Ab- initio calculation A.Mauri, N.Castellani*, D.Erbetta. * Mi- Bicocca Student
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1 Ab- initio calculation A.Mauri, N.Castellani*, D.Erbetta * Mi- Bicocca Student
2 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- body Schrödinger equation solution: Hatree- Fock Density functional Theory (LDA, CGA, hybrid method)
3 Ab- initio calculations A new time scale..for electronics industries Standard approach KMC approach Courtesy of: B.Civalleri
4 Used software Most of the software for DFT are university- type (some of them 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).
5 Software and super- computing All the previous sws require high parallization super- computing resources Our choice for super- computing is the ENEA cresco platform: Numonyx- farm is not suitable The CPMD software has been used as currently simulator
6 Physical problem The first applications is the study of Silicon nitride amorphous used for charge trapping devices
7 Pseudo- potential choice based on dimer Dimers Si- Si, N- N- SiN has been study in a isolated system The dimer total energy has been calculated to test wave function cutoff Functional chosen: Functional tested: Wave function optimization Geometrical optimization
8 Dimer energy v.s. distance Minimum of vibration energies have been calculated for the different dymer: Si- Si: A N- N: A Si- N: A
9 Silicon nitride crystalline phase Hexagonal Beta phase Hexagonal Alpha phase Crystal point group: c1 Crystal point group: c6h Lattice par.: a= Å, c= Å Lattice par.: a= Å, c= Å Unit cell: 28 atoms Unit cell: 14 atoms N.Ruddlesen Acta Crystal. (1958) 11,465
10 Silicon nitride super- cell Hexagonal Alpha phase Hexagonal Beta phase Number of unit cells: 8 Number of unit cells: 16 Total atoms: 224 atoms Total atoms: 224 atoms
11 G(r): beta phase Implemented sw to calculate Pair correlation function (i.e g(r)) from CPMD output data G(r) has been evaluated for beta phase for different temperature below the melting point
12 G(r): beta phase pbc p.b.c off p.b.c on To test g(r) we increased the considered cell volume: at long distance g(r) goes to 1 as expected G(r) has been evaluated with and without periodic boundary conditions
13 G(r): beta phase F.Alvaretz,.. Solid state com.(2003) 127,483 The calculated distances between the first and the second neighbours are in agreement with published data
14 RDF for beta phase Implemented sw to calculate Radial distribution function (i.e RDF) from CPMD output data RDF has been evaluated for beta phase for different temperature below the melting point (comparison with literature data not meaningful) T.Fukunaga,.. J.non.cystalline solid.(1987) 1119
15 Coordination number for beta phase Implemented sw to calculate coordination number (i.e CN) from CPMD output data CN has been evaluated for beta phase for different temperature below the melting point The number of first neighbour is in agreement with experimental data
16 Crystal vibrations
17 Angular distribution: beta phase Implemented sw to calculate angular distribution (i.e AD) from CPMD output data Comparison with experimental data is available only for the amorphous phase P.Kroll,.. J.non.cystalline solid.(2001) 238
18 Bands: beta phase R.Wang,.. Chin.Phys.Letters.(1993) 741 Implemented sw to calculate solid bands from CPMD output data Comparison with experimental data are in good agreement
19 Bands: alpha phase R.Shaposhnikov,., Phys.of the Solid states (2007) 1628 Good agreement found also for the alpha phase
20 DOS: beta phase K.Tastumi,.. PRB (2002) R.Wang,.. Chin.Phys.Letters.(1993) 741 Implemented sw to calculate DOS (density of states) from CPMD output data Comparison with published data are in good agreement Calculated band- gap: 4.33 ev
21 DOS: beta phase optimized non- optimized DOS as band structure depends of the optimized structure We have performed the test on beta phase structure
22 DOS: alpha phase Calculated band- gap: 4.9eV
23 Simulation of defects: Si vacancy Calculation of the defects formation energy We have estimated a formation energy in a perfect crystal for a silicon vacancy of: Ef = 3.1 ev
24 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 formation calculation): Si vacancy N vacancy Si interstitial N interstitial Calculation of the structural factor?
25 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 coefficient calculations is already developed) Quenched of the amorphous phase to generate defects
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