comparisons of dft-md, tb- md and classical md ... · comparisons of dft-md, tb-md and classical md...

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Comparisons of DFT-MD, TB-MD and classical MD calculations of radiation damage and plasma-wallinteractions

Kai Nordlund

Department of Physics and Helsinki Institute of Physics

University of Helsinki, Finland

Kai Nordlund, Department of Physics, University of Helsinki 2

Contents

0. Levels of molecular dynamics

1. Examples of comparisons of classical and

quantum mechanical methods

- Si: threshold displacement energy:

DFT-MD vs. classical

- Erosion and sticking of hydrocarbons in

fusion reactors:

TB-MD vs. classical


0. Levels of molecular dynamics

By increasing order of realism: Coarse-grained MD

- Multimillions of objects

- Now popular in biophysics

Classical (analytical potential) MD

- Hundreds of millions of atoms

- Dominating by scopes of use

Tight-binding MD

- ~ A few hundred atoms

- Has been used for some 20 years

Density-functional theory MD

- ~ One hundred atoms

- Use widely increasing now

Time-dependent density functional

theory MD

- ~ A few tens of atoms

- Practical uses limited so far

“True” Hartree-Fock ab initio

- ~ A few tens of atoms

- Practical uses limited so far

Relevant for

sputtering

simulations

But because

of need for

statistics,

classical still

dominates!

- Although

ideally

everything

better be done

by DFT MD…


Threshold displacement energy in Si

- Introduction

The threshold displacement energy

is the smallest amount of kinetic

energy needed to permanently

displace an atom from its lattice site

to an interstitial position

A vacancy is left behind so a Frenkel pair is produced

Mathematically, where p is the probability for displacement,

(α,φ) is the direction of recoils in spherical coordinates, T is

the energy of the recoil, and Td (α,φ) is the threshold energy

surface in 3D:

Typically Td ~ 10 - 50 eV



- Introduction

Minimum vs. average threshold displacement energy:

Direction-specific

thresholds: Td,100, Td,110, …

Average threshold

displacement energy:

Minimum threshold

displacement energy:

- Usually in one of principal directions

<100>

<111>:

B Open

A Closed

<110>

AVERAGE

,min min ( , )d dT T

,ave ave ( , )d dT T



Introduction: why?

Why does Td matter?

It is the single most important quantity in determining

radiation damage in solids

It determines directly the number of Frenkel pairs created

NFP by high-energy electron irradiation

It is also used to estimate the damage caused by neutron

and ion irradiation via the Kinchin-Pease/NRT equation:

From here also the “displacement-per-atom” (dpa) value is

obtained

It is the threshold for vacancy production in TRIM/SRIM

,

Nuclear deposited energy0.8

2FP

d ave

NT



Introduction

Why study Td in silicon?

Silicon is the foundation for

the semiconductor industry,

where ion implantation is the most

commonly used doping method

Silicon appears in many other

applications, where radiation

is omnipresent (radiation

detectors, sensors, etc.)

In spite of this, Td is poorly known

There is even confusion

between the minimum and

average of Td



Introduction

Why use molecular dynamics (MD) to study Td?

The threshold displacement energy is difficult to determine

experimentally: The experimental methods, which

practically all rely on electron irradiation, cause problems in

interpreting the results (spreading of the beam, isolated

defects vs. clustered defects, annealing of damage etc.)

MD (=simulation of atom motion) can determine it directly

without these problems

Why use Density Functional Theory (DFT) to study Td?

The choice of classical MD potentials is a source of

considerable deviation in the results – values range around

10 – 23 eV

DFT is a quantum mechanical, more basic level of theory



Simulation methodology

DFT MD is veeery slow

Hence we took a 4-step approach:

1. Use classical MD in very large systems (thousands of

atoms) for long times (~ 10 ps) to find a reliable value

within the model used:

Two widely different potentials: Stillinger-Weber and Tersoff

2. Scale down the system size and simulation time in the

classical as much as possible while checking that the result

does not change too much in either model

3. Find minimal basis set in DFT which keeps point defect

energies ~ unchanged

4. Use DFT MD with the minimal system size and basis set to

get a more reliable value of Td



Simulation methodology

Choose a random direction (α,φ), set E = E0 (8 eV)

Simulate a recoil in the direction (α,φ) with energy E

Frenkel pair formed?

E = E + ΔE

NO

Threshold energy in the direction (α,φ) found

YES



Simulation methodology: scaling results

Results of the classical

scaling tests:

Natoms

has to be > 100

We chose 144 atom

periodic non-cubic cell

Simulation time was

similarly optimized

Time has to be >= 3 ps

We chose 3 ps



II. Simulation methodology:

DFT Parameter Scanning

The general parameters of the

dynamical simulation were now

optimized

The next step was to optimize

the DFT parameters

The goal was to find one suitable

LDA set and one suitable GGA set

Criteria for a suitable set:

Reasonable calculation time (a few days per recoil simulation)

Good energetics for the basic point defects

The DFT code we used was SIESTA

Final sets:

LDA: SZ, 4 k points, 100 Ry cutoff, Ceperley-Alder

GGA: SZ, 4 k points, 250 Ry cutoff, Perdew-Burke-Ernzerhof



Results

Formation of close FP in closed 111 direction:



Results

Recombination effects are major:

110 direction, 20 eV



The DFT simulations

Our goal was to find the average

threshold displacement energy

of silicon within a statistical

error limit of 2 eV

The average threshold energy in

the LDA scheme

40 random directions for A

40 random directions for B

The GGA scheme was used to

confirm the average obtained by

LDA

10 random directions for A

10 random directions for B





The DFT simulations: Results

Two surprising effects were observed:

A large fraction of defects

formed were IV pairs

(= Bond Defects, BD)

These usually formed at

lower E‟s than Frenkel pairs

Big difference to classical MD

Majority of „real‟ Frenkel pairs

contained a tetrahedral rather

than a dumbbell interstitial

Explanation: Frenkel pair

with tetrahedral interstitial

lower in E



The DFT simulations: Results

Results for minimum threshold:

DFT: Td, min = 12.5 ± 1.5SYST eV, open 111 direction

Experiment: Td, min = 12.9 ± 0.6 eV, 111 direction

Excellent agreement!

This gave us great confidence that we can reliably predict

the average threshold displacement energy

Results for average threshold:

Counting IV pair or Frenkel pairs:

- LDA DFT: Td, ave = 24 ± 1STAT

± 2SYST

eV

- GGA DFT: Td, ave = 23 ± 2STAT

± 2SYST

eV

Counting only Frenkel pairs:

- LDA DFT: Td, ave = 36 ± 2STAT

± 2SYST

eV

- GGA DFT: Td, ave = 35 ± 4STAT

± 2SYST

eV

[Loferski and Rappaport, Phys. Rev. 111 (1958) 432]



How good are the classical models?

We also compared the classical potentials systematically

with the quantum mechanical ones

=> Stillinger-Weber (SW) does best of the classical

potentials

[E. Holmström et al, Phys. Rev. B 78, 045202 (2008)]



3D displacement energy surface

The classical models have sufficient statistics that we can

plot the full 3D displacement energy surface Td (α,φ)

Minimum in all around open 111 direction

Maximum in all around <144> directions

(~ 45o off closed 111)

A bit below straight impact to

2nd-nearest neighbor from A



Conclusions

There are considerable differences between DFTMD and

classical MD results of the threshold displacement energy

in Si

Even qualitative: the large production of Bond Defects is not

reproduced by any of the classical potentials

Even so, classical MD can help DFT-MD:

Use first classical MD to determine acceptable system size

and simulation conditions for DFT!

[E. Holmström et al, Phys. Rev. B 78, 045202 (2008)]


And now…

Let's switch gears…


Erosion of carbon in fusion reactors

Erosion of hydrocarbons: classical vs. TB

In 1999-2001 we

showed that the

athermal part of

the carbon

erosion can be

explained by the

swift chemical

sputtering

mechanism

Athermal, rapid,

endothermal

[Salonen et al, Europhys. Lett. 52 (2000)

504; Phys. Rev. B 63 (2001) 195415]


Erosion of carbon in fusion reactors

Comparison of classical vs TB MD

Results of

comparison:

Exactly same

simulation cell,

about 200 atoms

Relaxed in each

model before

bombardments


Sticking of radicals on dangling bonds

Introduction: Radicals in the reactor

The MD simulations show both CHx and C2Hy erosion

As well as larger hydrocarbons

Fraction depends on surface structure and ion energy

Experiments show that ”CH3 and C2H2 are the most

abundantly sputtered species from plasma-facing carbon

materials in fusion devices”

[E Vietzke and A. A. Haasz, in Physical Processes of the Inaction of Fusion Plasmas with Solids, Chap. 4 (1996)]



Methods

We have carried out simulations of radical sticking

We have limited ourselves to model surfaces with a well-

defined dangling bond nature (or lack of it)

Classical:

Brenner (1st generation) potential with bond conjugation

terms

- But cutoff extended to 2.46 Å (this reproduces better the

diamond-to-graphite phase transition [Nordlund et al, PRL

77, 699 (1996)] )

Tight-binding:

Density-functional based tight-binding model of Frauenheim

et al.

Implemented into our own code as force model



Sticking of CH3: dependence on db

neighbourhood

7 DB: sticking cross section =

average area per surface site,

5.9 Å2



Sticking of CH3: angular dependence

We find a major dependence of the sticking probability

vs. distance from unsaturated carbon site at different

angles of incidence of CH3

angles of incidence

[Träskelin et al, J. Appl. Phys. 93, 1826 (2003)]



Sticking of CH3: animation of TB case



Sticking of CH3: model dependence

There is a model dependence between the TB and

classical results

TB likely to be more reliable

[Träskelin et al, J. Nucl. Mater. 334, 65 (2004).)]



Sticking of CH3: comparison to experiments

and analytical model

The TB results are in excellent agreement with

experiments

Angular dependence can be explained by a simple

analytical model

[Träskelin et al, J. Nucl. Mater. 334, 65 (2004).)]



Sticking of C2Hx

We have also studied the sticking of C2Hx molecules on

similar model surfaces

Incoming molecule equilibrated at 300 or 2100 K

Surface at 0 K initially



Animation...

C2H2 on 7db

surface



Results at 300 K, 1db surface

Sticking

probability

decreases with

increasing

amount of H

atoms

Not surprising

at all => more

H makes them

less chemically

reactive

[Träskelin, J. Nucl. Mater. 375, 270 (2008)].



Results at 2100 K, 1db surface




Comparison of results with amount of H

What is very

interesting is that

the sticking

cross section is

non-monotonous

with x in C2Hx

Reason: basic

chemistry: odd x

are radicals,

even x not!

x = Number of H atoms

Sti

ckin

g c

ross

sec

tion

(Å

)




New results: DFT MD of hexane on Si

C6H14 deposition on

Si (100) surface

No sticking because of

no dangling bonds in

molecule



Conclusions

Our results show that hydrocarbon sticking on dangling

bonds in carbon-based materials is:

Not so sensitive to the incoming molecule temperature

Somewhat sensitive to the simulation model used

Very sensitive to the dangling bond neighbourhood

Very sensitive to the incoming angle

Very sensitive to the number of hydrogens in the molecule


Conclusions

- Overall conclusions

Classical interatomic potentials can easily have

systematic errors

DFT-MD starts to be of practical value now w.r.t. sticking

and reflection calculations

But will remain out of reach for larger systems for years

DFT checks and calibrations of classical MD a good way to

assess their reliability

comparisons of dft-md, tb- md and classical md ... · comparisons of dft-md, tb-md and classical md...

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