This Example is based on the understanding of the DSMC example, so look at this one first.

In this example, we simulate the plasma flow through an A700V sputtering chamber provided with a PK750 magnetron. We have a 2D-model of the chamber and a 3D-model of the magnetron (see Fig. 1).

Figure 1: 2D-model of an A700V sputtering chamber & 3D-model of a PK750 magnetron

Unzip a700v_pk750.zip in the same directory. The file contains the GMSH models for this example.

Create a parameter file:

$ initpicmc a700v

Edit the “a700v.par”-file.

First we need a good time resolution for the plasma simulation:

DT       = 5e-11;
TSIM     = 10e-6;

Set the workmode to plasma simulation:

WORKMODE = 1;

We have to adjust the power dissipation:

PSOLL = 10/750;

This corresponds to 10 W distributed over 750 mm target length. We simulate only a 1mm-slice of the target, so the power dissipation has to be adjusted accordingly. Since we want to simulate a plasma, we need some particles:

SPECIES = ["Ar", "Arplus", "e"];

The “NREAL”-parameter is the factor between the number of simulated and real particles and the “P0”-parameter is the pressure (for neutral particles like Ar) or the initial density (for charged Particles like Ar+ and e-). The appropriate “NREAL_Ar”-parameter can be calculated (formula further down, because it depends on other parameters). Possible values for the other parameters are:

NREAL_Ar     = 5e9;
P0_Ar        = 0.5;
NREAL_Arplus = 1e5;
P0_Arplus    = 1e13;
NREAL_e      = 1e5;
P0_e         = 1e13;

Depending on what plots you are interested in, insert the species into the desired category:

NUMBER   = ["Arplus", "e"];
DENSITY  = ["Arplus", "e"];
PRESSURE = ["Ar", "Arplus", "e"];
VELOCITY = ["Arplus", "e"];

The unit of the mesh geometry depend on the person who generated the mesh file. In our case it is in [m], so the 1.0 is ok. The extent of the bounding box is calculated automatically from the a700v.msh-file, but we have to adjust the cell spacing. The bounding box has a volume of 360*105*1 mm³. For a simulation with a reasonable plasma density, a cell dimension of 1x1x1 mm³ is appropriate. We also segment the total volume into subvolumes, to speed up the simulation, because the calculation can be parallelized. A possible cell resolution with 12 subvolumes (4x3x1) looks like:

NX   = [90, 90, 90, 90];
NY   = [35, 35, 35];
NZ   = [1];

Since we have a 2D-xy-model of the sputtering chamber, we have to change the border types in z-direction:

TYPE_z1 = "periodic";
TYPE_z2 = "periodic";

We also want so simulate the magnetic field, so the mesh file for the PK750 magnetron is needed:

BEMMESH  = "pk750-single_standard_unbalanced.msh";

Now we need to specify the reactions wich occour on our surfaces. Additionally the wall of the sputtering chamber should be set to ground potential:

Border Wall = {
   ⋮
  vf = "0";
  reactions: {
    add_absorption("Arplus", 1.0);
    add_absorption("e",      1.0);
  };
};

If the simulated substrate should be an insulator instead of a metal, e.g. a glass:

Border Substrate = {
   ⋮
  epsr = 6.0;
  reactions: {
    add_absorption("Arplus", 1.0);
    add_absorption("e",      1.0);
  };
};

The voltage function of the target T1 should be set to “-VP”, which is an internal variable. In the actual example the second target is not powered, so it gets the same parameters as the chamber wall:

Border T1 = {
   ⋮
  vf = "-VP";
  reactions: {
    add_plain_reaction("Arplus", 1, 1, ["Ar", "e"], [1, 0.1]);
    set_emission_energy("e", 0, 5, 1);
    add_absorption("e",      1.0);
  };
}; 
 
Border T2 = {
   ⋮
  vf = "0";
  reactions: {
    add_absorption("Arplus", 1.0);
    add_absorption("e",      1.0);
  };
};

As mentioned above, the “NREAL_Ar”-parameter has to be calculated, depending on some other parameters. The number of particles in each cell, has a big impact on the simulation time. A good benchmark are ca. 20 simulated particles/cell. Depending on the Ar pressure (P0_Ar = 0.5 Pa), temperature (T0 = 300 K) and the cell dimension (1x1x1 mm³) you can calculate the number of real particles per cell and then adjust the “NREAL-Ar”:

Create a template for the magnetic fieldsolver:

$ initbfield a700v

Edit the “a700v.bem”-file. The relative permeabilities of the three domains (vacuum, magnets and yoke) can stay the same:

Domains = [1, 1.05, 1000];

Then you have to define and correlate all physical surfaces. The “val”-parameter is the magnetic remanence value. The “domain”- and “neighbourdomain”-parameter correspond to the above defined domains. The bottom of the inner and outer magnet are connected to the yoke and all other surfaces are connected to vacuum:

Boundary Outer_Magnet_Top    = {icodec = 1; type = "interface"; val = -1.40;  domain = 1; neighbourdomain = 0;};
Boundary Outer_Magnet_Bottom = {icodec = 2; type = "interface"; val =  1.40;  domain = 1; neighbourdomain = 2;};
Boundary Inner_Magnet_Top    = {icodec = 3; type = "interface"; val =  1.40;  domain = 1; neighbourdomain = 0;};
Boundary Inner_Magnet_Bottom = {icodec = 4; type = "interface"; val = -1.40;  domain = 1; neighbourdomain = 2;};
Boundary Magnet_Skin         = {icodec = 5; type = "interface"; val =     0;  domain = 1; neighbourdomain = 0;};
Boundary Yoke                = {icodec = 6; type = "interface"; val =     0;  domain = 2; neighbourdomain = 0;};

A complete version of the model including both parameter files can be found here.

Start the computation with n processes. In our case with n = 12 just enter:

$ rvmmpi -bem 12 a700v

In the output look for the following lines:

MASTER <- {BEM 10}:     [MESSAGE]        domain:   2 checksum:  1.0319e-13
MASTER <- {BEM  6}:     [MESSAGE]        domain:   1 checksum: -5.0333e-13
MASTER <- {BEM  1}:     [MESSAGE]        domain:   0 checksum:  1.2566e+01

For all areas the sum should be exactly 4π = 12.5664 or 0 (round-off errors like 1e-12 are ok).

Start the simulation with n processes (n may not exceed the number of subvolumes). In our case with n = 12 just enter:

$ rvmmpi -picmc 12 a700v

The plasma in a 2D set-up is not coupled and thus, more sensitive to the anode configuration. With the substrate on ground potentialthe right plasma is as bright as the left one (see figure 1).

Substrate on ground potential

Figure 1: Electric potential (left) and electron density (right) during simulation with substrate on ground potential (0 V).

Here the left plasma is conductively connected to the ajacent chamber wall, the right one however is connected with the top of the chamber wall. Thus, with the substrate on floating potential some of the anodic surface is shielded causing the right plasma to fade (see figure 2). Due to the uncoupled electron drift current in a 2d setup this effect is even more pronounced. Thus, if using constant power the voltage can drop below ignition point causing the right plasma to diminish.

Substrate on floating potential

Figure 2: Electric potential (left) and electron density (right) during simulation with substrate on floating potential.

As seen in the pictures below we get some anomalies if using our coater geomtry settings together with a balanced magnetron. A spacing of 1 mm between target and dark space shielding causes an distortion of the electric field. Thus, we get an extensive electric field strength parallel to the target surface. Thus, electrons are shifted sideways in the magnetic confinement and can escape more easily. Therefore excessively high voltages are needed to get a self sustaining plasma which is even so quite unstable.

Short-circuit with the edge of the dark space shielding

Figure 1: Electric potential (left) and electron density (right) during simulation with balanced magnetron.

Short-circuit with the edge of the dark space shielding

Figure 2: Electron density overlayed with electric potential (left) and magnetic field By (right) isolines.