Download John T. Yim, Michael Keidar, and Iain D. Boyd

Molecular Dynamics Simulation of
Sputtering and Pathway for
Use in Thruster and Plume Analyses
Iain D. Boyd and Brandon Smith
Department of Aerospace Engineering
University of Michigan
Ann Arbor, MI 48109
Background (1)
• Electric propulsion (EP):
– being implemented in various forms by DOD, NASA,
and industry for several functions
– due to lower thrust compared to chemical propulsion
systems, EP thruster operation time requirements are
much longer (e.g. 10,000 hours)
Background (2)
• EP thruster erosion:
– arises from accelerated ions
impacting thruster walls and
causing sputtering
– leads to beam divergence
and performance degradation
– can lead to thruster failure
– enormously expensive to
study experimentally
Sputter Modeling
• Objective:
– to accurately calculate sputter yields for boron nitride
under low energy xenon ion impacts
• Motivation:
– erosion of BN channel walls is main life-limiter for Hall
thrusters
– no measurements of sputter yield exist for BN at
Xe+ energies below 100 eV
– this region of the sputter yield profile has a large
influence on Hall thruster erosion
Modeling Approach
• Binary collision approximation (BCA)
– Monte-Carlo approach to model molecular systems
– not well suited for low-energy regimes
– sputter yields highly sensitive to binding energy
• Molecular dynamics (MD)
– slower than BCA method
– provides greater accuracy and more detail
B-N Interaction
• Boron nitride interatomic potentials
– modified version of Tersoff potential proposed by
Albe et al.
•
•
•
•
•
rij is the distance between particle i and particle j
fc is a cutoff function which limits the interaction range
fR is the repulsive component of the force
fA is the attractive component of the force
bij incorporates bond stretching and bending terms
B-N Potential
• Repulsion and attraction terms
BN Bond Modeling
• Bond bending and stretching terms
– Attraction term modifier
j
– Sum over all three-body sites
rij
– Bond bending term
jik
i
k
rik
– Bond stretching term
k''
k'
Xe-B/N Interaction
• Xenon ion interatomic potential
– Purely repulsive shielded Molière potential
• aF is the Firsov screening length, based on Bohr radius
– Purely repulsive force is acceptable since
van der Waals interaction of Xe with B or N is much
weaker than the strength of BN covalent bonds
BN Structural Model
• Consider hexagonal BN:
– has structure akin to graphite: hexagonal sheets
– 5200 boron and nitride atoms modeled as 13 10x10
hexagon sheets in a 4.3 nm x 4.2 nm x 2.5 nm box
– periodic boundary
conditions applied in
the lateral directions
– bottommost layer
kept immobile to
prevent translation
BN Surface Topology
• Amorphized layer:
– after a number of ion impacts, the near surface region
of the BN block becomes amorphized
– reduces effect of crystal orientation on sputtering
– once a steady state is reached,
generate sputter yield
statistics beginning from
this state instead of
starting from initial
ordered structure
Sputtering Event
Sputter Yield
Tw=423 K; Xe+: =45 deg.
Reflected Xe Properties
Tw=423 K; Xe: e=50 eV, =45 deg.
Pathway for Analysis
Of Thruster and Plume
• Large computational database to be generated:
– variation of xenon impact energy and angle
– output of nonequilibrium probability density functions:
• properties of reflected xenon particles (accommodation)
• properties of sputtered products (B, N, BN, etc.)
• required for use in thruster plasma analysis simulations
• also needed for plume contamination assessment
• Validation:
– measurements of differential sputter yield (Yalin, CSU)
– need to characterize nonequilibrium material effects
– measurements of BN plume transport (Gallimore, UM)
Plume Simulation
BN
Xe+