Alec Goodyear

Comparison of an self-organizing migration algorithm with simulated annealing and differential evolution for automated waveform tuning

In this article, the performance of a self-organizing migration algorithm (SOMA), a new stochastic optimization algorithm, has been compared with simulated annealing (SA) and differential evolution (DE) for an engineering application. This application is the automated deduction of 14 Fourier terms in a radio-frequency (RF) waveform to tune a Langmuir probe. Langmuir probes are diagnostic tools used to determine the ion density and the electron energy distribution in plasma processes. RF plasmas are inherently non-linear, and many harmonics of the driving fundamental can be generated in the plasma. RF components across the ion sheath formed around the probe distort the measurements made. To improve the quality of the measurements, these RF components can be removed by an active-compensation method. In this research, this was achieved by applying an RF signal to the probe tip that matches both the phase and amplitude of the RF signal generated from the plasma. Here, seven harmonics are used to generate the waveform applied to the probe tip. Therefore, 14 mutually interacting parameters (seven phases and seven amplitudes) had to be tuned on-line. In previous work SA and DE were applied successfully to this problem, and hence were chosen to be compared with the performance of SOMA. In this application domain, SOMA was found to outperform SA and DE.

Measurements of characteristic transients of planar electrostatic probes in cold plasmas

This article describes how to extract accurate information about a plasma from a capacitively coupled planar probe that is biased using pulsed radio-frequency excitation. The conditions necessary to observe correct saturation of the probe current are investigated, particularly the use of correct geometry and biasing for the guard ring. With these precautions the probe is an effective diagnostic for electron tail temperature at energies beyond those probed by conventional cylindrical probes. The dynamic response of the probe is investigated using conventional sweep voltages and shows the onset of displacement current and inertial effects associated with ions and electrons. In addition the effect of insulating films on the probe surface is examined, showing how the probe continues to operate even when it is coated. Characteristic changes caused by the presence of an insulating film give information about its electrical properties and its thickness.

The role of ions in the continuous-wave plasma polymerisation of acrylic acid

Ion flux, mass spectral and mass deposition rate measurements have been made in radiofrequency-induced continuous-wave plasmas of acrylic acid. At 1 W input power, an ion flux of 0.05±0.1×1018 ions m-2 s-1 was measured for acrylic acid. At this power, ions corresponding to (2M+H)+ and (3M+H)+ were prominent in the positive-ion mass spectrum. When this spectrum was corrected for the transmission function of the quadrupole mass spectrometer (conservatively taken as intensity∝m-1), it was evident that the cationic portion of plasma contained many ions of high m/z, as opposed to small fragments of acrylic acid. The m/z of the ‘average’ ion was calculated as 115. The mass of ions arriving at a solid surface in the centre of the plasma was then calculated by multiplying the flux by the average mass to give 9.6 µg m-2 s-1. This value represents a significant fraction of the total mass deposited, determined by means of a quartz crystal mass balance (45.5 µg m-2 s-1). Repeating the calculation for a 5 W plasma yields an ion mass flux of 39.6 µg m-2 s-1 (measured mass deposition of 57.3 µg m-2 s-1). At 15 W, the calculated mass deposited (based on ion flux) exceeds that measured by the quartz mass balance. The ‘average’ ion mass decreased as plasma input power increased.Based on these data, and XPS measurements of the solid-phase deposit we make a first attempt at describing semi-quantitatively the possible role of ions in deposit formation.

Tailoring of electron energy distributions in low temperature plasmas

Assuming a background Maxwellian electron distribution we investigate the effects of tailoring the tail of the distribution upon the plasma density and electron temperature in a capacitive discharge. Taking the latter to be in the intermediate pressure regime the main effect of the tail is to modify the rate coefficients for ionization and excitation, and hence to alter the collisional energy loss per electron-ion pair created. We demonstrate that the background temperature can be suppressed and the electron density increased by enhancing the tail population. The model is applied to a typical set of low temperature conditions in argon and the changes in temperature and density calculated. Injecting 100 eV electrons into an argon plasma under very similar conditions to those of the application of our model, the corresponding densities and temperatures are measured. Good qualitative agreement is found.

Automated control of an actively compensated Langmuir probe system using simulated annealing

A simulated annealing (SA) method has been developed to deduce 14 Fourier terms in a radio frequency waveform for active compensation of a Langmuir probe system. The active compensation system uses seven harmonics to generate a required waveform. Therefore, 14 heavily interacting continuous parameters need to be tuned before measurements can be taken. Because of the magnitude of the resulting search space, it is virtually impossible to test all possible solutions within an acceptable time. An automated control system employing SA has been developed for online tuning of the waveform. This control system has been shown to find better solutions in less time than skilled human operators. The results are also more reproducible and hence more reliable.

Optimization of plasma etch processes using evolutionary search methods with in situ diagnostics

This paper presents several approaches that have been used to control, optimize and characterize a low pressure (10–300 mTorr) plasma processing system. Methods such as contour following and differential evolution have been used to find contours of DC bias, total ion flux, ion energy flux, quadrupole mass spectrum (QMS) intensity ratios and line intensity ratios of the optical emission spectrum (OES) in argon and nitrogen plasmas. A mapping for a 4 × 4 multi-dimensional parameter space is also presented, in which the relationship between four control parameters (power, pressure, mass flow rates of two supplied gases) and four measurement outputs (DC bias, ion flux, QMS ratios and OES line intensity ratios) is determined in a plasma etching process. The use of these methods significantly reduces the time needed to re-configure the processing system and will benefit transfer of processes between different systems. A similar approach has also been used to find quickly an optimum condition for directional etching of a silicon wafer.

Ion flux and deposition rate measurements in the RF continuous wave plasma polymerisation of acrylic acid

Ion flux and deposition rate measurements made in plasmas of acrylic acid support the view that at low plasma power ions are primarily responsible for deposit growth.

Importance of fluorine surface diffusion for plasma etching of silicon

Dry etching of silicon is an important process in the manufacturing of integrated circuits and micromachined devices. Traditionally, the etch rate limiting step for an isotropic silicon etching process is considered to be the arrival of fluorine atoms directly from the gas phase onto the silicon surface, and the mechanism to promote anisotropy is the prevention of lateral etching by the formation of an inhibiting layer on the vertical walls. Furthermore, isotropic dry etching is considered to etch features in the same way as isotropic wet etching. Conventional mechanisms cannot explain, however, the perfect anisotropic etching of silicon with pure SF6, when no polymer is formed. Neither can it be understood how a deep (>50 μm), isotropic, dry etching process applied to silicon can result in structures with a pinched neck and sharp ridges, in contrast with a wet etching process, where the corners are rounded and no pinching of the neck is observed. It is proposed that long-range diffusion of fluorine atoms...

Improved simulated annealing with step width adaptation for Langmuir probe tuning

In a previous investigation, a simulated annealing (SA) method was developed to optimize 14 Fourier terms in a radio-frequency waveform for active compensation of a Langmuir probe system. This approach was shown to find better solutions in less time than skilled human operators. However, variations in fitness indicated that the SA algorithm did not always find the precise global solution, although it came consistently close to it. This variability was caused by the limited number of fitness evaluations available due to time constraints. In this research, the chosen maximum step width has been shown to have a significant effect on the overall performance of the algorithm. A scaling function has been developed to adapt the maximum step width of the SA algorithm, on-line, as a function of the number of elapsed iterations. The modified algorithm has been shown to find fitter solutions with reduced variability in fitness.

Intelligent control of low pressure plasma processing

Several parameters characterize systems for materials processing that use radio frequency electrical discharges in gases at low pressure. These include directly measurable quantities such as a DC bias voltage, an ion current, an energy flux, masses of charged species, and spectrally resolved optical emission. None of these is directly controllable but all are dependent on several variables that can be controlled such as radio-frequency (RF) power, chamber pressure, and gas flow rates. There is a rich parameter space that must be painstakingly searched for optimum conditions for any particular process. In place of the relatively slow manual procedure, an artificial intelligence (AI) approach has been used to map out contours for all of the above characteristic parameters in the control space. Automatic characterization of plasma systems in this way could significantly reduce the time to re-configure them and to transfer processes between different systems.