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Ab- initio calculationA.Mauri, N.Castellani*, D.Erbetta

* Mi- Bicocca Student

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Copyright 2008 Numonyx B.V.

Introduction

Ab initio calculations can be used to: Determine material structural properties Study defects in material Study molecular dynamics in general (reactions, stoichiometry

etc) Ab- initio can be applied to:

Crystalline material

Amorphous material Ab- initio is a general identification for methods of a multi- bodySchrdinger equation solution:

Hatree- Fock

Density functional Theory (LDA, CGA, hybrid method)

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Ab- initio calculations

A new time scale ..for electronics industriesStandard approach

KMC approach

Courtesy of: B.Civalleri

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Used software

Most of the software for DFT are university- type (some ofthem are not free of charge)

Most common software: Quantum espresso (Theoretical school of Trieste SISSA) CPMD, CP2K (ETH Zurigh_ _ > Parriniello) VASP (univeristy of Vienna) Ab- init (Catholique Un. of Belgium) Gaussian (commercial tools).

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Software and super- computing

All the previous sws require high parallizationsuper- computing resources

Our choice for super- computing is the ENEAcresco platform: Numonyx- farm is not suitableThe CPMD software has been used as currentlysimulator

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Physical problem

The first applications is the study of Silicon nitrideamorphous used for charge trapping devices

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Pseudo- potential choice based on dimer

Dimers Si- Si, N- N- Si-N has been study in aisolated system

The dimer total energyhas been calculated to

test wave function cut-off

Functional chosen:

Functional tested:

Wave function optimization Geometrical optimization

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Dimer energy v.s. distance

Minimum of vibration energies havebeen calculated for the different dymer:

Si- Si: 2.359 A N- N: 1.105 A

Si- N: 1.645 A

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9/25Copyright 2008 Numonyx B.V.

Silicon nitride crystalline phase

Hexagonal Beta phase

Crystal point group: c6h

Lattice par.: a= 7.606 , c= 2.909 Unit cell: 14 atoms

Hexagonal Alpha phase

Crystal point group: c1

Lattice par.: a= 7.753 , c= 5.618 Unit cell: 28 atoms

N.Ruddlesen Acta Crystal. (1958) 11,465

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Silicon nitride super- cell

Hexagonal Beta phase

Number of unit cells: 16

Total atoms: 224 atoms

Hexagonal Alpha phase

Number of unit cells: 8

Total atoms: 224 atoms

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G(r): beta phase

Implemented sw to calculate Paircorrelation function (i.e g(r)) fromCPMD output data

G(r) has been evaluated for betaphase for different temperaturebelow the melting point

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G(r): beta phase pbc

To test g(r) we increased the considered cell volume: at long distanceg(r) goes to 1 as expected

G(r) has been evaluated with and without periodic boundary conditions

p.b.c off p.b.c on

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G(r): beta phase

The calculated distances between the first and the second neighbours arein agreement with published data

F.Alvaretz,.. Solid state com.(2003) 127,483

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RDF for beta phase

Implemented sw to calculate Radialdistribution function (i.e RDF) fromCPMD output data

RDF has been evaluated for betaphase for different temperaturebelow the melting point (comparisonwith literature data not meaningful)

T.Fukunaga,.. J.non.cystalline solid.(1987) 1119

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Coordination number for beta phase

Implemented sw to calculatecoordination number (i.e CN) fromCPMD output data

CN has been evaluated for betaphase for different temperaturebelow the melting point

The number of first neighbour is inagreement with experimental data

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Crystal vibrations

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Angular distribution: beta phase

Implemented sw to calculate angulardistribution (i.e AD) from CPMD outputdata

Comparison with experimental data isavailable only for the amorphous phase

P.Kroll,.. J.non.cystalline solid.(2001) 238

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Bands: beta phase

Implemented sw to calculate solid bands from CPMD output data

Comparison with experimental data are in good agreement

R.Wang,.. Chin.Phys.Letters.(1993) 741

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Bands: alpha phase

Good agreement found also for the alpha phase

R.Shaposhnikov,. , Phys.of the Solid states(2007) 1628

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DOS: beta phase

K.Tastumi,.. PRB (2002) 165210

Implemented sw to calculate DOS (density of states) from CPMD outputdata

Comparison with published data are in good agreement

Calculated band- gap: 4.33 eV

R.Wang,.. Chin.Phys.Letters.(1993) 741

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DOS: beta phase

DOS as band structure depends of the optimized structure

We have performed the test on beta phase structure

optimized non- optimized

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DOS: alpha phase

Calculated band- gap: 4.9eV

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Simulation of defects: Si vacancy

Calculation of the defects formation energy

We have estimated aformation energy in a perfec

crystal for a silicon vacancyof:

eVEf 1.3=

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Crystal simulations

We have planned the following simulations for beta phase MD at 900C and 1500C (..g(r), angular distribution) MD of the liquid phase T> 1900C (..g(r), angular distribution)

Defects study in a perfect crystal (geometry optimization, energy formationcalculation):

Si vacancy

N vacancy

Si interstitial

N interstitial

Calculation of the structural factor?

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Amorphous simulations

We have planned the following simulations for amorphous phase MD of the liquid phase T> 1900C (..g(r), angular distribution)

Study of Si and N diffusion in a liquid (sw for diffusion coefficientcalculations is already developed)

Quenched of the amorphous phase to generate defects

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