Self Consistent

A. Self - Consistent Fluid and hybrid Models in PTLUP

PTLUP has been involved to the development of  self-consistent fluid and hybrid models since 2001. The self-consistent approach is required in order to simulate plasma reactors were typical plasma diagnostics measurements cannot be applied as medium and industrial scaled systems.

Such types of models require a minimum number of inputs and counts for all physical and chemical processes that take place during the Plasma Processing of materials. PTLUP model involves the following modules:  

Flow module
Equations:                               Navier –Stokes
Results:                                   Flow field – Gas velocity – Gas density distribution
Time:                                      Slow step ~ 1-2 sec



Heat module
Equations:                                Heat conduction - convection – diffusion – radiation
Results:                                    Temperature and gas enthalpy maps
Time:                                       Slow step ~ 1-2 sec

Chemistry module
Equations:                                 Mass balance of species
Results:                                     Reactions rate, species density distribution, species flux towards surfaces
Time:                                       Intermediate step ~ 1 – 300 msec

Plasma Module
Equations:                                  Mass balance of electrons and ions, Energy balance of electrons and ions
Results:                                      Electrons and ions density distribution, ions flux towards surfaces, electron –  molecule collision rates
Time:                                         Fast step ~ 1-10 μsec

Electromagnetic module
Equations:                                   Poisson’s equation
Results:                                       Distribution of electrostatic field and voltage
Time:                                          Fast step ~ 1-10 μsec

The main problem of such type of simulation is the large scattering of time scales that are required for the convergence of the different modules and the extensive in some cases gas phase and surface chemistry of the processes. Advanced numerical algorithms are necessary for fast convergence while High Performance Computing systems and parallel processing are required especially in the case of industrial systems

PTLUP has already develop and use self-consistent model for the simulation of

- Amorphous and microcrystalline silicon deposition from SiH4/H2 plasmas
- Diamond-like thin film deposition from CH4/H2 discharges
- Treatment of polymers from He and He/O2 discharges

Typical steps that are required for the simulation of the plasma process are:

- Geometry creation and meshing
- Problem solution
- Post - Processing of the data


The model counts for flow, heat, chemistry, plasma and electromagnetism that produces outputs for all these modules

Characteristic example of flow in a PECVD reactor


Characteristic example of heating in a PECVD reactor


Characteristic example of plasma electrical properties in a PECVD reactor

Power dissipation


Electron flux


Characteristic example of species distribution in SiH4/H2 discharges

H atoms density distribution for different SiH4/H2 mixtures


picture1a            picture1b           picture1c         picture1d

                                                         1 % SiH4             2 % SiH4            3 % SiH4             4 % SiH4

Characteristic example of species distribution in SiH4/H2 discharges



Sheath expansion/contraction cycle in large area Argon CCP,

when electromagnetic (standing wave) effect is included:

- Electron density spatiotemporal mapping 

- Electric potential profile in the powered electrode and
axial electron density graphs.



Creation of detailed geometries and detailed meshing of simulated areas are extremely important for accurate solutions

PTLUP has years of experience in creating geometries of reactors either installed in the lab or of industrial and R/D partners

Examples of 2 and 3d geometries












For simulation of large area reactors and geometries above 0.5 Mcells parallel processing has been developed and problems are solved in cluster of PC's


64 cores are available of Intel® Xeon® Processor E5540 for modelling of large scale systems


Click here to download a presentation of the model

 Recent publications of the group related to self consistent modeling:

"Growth kinetics of plasma deposited microcrystalline silicon thin Flms",

Surf. Coat. Technol., Accepted for publication - Corrected Proofs,

E. Amanatides and D. Mataras ©


"Simulation of cylindrical electron cyclotron wave resonance argon discharges", 

S. Sfikas, E. Amanatides, D. Mataras and D.E. Rapakoulias

J. Phys. D - Appl. Phys., 44 (2011) 165204 ©


"Fluid Model of an Electron Cyclotron Wave Resonance Discharge

S. A. Sfikas, E. K. Amanatides, D. S. Mataras and D. E. Rapakoulias

IEEE Trans. Plasma Science 10.1109/TPS.2007.905946 Page(s): 1420-1425 (2007) ©


Simulation of The Electrical Poperties of SiH4/H2 RF Discharges

B. Lyka, E. Amanatides and D. Mataras

Jap. J. Appl. Phys. 45 (2006) 8172-8176 ©


"Relative importance of hydrogen atom flux and ion bombardment to the growth of μc-Si:H thin films"

B. Lyka, E. Amanatides and D. Mataras

Journal of Non-Crystalline Solids, 352 1049 2006 ©


"Plasma 2D modeling and diagnostics of DLC deposition on PET"

E. Amanatides, P. Gkotsis, Ch. Syndrevelis and D. Mataras

Diamond and Related Materials, 15 904 (2006) ©


"Plasma Enhanced Chemical Vapor Deposition of Silicon under Relatively High Pressure Conditions"

E. Amanatides, B. Lykas and D. Mataras

IEEE Trans. Plasma Sci. 33, 372 (2005)  ©


"Power consumption effect on the microcrystalline silicon deposition process: a comparison between model and experimental results" 

B. Lykas, E. Amanatides, D. Mataras, D. E. Rapakoulias 

J. Phys.: Conf. Ser. 10 (2005) 198-201 ©

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