Multiscale modeling of PECVD generated Silicon films ... - Lammps

LAMMPS User Group MeetingAugust 7-8, 2013PECVD generated Silicon films withkinetic Monte Carlo and LAMMPSmolecular dynamicsDr. Andreas BickAlbuquerque, 2013

Motivation: Silicon is everywhere

Plasma Enhanced Vapor Deposition Chemical Reaction SiH 4-> Si + 2 H 2 Deposits thin films from a gas state (vapor) to a solid state on asubstrate Used for electronics, optoelectronics and photovoltaic applications Fast deposition at low temperatures Surface interactions and film growth not yet fully understood

Combine KMC and MDExperiment conditionsFullgrowthKMCStepwisegrowthKMCmap to atomisticmap to atomisticMDMDmap to KMCFilm properties

Kinetic Monte Carlo(n- fold method) Based on Diamond lattice Complex chemical reaction involving different radicalspecies Physisorptions & Chemisorptions of gas phase radicals Bulkilization of Hydrogen passivated Si Subsequent abstraction of surface atoms (Eley-Rideal HydrogenAbstractions) Surface diffusion of physisorbed radicals Two separate reaction steps (Decoupled diffusionmethodology) Diffusion (Markovian Random Walk) All the other reactions

Kinetic Monte Carlo(n- fold method) II At each step a complete list of possible reactions for allsurface sites is considered Reaction event j is randomly selected according to:Ri=M= ∑ i = 1ri∑i= j − 1i=jr( )i= 1 ii=1 i< ξ < 11R∑Rrwith the random number chi, the total number of possiblereactions per step M and the reaction rate r The time increment delta R is calculated asδ t = −ln( ξ )R22( )

KMC Results: Snapshot of KMC generated surface visualized in MAPS:

KMC Results: Surface thickness dependent on SiH content:5 % SiH 6 % SiH

KMC Results: Void distribution

Molecular Dynamics (LAMMPS) Newton’s equation of motionF =m a The force can be written as the gradient of the potentialenergyF =−∇ V Combine the two equations to getdVdr =−m d 2 rdt 2 A trajectory is obtained by solving this differentialequation NVT Simulations using the Nose Hover thermostat at 180K performed for this study

Tersoff Potential Bond Order Potential Strength of a chemical bond depends on the bondingenvironment, including the number of bonds and possiblyalso angles and bond length Exists in several modifications Implementation in LAMMPS needed modification to thefunctional form developed by Ohira( ) ⎡ ( ) ( )V = f r⎣a f r + b f rij C ij ij R ij ij A ijWhere the interaction parameter aij describes therepulsive Si-H interaction Implemented in LAMMPS for this project by Scienomics⎤⎦

Tersoff Potential Validation Reproducing structural characteristics: Si(100)–2x1 reconstruction Si(100)-2x1 reconstructed, H terminated Si-Si : 2.4 Å Si-H : 1.521 Å Si-Si-H : 111.9 degOhira et al, Phys. Rev. B, 52, 8283, 1995Ohira et al, Surface Science, 458, 216–228, 2000

LAMMPS MD Results: Convergence of total energy:Total Energy (MeV)-2.6-2.7-2.8-2.9-3.0-3.1Total Energy (MeV)-3.180-3.182-3.184-3.186-3.188DR=6%-3.1905.0 5.5 6.0 6.5time (ns)DR=6%Total Energy (MeV)-1.80-1.81-1.82Total Energy (MeV)-1.821-1.822-1.823DR=5%DR=5%-1.8246.0 6.5 7.0 7.5 8.0time (ns)-3.20 1 2 3 4 5 6 7time (ns)-1.830 1 2 3 4 5 6 7 8time (ns)

LAMMPS MD Results: Diffusion and Mean Square Displacement:4msd of film with DR=5%4msd of film with DR=6%3HSi3HSimsd2msd21100 2 4 6 8 10 1200 2 4 6 8 10 12t [ns]t [ns]DR = 5 % DR = 6 %

LAMMPS MD Results: Autocorrelation functions:1DR 5%1DR 6%ACF Si-Si0.90.82.0 A2.5 A3.0 A3.5 A4.0 A4.5 A5.0 A5.5 AACF Si-Si0.90.82.0 A2.5 A3.0 A3.5 A4.0 A4.5 A5.0 A5.5 A0.70 2 4 6 8 10 12 14 16t [ns]0.70 2 4 6 8 10 12t [ns]DR = 5 % DR = 6 %

LAMMPS MD Results: Bond Angle Distribution:0.6000Si-Si-Z angle : DR 5%0.0100Si-Si-Z angleP0.50000.40000.30000.2000P0.00800.00600.0040DR=5%DR=6%0.10000.00200.00000 20 40 60 80 100 120 140 160 180 200θ [deg]0.00000 20 40 60 80 100 120 140 160 180 200θ [deg]After MCAfter MD

LAMMPS MD Results: Bond Angle Distribution:

LAMMPS MD Results: Pair Correlation functions:

Figure 12 - Example Attack Tree for VPN partner connectionThe attack tree in Figure 12 is a horizontal tree that adheres to the guidelines discussed in the previoustree’s description. In this tree, the grey nodes are the conditional nodes of the tree, the red nodes areresultant conditions, green nodes are security controls and the orange nodes are threat actors/attackagents. This tree is shown as a comparison to the tree in Figure 11 – to illustrate the flexibility andcreativity possible with attack trees.Threat ProfilesFor the purposes of this paper, a threat profile is defined as a tabular summary of threats, attacks andrelated characteristics. The tabular format allows for a large degree of flexibility in terms of the columnsand rows selected for each profile. Threat profiles are an excellent tool for communicating the results ofcompleted threat models and/or attack trees. They also allow for consolidation, sorting, pivoting and othercommon data manipulation functions. Providing detailed descriptions of both the cause and effect ofthreats and attack vectors is an ideal use case for threat profiles.For comparison, some assessment practices use the term threat profile to describe a decomposition that ismuch more analogous to an attack tree [5], while others are more congruent with the description providedin this paper [13]. More recently, the term threat profile has been used in the development of cyber threatintelligence.Table 2 presents a generic threat profile template. Table 3, along with Listing 1, and Table 4 illustratecase study threat profiles. The differences in scope and applicability between Tables 3 and 4 are describedas follows: Table 3 is a more granular profile and Table 4 is an example of a large-scale, detailed analysispresented as a summarized and aggregate data set. These two examples demonstrate the flexibility andscalability of threat profiles.© Lockheed Martin Corporation19

LAMMPS MD Results: Local Growth Zone in some detail

LAMMPS MD Performance with modifiedTersoff potential: Execution time over 10000 MD steps System size 965902 atoms, 80000 fixed NVT with PBC in xand yExecution time (s)250020001500100050000 200 400 600 800 1000 1200Number of CoresParallel Efficiency (%)1009590850 200 400 600 800 1000 1200Number of Cores

Classical Engines & Tools in MAPS

Monte Carlo based Tools

Scienomics LAMMPS additions Tersoff with repulsive three body interactions(tersoff/rep) – will be committed soon Bond angle: fourier, fourier/simple, quartic Dihedral: quadratic, nharmonic Improper: fourier

Conclusions Silicon films growth by PECVD modeled using KMCcombined with MD With KMC: overcome the problem of multiple time scales of the reactionsinvolved in the process good qualitative prediction of the deposition rate for a range ofconditions good qualitative prediction of the final composition in H for a rangeof conditions Film thickness of several 10 nm simulated With the MD simulations we target: Relaxation of the films produced from KMC Gradual relaxation of the film as it is developed fro KMC Study the molecular mechanisms relevant to properties such ascrystallinity and surface roughness

Thank you for yourattentionContact:Andreas.Bick@scienomics.comVisit: www.scienomics.com