Strain field calculations in embedded quantum dots and wires

Journal of Computational and Theoretical Nanoscience

Volumn 4, Issue 4, 2007, Pages 715-738

  Maranganti, Ravi ^a   Sharma, Pradeep ^a,b  

^a UNIVERSITY OF HOUSTON   (United States)

^b University of Houston   (United States)

Author keywords

Elasticity; Inclusion; Quantum dot; Quantum wire; Size dependent; Strain

Indexed keywords

CRYSTALLOGRAPHY; ELASTICITY; INCLUSIONS; NANOCRYSTALS; NANOWIRES; NUMERICAL METHODS; QUANTUM THEORY; SEMICONDUCTOR QUANTUM WIRES; STRAIN; WIRE;

ANALYTICAL EXPRESSIONS; ATOMISTIC SIMULATIONS; CONTINUUM ELASTICITY THEORY; ELASTIC NON-LINEARITY; EMBEDDED QUANTUM DOTS; NON-LOCAL ELASTICITIES; SIZE DEPENDENT; SIZE-DEPENDENT EFFECT;

SEMICONDUCTOR QUANTUM DOTS;

EID: 60649101141     PISSN: 15461955     EISSN: None     Source Type: Journal    
DOI: 10.1166/jctn.2007.2359     Document Type: Review

References (198)

1. Y. Arakawa, IEEE J. Sel. Top. Quantum Electron. 8, 823 (2002).
2. S. Nakamura, S. Pearton, and G. Fasol, The Blue Laser Diode: The Complete Story, Springer, Berlin (2000).
3. D. G. Deppe and D. L. Huffaker, Appl. Phys. Lett. 77, 3325 ( 2000).
4. P. Bhattacharya and S. Ghosh, Appl. Phys. Lett. 80, 3482 (2005).
5. T Lundstrom, W. Schoenfeld, H. Lee, and P. M. Petroff, Science 286, 2312 (1999).
6. Y. Chye, M. E. White, E. Johnston-Halperin, B. D. Gerardot, D. D. Awschalom, and P. M. Petroff, Phys. Rev. B 66, 201301 (2002).
7. P. M. Petroff, Top. Appl. Phys. 90, 1 (2003).
8. P. Alivisatos, Quantum Electronics and Laser Science Conference (QELS 2000). Technical Digest. Post conference Edition. TOPS 40, 86 ( 2000).
9. P. Bhattacharya, A. D. Stiff-Roberts, S. Krishna, and S. Kennerly, Int. J. High Speed Electronics and Systems 12, 969 (2002).
10. J. Tersoff, C. Teichert, and M. G. Lagally, Phys. Rev. Lett. 76, 1675 (1996).
11. D. Bimberg, Semiconductors 33, 951 (1999).
12. D. Bimberg, M. Grundmann, and N. N. Ledentsov, Quantum Dot Heterostructures, Wiley, New York (1998).
13. J. O. Winter, T. Y. Liu, B. A. Korgel, and C. E. Schmidt, Adv. Mater. 13, 1673 (2001).
14. J. C. Chen, A. M. Chang, and M. R. Melloch, Phys. Rev. Lett. 92, 176801 (2004).
15. I. L. Medintz, A. R. Clapp, H. Mattoussi, E. R. Goldman, B. Fisher, and J. M. Mauro, Nat. Mater. 2, 630 (2003).
16. L. B. Freund and H. T. Johnson, J. Mech. Phys. Solids 49, 1925 ( 2001).
17. H. T. Johnson and L. B. Freund, Int. J. Solids. Struct. 38, 1045 (2001).
18. E. P. O'Reilly, Semicond Sci. Technol. 4, 121 (1989).
19. E. P. O'Reilly and A. R. Adams, IEEE J. Quantum Electron. 30, 366 (1994).
20. A. Alizadeh, P. Sharma, S. Ganti, S. F. LeBoeuf, and L. Tsakalakos, J. Appl. Phys. 95, 8199 (2004).
21. P. Harrison, Quantum Wells, Wires and Dots: Theoretical and Computational Physics, Wiley, New York (2000).
22. J. Singh, Physics of Semiconductors and Their Heterostructures, McGraw-Hill College, New York (1992).
23. M. Yang, J. C. Strum, and J. Provost, Phys. Rev. B 56, 1973 ( 1997).
24. M. S. Miller, J.-O. Malm, M. E. Pistol, S. Jeppesen, B. Kowalski, K. Georgsson, and L. Samuelson, J. Appl. Phys. 80, 3360 (1996).
25. G. S. Solomon, J. A. Trezza, A. F. Marshall, and J. S. Harris, Jr., Phys. Rev. Lett. 76, 952 (1996).
26. Q. Xie, A. Madhukar, P. Chen, and N. P. Kobayashi, Phys. Rev. Lett. 75, 2542 (1995).
27. M. Grundmann, O. Stier, and D. Bimberg, Phys. Rev. B 52, 11969 ( 1995).
28. M. Moreno, A. Trampert, B. Jenichen, L. Daweritz, and K. H. Ploog, J. Appl. Phys. 92, 4672 (2002).
29. A. Lenz, R. Timm, H. Eisele, Ch Hennig, S. K. Becker, R. L. Sellin, U. W. Pohl, D. Bimberg, and M. Dahne, Appl. Phys. Lett. 81, 5150 ( 2002).
30. J. D. Eshelby, Proc. R. Soc. London, Ser. A 241, 376 (1957).
31. J. D. Eshelby, Proc. R. Soc. London, Ser. A 252, 561 (1959).
32. J. D. Eshelby, Progress in Solid Mechanics, edited by 1. N. Sneddon and R. Hill, North Holland, Amsterdam (1961), Vol. 2.
33. S. Nemat-Nasser and M. Hori, Micromechanics: Overall Properties of Heterogeneous Solids, Elsevier Science Publishers, Amsterdam (1999).
34. L. D. Landau and E. M. Lifsthitz, The Classical Theory of Fields: Butterworth-Heinemann, Oxford (1980), Vol. 2.
35. T. Mura, Micromechanics of Defects in Solids, Martinus Nijhoff, Dordrecht, The Netherlands (1987).
36. O. D. Kellogg, Foundations of Potential Theory, Dover, New York (1954).
37. D. H. Armitage and S. J. Gardiner, Classical Potential Theory, Springer, London (2000).
38. A. Blech and E. S. Meieran, J. Appl. Phys. 38, 2913 (1967).
39. S. M. Hu, J. Appl. Phys. 50, 4661 (1979).
40. A. Fischer and H. Richter, Appl. Phys. Lett. 61, 2656 (1992).
41. P. A. Kirkby, P. R. Selway, and L. D. Westbrook, J. Appl. Phys. 50, 4567 (1979).
42. S. Christiansen, M. Albrecht, H. P. Strunk, and H. J. Meier, Appl. Phys. Lett. 64, 3617 (1994).
43. J. Massies and N. Grandjean, Phys. Rev. Lett. 71, 1411 (1993).
44. F. Glas, J. Appl. Phys. 70, 3556 (1991).
45. M. Grundmann, O. Stier, and D. Bimberg, Phys. Rev. B 52, 11969 ( 1995).
46. J. Y. Marzin and G. Bastard, Solid State Commun. 92, 437 (1994).
47. C. Priester, I. Lefebvre, G. Allan, and M. Lannoo, Mechanisms of Thin Film Evolution, MRS Symposia Proceedings 317 (1994).
48. S. Christiansen, M. Albrecht, H. P. Strunk, and H. J. Maier, Appl. Phys. Lett. 64, 3617 (1994).
49. J. R. Downes, D. A. Faux, and F. P. O'Reilly, J. Appl. Phys. 81, 6700 (1997).
50. Y. P. Chiu, J. Appl. Mech. 45, 302 (1978).
51. T. Bennabas, P. Francios, Y. Androussi, and A. Lefebvre, J. Appl. Phys. 80, 2763 (1996).
52. G. S. Pearson and D. A. Faux, J. Appl. Phys. 88, 730 (2000).
53. J. H. Davies, J. Appl. Phys. 84, 1358 (1998).
54. K. Nishi, A. A. Yamaguchi, J. Ahopelto, A. Usui, and H. Sakaki, J. Appl. Phys. 76, 7437 (1994).
55. C. Pryor, M. E. Pistol, and L. Samuelson, Phys. Rev. B 56, 10404 (1997).
56. C. Pryor, Phys. Rev. B 57, 7190 (1998).
57. C. Pryor, J. Kim, L. W. Wang, A. J. Williamson, and A. Zunger, J. Appl. Phys. 83, 2548 (1998).
58. M. Tadić, F. M. Peeters, K. L. Janssens, M. Korkusinski, and P. Hawrylak, J. Appl. Phys. 92, 5819 (2002).
59. M. Korkusinski and P. Hawrylak, Phys. Rev. B 63, 195311 (2001).
60. H. Shin, W. Lee, and Y. H. Yoo, J. Phys. Condens. Mat. 15, 3689 (2003).
61. S. H. Bellaiche, L. Wei, and A. Zunger, Phys. Rev. B 54, 18568 ( 1996).
62. J. Bernard and A. Zunger, Appl. Phys. Lett. 65, 165 (1994).
63. M. Cusack, P. Briddon, and M. Jaros, Phys. Rev. B 54, R2300 ( 1996).
64. H. Jiang and J. Singh, Phys. Rev. B 56, 4696 (1997).
65. P. N. Keating, Phys. Rev. 145, 637 (1966).
66. R. M. Martin, Phys. Rev. B 1, 4005 (1970).
67. F. H. Stillinger and T. A. Weber, Phys. Rev. B 31, 5262 (1985).
68. W. Yu and A. Madhukar, Phys. Rev. Lett. 79, 905 (1997).
69. W. Yu and A. Madhukar, Phys. Rev. Lett. 79, 4939 (1997).
70. M. A. Makeev and A. Madhukar, Phys. Rev. B 67, 073201 (2003).
71. M. A. Migliorato, A. G. Cullis, M. Feam, and J. H. Jefferson, Phys. Rev. B 65, 115316 (2002).
72. Y. Kikuchi, H. Sugii, and K. Shintani, J. Appl. Phys. 89, 1191 ( 2001).
73. J. Stangl, V. Holy, and G. Bauer, Rev. Mod. Phys. 76, 725 (2004).
74. O. Brandt, K. Ploog, R. Bierwolf, and M. Hosenstein, Phys. Rev. Lett. 68, 1339 (1992).
75. J. R. Downes and D. A. Faux, J. Appl. Phys. 77, 2444 (1995).
76. D. A. Faux, S. G. Howells, U. Bangert, and A. J. Harvey, Appl. Phys. Lett. 64, 1271 (1994).
77. E. Kapon, M. Walther, J. Christen, M. Grundmann, C. Caneau, D. M. Hwang, E. Colas, R. Bhat, G. H. Song, and D. M. Bimberg, Superlattices Microstruct. 12, 491 (1992).
78. T. Arakawa, S. Tsukamoto, Y. Nagamune, M. Nishioka, J.-H. Lee, and Y. Arakawa, Jpn. J. Appl. Phys. 32, L1377 (1993).
79. N. Usami, T. Mine, S. Fukatsu, and Y. Shiraki, Appl. Phys. Lett. 64, 1126 (1994).
80. T. J. Gosling and J. R. Willis, J. Appl. Phys. 77, 5601 (1995).
81. T. Yamauchi, Y. Arakawa, and J. N. Schulman, Surf. Sci. 267, 291 (1992).
82. Y. Arakawa, IEEE Trans. Fundamentals E75-A, 20 (1992).
83. T. Yamauchi, T. Takahashi, J. N. Schulman, and Y. Arakawa, IEEE J. Quantum Electron. QE-29, 2109 (1993).
84. T. J. Gosling and L. B. Freund, Acta Mater. 44, 1 (1996).
85. G. Bilalbegovic, Phys. Rev. B 58, 15412 (1998).
86. I. A. Ovid'ko, Phys. Rev. Lett. 88, 046103 (2002).
87. M. E. Sherwin, T. J. Dummond, and D. J. Srolovitz, J. Appl. Phys. 69, 717 (1991).
88. D. A. Faux, J. R. Downes, and E. P. O'Reilly, J. Appl. Phys. 80, 2515 (1996)
89. K. Nishi, A. A. Yamaguchi, J. Ahopelto, A. Usui, and H. Sakaki, J. Appl. Phys. 76, 7437 (1994).
90. J. R. Downes, D. A. Faux, and E. P. O'Reilly, J. Appl. Phys. 92, 3754 (1997).
91. R. W. Keyes, J. Appl. Phys. 33, 3371 (1962).
92. A. D. Prins and D. J. Dunstan, Philos. Mag. Lett. 58, 37 (1988).
93. A. D. Andreev, J. R. Downes, D. A. Faux, and E. P. O'Reilly, J. Appl. Phys. 86, 297 (1999).
94. A. E. Romanov, P. M. Petroff, and J. S. Speck, Appl. Phys. Lett. 74, 2280 (1999).
95. H. Lee, J. A. Johnson, J. S. Speck, and P. M. Petroff, J. Vac. Sci. Technol. 18, 2193 (2000).
96. R. D. Mindlin and D. H. Cheng, J. Appl. Phys. 21, 926 (1950).
97. R. D. Mindlin and D. H. Cheng, J. Appl. Phys. 21, 931 (1950).
98. J. N. Goodier, Philos. Mag. 23, 1017 (1937).
99. S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, McGraw-Hill, New York (1970), 3rd edn.
100. J. H. Davies, J. Appl. Mech. 70, 655 (2003).
101. R. D. Mindlin, Midwestern Conf. Solid Mech. 56 (1953).
102. K. Seo and T. Mura, J. Appl. Mech. 46, 568 (1979).
103. F. Glas, J. Appl. Phys. 90, 3232 (2001).
104. F. Glas, Appl. Surf. Sci. 188, 9 (2002).
105. F. Glas, Philos. Mag. A 82, 2591 (2002).
106. R. I. Barabash and M. A. Krivoglaz, Fiz Tverd Tela+ 29, 3081 ( 1987).
107. A. E. Romanov, G. E. Beltz, W. T. Fischer, P. M. Petroff, and J. S. Speck, J. Appl. Phys. 89, 4523 (2001).
108. D. A. Faux and J. Haigh, J. Phys. Condens. Matter 2, 289 (1990).
109. P. H. Dederichs and G. Leibfried, Phys. Rev. 188, 1175 (1969).
110. J. W. Flocken and J. R. Hardy, Phys. Rev. B 1, 2447 (1970).
111. R. A. Masamura and G. Sines, J. Appl. Phys. 41, 3930 (1970).
112. P. H. Dederichs and J. Pollman, Z. Physics 255, 315 (1972).
113. T. Mura and N. Kinoshita, Phys. Status Solidi B 47, 607 (1971).
114. I. M. Lifshits and L. N. Rosentsverg, Zh. Eks. Teor. Fiz 17, 9 ( 1947); i Sov. Phys. JETP].
115. D. A. Faux and G. S. Pearson, Phys. Rev. B 62, R4798 (2000).
116. E. Pan and F. G. Yuan, Int. J. Sol. Struct. 37, 5329 (2000).
117. J. R. Barber and F. A. Sturla, J. Mech. Phys. Solids 40, 17 ( 1992).
118. J. C. T. Ting, Anisotropic Elasticity, Oxford University Press, Oxford, UK (1996).
119. K. C. Wu, J. Elast. 51, 213 (1998).
120. Y. C. Pan and T. W. Chou, Int. J. Eng. Sci. 17, 545 (1979).
121. E. Pan, ASME J. Appl. Mech. 70, 101 (2003).
122. Q. X. Pei, C. Lu, and Y. Y. Wang, J. Appl. Phys. 93, 1487 (2003).
123. S. W. Ellaway and D. A. Faux, J. Appl. Phys. 92, 3027 (2002).
124. M. J. Mehl, J. E. Osburn, D. A. Papaconstantopoulos, and B. M. Klein, Phys. Rev. B 41, 10311 (1990).
125. M. J. Mehl, J. E. Osburn, D. A. Papaconstantopoulos, and B. M. Klein, Phys. Rev. B 42, 5362 (1990).
126. M. J. Mehl, Phys. Rev. B 47, 2493 (1993).
127. M. Ichimma, Phys. Status. Solidi A 153, 431 (1996).
128. S. W. Ellaway and D. A. Faux, Phys. Status Solidi B 235, 437 ( 2003).
129. M. D. Frogley, J. L. Sly, and D. J. Dunstan, Phys. Rev. B 58, 12579 (1998).
130. M. D. Frogley, J. R. Downes, and D. J. Dunstan, Phys. Rev. B 62, 13612 (2000).
131. S. P. Lepkowski and 1. A. Majewski, Acta Phys. Pol. A 105, 559 ( 2004).
132. S. P. Lepkowski and J. A. Majewski, Solid State Commun. 131, 763 (2004).
133. B. W. Kim, J. Appl. Phys. 89, 1197 (2001).
134. S. Sanguinetti, M. Gurioli, E. Grilli, M. Guzzi, and M. Henini, Thin Solid Films 380, 198 (2000).
135. A. Patane, A. Levin, A. Polimeni, F. Schindler, P. C. Main, L. Eaves, and M. Henini, Appl. Phys. Lett. 77, 2979 (2000).
136. J. F. Nye, Physical Properties of Crystals, Clarendon, Oxford (1985).
137. B. Jogai, J. Appl. Phys. 90, 699 (2001).
138. E. Pan, J. Appl. Phys. 91, 3785 (2002).
139. E. Pan, Proc. R. Soc. London Ser. A 458, 181 (2002).
140. D. M. Barnett and J. Lothe, Phys. Norv. 8, 13 (1975).
141. E. Pan, J. Appl. Phys. 91, 6379 (2002).
142. P. Sharma and S. Ganti, Phys. Status Solidi B 234, R10 (2002).
143. A. Alizadeh, P. Sharma, S. Ganti, S. LeBoeuf, and L. Tsakalakos, J. Appl. Phys. 95, 8199 (2004).
144. P. Sharma and S. Ganti, J. Appl. Mech. 71, 663 (2004).
145. R. E. Miller and V. B. Shenoy, Nanotechnology 11, 139 (2000).
146. R. C. Carnmarata, K. Sieradzki, and F. Spaepen, J. Appl. Phys. 87, 1227 (2000).
147. R. Kukta, A. Peralta, and D. Kouris, J. Appl. Mech. 69, 443 ( 2002).
148. D. A. Kouris, E. Tsuchida, and T. Mura J. Appl. Mech. 53, 724 ( 1986).
149. M. E. Gurtin and A. I. Murdoch, Arch. Ration. Mech. Anal. 59, 389 (1978).
150. A. I. Murdoch, Quart. J. Mech. Appl. Math. 29, 245 (1976).
151. M. E. Gurtin, J. Weissmuller, and F. Larche, Philos. Mag. A 78, 1093 (1998).
152. H. Ibach, Surf. Sci. Rep. 29, 193 (1997).
153. P. Sharma and S. Ganti, Philos. Mag. Lett. 83, 745 (2003).
154. P. Sharma, S. Ganti, and N. Bhate, Appl. Phys, Lett. 82, 535 ( 2003).
155. P. Sharma and S. Ganti, J. Appl. Mech. 71, 663 (2004).
156. X. Peng, S. Ganti, A. Alizadeh, P. Sharma, S. K. Kumar, S. K. Nayak, Phys. Rev. B. 74, 035339-1 (2006).
157. C. Eringen, Nonlocal Continuum Filed Theories, Springer- Verlag, New York (2002).
158. H. Kleinert, Gauge Fields in Condensed Matter, World Scientific, Singapore (1989), Vol. 2.
159. B. Delley and E. F. Steigmeier, Appl. Phys. Lett. 67, 2370 ( 1995).
160. X. Zhang and P. Sharma, Int. J. Solids Struct. 42, 3933 (2005).
161. X. Zhang and P. Sharma, Phys. Rev. B. 72, 195345 (2005).
162. D. P. DiVincenzo, Phys. Rev. B 34, 5450 (1986).
163. R. Furuhashi, J. H. Huang, and T. Mura, J. Appl. Mech. 59, 783 ( 1992).
164. C. Q. Ru and P. Schiavone, Proc. R. Soc. London A 453, 2551 ( 1997).
165. Z. Zhong and S. A. Meguid, J. Appl. Mech. 63, 877 (1996).
166. J. Qu, Mech. of Mat. 14, 269 (1993).
167. J. Qu, J. Appl. Mech. 60, 1048 (1993).
168. L. J. Walpole, Math. Proc. Cambridge 83, 495 (1978).
169. H. A. Luo and G. J. Weng, Mech. Mater. 8, 77 (1989).
170. M. Cherkaoui, H. Sabar, and M. Berveiller, J. Eng. Mater. 116, 274 (1994).
171. G. P. Sendeckyj, Ellipsoidal inhomogenity problem, Ph.D. Dissertation, Northwestern University, Evanston (1967).
172. Z. A. Moschovidis, Two ellipsodal inhomogenities and related problems treated by the equivalent inclusion method, Ph.D. Dissertation, Northwestern University, Illinois (1975).
173. R. J. Asaro and D. M. Barnett, J. Mech. Phys. Solids 23, 77 ( 1975).
174. T. Mura and N. Kinoshita, Phys. Status Solidi A 48, 447 (1978).
175. M. Rahman, J. Appl. Mech. 69, 593 (2002).
176. A. C. Eringen, Microcontinuum Field Theories I: Foundations and Solids, Springer-Verlag, New York (1999).
177. Z. Q. Cheng and L. H. Le, Int. J. Eng. Sci. 33, 389 (1995).
178. Z. Q. Cheng and L. H. Le, Int. J. Eng. Sci. 35, 659 (1997).
179. P. Sharma and A. Dasgupta, Phys. Rev. B 66, 224110 (2002).
180. C. Q. Ru, Acta Mech. 160, 219 (2003).
181. J. Y. Li and M. L. Dunn, Philos. Mag. A. 77, 1341 (1998).
182. E. Pan and B. Yang, J. Appl. Phys. 93, 2435 (2003).
183. G. J. Rodin, J. Mech. Phys. Solids 44, 1977 (1996).
184. H. Nozaki and M. Taya, J. Appl. Mech. 68, 441 (2001).
185. K. Markov and L. Preziosi, Heterogeneous Media: Micromechanics Modeling Methods and Simulations, Birkhauser Verlag, Switzerland (2000).
186. G. J. Weng, M. Taya, and H. Abe, Micromechanics and Inhomogenity: The Toshio Mura Anniversary Volume, Springer Verlag, London (1990).
187. B. A. Bilby, K. J. Miller, and J. R. Willis, IUTAM/IFC/ICM Symposium on Fundamentals of Deformation and Fracture, Cambridge University Press, Cambridge (1984).
188. T. Mura, H. M. Shodja, and Y. Hirose, Appl. Mech. Rev. 49, S118 (1996).
189. T. Mura, Mat. Sci. Eng. A- Struct. A285, 224 (2000).
190. W. J. Drugan and J. R. Willis, J. Mech. Phys, Solids 44, 497 ( 1996).
191. A. Alizadeh, Personal Communication (2005).
192. G. E. Pikus and G. L. Bir, Sov. Phys. Solid State 1, 1502 (1960).
193. G. E. Pikus and G. L. Bir, Symmetry and Stain Induced Effects in Semiconductors, Wiley, NY, USA (1974).
194. T. B. Bahder, Phys. Rev. B 41, 11992 (1989).
195. T. B. Bahder, Phys. Rev. B 46, 9913 (1992).
196. Y. Zhang, Phys. Rev. B 49, 14352 (1994).
197. R. Maranganti and R Sharma, J. Mech. Phys. Solids (2007).
198. R. Maranganti and P. Sharma, Phys. Rev. Lett. 98, 195504 (2007).