Iain D. Boyd and Brandon SmithDepartment of Aerospace Engineering

University of MichiganAnn Arbor, MI 48109

Molecular Dynamics Simulation of Sputtering and Pathway for

Use in Thruster and Plume Analyses

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

• 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

Modeling Approach

• 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 Interaction

• Repulsion and attraction terms

B-N Potential

• Bond bending and stretching terms– Attraction term modifier

– Sum over all three-body sites

– Bond bending term

– Bond stretching termi

j

kjik

rik

rij

k'k''

BN Bond Modeling

• 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

Xe-B/N Interaction

• 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 inthe lateral directions

– bottommost layerkept immobile toprevent translation

BN Structural Model

• 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

BN Surface Topology

Sputtering Event

Sputter Yield

Tw=423 K; Xe+: =45 deg.

Reflected Xe Properties

Tw=423 K; Xe: =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+