Size dependence of the bulk modulus of semiconductor nanocrystals from first-principles calculations

Physical Review B - Condensed Matter and Materials Physics

Volumn 82, Issue 23, 2010, Pages

  Cherian, R ^a,e   Gerard, C ^a,b   Mahadevan, P ^a   Cuong, Nguyen Thanh ^c   Maezono, Ryo ^d  

^a S N BOSE NATIONAL CENTRE FOR BASIC SCIENCES   (India)

^b INDIAN INSTITUTE OF SCIENCE   (India)

^c NATIONAL INSTITUTE OF ADVANCED INDUSTRIAL SCIENCE AND TECHNOLOGY AIST   (Japan)

^d JAPAN ADVANCED INSTITUTE OF SCIENCE AND TECHNOLOGY   (Japan)

^e MAX PLANCK INSTITUT FÜR FESTKÖRPERFORSCHUNG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78650916685     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.82.235321     Document Type: Article

References (52)

1. M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, Phys. Rev. Lett. 65, 96 (1990) 10.1103/PhysRevLett.65.96
2. J. R. Heath, Science 270, 1315 (1995). 10.1126/science.270.5240.1315
3. Y. Kayanuma, Phys. Rev. B 44, 13085 (1991) 10.1103/PhysRevB.44.13085
4. M. B. Mohamed, C. Burda, and M. A. El-Sayed, Nano Lett. 1, 589 (2001) 10.1021/nl0155835
5. J. Hu, L. Li, W. Yang, L. Manna, L. Wang, and A. P. Alivisatos, Science 292, 2060 (2001) 10.1126/science.1060810
6. A. Shabaev and Al. L. Efros, Nano Lett. 4, 1821 (2004) 10.1021/nl049216f
7. M. Simurda, P. Nemec, F. Trojanek, K. Neudert, T. Miyoshi, K. Kasatani, and P. Maly, Physica E 36, 205 (2007). 10.1016/j.physe.2006.10.018
8. M. Reibold, P. Paufler, A. A. Levin, W. Kochmann, N. Pätzke, and D. C. Meyer, Nature (London) 444, 286 (2006). 10.1038/444286a
9. C. Q. Chen, Y. Shi, Y. S. Zhang, J. Zhu, and Y. J. Yan, Phys. Rev. Lett. 96, 075505 (2006). 10.1103/PhysRevLett.96.075505
10. Z. Wang, K. Tait, Y. Zhao, D. Schiferl, C. S. Zha, H. Uchida, and R. T. Downs, J. Phys. Chem. B 108, 11506 (2004). 10.1021/jp048396e
11. Z. Wang, S. K. Saxena, V. Pischedda, H. P. Liermann, and C. S. Zha, Phys. Rev. B 64, 012102 (2001). 10.1103/PhysRevB.64.012102
12. S. H. Tolbert and A. P. Alivisatos, Science 265, 373 (1994) 10.1126/science.265.5170.373
13. S. H. Tolbert and A. P. Alivisatos, Annu. Rev. Phys. Chem. 46, 595 (1995) 10.1146/annurev.pc.46.100195.003115
14. J. Z. Jiang, L. Gerward, D. Frost, R. Secco, J. Peyronneau, and J. S. Olsen, J. Appl. Phys. 86, 6608 (1999) 10.1063/1.371631
15. J. Z. Jiang, L. Gerward, R. Secco, D. Frost, J. S. Olsen, and J. Truckenbrodt, J. Appl. Phys. 87, 2658 (2000). 10.1063/1.372235
16. S. H. Tolbert and A. P. Alivisatos, J. Chem. Phys. 102, 4642 (1995). 10.1063/1.469512
17. G. Ouyang, W. G. Zhu, C. Q. Sun, Z. M. Zhu, and S. Z. Liao, Phys. Chem. Chem. Phys. 12, 1543 (2010). 10.1039/b919982a
18. R. E. Miller and V. B. Shenoy, Nanotechnology 11, 139 (2000). 10.1088/0957-4484/11/3/301
19. G. M. Dalpian, M. L. Tiago, M. L. Puerto, and J. R. Chelikowsky, Nano Lett. 6, 501 (2006). 10.1021/nl0525094
20. R. Cherian and P. Mahadevan, Phys. Rev. B 76, 075205 (2007). 10.1103/PhysRevB.76.075205
21. K. Shiraishi, J. Phys. Soc. Jpn. 59, 3455 (1990). 10.1143/JPSJ.59.3455
22. G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11169 (1996) 10.1103/PhysRevB.54.11169
23. G. Kresse and J. Furthmüller, Comput. Mater. Sci. 6, 15 (1996). 10.1016/0927-0256(96)00008-0
24. G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999). 10.1103/PhysRevB.59.1758
25. The thickness of the vacuum was determined by evaluating total-energy differences for smaller unit cells as a function of the vacuum layer. The total energies by themselves do not converge fast enough but the differences converge fast.
26. The convergence with respect to k points was tested by increasing the mesh density from 8 × 8 × 8 to 12 × 12 × 12. The total energies changed by 0.02 meV.
27. C. B. Barber, D. P. Dobkin, and H. T. Huhdanpaa, ACM Trans. Math. Softw. 22, 469 (1996). 10.1145/235815.235821
28. F. D. Murnaghan, Proc. Natl. Acad. Sci. U.S.A. 30, 244 (1944). 10.1073/pnas.30.9.244
29. B. L. Hammond, W. A. Lester, Jr., and P. J. Reynolds, Monte Carlo Methods in Ab Initio Quantum Chemistry (World Scientific, Singapore, 1994).
30. GAUSSIAN 03, REVISION E.01, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery, Jr., T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez, and J. A. Pople, Gaussian, Inc., Wallingford CT (2004).
31. M. Burkatzki, C. Filippi, and M. Dolg, J. Chem. Phys. 129, 164115 (2008). 10.1063/1.2987872
32. R. J. Needs, M. D. Towler, N. D. Drummond, and P. López Ríos, J. Phys.: Condens. Matter 22, 023201 (2010). 10.1088/0953-8984/22/ 2/023201
33. N. D. Drummond, M. D. Towler, and R. J. Needs, Phys. Rev. B 70, 235119 (2004). 10.1103/PhysRevB.70.235119
34. N. D. Drummond and R. J. Needs, Phys. Rev. B 72, 085124 (2005). 10.1103/PhysRevB.72.085124
35. P. Vinet, J. H. Rose, J. Ferrante, and J. R. Smith, J. Phys.: Condens. Matter 1, 1941 (1989). 10.1088/0953-8984/1/11/002
36. R. Maezono, A. Ma, M. D. Towler, and R. J. Needs, Phys. Rev. Lett. 98, 025701 (2007). 10.1103/PhysRevLett.98.025701
37. F. Birch, Phys. Rev. 71, 809 (1947). 10.1103/PhysRev.71.809
38. C. Kittel, Introduction to Solid State Physics, 8th ed. (Wiley, New York, 2005).
39. S. Adachi, J. Appl. Phys. 58, R1 (1985). 10.1063/1.336070
40. R. W. G. Wyckoff, Crystal Structures (Interscience, New York, 1963), Vol. 1.
41. Crystal and Solid State Physics, edited by, O. Madelung, Landolt-Börnstein, New Series, Group III (Spinger, Berlin, 1984).
42. H. J. McSkimin, A. Jayaraman, and Jr. Andreatch, J. Appl. Phys. 38, 2362 (1967). 10.1063/1.1709884
43. O. Madelung and M. Schultz, Landolt-Börnstein, New Series, Group III Vol. 22 (Springer-Verlag, Berlin, 1987).
44. H. Sowa, Solid State Sci. 7, 1384 (2005). 10.1016/j.solidstatesciences. 2005.09.003
45. G. Simmons and H. Wang, Single Crystal Elastic Constants and Calculated Aggregrate Properties: A Handbook, 2nd ed. (MIT Press, Cambridge, 1971).
46. W. A. Harrison, Electronic Structure and Properties of Solids (Freeman, San Fransico, 1980).
47. X.-P. Li, D. M. Ceperley, and R. M. Martin, Phys. Rev. B 44, 10929 (1991). 10.1103/PhysRevB.44.10929
48. D. Alfè, M. J. Gillan, M. D. Towler, and R. J. Needs, Phys. Rev. B 70, 214102 (2004). 10.1103/PhysRevB.70.214102
49. R. Maezono, N. D. Drummond, A. Ma, and R. J. Needs, Phys. Rev. B 82, 184108 (2010). 10.1103/PhysRevB.82.184108
50. M. L. Cohen, Phys. Rev. B 32, 7988 (1985). 10.1103/PhysRevB.32.7988
51. R. Cherian and P. Mahadevan, Appl. Phys. Lett. 92, 043130 (2008). 10.1063/1.2839372
52. J. Z. Jiang, J. S. Olsen, L. Gerward, and S. Mørup, Europhys. Lett. 44, 620 (1998). 10.1209/epl/i1998-00563-6