Three-Dimensional Electromagnetic Diffraction by a Slot System With Parallel Plane Dielectric Interfaces

Titovitsky, Joseph A.

doi:10.2528/pierm10041402

Cited by 3 publications

(2 citation statements)

References 19 publications

(38 reference statements)

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“…Using the first approach results in an asymmetric set of equations for boundary conditions, thus producing asymmetric matrices in the EM field computations. This problem is overcome uti lizing the second approach [22]. Since there is no net volu metric electrical charge in either the plasma nor the quartz, the second approach uses a set of two independent vector potentials, A and F. This strategy produces symmetry in all equations and symetric matrices with simpler terms.…”

Section: Electromagnetic Formulationmentioning

confidence: 99%

Analytical investigation into the resonance frequencies of a curling probe

Arshadi¹,

Brinkmann²

2016

Plasma Sources Sci. Technol.

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The term 'active plasma resonance spectroscopy' (APRS) denotes a class of closely related plasma diagnostic methods which utilize the natural ability of plasmas to resonate on or near the electron plasma frequency ω pe ; an electrical radio frequency signal (in the GHz range) is coupled into the plasma via an antenna or a probe, the spectral response is recorded and a mathematical model is employed to determine plasma parameters such as the plasma density and the electron temperature. The curling probe, recently invented by Liang et al (2011 Appl. Phys. Express 4 066101), is a novel realization of the APRS concept which has many practical advantages. In particular, it can be miniaturized and flatly embedded into the chamber wall, thus allowing the monitoring of plasma processes without contamination nor disturbance. Physically, the curling probe can be understood as a 'coiled' form of the hairpin probe (Stenzel 1976 Rev. Sci. Instrum. 47 603). Assuming that the spiralization of the probe has little electrical effect, this paper investigates the characteristcs of a 'straightened' curling probe by modeling it as an infinite slottype resonator that is in direct contact with the plasma. The diffraction of an incident plane wave at the slot is calculated by solving the cold plasma model and Maxwell's equations simultaneously. The resonance frequencies of the probe are derived and are found to be in good agreement with the numerical results of the probe inventors.

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Section: Electromagnetic Formulationmentioning

confidence: 99%

Analytical investigation into the resonance frequencies of a curling probe

Arshadi¹,

Brinkmann²

2016

Plasma Sources Sci. Technol.

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“…With the explicit seperation of the incident and reflected waves [29], for each of these regions the field will be sought as a Fourier integral on plane waves: in quartz ( ⩽ )…”

Section: Evaluation Of Em Fieldsmentioning

confidence: 99%

Analytical investigation of microwave resonances of a curling probe for low and high-pressure plasma diagnostics

Arshadi

Brinkmann

2016

Plasma Sources Sci. Technol.

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The concept of 'active plasma resonance spectroscopy' (APRS) has attracted greater interest in recent years as an established plasma diagnostic technique. The APRS describes a class of related methods utilizing the intrinsic ability of plasma to resonate at or near the electron plasma frequency ω pe . The Curling probe (CP) as a novel realization of the APRS idea, is a miniaturized spiral slot embedded flatly in the chamber wall. Consequently, a plasma diagnostic technique with minimum disturbance and without metal contamination can be developed. To measure the plasma parameters the CP is fed with a weak frequency-swept signal from the exterior of the plasma chamber by a network analyzer which also records the response of the plasma versus the frequency. The resonance behavior is strongly dependent on the electron density and the gas pressure. The CP has also the advantage of resonating at a frequency greater than ω pe which is dependent on the spiral's length. The double resonance characteristic gives the CP the ability to be applied in varying plasma regimes. Assuming that the spiralization does not have a considerable effect on the resonances, a 'straightened' infinite length CP has recently been investigated (Arshadi and Brinkmann 2016 Plasma Sources Sci. Technol. 25 045014) to obtain the surface wave resonances. This work generalizes the approach and models the CP by a rectangular slot-type resonator located between plasma and quartz. Cold plasma theory and Maxwell's equations are utilized to compute the electromagnetic fields propagating into the plasma by the diffraction of an incident plane wave at the slot. A mathematical model is employed and both kinds of resonances are derived. The analytical study of this paper shows good agreement with the numerical results of the probe inventors.

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Integrated evaluation of diffraction image quality in optical lithography using the rigorous diffraction solution for a slot

Rudnitsky

2012

Tech. Phys.

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Three-Dimensional Electromagnetic Diffraction by a Slot System With Parallel Plane Dielectric Interfaces

Cited by 3 publications

References 19 publications

Analytical investigation into the resonance frequencies of a curling probe

Analytical investigation into the resonance frequencies of a curling probe

Analytical investigation of microwave resonances of a curling probe for low and high-pressure plasma diagnostics

Integrated evaluation of diffraction image quality in optical lithography using the rigorous diffraction solution for a slot

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