Wave Cutoff Method Research Articles

Measurement of sheath thickness at a floating potential

In a cylindrical Langmuir probe measurement, ion current is collected from the surface of the sheath surrounded at probe tip, not at the surface of the probe tip. By using this, the sheath thickness can be obtained, if we know some unknown parameters, such as ion current, plasma density, and electron temperature. In this paper, we present a method to measure sheath thickness by using a wave cutoff method and a floating harmonic method. The measured result is in a good agreement with Allen-Boyd-Reynolds theory.

A restoration model of distorted electron density in wave-cutoff probe measurement

This study investigates the problem of electron density distortion and how the density can be restored in a wave-cutoff probe. Despite recent plasma diagnostics research using a wave-cutoff probe, the problem of electron density distortion caused by plasma conditions has not been resolved. Experimental results indicate that electron density measured using the wave-cutoff method is highly susceptible to variations in the probe tip gap. This electron density distortion is caused by the bulk plasma disturbance between probe tips, and it must be removed for calculating the absolute electron density. To do this, a detailed analytic model was developed using the power balance equation near probe tips. This model demonstrates the characteristics of plasma distortion in wave-cutoff probe measurement and successfully restored the absolute value of electron density with varying probe tip gaps.

Calculation of renormalized fermion effective actions in radially symmetric non-Abelian backgrounds

Our recent method to calculate renormalized functional determinants, the partial wave cutoff method, is extended for the evaluation of 4-D fermion one-loop effective action with arbitrary mass in certain types of radially symmetric, non-Abelian, background gauge fields (including instanton-like and instanton-antiinstanton-like configurations). A detailed study on functional determinants for matrix-valued radial differential operators is presented, explicating both our analytic treatment on the high partial wave contribution and the application of the generalized Gel'fand-Yaglom formula to determine the low partial wave contribution. In general, some numerical work is needed for the low partial wave part. In the massless limit, however, the factorizable nature of our partial-wave radial differential operators can be exploited to evaluate semi-analytically even the low partial wave part, and we thus have the full fermion effective action calculated explicitly in a class of non-Abelian background gauge fields. With nonzero mass, we also perform necessary numerical analysis as regards the low partial wave contribution to produce numerically exact results for the massive effective action. Comparing these against the results of the large mass expansion, the validity range of the large mass expansion is addressed. Also studied is the fermion mass dependence of the effective instanton-antiinstanton interaction.

Wave-Cutoff Method: Theory, Apparatus, Characteristics, and Applications

In this paper, we present an overview of recent studies of the wave-cutoff method, so that researchers who are not familiar with it can use this method easily. This method uses a wave-cutoff probe to acquire plasma parameters from the transmission or reflection spectra of plasma. Since this method was developed, some applications and analysis methods have been attempted and much progress has been achieved. The wave-cutoff method can measure electron density and electron temperature simultaneously, and is usable even in processing plasma. This method can measure the plasma parameters very accurately in a very short time.

Pressure limitation of electron density measurement using a wave-cutoff method in weakly ionized plasmas

Pressure limitation of electron density measurement is presented using a wave-cutoff method. As gas pressure builds up, the electron motion at ω=ωp is disturbed by an electron-neutral collision and cannot catch up to the movement of the electromagnetic wave. For this reason, electromagnetic waves begin to penetrate into plasma and the wave-cutoff signal disappears as the gas pressure increases. This was also confirmed by using an impedance analysis of the probe system. The results corresponded well with the measured wave transmission characteristics at the plasma frequency.

Photodissociation effects on the electron density and on FTIR measurements in a BTMSM/Ar discharge

For precise measurements of the absolute electron density in a bis-trimethylsilymethane (BTMSM) and argon plasma, the authors adapted a wave cutoff method and used the plasma frequency. The films were deposited on a p-type Si(1 0 0) substrate by means of UV-assisted inductively coupled plasma-enhanced chemical vapour deposition. Fourier transform infrared spectroscopy was used to investigate the bonding configuration of the SiCH films. With UV illumination, the electron density was found to increase in the low power region and decrease in the high power region. The peak intensity of Si-CH3 decreases with UV illumination under all conditions. Moreover, when the UV source illuminates the plasma, the peak intensity of CH2 increases whereas the peak intensity of CH3 decreases.

Renormalized effective actions in radially symmetric backgrounds: Partial wave cutoff method

The computation of the one-loop effective action in a radially symmetric background can be reduced to a sum over partial-wave contributions, each of which is the logarithm of an appropriate one-dimensional radial determinant. While these individual radial determinants can be evaluated simply and efficiently using the Gel'fand-Yaglom method, the sum over all partial-wave contributions diverges. A renormalization procedure is needed to unambiguously define the finite renormalized effective action. Here we use a combination of the Schwinger proper-time method, and a resummed uniform DeWitt expansion. This provides a more elegant technique for extracting the large partial-wave contribution, compared to the higher-order radial WKB approach which had been used in previous work. We illustrate the general method with a complete analysis of the scalar one-loop effective action in a class of radially separable SU(2) Yang-Mills background fields. We also show that this method can be applied to the case where the background gauge fields have asymptotic limits appropriate to uniform field strengths, such as, for example, in the Minkowski solution, which describes an instanton immersed in a constant background. Detailed numerical results will be presented in a sequel.

Characterization of remote inductively coupled CH4–N2 plasma for carbon nitride thin-film deposition

We investigated reaction characteristics in a CH4∕N2 plasma for deposition of amorphous CNx thin films (a-CNx) by evaluating the change in electron density using the wave cutoff method, and the behavior of ions and radicals with an optical emission spectroscopy (OES). An inductively coupled plasma source that was 30cm away from the substrate stage was used for the discharge. The change in electron density in the substrate region and OES spectra in the plasma-source region were evaluated to investigate both the reaction mechanism and the remote effect while varying process conditions such as rf power, pressure, and gas-mixing ratio. We found that the electron density in the remote CH4∕N2 plasma was closely related to recombination reactions of major ions such as N2+, CH4+, CH3+, and H2+ during diffusion from the plasma source to the substrate. The electron density and optical emission of major ions and radicals in the CH4∕N2 plasma increase at higher rf power. The ratio [N]∕([N]+[C]) in a-CNx films, as measured by auger electron spectroscopy, also increases with rf power since more excited N and C species are generated. For increasing pressure, the change in electron density and emission spectra showed different behavior, which arose from recombination of ions that generated more CH4, Nx (x=1,2), and CN radicals. The majority of positive ions generated from N2 species are greatly affected by the remote effect, while the majority of positive ions generated from CH4 species are not significantly influenced, since each species has different losses dependent on the pressure. A higher N2 gas fraction in the gas mixture generated more CN radicals, which resulted not only in more N incorporated into a-CNx films but also to a reduction of H passivation that retards formation of hybrid bonding between C and N in the films. These results suggest that efficient H abstraction is required to achieve more NC triple bonding in CH4∕N2 plasma deposition.

Analysis of the uncertainty in the measurement of electron densities in plasmas using the wave cutoff method

We have analysed the uncertainty of a measured electron density using a wave cutoff probe and compared it with that obtained using a double Langmuir probe and plasma oscillation probe. The wave cutoff probe gives an electron density from a measured plasma frequency, using a network analyser and radiating and detecting antennae. It can also measure the spatial distribution of the electron density. The cutoff method is free of many difficulties often encountered with Langmuir probes, such as thin film deposition and plasma potential fluctuation, and the uncertainty of the cutoff probe is not affected by the complex plasma environment. Here, the measurement technique is theoretically analysed and experimentally demonstrated in density measurements of an inductively coupled radio frequency plasma, and a comparison with the double probe and a plasma oscillation method with uncertainty analysis is also made.

Ion species and electron behavior in capacitively coupled Ar and O2 plasma

We investigated the change in electron density using the plasma frequency by the wave cutoff method, and the behavior of ion species with a quadrupole mass spectrometer (QMS) in pure Ar and O2 and mixed O2∕Ar plasmas. The change in electron and ion density in pure Ar and O2 plasmas was evaluated while varying such process conditions as rf power and pressure. We found that electron density in a pure Ar and O2 discharge is closely correlated to loss and generation of ions. The electron densities in both pure Ar and O2 plasmas increase with rf plasma power but show different dependence on pressure due to different loss mechanism for each type of gas. The addition of Ar to an O2 plasma significantly enhances the electron density due to the rapid increase of Ar+ ions regardless of the pressure. Also, Ar addition results in more dissociation of O2, which gives more atomic O. These results indicate that the electron density calculated from the plasma frequency, measured by the wave cutoff method, is well explained by the ion behavior, as characterized by QMS.

Wave cutoff method to measure absolute electron density in cold plasma

A method for precise measurements of absolute electron density in plasma using wave cutoff is described. This method of measurement uses a network analyzer with radiating and detecting antenna A microwave signal of 10 kHZ–3 GHz frequency is introduced into the plasma from a radiating port of the network analyzer and propagates in the plasma. The transmitted wave is monitored at a distance from a radiating antenna using an antenna connected to the receiving port of the network analyzer. The transmitted wave decays rapidly at a cutoff plasma frequency, which is a direct measure of the absolute electron density. This cutoff method is free of many difficulties often encountered with a Langmuir probe, such as thin film deposition and plasma potential fluctuation. The cutoff probe can also measure the spatial distribution of the electron density. The measurement technique is analyzed theoretically and experimentally, demonstrated in density measurements of an inductively coupled radio-frequency plasma, and is compared with the double probe and a plasma oscillation methods.

Plasma frequency measurements for absolute plasma density by means of wave cutoff method

A method for precise measurements of absolute electron density in the plasma using plasma frequency is developed. A microwave perturbation of a frequency is introduced to plasma from a network analyzer and transmits in the plasma. The transmitting wave at a distance from a radiating antenna is monitored using a spectrum analyzer to scan the perturbing frequency. The transmitting wave rapidly decays by a cutoff at the plasma frequency, which gives the absolute electron density. The transmitting waves of some frequency including plasma frequency are characterized. The measured plasma frequency by this method is coincident with that obtained by the plasma oscillation method.