Kinetic Study on Channelling of Protons in Metallic Carbon Nanotubes

Based on the kinetic model and the dielectric response theory, a theoretical model is put forward to describe the transport of protons along nanotube axes. With the introduction of electron band structure for different nanotubes like zigzag and armchair nanotubes of metallic properties, the collective excitation of electrons on the cylinders induced by the incident ions is studied, showing several distinct peaks in the curves of the energy loss function. Furthermore, the stopping power and the self-energy are calculated as functions of ion velocities, especially taking into account the influence of damping coefficients. It is conceivable from the results that, in the kinetic formulation, plasmon excitation plays a major role in the stopping. And as the damping increases, the peaks of the stopping power shift to the lower velocities, with the broadening of the plasmon resonance.

Influence of Discharge Parameters on Tuned Substrate Self-Bias in an Radio-Frequency Inductively Coupled Plasma

The tuned substrate self-bias in an rf inductively coupled plasma source is controlled by means of varying the impedance of an external LC network inserted between the substrate and the ground. The influencing parameters such as the substrate axial position, different coupling coils and inserted resistance are experimentally studied. To get a better understanding of the experimental results, the axial distributions of the plasma density, electron temperature and plasma potential are measured with an rf compensated Langmuir probe; the coil rf peak-to-peak voltage is measured with a high voltage probe. As in the case of changing discharge power, it is found that continuity, instability and bi-stability of the tuned substrate bias can be obtained by means of changing the substrate axial position in the plasma source or the inserted resistance. Additionally, continuity can not transit directly into bi-stability, but evolves via instability. The inductance of the coupling coil has a substantial effect on the magnitude and the property of the tuned substrate bias.

A Numerical Study on Tuned Substrate Self-Bias in a Radio-Frequency Inductively Coupled Plasma

The tuned substrate self-bias in a radio-frequency inductively coupled plasma is controlled by varying the impedance of an external tuning LCR （inductor, capacitor and resistor） network inserted between the substrate and the ground. In experiments, it was found that the variation of the tuned substrate self-bias with the tuning capacitance demonstrated three features, namely, continuity, instability and bistability. In this paper, a numerical study is focused on the elucidation of the physical mechanisms underlying continuity and bistability. For the sake of simplicity and feasibility to include the key factors influencing the tuned substrate bias, the tedious calculation of inductive-coupling to obtain the plasma density axtd electron temperature is omitted, and discussion of the tuned substrate self-bias is made under the prescribed plasma density and electron temperature. On the other hand, the parameters influencing capacitive- coupling are retained in modeling the system with an equivalent circuit. It is found that multi-stable state appears when one of the parameters, such as the resistance in LCR, substrate area and plasma density, decreased to its critical value, or the rf voltage or electron temperature increased to the critical value individually. In the reverse cases, the tuned substrate self-bias varies continuously with the tuning capacitance.

The Tuned Substrate Self-bias in a Radio-frequency Inductively Coupled Plasma

The radio frequency (rf) self-bias of the substrate in a rf inductively coupled plasma is controlled by means of varying the impedance of an external LC network inserted between the substrate and the ground. Experimental studies were done on the relations of the tuned substrate self-bias with varying discharge and external circuit parameters. Under a certain discharge gas pressure, the curves of tuned substrate self-bias Vtsb versus tuning capacitance Ct demonstrate jumps and hysteresises when rf discharge power is higher than a threshold. The hysteresis loop in terms of △Ctcrit1(= Ccrit1-Ccrit2, here,Ccrit1, Ccrit2 are critical capacitance magnitudes under which the tuned substrate self-bias jumps) decreases with increasing rf discharge power, while the maximum |Vtsbimn| is achieved in the middle discharge-power region. Under a constant discharge power |Vtsb min|, Ccrit1 and Ccrit2 achieve their minimums in the middle gas-pressure region. When the tuning capacitance is pre-set at a lower value, Ttsb varies slightly with gas-flow rate; in the case of tuning capacitance sufficiently approaching Ctcriti, Vtsb undergoes the jump and hysteresis with the changing gas-flow rate. By inserting a resistor R into the external network, the characteristics of Vtsb-Ct curves are changed with the reduced quality factor Q depending on resistance values. Based on inductive- and capacitive-coupling characteristics of inductively coupled plasma, the dependence of a plasma sheath on plasma parameters, and the impedance properties of the substrate branch, the observed results can be qualitatively interpreted.