic and ionic debris in the EUV chamber. Steady state and pulsed electric fields^6,7 and magnetic fields in different configurations^8–11 were studied and optimized to reduce ion energy and flux to the collecting optics. Additionally, secondary plasma systems¹² were proposed to ionize Sn neutrals which then can be deviated by electric or magnetic fields or a combination of both. Modeling of LPPs in axial magnetic field showed spatial and temporal effects of magnetic field on plasma evolution and ion distribution and suggested that the time-varying magnetic fields as a magnetic pinch would be more efficient for the mitigating purposes.¹³ Gas flow near the mirror surfaces is currently considered as the main method for in-situ optics cleaning from the deposited Sn debris.^8,14 However, buffer gases in the chamber even at relatively low pressure, 1–10 Pa, can absorb in-band and out-band EUV light that results in EUV induced plasma formation and development of various related phenomena.^15,16 For example, such plasma can lead to the formation of electric field near mirror surfaces accelerating Sn ions towards collecting optics.¹⁵ Several experimental and modeling studies predicted EUV induced plasma parameters such as electron density and temperature in dependence on gas pressure and EUV pulse energy.^17,18 These studies used an external source of EUV radiation and estimated the parameters of plasma induced in gas filled chambers without connection to the original EUV created plasma. However, in the LPP chamber, EUV induced plasma developed near the mirror system can also be affected by the original plasma created from the target by single- or double-pulse laser beams. Reduced collision and recombination rates at low pressure in the chamber will result in free electron propagation from the actual source area that can further affect EUV induced plasma properties. These studies require consideration of a mixed environment in the chamber and dynamics and interaction of two flows, original plasma and injected gas.

Our previous simulation results showed strong dependence of the CE on the properties of mist developed by the short pre-pulse lasers.¹⁹ It was shown that, for example, the density in the vapor cloud surrounding the micro-fragments has a large effect on the source efficiency and resulted in an increase from 2.1% to 3.3% in the CE. Recent experimental results showed that a CE as high as 5% can be achieved using picosecond (ps) lasers for the pre-pulse. Lasers with a short pulse duration interacting with 20 μm droplets can break the droplet into smaller submicron fragments. This leads to high evaporation and ionization rates of the developed mist particles by the following main laser pulse.

Increasing the frequency of droplet generation and laser pulses will lead to accumulation of tin dust in the area surrounding EUV source production. Assessment of this issue and its effect is especially important for high volume manufacture (HVM) and the development of higher power sources where larger droplets are required to produce a larger volume of EUV generating plasma. Allowing a higher power of the EUV source, larger droplets, however, will require higher pre-pulse laser intensities³ and will lead to more and larger fragments and mist generation.

In this work, the effects of possible accumulation of tin vapor on the EUV source evolution were studied. Modeling of the source environment consisting of tin droplets and micro-fragments surrounded by a vapor cloud with different pressures was performed using the comprehensive HEIGHTS simulation package.

Studying the effect of different vapor volumes and densities around the droplet, we found regimes with transition from the degradation of EUV source efficiency to enhancement of EUV photon emission. The effect of chamber conditions on further fragments/vapor distribution was also analyzed. The maximum source operation frequency and efficiency could be affected and limited by the background environment inherited during source operation.

The HEIGHTS package includes advanced state-of-the art 3-D models for various interactions of laser photons with liquid/vapor/plasma, plumes hydrodynamics, and radiation and thermal processes. We continued to upgrade our HEIGHTS package for the analysis and optimization of EUV sources from LPPs. Our modeling and simulation include all phases of laser-target evolution: from laser/droplet interaction, energy deposition, target vaporization and fragmentation, ionization, plasma hydrodynamic expansion, thermal and radiation energy redistribution, and EUV photon collection as well as detailed mapping of the photon source location and size. These models were described in several publications.^20,21 Brief physics descriptions included in the package are given below.

The HEIGHTS package consists of a set of independent modules for describing the main processes taking place in laboratory plasma devices. These integrated processes can be described by the general form of the hydrodynamic equation set for modeling of LPPs with a two-temperature approximation model given by:

Here, $ρ$ is the density of plasma; $v$ is the velocity of plasma; $ph$ is the hydrodynamic pressure; $eh=ee+ei+ekin$ is the total energy; $ee$ is the electronic component of the plasma energy, which includes thermal energy of electrons and ionization energy; $ei$ is the ion component of the plasma energy; and $ekin=ρ v22$ is the kinetic energy of the plasma. Pressure has electron and ion parts $ph=pe+pi$⁠. Thermal conduction in the plasma is considered as the combined result of the electron $λe ∇Te$ and ion $λ i∇Ti$ components, where $λ$ is the conductivity coefficient and $T$ is the temperature. Laser and plasma radiation processes are represented here as the laser heating source as $Qlas$ and flux $Srad$⁠. The $Qei$ term is the energy interchange between electrons and ions.

Splitting methods are used to separate the hyperbolic and parabolic parts of the above equations that allow implementation of different numerical methods for efficient modeling of hydrodynamic fluxes, heat conduction in plasma, laser heating, and radiation transport (RT). These models for plasmas processes are integrated with models for the description of target evolution which include laser energy absorption/reflection at the surface, heat conduction in material, melting, and evaporation.

Radiation transport (RT), one of the critical parts in the modeling of plasma evolution, has two implementations in the HEIGHTS package. These include a direct numerical solution of the RT equation using the Gaussian quadrature method for volume integration along the path of photons, and Monte Carlo models. Both methods were compared regarding the accuracy of produced results and requirements for the solid angle discretization (for the Gaussian quadrature integration) or pseudophoton number (for Monte Carlo integration).²² 

The HEIGHTS models continued to be well benchmarked at each interaction physics phase during plasma evolution as well as in the whole integrated LPP systems. The results were extensively benchmarked against experimental studies for the in-band EUV photon production and for debris and ion generation.¹⁹ 

To study the effects of the residual tin gas pressure, several background conditions were considered in this analysis. A CO₂ laser with 30 ns duration and 100 mJ total energy and a Nd:YAG laser with 10 ns pulse and 40 mJ total energy were used in these simulations. A CO₂ laser having 200 μm spot size and a Nd:YAG laser having 100 μm spot size heated 100 μm droplets. This resulted in intensities of 10¹⁰ W/cm² and 5 × 10¹⁰ W/cm², respectively. Gaussian temporal and spatial profiles were used in all cases. A much larger spot than the droplet size in the case of the CO₂ laser was chosen to produce a more efficient EUV source that is due to longer duration of this laser and more efficient interaction with expanded plasma.²³ Figure 1 illustrates the modeling approach corresponding to the mist cloud which might be formed at the conditions of the high-frequency operation of the LPP source. Among the main components of the HEIGHTS package, Monte Carlo radiation transport and Monte Carlo modeling of laser photon interaction with tin droplets, vapor, and plasma include all possible mechanisms of interaction, absorption, reflection, and reabsorption. These allow simulating all processes' evolution self-consistently, e.g., it takes into account reduction of target heating due to laser absorption in evolving vapor/plasma; at the same time, heating of the target by radiation from hot plasma; heating and ionization of the vapor cloud around expanding plasma; changing of plume dynamics around the droplet due to high pressure in the plasma layer absorbing most of the laser photons that again affects laser photon absorption and reflection.

The above approach was used to find conditions affecting EUV source characteristics. Comparison of the results for relatively low pressure, relevant to the pressure of the mitigating gas, and extremely high pressure for EUV devices was done to find the regimes affecting EUV photon generation and collection. Figures 2(a) and 2(b) show the difference in the evolution of the plasma plume created by the CO₂ laser with 30 ns duration from 100 μm droplet surrounded by tin vapor at pressures of 3 Pa [Fig. 2(a)] and 300 Pa [Fig. 2(b)]. Such a difference in background conditions changes significantly both the density and temperature distribution in the evolving plasma.

Figures 3(a) and 3(b) illustrate the effect of the background conditions on the EUV source intensity and shape. In the case of low pressure, combination of relatively high electron temperature of 60 eV and density of ∼10¹⁸ cm⁻³ above the target results in a low concentration of EUV producing ions²⁵ that explains low intensity of EUV production in this area [Fig. 3(a)]. However, at higher pressure conditions [Fig. 3(b)], a large volume with densities of 10¹⁷–10¹⁸ cm⁻³ and temperatures appropriate for 13.5 nm photon absorption/emission is formed around the actual source near the target. A significant portion of EUV photons emitted in most productive plasma can be absorbed in this volume [Figs. 2(b) and 3(b)]. Thus, this source has a lower intensity and smaller size compared with the source produced at lower pressure. A small portion of collectable EUV photons is produced in the plasma layer formed far above the target with 10¹⁷ cm⁻³ electron density and 30 eV temperature [Fig. 2(b)]. However, the intensity of these peripheral sources is much smaller due to two orders of magnitude lower density in comparison with the main source located near the target. Formation of such a region in the presence of background pressure was discussed in detail previously.²⁵ 

The difference in the CE of the above sources is ∼30%. The pressure of 1–5 Pa can be considered as the highest pressure when the background tin vapor does not result in any effects on the source efficiency in comparison with vacuum chamber conditions. Ten times increase in this pressure, for example, to 30 Pa, results in only ∼5% decrease in the CE even in the case of a relatively large vapor volume expanded up to 1 cm. These are encouraging results considering that very high pressure of 300 Pa would unlikely be established in the EUV chamber with an efficient mitigating system as well as a good vacuum system in the chamber without perturbing the droplet injection system. However, a strong vacuum system in the chamber could affect the target system performance and its stability. Also, depending on the type of the mitigation system, more background gas can be produced. Therefore, it is important to study the limits of the background gas on source performance during the high frequency operation required for future high power devices needed for the HVM.

The effect of background conditions also depends on the volume of the surrounding vapor plume. A decrease in the CE can be even at lower pressure if the background volume size is increased.¹¹ Increasing the pressure from 3 Pa to 300 Pa in the volume with around 10 cm layer thickness above the target results in a six times drop in the CE. Figures 4(a) and 4(b) show simulation results of Nd:YAG laser interaction with droplets surrounded by vapor assuming a constant pressure of 300 Pa [Fig. 4(a)] and pressure gradient with the lowest value of 3 Pa and highest value of 300 Pa near the target [Fig. 4(b)].

High constant vapor pressure confines plasma around the source increasing EUV reabsorption near the source and in cold relatively dense vapor/plasma above. Comparison of EUV photon absorption (in the range of 13.5 ± 1%) for the two cases considered above is given in Fig. 5. Figure 5 shows a high absorption rate in the area surrounding actual EUV source. The source location can be determined by the combination of 30–40 eV temperature and 10²⁰ cm⁻³ electron density in the case of Nd:YAG produced plasma (Fig. 4). Relatively high EUV absorption in cold layers above, especially in the case of 300 Pa pressure conditions, is related to photoionization of atoms and low charged ions. Lower absorption of photons with energies of 91–93 eV in plasma with 5–15 eV temperatures can be explained by prevailing concentration of Sn⁵⁺–Sn⁷⁺ ions in this area which have higher ionization energy than considered EUV photons (94 eV for Sn⁵⁺) and do not contribute to these photon emission/absorption processes due to EUV transitions.²⁴ 

The above results showed that the efficiency of the EUV source can be reduced at higher pressure of the surrounding vapor and at larger vapor volume. However, there are also conditions when the CE of the source can be increased due to the presence of tin vapor surrounding solid/liquid droplets or fragments. Previous studies showed that this effect is different for CO₂ and Nd:YAG lasers.²⁵ Background vapor in a volume with a radius of 500 μm allows an almost two times increase in the CE of the source produced by the CO₂ laser.

More detailed analysis of plasma evolution at various background and laser conditions allowed identifying the regimes for positive effects of background vapor on the EUV photon emission and collection. These results are presented for single CO₂ laser interaction with 50 μm droplets. Such systems in vacuum chamber conditions produce sources with very low efficiency.²⁶ However, the efficiency can be increased if the proper vapor plume will surround the droplet. Figures 6 and 7 show simulation results for the conditions when small (100 μm in diameter) and large (700 μm in diameter) volumes of vapor surrounded a 50 μm droplet. In the case of a smaller volume, vapor did not contribute much to the development of the EUV source—the CE of this source is similar to the CE produced from the droplet in high vacuum conditions.

A larger volume of the vapor with an atom concentration of 5 × 10¹⁷ cm⁻³, corresponding to a pressure of 3.5 kPa, has led to a larger EUV source and contributed ∼40% of additional EUV output [Fig. 7(b)].

Further increase in the vapor layer above the droplet allowed achieving source efficiency similar to the efficiency of planar targets created by lasers with a large spot size. Figure 8 shows dependence of the source efficiency on the vapor volume indicating the transition to the negative effect of background on the CE.

The above analysis showed the important effects of the conditions around the droplet on EUV source evolution and production. These studies can be extrapolated to dual-beam systems, when droplets can be split into small fragments and mix created by a short pre-pulse laser.²⁷ These studies should be important for the development of higher power sources for HVM when larger targets will be required to produce a larger volume of EUV producing plasma and due to increasing difficulty of preparing such larger droplets for the second, CO₂, pulsed laser heating.

The success and the economic cost of the next generation computer chips will depend on the performance of EUV sources and on the efficient operation and lifetime of these nanolithography devices. While the efficiency of the sources is continuously being improved, their operational cycle is still highly restricted due to the degradation of the optical mirrors as well as the necessity of maintaining a clean chamber environment and components. These issues will even be more pronounced since the requirements for higher EUV power become more demanding.

Continued improvement and optimization of EUV lithography technology requires, among others, improving the processes of EUV source development. Increasing the power of sources requires increasing the size of Sn droplets that will lead to more complex processes of target preparation by pre-pulse lasers. It is expected that the source chamber will have some residual gas pressure and fine mist due to the required high frequency operation for the high-volume manufacture (HVM). A strong vacuum system in the chamber could affect the target system, its stability, and cost. In addition, depending on the type of the mitigation system, more background gas can be produced. Therefore, it is important to carefully study the limits of the background gas on the overall source performance.

Detailed analysis of various mix compositions is required to optimize the source and to reduce debris accumulation in the chamber. The comprehensive HEIGHTS 3D package was used for the analysis of the effect of background pressure and volume on EUV photon emission and collection. It was found that background pressure in the range of 1–5 Pa does not significantly influence the EUV source produced by the CO₂ laser. A larger volume with this pressure condition, however, can reduce the efficiency of the source. On the other hand, an optimized volume of mix with proper density could increase the efficiency of the sources produced by CO₂ lasers.

This work was supported by the National Science Foundation, PIRE Project. We gratefully acknowledge the computing resources provided by the Blues cluster operated by the Laboratory Computing Resource Center at Argonne National Laboratory.