Browsing by Author "Gu, Bi-Ren"

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Effect of Reconstruction Scheme on the Plasma Fluid Modeling With Original and Reformulated Ion-Related Modeling Equations Using HLL Flux Scheme
(2019-02-01)
Chen, Kuan-Lin
;
Tseng, Meng-Fan
;
Gu, Bi-Ren
;
Sharma, Sarveshwar
;
Wu, Jong-Shinn
In this paper, we would like to investigate the effect of spatial reconstruction schemes on the plasma fluid model with original and reformulated ion-related modeling equations by using the Harten-Lax-van Leer (HLL) flux scheme. The results based on the 1-D fluid model equations for electropositive plasma show that the appearance of unphysical oscillations near-sheath edges strongly depends on the reconstruction schemes (e.g., kappa = 1/2, 1/3, and first-order scheme) when the original ion equations utilize the incorrect ion sound speed. The unphysical oscillations disappear no matter what the spatial reconstruction scheme is applied if the reformulated ion equations with correct ion sound speed are used instead. For electronegative plasma, the kappa reconstruction scheme causes numerical instability when using either the incorrect or correct numerical ion sound speed, but the min-mod reconstruction scheme does not. The numerical results show that for either electropositive or electronegative discharges, both the second-order HLL scheme with min-mod reconstruction and the first-order HLL schemes can produce stable solution, while the accuracy of the former is slightly better than the later. Finally, some examples with an extension to the 2-D-axisymmetric electropositive and electronegative plasmas are demonstrated.
Numerical Investigation on Ion Inertia Force in Low-Temperature Plasma Using Fluid Model Considering Ion Momentum Equation
(2016-12-01)
Chen, Kuan-Lin
;
Tseng, Meng-Fan
;
Gu, Bi-Ren
;
Hung, Chieh-Tsan
;
Wu, Jong-Shinn
In this paper, we would like to numerically investigate the effect of ion inertia force in a typical argon gas discharge using fluid model considering the ion momentum equation, which becomes important under various operating conditions. The proposed self-consistent fluid model consists of the electron continuity equation with the drift-diffusion approximation, the ion continuity equation, the electron energy density equation, the ion momentum equation, and the Poisson equation for electric potential. We studied the plasma properties affected by the inertia force by comparing between the use of momentum equation and drift-diffusion approximation for ion momentum. The results show that the ion inertia force is significant under the low-pressure conditions (<100 mtorr) as expected, e.g., for plasma etching and radio frequency magnetron sputtering plasma. In addition, we also found when the pressure is higher than 100 mtorr, the inertia force becomes important (e.g., more than 15%) in the sheath region when the driving frequency is high enough (e.g., 60 MHz), e.g., for high-frequency plasma-enhanced chemical vapor deposition. Thus, inclusion of inertia force in the modeling of momentum equation becomes necessary under these operating conditions.
Numerical Investigation on Ion Inertia Force in Low-Temperature Plasma Using Fluid Model Considering Ion Momentum Equation
(2016-12)
Chen, Kuan-Lin
;
Tseng, Meng-Fan
;
Gu, Bi-Ren
;
Hung, Chieh-Tsan
;
Wu, Jong-Shinn
In this paper, we would like to numerically investigate the effect of ion inertia force in a typical argon gas discharge using fluid model considering the ion momentum equation, which becomes important under various operating conditions. The proposed self-consistent fluid model consists of the electron continuity equation with the drift-diffusion approximation, the ion continuity equation, the electron energy density equation, the ion momentum equation, and the Poisson equation for electric potential. We studied the plasma properties affected by the inertia force by comparing between the use of momentum equation and drift-diffusion approximation for ion momentum. The results show that the ion inertia force is significant under the low-pressure conditions (<100 mtorr) as expected, e.g., for plasma etching and radio frequency magnetron sputtering plasma. In addition, we also found when the pressure is higher than 100 mtorr, the inertia force becomes important (e.g., more than 15%) in the sheath region when the driving frequency is high enough (e.g., 60 MHz), e.g., for high-frequency plasma-enhanced chemical vapor deposition. Thus, inclusion of inertia force in the modeling of momentum equation becomes necessary under these operating conditions.