『はじめてのVASP 原理から使用法，適用例まで』

1 VASP .. 23 11 8 .. 1 2.. 2.. 5.. 7.. 7.. 7.. 8.. 8.. 9. 2 12.. 12. SiO2 E-V .. 14.. 14. Si O .. 16. ZrCr2 Laves phonon .. 18. SiC .. 20. SiC C .. 22. SiC .. 24.. 24.. 24. P B Si .. 27.. 29. 1. 3 VASP 33.. 33. VASP .. 33. E-V .. 35. Linux .. 38.. 41. INCAR .. 41. POSCAR .. 45. KPOINTS .. 48. POTCAR .. 48.. 49.. 49. DOS .. 50. DOS .. 50. 4 , 53. GUI VASP MedeA .. 53. MedeA .. 53.. 53.. 57. spin .. 58. Phonon .. 61. 1 .. Schro dinger .. adiabatic approximation . Schro dinger . H = . ( ). d + V = (1). dx (Hamiltonian:H) (wave function: ) . (energy Eigen value: ) (Kinetic Energy). (d /dx) (V ) . (potential:V ) (nuclear potential) ( exchange-correlation interaction) . 2.. (1) .. self consistent loop . 1: .. Full Potential . pseudo potential 2 PseudoP . ultra soft, norm (.)

2 (Atomic Orbital) (Plane Wave) 2 . AO (Linear Combination) LCAO, . PW (augument) APW (Linearlized) . AO PW Mu n Tin Orbital . FP All Electron . AE Projector augmented Wave Pseudo P . (Local Density Approxima- tion) (Generalized Gradient Approximation) . version Perdew-Wang 91 . (Van der Waals) . GGA GW . GW G . W . 3. PW (k-space) . (Fast Fourier Transformation) . (real space) . PW (periodic boundary condition) .. PseudoP+PW . FP+LAPW .. 4.. orbital orbit( ) (tal) .. 2 .. 2: . 2 VASP . 2 . 2 2 . s 1 . 2 . (Molecular Orbital) . (energy level) (bonding energy level, E + ) (antibonding energy level, E ) .. E = E + |h|S 4h2 + E 2 (2). E 2 h . (bond integral) S (overlap integral) E 2 .. 2 .. 2 . 2 2 .. Etotal = 2 EAB (1 EA + 1 EB ) (3). 5. E .. (total energy).. (formation energy: H).

3 A B .. Etotal = Ei ni (4). i (i) (Ei ) (ni ) . ni 0. (Highest Occupied MO), . (Lowest Unoccupied MO) . 0 (zero point, level) .. Mu n Tin .. 2 1023 .. (Valence Band) . (Conduction Band) (band gap:Eg ) .. EF. Etotal = En(E)dE (5).. EF Fermi n(E) . (Density Of States) . (dielectrics) . (bound) (localized) AO (unbound, extended). PW Na (simple metals) . (transition metals) . (dielectric polarization) . (spontaneous polarization) . ( Madelung energy) . (Ewald method, sum) . (screening e ect) .. 6.. (perfect lattice) (stability) . (relaxation) .. (unit cell).. (defect) (microstructure) .. 0 (point) (vacancy) (substitutional) (inter- stitial) .. (lattice) (tetragonal site) . (octahedral site) (bond center) .. 1 (dislocation) . (edge) full relax . extra half plane .. (screw).

4 Exible boundary condition .. 2 (stacking fault) (surface) (interface) . 2 . (slab) . (polarized plane) (non-polarized plane) . (surface reconstruction) .. (coherent interface) . ( 3, 5 ) . (tilt) (twist) 2 .. (ground states) ( nite temperature) . 7. (formation enthalpy: H) . A + B AB (6). 2 .. A B (segregation limit) . phonon (vibrational e ect) (time constant) . (force constant) phonon . (pseudo harmonic oscillator approximation) (thermal expansion) . (con guration) 2 . Bragg-Williams 3 4 . (cluster variation method) . CALPHAD .. (di usion) (activation energy, barrier) (path) . (saddle point) . nudged elastic band . (nucleation) .. phase eld . ( rate-determining step control mechanism ) (additives) . 8.. E-V E V (energy-volume curve) 3 Si E V . E V . B . V . 1 d2 E.

5 B= (7). V dV 2.. E V . 3: Si E-V (energy-volume curve ) .. 4 .. (force) . 9. cell .. 4: .. (adiabatic potential surface) .. 4 a,b,c 3 3 b .. Si . ( ) 5 9 .. 6 .. 5: Si 6: . 9 .. Force . 10.. 11. 2 .. Zincblende (ZB) Wurtzite (WZ) WZ ZB . 0 ZB WZ EZB-WZ . 7 0 . e* WZ c/a . 7: 0 (a) e* (b)WZ c/a . III-V II-VI ZB WZ . VASP EZB-WZ WZ c/a . ZB WZ . 1000eV . 8 0 EZB-WZ . 0 EZB-WZ .. 2 CdSe . VASP .. 9 EZB-WZ WZ c/a . EZB-WZ WZ c/a ZB . c/a = WZ . 12. 7(b) 0 c/a 8 0 EZB-WZ . 0 EZB-WZ ZB WZ . EZB-WZ c/a . 8: ( 0 ) ZB WZ ( E ZB W Z ) . 9: ( E ZB W Z ) WZ c/a . [1] S. Takeuchi, and K. Suzuki, Stacking Fault Energies of Tetrahedrally Coordi- nated Crystals, Phys. Stat. Sol., (a) 171 (1999), 99-103. 13. SiO2 E-V . VASP E-V . SiO2 10 SiO2 . Stishovite . SiO4 . 2 18 SiO2 . [1] Cristobalite Tridymite 2.

6 [2]. 10: SiO2 . 11(a) VASP SiO2 E-V .. Stishovite .. VASP E-V . dE Q W . dE = Q W (8). Q = 0 Wrev = P dV . dE = P dV (9). P . dE. P = (10). dV. (10) E-V . 2 E-V . 14. 11: SiO2 E-V . a 8 E-V . b stishovite coesite coesite low quartz . 11(b) Stishovite Coesite Low Quartz E-V . E-V eV/A GPa . 1[GPa] = [eV/A ] (11). Stishovite Coesite Coesite Low Quartz E-V ,- (11) 1 .. 1: 2 . [GPa] [GPa][3]. Stishovite Coesite Coesite Low Quartz . [1] , . , ( . 1995) . [2] . ,( 2003) . [3] . ,( 1968) . 15. Si O . VASP (IBRION) .. (P1 ) .. Si O . O Si-Si (o -center) . O Si Si8 . 3 2 2x2x2 64 . Si-Si 1 12(a) . O Si-Si . 111 Si-Si site1 9 . 12(b) Si-Si 1/8. O Si 8.. 12: Si O (a) Si (b) O . 13(a) site1 3 7 9 ( ) ( . ) ( ) ( ) 9 . site1 2 4 5 .. 13(b) 5 O site1 2 4 5 . 25 13(a) . site . 13(c) 13(c).

7 13(b),(c) Si-Si site1 . 16. 13: O a . b site1 . 2 4 5 c (b). 3.. site2 4 . site5 . Si-Si . 1/8 . Si . Si . VASP 12(b) site1 . VASP . 17. ZrCr2 Laves phonon .. AB2 ZrCr2 Laves 14. ZrCr2 Laves MgCu2 (C14) MgZn2 (C15) , MgNi2 (C36) 3 . 15 C15 C36 C14 . [?] . 14: ZrCr2 Laves . 15: Zr-Cr .. Phonon-DOS ?? Phonon-DOS . 18.. Phonon-DOS C36 .. 16 C15 C15. C14 15 1800. 1900 K C36 . 16: ZrCr2 Laves .. [1] J. Pavlu, J. Vrestal, , Stability of Laves Phases in the CrZr System , CALPHAD- COMPUTER COUPLING OF PHASEDIAGRAMS AND THERMOCHEMISTRY, 2009. 19. SiC . MedeA-Phonon .. 3C 4H-SiC. MedeA-Phonon . 3C-SiC c/a = 1 4H-SiC hexagonal . c/a VASP . c/a = ( 2) 3C-SiC . 4H-SiC a c . MedeA-Phonon . 3C-SiC a c . 4H-SiC a c .. a c .. 17 3C-SiC . a/a0 a0 .. 17: 3C-SiC . 18 4H-SiC a c . (a/a0 , c/c0 )=( , ) (a)500K.

8 (b)1000K (c)1500K 3C-SiC .. 20. 18: (a) 500K (b) 1000K (c)1500K 4H-SiC . 19 17 18 (a)3C (b)4H-SiC .. 19: (a)3C-SiC (b) 4H-SiC . 21. SiC C .. SiC C .. SiC . (Metastable Solvent Epitaxy) Si 4H-SiC. 20 MSE 4H-SiC {0001} C-face Si-face MSE C. Si C . C .. 20: 4H-SiC (a) Si-face (b) C-face . 21(a) Si-face . (b) C-face 3 C . C .. 22 Si-face C-face C . 3 C 2 1 2 1. 3 Si-face C-face . C-face .. face . 22. 21: 4H-SiC (a) Si-face (b) C-face C . 22: (a)Si-face (b)C-face C . 23. SiC .. slab . (surface reconstruction) . SiC (0001) .. SiC h0001i Si C . (0001) (0001 ) . 23 Si ( . coverage ratio) Si .. 23 Si = . Si C 1:1 .. 23: Si Si Si-rich C-rich . Si = a-type b-type .. Si-C 24 . Si100% C100% SiC 1:1 . Si C SiC . 24. SiC line compound . SiC Si . 2 A . ( Si , C ) SiC Si . Si-rich.

9 24: Si-C Si100 % C100 % . SiC 1:1 . SiC . Si(Si-rich) = Si(bulk). C(Si-rich) = C(bulk) + Hf (12). Hf SiC [eV/SiC pair] SSi(bulk) Si . C(bulk) C C-rich .. C(C-rich) = C(bulk). Si(C-rich) = Si(bulk) + Hf (13).. Si-rich C-rich . ESiC(suface) Si C nSi , nC . ESiC(suface) = ESiC(slab) nSi Si(bulk) nC ( C(bulk) + Hf ) (Si-rich). ESiC(suface) = ESiC(slab) nSi ( Si(bulk) + Hf ) nC C(bulk) (C-rich) (14). Si C-rich, Si-rich . C-rich Si . Si . 25. Si-rich C-rich SiC . 25 (112 0), (11 00) (0001) Si C . (a) Si-rich 3C 4H 6H . (0001) (b) C-rich . Si-rich (0001) .. 25: SiC . 26. P B Si . 2 .. (P) Si . [1] 26 week beam . stacking fault energy dopant P dopant . stacking fault energy B . dopant P .. 073514-2 Ohno et al. J. Appl. Phys. 108, 073514. 091915-2 Ohno et al. P. FIG. 1. Color online TEM images of a dissociated dislocation in Si; doped with P with a concentration of 3 1019 cm 3, tan = a and b h or c nondoped tan = h.

10 The left, center, and right images in each figure 073514-3 are, Ohno respectively, et with the reflection g = 02 2 , 22 0 , and 202 . A J. Appl. Phys. 108. double arrowhead in b indicates a P agglomerate. The structural nature of Color online A TEM image of the node between a dissociated each dislocation in a c is schematically shown in d . segment and a constricted one; with a 90 edge or b 60 segregation energy results from electronic effects. Indeed, orientation. III. RESULTS p-type and isoelectronic dopant atoms did not affect the The inset in each figure shows a schematic view of the geometry stacking of faultthe energy Fig. 3 , even though it is suggested Effects of annealing on the structural nature of disloca- that those atoms also segregate nearby dislocations.