where rpbnew is the post-collision value of the accumulated variable,
rpb is the pre-collision value,
R is a source term, and
V is the mesh element length (in 2D) or surface area (in 3D). Each of the accumulated variables in this section is defined by the physical quantity that it represents and the expression for its source term.
The Surface Charge Density feature adds an accumulated variable for the charge density
σ (SI unit: C/m
2) on a set of boundaries that the particles hit. The source term for this accumulator type is
where e = 1.602176634 × 10-19 C is the elementary charge and
Z (dimensionless) is the charge number of the incident particle.
The Current Density feature adds an accumulated variable for the current density of the incident particles on a set of boundaries.
If the Type is set to
Normal current density, the accumulated variable is the normal current density
Jn (SI unit: A/m
2), and the source term is
If the Type is set to
Current density, one accumulated variable is defined for each component of the current density vector
Js. The source term for the
ith component is
where v (SI unit: m/s) is the incident particle velocity.
The Heat Source feature adds an accumulated variable for a heat source
Q (SI unit: W/m
2) equal to the total kinetic energy of the incident particles. The source term is
where frel (SI unit: 1/s) is the effective frequency of release of the incident particle and
E (SI unit: J) is the kinetic energy of the incident particle.
The Etch feature uses accumulated variables to calculate the etch rate due to physical sputtering as energetic ions hit a surface. The dependence of the sputtering yield on the energy of particles and their angle of incidence has been described by Yin and Sawin (
Ref. 13) and by Guo and Sawin (
Ref. 14).
If the Plasma type is
Collisionless, then the number of real ions represented by each model particle can be deduced directly from the particle release feature via the effective frequency of release. A single accumulated variable
EE is defined for the etch rate on the surface (SI unit: m/s). The corresponding source term is
If the Plasma type is
Collisional, the effective frequency of release is no longer a reliable indicator of the incident charged particle current. Instead, incident particles in each boundary element are assigned a weighting factor
Γi (SI unit: 1/(m
2·s)), defined as
where the numerator n · Ji (SI unit: A/m
2) is the normal current of charged particles at the surface. Usually the incident current from a collisional plasma is computed using the Plasma Module. The sum in the denominator is taken over all particles that hit the
ith boundary mesh element. The etch rate in this element is then defined as