Fluid, particle-in-cell and hybrid models are the numerical simulation techniques commonly used for simulating low-temperature plasma discharges. Despite the complexity of plasma systems and the challenges in describing and modelling them, well-organized simulation methods can provide physical information often difficult to obtain from experiments. Simulation results can also be used to identify research guidelines, find optimum operating conditions or propose novel designs for performance improvements. In this paper, we present an overview of the principles, strengths and limitations of the three simulation models, including a brief history and the recent status of their development. The three modelling techniques are benchmarked by comparing simulation results in different plasma systems (plasma display panels, capacitively coupled plasmas and inductively coupled plasmas) with experimentally measured data. In addition, different aspects of the electron and ion kinetics in these systems are discussed based upon simulation results.

Gas breakdown in large scale systems has been widely studied and is reasonably well understood. Deviations from the well-known Paschen law, however, have been reported in microgaps. One possible mechanism responsible for these deviations is the increase of the secondary electron emission yield due to the quantum tunnelling of electrons from the metal electrodes to the gas phase. The high electric fields obtained in small gaps combined with the lowering of the potential barrier seen by the electrons in the cathode as an ion approaches lead to the onset of ion-enhanced field emissions. Particle-in-cell/Monte Carlo simulations including ion-enhanced field emission have been performed to evaluate the importance of these mechanisms in the discharge breakdown. Deviations from the Paschen curve in gaps smaller than 5 µm can be explained based on this mechanism.

The phenomenon of field emission plays a significant role in the deviation of the breakdown voltage from that predicted by Paschen's law within the range of high electric fields. High fields obtained in small gaps may enhance the secondary electron emission and such enhancement could lead to a lowering of the breakdown voltage and a departure from the Paschen curve. In this paper, the dc breakdown characteristics of the discharge in the micrometric regime were extensively studied by the theoretical approach including ion-enhanced field emission. In addition, semi-empirical expressions for the dependence of the breakdown voltage on the gap spacing and on the pressure based on the numerical solutions of the equation that describes the dc breakdown criteria have been proposed.

This paper contains the results of the detailed simulation study of the role of ion-enhanced field emission on the breakdown voltage in argon, xenon and krypton at high frequencies. Calculations were performed by using a one-dimensional particle-in-cell/Monte Carlo collisions (PIC/MCC) code with the secondary emission model adjusted to include field emission effects in microgaps. The obtained simulation results clearly show that electrical breakdown across micron-size gaps may occur at voltages far below the minimum predicted by the conventional Paschen curve. The observed breakdown voltage reduction may be attributed to the onset of ion-enhanced field emission.

This work represents the investigation of the dependence of the breakdown voltage on the gas pressure and on the frequency in radio-frequency argon discharges. Calculations were performed by using a one-dimensional particle-in-cell/Monte Carlo code with three velocity components with a new secondary emission model. The obtained results show that the multivalued nature of the left-hand branch of the breakdown curve can be achieved only by taking into account energy dependence of the yield per ion. The multivalued nature of the left-hand branch of the breakdown curve is attributed to the influence of the secondary emission characteristics of the electrodes on the breakdown voltage. Simulation results show a good agreement with the available experimental data. Disagreements between simulation results and theoretical predictions based on the phenomenological method indicate that a more accurate determination of molecular constants is needed. As a result of the satisfactory agreement between simulation and experimental data for dependence of the breakdown voltage on the frequency, a frequency scaling law is proposed.