Rađenović, Branislav M.

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  • Rađenović, Branislav M. (7)
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Author's Bibliography

Eigenmodes of finite length silicon-on-insulator microring resonator arrays

Rađenović, Branislav M.; Radmilović-Rađenović, Marija; Beličev, Petar

(2017)

TY  - JOUR
AU  - Rađenović, Branislav M.
AU  - Radmilović-Rađenović, Marija
AU  - Beličev, Petar
PY  - 2017
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1544
AB  - In this paper the eigenmodes of finite length microring resonator arrays have been systematically studied, both analytically using temporal coupled mode theory (CMT), and numerically using two-dimensional finite element method (FEM). The method for obtaining the values of parameters appearing in simplified CMT model using results of FEM calculations is presented. Calculations were carried out by COMSOL FEM packages for a wide range of distances between the rings. The obtained results reveal that the rotational degeneracy is preserved for a wide range of interrings distances. It is shown how the eigenvalue spectrum depends on the number of cavities in the system. The differences for the cases of odd and even numbers of rings, and its implications on actual applications, are discussed in details. The central branch appearing in odd-number arrays plays significant role for the delay-lines and optical buffering applications. Based on the first order perturbation theory, an analytical expressions for the eigenfrequencies of arbitrary (finite) length linear array of microring resonators are derived. The analytical expressions describing eigenfrequencies are useful for determining positions of the maxima in transfer characteristics in microring arrays with external buses.
T2  - Optical and Quantum Electronics
T1  - Eigenmodes of finite length silicon-on-insulator microring resonator arrays
VL  - 49
IS  - 4
DO  - 10.1007/s11082-017-0984-9
ER  - 
@article{
author = "Rađenović, Branislav M. and Radmilović-Rađenović, Marija and Beličev, Petar",
year = "2017",
abstract = "In this paper the eigenmodes of finite length microring resonator arrays have been systematically studied, both analytically using temporal coupled mode theory (CMT), and numerically using two-dimensional finite element method (FEM). The method for obtaining the values of parameters appearing in simplified CMT model using results of FEM calculations is presented. Calculations were carried out by COMSOL FEM packages for a wide range of distances between the rings. The obtained results reveal that the rotational degeneracy is preserved for a wide range of interrings distances. It is shown how the eigenvalue spectrum depends on the number of cavities in the system. The differences for the cases of odd and even numbers of rings, and its implications on actual applications, are discussed in details. The central branch appearing in odd-number arrays plays significant role for the delay-lines and optical buffering applications. Based on the first order perturbation theory, an analytical expressions for the eigenfrequencies of arbitrary (finite) length linear array of microring resonators are derived. The analytical expressions describing eigenfrequencies are useful for determining positions of the maxima in transfer characteristics in microring arrays with external buses.",
journal = "Optical and Quantum Electronics",
title = "Eigenmodes of finite length silicon-on-insulator microring resonator arrays",
volume = "49",
number = "4",
doi = "10.1007/s11082-017-0984-9"
}
Rađenović, B. M., Radmilović-Rađenović, M.,& Beličev, P.. (2017). Eigenmodes of finite length silicon-on-insulator microring resonator arrays. in Optical and Quantum Electronics, 49(4).
https://doi.org/10.1007/s11082-017-0984-9
Rađenović BM, Radmilović-Rađenović M, Beličev P. Eigenmodes of finite length silicon-on-insulator microring resonator arrays. in Optical and Quantum Electronics. 2017;49(4).
doi:10.1007/s11082-017-0984-9 .
Rađenović, Branislav M., Radmilović-Rađenović, Marija, Beličev, Petar, "Eigenmodes of finite length silicon-on-insulator microring resonator arrays" in Optical and Quantum Electronics, 49, no. 4 (2017),
https://doi.org/10.1007/s11082-017-0984-9 . .
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Modeling FAMA ion beam diagnostics based on the Ptolemy II model

Balvanović, Roman V.; Beličev, Petar; Rađenović, Branislav M.

(2012)

TY  - JOUR
AU  - Balvanović, Roman V.
AU  - Beličev, Petar
AU  - Rađenović, Branislav M.
PY  - 2012
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5046
AB  - The previously developed model of ion beam transport control of the FAMA facility is further enhanced by equipping it with the model of ion beam diagnostics. The model of control, executing once, is adjusted so that it executes in iterative mode, where each iteration samples the input beam normally distributed over initial phase space and calculates a single trajectory through the facility beam lines. The model takes into account only the particles that manage to pass through all the beam line apertures, emulating in this way a Faraday cup and a beam profile meter. Generated are also beam phase space distributions and horizontal and vertical beam profiles at the end of the beam transport lines the FAMA facility consists of. By adding the model of ion beam diagnostics to the model of ion beam transport control, the process of determining optimal ion beam control parameters is eased and speeded up, and the understanding of influence of control parameters on the ion beam characteristics is improved. (C) 2012 Elsevier B.V. All rights reserved.
T2  - Nuclear Instruments and Methods in Physics Research. Section A: Accelerators, Spectrometers, Detectors, and Associated Equipment
T1  - Modeling FAMA ion beam diagnostics based on the Ptolemy II model
VL  - 690
SP  - 17
EP  - 26
DO  - 10.1016/j.nima.2012.06.028
ER  - 
@article{
author = "Balvanović, Roman V. and Beličev, Petar and Rađenović, Branislav M.",
year = "2012",
abstract = "The previously developed model of ion beam transport control of the FAMA facility is further enhanced by equipping it with the model of ion beam diagnostics. The model of control, executing once, is adjusted so that it executes in iterative mode, where each iteration samples the input beam normally distributed over initial phase space and calculates a single trajectory through the facility beam lines. The model takes into account only the particles that manage to pass through all the beam line apertures, emulating in this way a Faraday cup and a beam profile meter. Generated are also beam phase space distributions and horizontal and vertical beam profiles at the end of the beam transport lines the FAMA facility consists of. By adding the model of ion beam diagnostics to the model of ion beam transport control, the process of determining optimal ion beam control parameters is eased and speeded up, and the understanding of influence of control parameters on the ion beam characteristics is improved. (C) 2012 Elsevier B.V. All rights reserved.",
journal = "Nuclear Instruments and Methods in Physics Research. Section A: Accelerators, Spectrometers, Detectors, and Associated Equipment",
title = "Modeling FAMA ion beam diagnostics based on the Ptolemy II model",
volume = "690",
pages = "17-26",
doi = "10.1016/j.nima.2012.06.028"
}
Balvanović, R. V., Beličev, P.,& Rađenović, B. M.. (2012). Modeling FAMA ion beam diagnostics based on the Ptolemy II model. in Nuclear Instruments and Methods in Physics Research. Section A: Accelerators, Spectrometers, Detectors, and Associated Equipment, 690, 17-26.
https://doi.org/10.1016/j.nima.2012.06.028
Balvanović RV, Beličev P, Rađenović BM. Modeling FAMA ion beam diagnostics based on the Ptolemy II model. in Nuclear Instruments and Methods in Physics Research. Section A: Accelerators, Spectrometers, Detectors, and Associated Equipment. 2012;690:17-26.
doi:10.1016/j.nima.2012.06.028 .
Balvanović, Roman V., Beličev, Petar, Rađenović, Branislav M., "Modeling FAMA ion beam diagnostics based on the Ptolemy II model" in Nuclear Instruments and Methods in Physics Research. Section A: Accelerators, Spectrometers, Detectors, and Associated Equipment, 690 (2012):17-26,
https://doi.org/10.1016/j.nima.2012.06.028 . .
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Characteristics of the 2nd Harmonic ECR Micro Plasma Sources by Using PIC/MCC Simulations

Radmilović-Rađenović, Marija; Rađenović, Branislav M.; Beličev, Petar

(2012)

TY  - JOUR
AU  - Radmilović-Rađenović, Marija
AU  - Rađenović, Branislav M.
AU  - Beličev, Petar
PY  - 2012
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/4977
AB  - In this paper we have presented our simulation studies of 2.4 GHz microwave plasma production under the electron cyclotron resonance with an idea to expand the plasma generation conditions into the much lower pressure range and much shorter gap length. As the first for this purpose, we have focused on the influences of applied magnetic field, gas pressure and gap length on the breakdown and maintenance of plasmas. Calculations were performed by using a one-dimensional particle-in-cell/Monte Carlo collisions code with three velocity components. The obtained simulation results are in a good agreement with the available experimental data providing an insight into the resonant electron acceleration for ECR condition and the resonant electron confinement for the 2nd harmonic ECR. In addition, analytical expressions for the breakdown voltage and the trapping field have been derived.
T2  - Acta Physica Polonica A
T1  - Characteristics of the 2nd Harmonic ECR Micro Plasma Sources by Using PIC/MCC Simulations
VL  - 122
IS  - 1
SP  - 128
EP  - 131
DO  - 10.12693/APhysPolA.122.128
ER  - 
@article{
author = "Radmilović-Rađenović, Marija and Rađenović, Branislav M. and Beličev, Petar",
year = "2012",
abstract = "In this paper we have presented our simulation studies of 2.4 GHz microwave plasma production under the electron cyclotron resonance with an idea to expand the plasma generation conditions into the much lower pressure range and much shorter gap length. As the first for this purpose, we have focused on the influences of applied magnetic field, gas pressure and gap length on the breakdown and maintenance of plasmas. Calculations were performed by using a one-dimensional particle-in-cell/Monte Carlo collisions code with three velocity components. The obtained simulation results are in a good agreement with the available experimental data providing an insight into the resonant electron acceleration for ECR condition and the resonant electron confinement for the 2nd harmonic ECR. In addition, analytical expressions for the breakdown voltage and the trapping field have been derived.",
journal = "Acta Physica Polonica A",
title = "Characteristics of the 2nd Harmonic ECR Micro Plasma Sources by Using PIC/MCC Simulations",
volume = "122",
number = "1",
pages = "128-131",
doi = "10.12693/APhysPolA.122.128"
}
Radmilović-Rađenović, M., Rađenović, B. M.,& Beličev, P.. (2012). Characteristics of the 2nd Harmonic ECR Micro Plasma Sources by Using PIC/MCC Simulations. in Acta Physica Polonica A, 122(1), 128-131.
https://doi.org/10.12693/APhysPolA.122.128
Radmilović-Rađenović M, Rađenović BM, Beličev P. Characteristics of the 2nd Harmonic ECR Micro Plasma Sources by Using PIC/MCC Simulations. in Acta Physica Polonica A. 2012;122(1):128-131.
doi:10.12693/APhysPolA.122.128 .
Radmilović-Rađenović, Marija, Rađenović, Branislav M., Beličev, Petar, "Characteristics of the 2nd Harmonic ECR Micro Plasma Sources by Using PIC/MCC Simulations" in Acta Physica Polonica A, 122, no. 1 (2012):128-131,
https://doi.org/10.12693/APhysPolA.122.128 . .

Particle-in-cell modelling of a neutral beam source for material processing in nanoscale structures fabrication

Radmilović-Rađenović, Marija; Petrovic, Z. Lj.; Nikitovic, Z.; Strinic, A.; Stojanovic, V.; Nina, A.; Rađenović, Branislav M.

(2007)

TY  - CONF
AU  - Radmilović-Rađenović, Marija
AU  - Petrovic, Z. Lj.
AU  - Nikitovic, Z.
AU  - Strinic, A.
AU  - Stojanovic, V.
AU  - Nina, A.
AU  - Rađenović, Branislav M.
PY  - 2007
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/6583
AB  - Neutral beam processing has evolved into one of the most promising methods for overcoming plasma process induced damage. Surface treatment by neutrals avoids problems with surface charging effects, frequently encountered when using common ion treatment, especially for low k-materials. In this paper, the influence of various parameters on the neutralization of ion beams in Ar-CF4 mixture based on a Particle in Cell with Monte Carlo collisions (PIC/MCC) simulation is studied. The efficiency of neutralization has been treated by considering both surface neutralization of ions and collisions of ions in the gas.
C3  - Materials Science Forum
T1  - Particle-in-cell modelling of a neutral beam source for material processing in nanoscale structures fabrication
VL  - 555
SP  - 47
EP  - +
DO  - 10.4028/www.scientific.net/MSF.555.47
ER  - 
@conference{
author = "Radmilović-Rađenović, Marija and Petrovic, Z. Lj. and Nikitovic, Z. and Strinic, A. and Stojanovic, V. and Nina, A. and Rađenović, Branislav M.",
year = "2007",
abstract = "Neutral beam processing has evolved into one of the most promising methods for overcoming plasma process induced damage. Surface treatment by neutrals avoids problems with surface charging effects, frequently encountered when using common ion treatment, especially for low k-materials. In this paper, the influence of various parameters on the neutralization of ion beams in Ar-CF4 mixture based on a Particle in Cell with Monte Carlo collisions (PIC/MCC) simulation is studied. The efficiency of neutralization has been treated by considering both surface neutralization of ions and collisions of ions in the gas.",
journal = "Materials Science Forum",
title = "Particle-in-cell modelling of a neutral beam source for material processing in nanoscale structures fabrication",
volume = "555",
pages = "47-+",
doi = "10.4028/www.scientific.net/MSF.555.47"
}
Radmilović-Rađenović, M., Petrovic, Z. Lj., Nikitovic, Z., Strinic, A., Stojanovic, V., Nina, A.,& Rađenović, B. M.. (2007). Particle-in-cell modelling of a neutral beam source for material processing in nanoscale structures fabrication. in Materials Science Forum, 555, 47-+.
https://doi.org/10.4028/www.scientific.net/MSF.555.47
Radmilović-Rađenović M, Petrovic ZL, Nikitovic Z, Strinic A, Stojanovic V, Nina A, Rađenović BM. Particle-in-cell modelling of a neutral beam source for material processing in nanoscale structures fabrication. in Materials Science Forum. 2007;555:47-+.
doi:10.4028/www.scientific.net/MSF.555.47 .
Radmilović-Rađenović, Marija, Petrovic, Z. Lj., Nikitovic, Z., Strinic, A., Stojanovic, V., Nina, A., Rađenović, Branislav M., "Particle-in-cell modelling of a neutral beam source for material processing in nanoscale structures fabrication" in Materials Science Forum, 555 (2007):47-+,
https://doi.org/10.4028/www.scientific.net/MSF.555.47 . .
1
1

A particle-in-cell simulation of the breakdown mechanism in microdischarges with an improved secondary emission model

Radmilović-Rađenović, Marija; Rađenović, Branislav M.

(2007)

TY  - JOUR
AU  - Radmilović-Rađenović, Marija
AU  - Rađenović, Branislav M.
PY  - 2007
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/3197
AB  - In this paper, the failure of the breakdown voltage from the Paschens law at extremely small electrode separations is studied. The electrical breakdown in microgaps occurs at the voltages far below the Paschen curve minimum breakdown limit and the modified Paschen curve should be used. Offered explanation for the departure from the Paschens law at small gap spacings is based on the increasing of the yield of the secondary electrons. The high electric fields existing in small gaps may enhance the secondary electron yield and this would lead to a lowering of the breakdown voltage and to the departure from the Paschens law. Particle-in-cell/Monte-Carlo (PIC/MCC) simulations with a new secondary emission model have been performed to estimate the importance of this mechanism in the discharge breakdown. Obtained simulation results suggest that deviations from the Paschen curve across the micron and submicorn gap spacing can be attributed to the ion-enhanced field emissions. (c) 2007 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim.
T2  - Contributions to Plasma Physics
T1  - A particle-in-cell simulation of the breakdown mechanism in microdischarges with an improved secondary emission model
VL  - 47
IS  - 3
SP  - 165
EP  - 172
DO  - 10.1002/ctpp.200710023
ER  - 
@article{
author = "Radmilović-Rađenović, Marija and Rađenović, Branislav M.",
year = "2007",
abstract = "In this paper, the failure of the breakdown voltage from the Paschens law at extremely small electrode separations is studied. The electrical breakdown in microgaps occurs at the voltages far below the Paschen curve minimum breakdown limit and the modified Paschen curve should be used. Offered explanation for the departure from the Paschens law at small gap spacings is based on the increasing of the yield of the secondary electrons. The high electric fields existing in small gaps may enhance the secondary electron yield and this would lead to a lowering of the breakdown voltage and to the departure from the Paschens law. Particle-in-cell/Monte-Carlo (PIC/MCC) simulations with a new secondary emission model have been performed to estimate the importance of this mechanism in the discharge breakdown. Obtained simulation results suggest that deviations from the Paschen curve across the micron and submicorn gap spacing can be attributed to the ion-enhanced field emissions. (c) 2007 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim.",
journal = "Contributions to Plasma Physics",
title = "A particle-in-cell simulation of the breakdown mechanism in microdischarges with an improved secondary emission model",
volume = "47",
number = "3",
pages = "165-172",
doi = "10.1002/ctpp.200710023"
}
Radmilović-Rađenović, M.,& Rađenović, B. M.. (2007). A particle-in-cell simulation of the breakdown mechanism in microdischarges with an improved secondary emission model. in Contributions to Plasma Physics, 47(3), 165-172.
https://doi.org/10.1002/ctpp.200710023
Radmilović-Rađenović M, Rađenović BM. A particle-in-cell simulation of the breakdown mechanism in microdischarges with an improved secondary emission model. in Contributions to Plasma Physics. 2007;47(3):165-172.
doi:10.1002/ctpp.200710023 .
Radmilović-Rađenović, Marija, Rađenović, Branislav M., "A particle-in-cell simulation of the breakdown mechanism in microdischarges with an improved secondary emission model" in Contributions to Plasma Physics, 47, no. 3 (2007):165-172,
https://doi.org/10.1002/ctpp.200710023 . .
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Modelling of breakdown behavior by PIC/MCC code with improved secondary emission models

Radmilovi-Radjenovic, M.; Petrovic, Z. Lj; Rađenović, Branislav M.

(2007)

TY  - CONF
AU  - Radmilovi-Radjenovic, M.
AU  - Petrovic, Z. Lj
AU  - Rađenović, Branislav M.
PY  - 2007
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/6706
AB  - This paper contains the results of the detailed theoretical and simulation studies of the role of the secondary emission process in the breakdown phenomena. Calculations were performed by using a Particle-in-cell/Monte Carlo collisions (PIC/MCC) code with the secondary emission model adjusted to include the energy dependence of the secondary electron yield at large separations as well as the enhancement of the secondary emission coefficient in microgaps. Furthemore, in the presence of the magnetic field, the breakdown voltage has been determined taking into account the effect of both the equivalent pressure and the variation of Townsends second coefficient in a magnetic field. The obtained simulation results clearly show that a proper choice of the secondary emission model in the PIC/MCC code may lead to a gratifying agreement with the experimental results for the breakdown voltage. The results discussed in this paper indicate that PIC/MCC code with the improved secondary emission models provides a good physical description of plasma for various gap sizes, not only in the presence of the electric field, but also under the simultanious action of both electric and magnetic fields.
C3  - Journal of Physics: Conference Series
T1  - Modelling of breakdown behavior by PIC/MCC code with improved secondary emission models
VL  - 71
DO  - 10.1088/1742-6596/71/1/012007
ER  - 
@conference{
author = "Radmilovi-Radjenovic, M. and Petrovic, Z. Lj and Rađenović, Branislav M.",
year = "2007",
abstract = "This paper contains the results of the detailed theoretical and simulation studies of the role of the secondary emission process in the breakdown phenomena. Calculations were performed by using a Particle-in-cell/Monte Carlo collisions (PIC/MCC) code with the secondary emission model adjusted to include the energy dependence of the secondary electron yield at large separations as well as the enhancement of the secondary emission coefficient in microgaps. Furthemore, in the presence of the magnetic field, the breakdown voltage has been determined taking into account the effect of both the equivalent pressure and the variation of Townsends second coefficient in a magnetic field. The obtained simulation results clearly show that a proper choice of the secondary emission model in the PIC/MCC code may lead to a gratifying agreement with the experimental results for the breakdown voltage. The results discussed in this paper indicate that PIC/MCC code with the improved secondary emission models provides a good physical description of plasma for various gap sizes, not only in the presence of the electric field, but also under the simultanious action of both electric and magnetic fields.",
journal = "Journal of Physics: Conference Series",
title = "Modelling of breakdown behavior by PIC/MCC code with improved secondary emission models",
volume = "71",
doi = "10.1088/1742-6596/71/1/012007"
}
Radmilovi-Radjenovic, M., Petrovic, Z. L.,& Rađenović, B. M.. (2007). Modelling of breakdown behavior by PIC/MCC code with improved secondary emission models. in Journal of Physics: Conference Series, 71.
https://doi.org/10.1088/1742-6596/71/1/012007
Radmilovi-Radjenovic M, Petrovic ZL, Rađenović BM. Modelling of breakdown behavior by PIC/MCC code with improved secondary emission models. in Journal of Physics: Conference Series. 2007;71.
doi:10.1088/1742-6596/71/1/012007 .
Radmilovi-Radjenovic, M., Petrovic, Z. Lj, Rađenović, Branislav M., "Modelling of breakdown behavior by PIC/MCC code with improved secondary emission models" in Journal of Physics: Conference Series, 71 (2007),
https://doi.org/10.1088/1742-6596/71/1/012007 . .
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Influence of charging on SiO2 etching profile evolution etched by fluorocarbon Plasmas

Rađenović, Branislav M.; Radmilovc-Radjenovic, M.; Petrovic, Z. Lj.

(2007)

TY  - CONF
AU  - Rađenović, Branislav M.
AU  - Radmilovc-Radjenovic, M.
AU  - Petrovic, Z. Lj.
PY  - 2007
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/6584
AB  - A comprehensive simulation of etching profile evolution requires knowledge of the etching rates at all points of the profile surface during the etching process. Electrons do not contribute directly to the material removal, but they are the source, together with positive ions, of the profile charging that has many negative consequences on the final outcome of the process especially in the case of insulating material etching. The ability to simulate feature charging was added to the 3D level set profile evolution simulator described earlier. The ion and electron fluxes were computed along the feature using the Monte Carlo method. The surface potential profiles and electric field for the entire feature were generated by solving the Laplace equation using finite elements method. Calculations were performed in the case of a simplified model of Ar+/CF4 non-equilibrium plasma etching Of SiO2.
C3  - Materials Science Forum
T1  - Influence of charging on SiO2 etching profile evolution etched by fluorocarbon Plasmas
VL  - 555
SP  - 53
EP  - +
DO  - 10.4028/www.scientific.net/MSF.555.53
ER  - 
@conference{
author = "Rađenović, Branislav M. and Radmilovc-Radjenovic, M. and Petrovic, Z. Lj.",
year = "2007",
abstract = "A comprehensive simulation of etching profile evolution requires knowledge of the etching rates at all points of the profile surface during the etching process. Electrons do not contribute directly to the material removal, but they are the source, together with positive ions, of the profile charging that has many negative consequences on the final outcome of the process especially in the case of insulating material etching. The ability to simulate feature charging was added to the 3D level set profile evolution simulator described earlier. The ion and electron fluxes were computed along the feature using the Monte Carlo method. The surface potential profiles and electric field for the entire feature were generated by solving the Laplace equation using finite elements method. Calculations were performed in the case of a simplified model of Ar+/CF4 non-equilibrium plasma etching Of SiO2.",
journal = "Materials Science Forum",
title = "Influence of charging on SiO2 etching profile evolution etched by fluorocarbon Plasmas",
volume = "555",
pages = "53-+",
doi = "10.4028/www.scientific.net/MSF.555.53"
}
Rađenović, B. M., Radmilovc-Radjenovic, M.,& Petrovic, Z. Lj.. (2007). Influence of charging on SiO2 etching profile evolution etched by fluorocarbon Plasmas. in Materials Science Forum, 555, 53-+.
https://doi.org/10.4028/www.scientific.net/MSF.555.53
Rađenović BM, Radmilovc-Radjenovic M, Petrovic ZL. Influence of charging on SiO2 etching profile evolution etched by fluorocarbon Plasmas. in Materials Science Forum. 2007;555:53-+.
doi:10.4028/www.scientific.net/MSF.555.53 .
Rađenović, Branislav M., Radmilovc-Radjenovic, M., Petrovic, Z. Lj., "Influence of charging on SiO2 etching profile evolution etched by fluorocarbon Plasmas" in Materials Science Forum, 555 (2007):53-+,
https://doi.org/10.4028/www.scientific.net/MSF.555.53 . .
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