Global kinetic models combined with Monte Carlo sheath models are developed for SF 6 and C 4 F 8 plasma discharges for silicon etching under the Bosch process. In SF 6 plasma, the dominant positive ions are SF + 5 , SF + 4 , SF + 3 and F + while in C 4 F 8 the dominant positive ions are CF + 3 and C 2 F + 3 . The simulation results show that the electrical parameters, such as the electron density and electron temperature, clearly affect the sheath dynamics and consequently the ion energy distribution function evolutions. In this context, we showed the effects of the operating conditions, such as the pressure and the radiofrequency power, on the electron density and electron temperature evolutions as well as the reactive particle fluxes (neutral and positive ions) involved in the plasma surface interactions for etching/deposition under the Bosch process. Ion energy distribution functions obtained from SF 6 and C 4 F 8 plasmas are compared with each other as regards the electrical properties of their associated plasmas. The simulation results show that the bimodal peaks of ion energy distribution functions are wider for SF 6 plasma than for C 4 F 8 plasma due to the high sheath thickness of SF 6 compared to that of C 4 F 8 . This is explained by the low electron density due to the high electronegativity of SF 6 in comparison to that of C 4 F 8 . The simulations also reveal that the bimodal peak of the ion energy distribution function is wider when the ion mass is low.
This paper describes an experimental and an analytical investigation into the collapse of 44 circular cylindrical composite tubes under external hydrostatic pressure. The results for 22 of these tubes were from a previous investigation and the results for a further 22 models are reported for the first time in this paper. The investigations concentrated on fibre‐reinforced plastic tube specimens made from a mixture of three carbon and two E‐glass fibre layers. The lay‐up was 0°/90°/0°/90°/0; the carbon fibres were laid lengthwise (0°) and the E‐glass fibres circumferentially (90°). The theoretical investigations were carried out using a simple solution for isotropic materials, namely a well‐known formula by ‘von Mises’. The previous investigation also used a numerical solution based on ANSYS, but this was found to be rather disappointing. The experimental investigations showed that the composite specimens behaved similarly to isotropic materials previously tested, in that the short vessels collapsed through axisymmetric deformation while the longer tubes collapsed through non‐symmetric bifurcation buckling. Furthermore, it was discovered that the specimens failed at changes of the composite lay‐up due to the manufacturing process of these specimens. These changes seem to be the weak points of the specimens. For the theoretical investigations, two different types of material properties were used to analyse the composite. These were calculated properties derived from the properties of the single layers given by the manufacturer and also the experimentally obtained properties. Two different approaches were chosen for the investigation of the theoretical buckling pressures, of the previously analysed models, namely a program called ‘MisesNP’, based on a well‐known formula by von Mises for single‐layer isotropic materials, and two finite element analyses using the famous computer package called ‘ANSYS’. These latter analyses simulated the composite with a single‐layer orthotrophic element (Shell93) and also with a multi‐layer element (Shell99). The results from Shell93 and Shell99 agreed with each other but, in general, their predictions were higher than the analytical solution by von Mises. The von Mises solution agreed better than the finite element solutions for the longer vessels, which collapsed by elastic instability, particularly when the experimentally obtained material properties were used. Thus, it was concluded that the results obtained from the finite element analyses predicted ‘questionable’ buckling pressures. The report provides design charts by all approaches and material types, which allow the possibility of obtaining a ‘plastic knockdown factor’ for these vessels. The theoretical buckling pressures obtained using the computer programs MisesNP or ANSYS can then be divided by the plastic knockdown factor obtained from the design charts, to give the predicted buckling pressures. It is not known whether or not this method can be used for the design of very large vessels.
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