The mainstream approach for obtaining a 13.5 nm extreme ultraviolet (EUV) lithography light source involves laser-excited plasma. This requires the use of a high-power, high-frequency, and high-beam-quality short-pulse CO₂ laser, as well as a droplet Sn target, to generate extreme ultraviolet light. To satisfy the power requirements of EUV lithography, a high-frequency CO₂ oscillator must be used to generate high-frequency CO₂ seeds. These seeds undergo multi-stage amplification to produce a high-power CO₂ laser that serves as the driving laser. Consequently, a power amplifier is the core device for driving a light source system. Therefore, this study aims to optimize the operating parameters of a radio frequency (RF)-excited fast axial-flow CO₂ laser power amplifier to achieve better gain performance and higher amplified output power. This optimization has significant practical significance for efficiently obtaining EUV light sources.

Generally, the output power of an RF-excited fast axial laser amplifier is intricately linked to several factors such as the seed optical power, gas composition ratio, RF injection power, discharge tube diameter, gas pressure, and flow rate. In this paper, we establish a six-temperature model for an RF-excited fast axial CO₂ laser amplifier. This model encompasses the most abundant energy levels for simulating and calculating steady-state and transient energy distributions, light intensity changes, gain coefficients, etc. in the amplification process. As optimizing a single parameter with a six-temperature model may result in local optimization and a considerable workload, we employ a global optimization approach for the amplifier. Multiple parameters of the amplifier are optimized simultaneously. Thus, a six-temperature model serves as the fitness function, and a genetic algorithm is applied to globally optimize the cavity pressure and gas pressure ratio of CO₂∶N₂∶He in a self-developed RF-excited fast axial CO₂ laser amplifier. Furthermore, by continuously adjusting the relevant parameters of the genetic algorithm, we obtain optimized results. Finally, the feasibility of this approach is confirmed through amplification experiments performed on an experimental platform.

In this study, a six-temperature model is employed to identify the optimal operating conditions for the amplifier. Initially, a fixed V(CO₂)∶V(N₂)∶V(He)=5%∶25%∶70% is used to simulate the changes in the small-signal gain coefficients with the excitation electron number density under varying cavity pressures. The results indicate that the small-signal gain coefficients exhibit a pattern of increasing, stabilizing, and then gradually decreasing with increasing excitation electron number density. Different electron number densities (corresponding to the RF injection power) result in distinct optimal cavity pressures, with optima of 80 mbar (1 bar=100 kPa) and 100 mbar for a lower and higher excitation electron number density, respectively (Fig.7). Based on the simulation results, an optimal gas ratio and gas pressure are determined, considering the impact of the amplifier gas pressure and ratio on the small-signal gain and incorporating experimental data. Subsequently, the steady-state solution is used as the initial boundary condition, and a seed pulse with a pulse width of 150 ns and an average power of 110 W is injected to obtain the transient solution. This involves capturing the time-domain pulse evolution waveforms of both the seed and amplified output lasers (Fig.8). Based on the preliminary optimization results from the six-temperature model, a relatively optimal solution is obtained, resulting in an output power measurement of 2504 W under the operating conditions. As the experiment primarily considers the scenario of a 100% duty cycle for the seed, the small-signal gain coefficients derived from the steady-state solution serve as the objective function. After optimization using a genetic algorithm, the output power increases to 3422 W. The sum of the three gas pressures is 80 mbar, and the gas V(CO₂)∶V(N₂)∶V(He)=12.2%∶15.3%∶72.5%. Notably, the optimized He gas pressure corresponds closely with the initial value, whereas the optimized CO₂ and N₂ gas pressures differ from the initial values. This validates the feasibility and effectiveness of the proposed method (Table 4).

In this study, we optimize the gas pressure ratio and barometric pressure in an RF-excited fast axial CO₂ laser amplifier by integrating a genetic algorithm with a six-temperature model. This optimization aims to achieve a higher small-signal gain, as indicated by the laser-amplified output power. In experiments injecting a 10.6 μm seed with 110 W using the gas pressure ratio optimized through the genetic algorithm, the laser amplified output power significantly increases from 2504 W in the unoptimized laser system to 3422 W. This model is valuable for enhancing the amplifier performance and offers practical guidance for designing and optimizing internally developed amplifiers. Owing to equipment constraints, the current optimization has focused on continuous seed amplification parameters, with further exploration planned for the optimal parameters in pulse amplification.