Content uploaded by Cihan Yesil

Author content

All content in this area was uploaded by Cihan Yesil on Sep 14, 2019

Content may be subject to copyright.

TRANSITION TO CHAOS IN PLANAR GAS

DISCHARGE-SEMICONDUCTOR SYSTEM IN

NITROGEN: EFFECT OF FLUID MODELLING

APPROACH

Cihan Yeşil

Department of Physics

Middle East Technical University

Supervisor: Prof. Dr. İsmail RAFATOV

Gas Discharge Modelling

•Fluid Models

- Simple Fluid Model

- Extended Fluid Model

•Kinetic Particle Models

- PIC/MC Methods

•Hybrid Models

A diagram illustrating a correct physical model for a

plasma system as functions of system size and pressure

Retrieved from V.Kolobov and R. Arslanbekov, Microelectron. Eng., 69, 606–615, 2003.

Pattern Formation in Gas Discharge Plasma

•The group of Purwins

(Münster, Germany)

•The group of Astrov (St.

Petersburg, Russia)

Planar DC gas discharge system with high ohmic cathode

Retrieved from https://www.uni-muenster.de/~Physik.AP/Purwins/DC/index-en.html.

Experimentally Observed Patterns and

Oscillating Modes

•2D Patterns •Oscillating Modes

Retrieved from https://www.uni-muenster.de/~Physik.AP/Purwins/DC/index-en.html.

Retrieved from C. Strümpel, Yu. A. Astrov and H.G. Purwins, Phys. Rev. E, 65, 066210, 2002.

Governing Equations

•Boltzmann Equation

It is supplemented with Maxwell’s Equations.

•Zeroth moment produces the contiunity

equation:

•First moment produces the momentum

equation:

•Second moment gives the energy equation:

Drift-diffusion approximation

•Two-fluid equations with drift-diffusion

approximation

•To have a self-consistent model, Poisson’s

equation for electric potential is added

• and reduces

momentum equation into a simpler form

with

Simple Fluid and Extended Fluid Models

•Set of Equations

•Local-field approximation (LFA)

•By adding electron energy equation to

the simple fluid equations

where ,

•Local-mean-energy approximation (LMEA)

Simple Fluid Model Extended Fluid Model

Basic Plasma Chemical Reactions

Phelps and pitchford. http://www.lxcat.net.

•Discharge parameters:

p = 30 Torr, d = 1.4 mm, ,

•Verification of models were done in given

reference:

I. Rafatov, C. Yesil, "Transition from

homogeneous stationary to oscillating

state in planar gas discharge–

semiconductor system in nitrogen: Effect of

fluid modelling approach", Phys. Plasmas,

vol. 25, no. 8, pp. 082107, 2018.

Numerical modelling of the GDSS in nitrogen

Stationary

solution

Obtaining Stationary Solutions

Load Line:

Subnormal

Regime

CVC curve:

•Nonlinear oscillations occur in Subnormal Regime

•Plasma medium length is very small

Bifurcation diagram

of

vs.

•Stable and unstable regions

and signature of Hopf

bifurcation

•Different types of oscillations

limit cycle, period doubling etc.

•Points where chaotic

oscillations initiate

Chaos initiated

Chaos initiated

: limit cycle

: period-doubling

: oscillation with four period

: Chaos

*

vs. diagram

A B

c

D

AB C D

A: 665 V C: 725 V

B: 708 V D: 827 V

Lorenz map

•Lorenz maps (the (n + 1)th local

maximum of the discharge current j(t)

versus its nth maximum) obtained for the

regimes corresponding to voltages Ut =

665 V, 708 V, 725 V and 827 V.

•Showing universal trend but with

different current density values

Conclusion:

•Two developed one dimensional discharge models

- Simple Fluid approach

- Extended Fluid approach

•Two bifurcation diagrams are obtained

-Determination of locations

-Classification of oscillations

•Future works

- Lyapunov exponents

- 2D and 3D models