Molecular dynamic simulation study of plasma etching L1 FePt media in embedded mask patterning (EMP) process

EMP process is proposed to enable ultra-small HAMR media grains by defining isolated L1₀-FePt grains through a granular hard-mask layer using ion-assisted methanol plasma etch process.¹ In our previous modeling of EMP process, we applied a levelset analytic model with Langmuir surface kinetics to study ion and neutral effect in patterning Ru hard-mask and FePt media grains.^2,3 We also found that it is critical to minimize the hard-mask erosion by reduce the ion sputtering yield on the hard-mask and to maximize the chemical etch selectivity between hard-mask and FePt media, in order to successfully define the nano-meter scaled FePt grains. For example, we showed that using He etch gas would reduce the hard-mask erosion by 1-2 orders of magnitude than using Ar gas, giving the promise to improve the etch process capability to nanometer scale. Furthermore, we would like to study the magnetic property change of remaining material that has been exposed to energetic particles (ions) and neutral etchants, which the analytic continuum model is unable to answer. Classical Molecular Dynamics (MD) simulation has been used to understand the ion sputtering and surface reaction kinetics during etching process.^9,12–14 In MD model of etch process, substrate atoms, etchant particles (ions) and neutrals (molecules) are constructed in one ensemble with defined interatomic potentials. The time evolution of these particles are tracked and updated via solution of Newton’s equation of motions. MD simulation has been used extensively in semiconductor research. Okada et al. have applied MD simulation to study plasma induced defects (PID) in reactive ion etch process in Ar-Si/SiO₂ system.¹³ They found the damaged layer thickness inside Si substrate is proportional to ion energy level to the 0.3 power. Barone et al. performed MD study of Si etch of F+ as well as Cl+ ions¹⁴ and characterized both physical sputtering and chemical sputtering process. Nakazaki et al. also performed MD simulation in study Si etching in Cl₂ and Br based plasma etch process,¹² with both Cl+/Br+ ions as well as Cl and Br neutrals in the same simulation process. Many-body Stillinger-Weber interatomic potential, which takes the form of summation of total 2-body and 3-body interatomic potential, is used in Si/SiO₂ etch process with halogen etch gas.^12–14 Moliere-type repulsive pair potential has been employed to account for Ar-Si^9,12,13 interactions. Recently Brault et al. studied the atomic processes of Pt sputtering with high energy Ar ions (500-1Kev range)⁹ in LAMMPS⁸ simulator, using embedded-atom method (EAM)⁴ potential (for Pt-Pt bond energy) and Moliere pair-potential (for Ar-Ar and Ar-Pt interactions). Their study found that sputter yield of Pt increases with Ar ion energy and the slope is in a good agreement with results from the Yamamura analytic model.^10,11

Our objectives are to construct a plasma etch MD model to study the interaction mechanism between gas ions (i.e. Ar or He ions) or neutral radicals (i.e. CH₃, H, CO in methanol plasma) and Fe-Pt media atoms including sputtering yield and etch rate, and material changes including amorphized surface layer and interstitial defects inside FePt lattice. We also want to compare the MD results with the conclusions made earlier with our analytic model,^2,3 particularly on the difference of Ar and He effect on sputter yield. In this report, we will focus on ion-metal impact (physical sputtering) study and we will update our research progress on neutral etch model in future publication. We use MD simulation tool LAMMPS to carry the modeling. LAMMPS stands for “Large-scale Atomic/Molecular Massively Parallel Simulator”. It is a classical MD code originally developed and maintained by Sandia National Labs.

The initial structure contains 20 mono layers (MLs) of atoms stacking alternatively of Fe and Pt layers with (002) planes in c-axis. Lattice parameters are a=3.861A and c=3.788A.⁷ as shown in Figure 1. Total number of atoms is 3800 (1900 each for Fe and Pt). The X-Y atomic footprint is 38nm x 38nm, or 1444nm² of top surface area. The bottom 4 layers are fixed to prevent these atoms translating into free space from the bottom direction. Atoms in the next 6 layers upwards are “thermostated” to maintain the system at the set temperature 300K.¹² The 10 MLs above the thermostat layer are “mobile” layers that are only constrained through interatomic metallic bonds. The source of etch ion particles is confined in a 3D “slab” about 5A above the top surface. In the sputter simulation with Helium ions we constructed a “deeper” structure with 20 mobile layers instead 10 used in simulation with Ar ion, considering He ions could travel deeper into crystal as the nuclear stopping power is lower for He ions. This will be discussed in more details later in Section III.

Many-body Embedded-Atom Method⁴ (EAM) interatomic potential is used for modeling metallic Fe-Fe, Pt-Pt and Fe-Pt interactions. Compared to pair potential, EAM provides better description on metallic bonds and it includes both pair-potential energy term and the embedding energy from the surrounding atoms. EAM defined as:⁴ 

where $ϕ(Rij)$ is the atom i to atom j pair potential, $Fi(ρh,i)$ is the embedding energy of atom i into the background electron density ρ, and $ρja$ is the electron density contributed by atom j. EAM potential for single metal elements are readily available from first-principle DFT calculations⁴ but difficult to obtain for metal alloys. Johnson⁵ and later, Zhou⁶ have developed a fitting method to determine EAM potentials for binary alloy atomic interactions directly from their mono-atomic potentials. The detailed method of creating EAM function on binary alloy can be found in reference 5 and 6. Figure 2 shows the computer generated EAM potential values as function of interatomic distance for Fe-Fe, Pt-Pt and Fe-Pt atoms using Johnson-Zhou alloy EAM model. It should be noticed that because EAM solution for L1₀-phase FePt is not readily available, we applied Johnson-Zhou EAM model only as a close mathematical approximation of Fe-Pt interatomic interactions in a 1:1 atomic ratio alloy form, instead of actual representation of L1₀-phase FePt lattice. For instance, with Johnson-Zhou EAM model, the calculated equilibrium atomic distances between the nearest neighboring Fe and Pt atom model is 0.2905 nm, compared to experimental L1₀-phase lattice parameters⁷ 0.2704 nm between Fe and Pt atoms. The solution of more accurate EAM potential specifically for L1₀-phase FePt will be addressed in our future study.

Ziegler-Biersack-Littmark (ZBL) screened nuclear repulsion is chosen for description of ion-metal interactions. ZBL potential is commonly used to describe high-energy collisions between atoms. In LAMMPS, ZBL potential form defined below as the product of Coulombic repulsion and screening function. Values of parameters are A=0.4685, B=0.23, C₁=0.18175, C₂=0.509, C₃=0.28022, C₄=0.02817, D₁=3.1998, D₂=0.94229, D₃=0.40290 and D₄=0.20162.

R_ij is the interatomic distance between atoms i and j, Zi, Zj are atomic numbers of the two interacting atom types, i.e. 2 for He, 18 for Ar, 26 for Fe and 78 for Pt. ZBL potential for He-Fe, He-Pt, Ar-Fe and Ar-Pt are plotted in Figure 3 in log-scale. To compare to ZBL potential to other pair potential forms, “12-6” Lennard-Jones (LJ) pair potential functions for ion-ion and ion-metal interactions. LJ has been used to describe van der Waals non-bonding potential in inert gases and molecular systems.¹⁵ LJ “12-6” pair potential is expressed as the following formula with two material-dependent LJ parameters:

where ε is often referred as “bond energy” and σ equals to interatomic distance R_ij when potential diminishes to zero. Using “Lorentz-Berthelot” combining rule shown in Equation (4) below, we can obtain LJ potential function on binary interaction from their mono-atomic LJ parameters.

LJ parameters for mono-atomic interaction and binary interactions are listed in Table I.

Simulation scripts were run on a 64-bit Windows LAMMPS simulator under non-MPI computing mode. Ion flux density is assumed to be larger than 10mA/cm² or no more than one ion impact onto the FePt top surface area per nanosecond. Brendesen temperature control is used in “thermostated” layer for heat removal with coupling time constant set to 300 femtoseconds. To ensure enough time thermal relaxation and reasonable computation speed, we set up total 500 ion injection at rate of one in every 500 time-steps with each time-step size is one femtosecond. Observed temperature readings in the “thermostated” layer range about +/-5K around the set value of 300K. Hybrid pair potential option in LAMMPS is used to incorporate many-body EAM potentials between metal atoms and ZBL or LJ potentials for ion-metal atoms. Ion injections along normal incidence (-Z direction) are initiated from the 3D box source placed above the surface. Specific kinetic energies are given to these ion particles. Range of ion velocities are given as set value of $V=2*Ekm$ where E_k is chosen at 50ev, 100eV,150eV, 200eV and 250eV respectively, and with 10% variation range. m is the atomic mass for injected Ar or He ions. Ejected parts are allowed to go out of the simulation space so that the number of atoms remained in the FePt lattice and number of atoms sputtered off can both be clearly counted. Snapshots of entire ensemble atom positions during the run are saved to data “dump” file for post-run analysis in MATLAB. Ovito¹⁹ and VMD²⁰ are used for post-run visualization.

The main results of simulation are shown in Fig. 4–11. Fig. 4 shows the cross-section view of the FePt lattice structure after 500 Ar ion impacts and Fig. 5 shows that after 500 He ion impacts, both under different kinetic energy ranges from 50 to 200 eV. Cross-sections of lattice under 250eV ion impacts are not included in the figures. Fig. 6 shows that number of amorphized atom layers increases significantly with Ar ion kinetic energy. The amorphous layer thickness reaches from 4 mono-layers (or °7.6A) at 50eV to 14 mono-layer (or ∼2.7nm) under Ar ion energy at 250eV. This amorphous layer will be considered losing almost all magneto-crystalline anisotropy (MCA). However, with He ions there are only one amorphized surface layer shown within the same energy range.

Sputter yields are shown in Fig. 7 and 8 respectively for both Ar and He with 50-250eV kinetic energy using LJ “12-6” potential and KBL potential for ion-metal interactions. With ZBL potential, it is shown a reasonable increasing trend of sputter yield vs. ion energy for both Ar and He. The sputter yield numbers can be seen closely matched to empirical model results^10,11 on Ar-Pt and He-Pt impact, shown in Fig. 9. On the contrary, calculation with LJ “12-6” potential shows unrealistically high sputter yield (0.57 for He and 0.9 for Ar) even at 50eV, compared to the experimental results. Therefore, LJ potential function cannot be used to accurately represent the interactions between ions and metal atoms.

Interstitial defects also important as embedded ion particles travel into the FePt lattice and causes lattice displacement or vacancy defects. These defects can significant change the local MCA, as MCA of L1₀-FePt strongly depends on the consistent lattice parameters such as a, c and c/a ratio. Maximum depth measurement of ions found inside the lattice vs. ion energy is shown in Fig. 10 for both Ar and He impacts. It shows defect depth of He ions is significantly higher than Ar within the ion energy range. This can be understood as the ZBL potential shown in Figure 3 also indicates the nuclear stopping power of FePt crystal to injected particles. ZBL potential of Fe or Pt for He is almost one order of magnitude lower than that for Ar, giving the result of higher depth of embedded He ions inside FePt lattice.Fig. 11 shows the number of embedded particles after 500 ion impacts. For Ar, this number increases with ion energy. However, for He the counts is in the opposite direction from Ar ions. This is likely an artifact related to the limited simulation X-Y-Z space as He ions are more likely to escape from the sides and uncounted from the lattice structure due to their low stopper power.

A L1₀-phase FePt-ion MD simulation model is constructed in LAMMPS to simulate energetic Ar and He ion impacts to FePt media using EAM interatomic potentials generated from Johnson-Zhou’s alloy EAM model. Sputter yield results showed in close agreement with result from empirical model with ZBL potential to describe the ion-metal interactions. We found within energy range from 50-250eV, He ions cause almost no amorphized (i.e. magnetically damaged) surface layer while Ar ions can cause significant surface amorphous layer (or “magnetic dead layer”), from ∼7.6 A at 50eV to as much as ∼2.7nm at 250eV in thickness only after 500 ion impacts. Simulation also shows that He ions can readily travel into FePt lattice as the nuclear stopper power of He ions is far smaller than that of Ar ions, results in deeper and likely more embedded He ions inside FePt lattice. Such interstitial defects can still cause more pinning sites and local MCA and magnetization loss. In the future research, we will study and integrate the neutral-ion and neutral-metal interactions to the existing MD model.