Abstract

The mechanism and kinetics of growth of nanocrystals considered as quantum dots (those used as electronic blocks in optoelectronic devices) is investigated for the case when the growth and solving of them is controlled in parallel by diffusion (surface of volume) and by the rate of chemical reaction at surface of the nanocrystals (Wagner’s mechanism of growth). It is shown that the total flow to and from the nanocrystal consists of two parts, viz. the diffusion and kinetic ones. Depending on the ratio x of the two parts of the total flow, the diffusion or Wagner’s mechanism of growth predominates. For that, the size distribution function is determined for the specified x either by the curve corresponding to the generalized Chakraverty–Wagner distribution or from the generalized Lifshitz–Slyozov–Wagner distribution. Comparison of theoretically computed distributions with the experimentally obtained histograms is carried out.

© 2014 Optical Society of America

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  1. I. N. Stranski and L. Krastanov, “Theory of orientation separation of ionic crystal,” Sitzungsberichte der Akademie der Wifienschaften Wien, Mathematisch Naturwifienschaftlich Klafie, Abt. Lib. Bd. 146, 797–810 (1937).
  2. L. Goldstein, F. Glas, J. Y. Marzin, M. N. Charasse, and G. LeRoux, “Growth by molecular beam epitaxy and characterization of InAs/GaAs strained-layer superlattices,” Appl. Phys. Lett. 47, 1099–1101 (1985).
    [CrossRef]
  3. D. E. Eaglesham and M. Cerullo, “Dislocation-free Stranski–Krastanow growth of Ge on Si (100),” Phys. Rev. Lett. 64, 1943–1946 (1990).
    [CrossRef]
  4. J.-W. Mo, D. E. Savage, B. S. Swartzentruber, and M. G. Lagally, “Kinetic pathway in Stranski–Krastanov growth of Ge on Si(001),” Phys. Rev. Lett. 65, 1020–1023 (1990).
    [CrossRef]
  5. D. Vanderbilt and L. K. Wickham, “Elastic relaxation energies of coherent germanium islands on silicon,” in Evolution of Thin Film and Surface Microstructures (Mater. Res. Soc. Symp. Proc.), C. V. Thompson, J. Y. Tsao, and D. J. Srolovitz, eds. (Materials Research Society, 1991), Vol. 202, pp. 555–560.
  6. C. Ratsch and A. Zangwill, “Equilibrium theory of the Stranski–Krastanov epitaxial morphology,” Surf. Sci. 293, 123–131 (1993).
    [CrossRef]
  7. D. Leonard, M. Krishnamurthy, C. M. Reaves, S. P. Denbaars, and P. M. Petroff, “Direct information of quantum sized dots from uniform coherent islands of InGaAs on GaAs surfaces,” Appl. Phys. Lett. 63, 3203–3205 (1993).
    [CrossRef]
  8. D. Leonard, K. Pond, and P. M. Petroff, “Critical layer thickness for self-assembled InAs islands on GaAs,” Phys. Rev. B 50, 11687–11692 (1994).
    [CrossRef]
  9. J.-M. Marzin, J.-M. Gerard, A. Izrael, and D. Barrier, “Photoluminescence of single InAs quantum dots obtained by self-organized growth on GaAs,” Phys. Rev. Lett. 73, 716–719 (1994).
    [CrossRef]
  10. U. Hartmann, Faszination Nanotechnologie (Elsevier, 2006).
  11. M. L. Steigerwald and L. E. Brus, “Semiconductor crystallites: a class of large molecules,” Acc. Chem. Res. 23, 183–188 (1990).
    [CrossRef]
  12. C. B. Murray, C. R. Kagan, and M. G. Bawendi, “Synthesis and characterization of monodisperse nanocrystals and close-packed nanocrystal assemblies,” Annu. Rev. Mater. Sci. 30, 545–610 (2000).
    [CrossRef]
  13. X. Peng, J. Wickham, and A. P. Alivisatos, “Kinetics of II-VI and III-V colloidal semiconductor nanocrystal growth: ‘focusing’ of size distributions,” J. Am. Chem. Soc. 120, 5343–5344 (1998).
    [CrossRef]
  14. W. W. Yu and X. Peng, “Formation of high-quality CdS and Ooher II–VI semiconductor nanocrystals in noncoordinating solvents: tunable reactivity of monomers,” Angew. Chem., Int. Ed. Engl. 41, 2368–2371 (2002).
    [CrossRef]
  15. J. Nanda, S. Sapra, D. D. Sarma, N. Chandrasekharan, and G. Hodes, “Size-selected zinc sulfide nanocrystallites: synthesis, structure, and optical studies,” Chem. Mater. 12, 1018–1024 (2000).
    [CrossRef]
  16. R. Viswanatha, S. Sapra, S. Sen Gupta, B. Satpati, P. V. Satyam, B. N. Dev, and D. D. Sarma, “Synthesis and characterization of Mn-doped ZnO nanocrystals,” J. Phys. Chem. B 108, 6303–6310 (2004).
    [CrossRef]
  17. P. Gangopadhyay, R. Kesavamoorthy, S. Bera, P. Magudapathy, K. G. M. Nair, B. K. Panigrahi, and S. V. Narasimhan, “Optical absorption and photoluminescence spectroscopy of the growth of silver nanoparticles,” Phys. Rev. Lett. 94, 047403 (2005).
    [CrossRef]
  18. S. Takakusagi, K. Fukui, R. Tero, F. Nariyuki, and Y. Iwasawa, “Self-limiting growth of Pt nanoparticles from MeCpPtMe3 adsorbed on TiO2110 studied by scanning tunneling microscopy,” Phys. Rev. Lett. 91, 066102 (2003).
    [CrossRef]
  19. A. F. Craievich, G. Kellermann, L. C. Barbosa, and O. L. Alves, “Structure characterization and mechanism of growth of PbTe nanocrystals embedded in a silicate glass,” Phys. Rev. Lett. 89, 235503 (2002).
    [CrossRef]
  20. R. D. Averitt, D. Sarkar, and N. J. Halas, “General vector basis function solution of Maxwell’s equations,” Phys. Rev. Lett. 78, 4217–4220 (1997).
    [CrossRef]
  21. J.-S. Lee, M. V. Kovalenko, J. Huang, D. S. Chung, and D. V. Talapin, “Band-like transport, high electron mobility and high photoconductivity in all-inorganic nanocrystal arrays,” Nat. Nanotechnol. 6, 348–352 (2011).
    [CrossRef]
  22. D. V. Talapin and C. B. Murray, “PbSe nanocrystal solids for n- and p-channel thin film field-effect transistors,” Science 310, 86–89 (2005).
    [CrossRef]
  23. T. Shimoda, Y. Matsuki, M. Furusawa, T. Aoki, I. Yudasaka, H. Tanaka, H. Iwasawa, D. Wang, M. Miyasaka, and Y. Takeuchi, “Solution-processed silicon films and transistors,” Nature 440, 783–786 (2006).
    [CrossRef]
  24. J. J. Urban, D. V. Talapin, E. V. Shevchenko, C. R. Kagan, and C. B. Murray, “Synergism in binary nanocrystal superlattices leads to enhanced p-type conductivity in self-assembled PbTe/Ag2Te thin films,” Nat. Mater. 6, 115–121 (2007).
    [CrossRef]
  25. D. B. Mitzi, M. Copel, and S. Chey, “Low-voltage transistor employing a high- mobility spin-coated chalcogenide semiconductor,” J. Adv. Mater. 17, 1285–1289 (2005).
    [CrossRef]
  26. B. S. Ong, C. Li, Y. Li, Y. Wu, and R. Loutfy, “Stable, solution-processed, high-mobility ZnO thin-film transistors,” J. Am. Chem. Soc. 129, 2750–2751 (2007).
    [CrossRef]
  27. L. A. Kosyachenko, ed., Solar Cells: Thin-Film Technologies (InTech, 2011), p. 456.
  28. L. A. Kosyachenko, ed., Solar Cells: Silicon Wafer-Based Technologies (InTech, 2011), p. 364.
  29. L. A. Kosyachenko, ed., Solar Cells: New Aspects and Solutions Edited (InTech, 2011), p. 512.
  30. L. A. Kosyachenko, ed., Solar Cells: Dye-Sensitized Devices (InTech, 2011), p. 492.
  31. W. Ostwald, “Uber die vermeintliche isomerie des rotten und gelben quecksilberoxyds und die oberflachenspannung fester korper,” Zs. Phys. Chem. 34, 495–503 (1900).
  32. I. M. Lifshits and V. V. Slyozov, “On kinetics of diffusion decay of oversaturated solid solutions,” J. Exp. Theor. Phys. 35, 479–492 (1958).
  33. C. Wagner, “Theorie der alterung von niderschlagen durch umlösen (Ostwald Reifung),” Zs. Electrochem. 65, 581–591 (1961).
  34. B. K. Chakraverty, “Grain size distribution in thin films. I. Conservative systems,” J. Phys. Chem. Solids Suppl. 28, 2401–2412 (1967).
  35. N. N. Ledentsov, V. M. Ustinov, V. A. Shchukin, P. S. Kop’ev, Z. I. Alferov, and D. Bimberg, “Quantum dot heterostructures: fabrication, properties, lasers,” Fiz. Tekh. Poluprovodn 32, 385–410 (1998).
  36. R. D. Vengrenovich, B. V. Ivans’kyi, and A. V. Moskalyuk, “Generalized Chakraverty–Wagner distribution,” Ukr. J. Phys. 53, 1101–1109 (2008).
  37. A. Layek, G. Mishra, A. Sharma, M. Spasova, S. Dhar, A. Chowdhury, and R. A. Bandyopadhyaya, “Generalized three-stage mechanism of ZnO nanoparticle formation in homogeneous liquid medium,” J. Phys. Chem. C 116, 24757–24769 (2012).
    [CrossRef]
  38. R. D. Vengrenovich, B. V. Ivanskii, and A. V. Moskalyuk, “Generalized Lifshitz–Slyozov–Wagner distribution,” J. Exp. Theor. Phys. 131, 1040–1047 (2007).
  39. S. Suraprapapich, Y. M. Shen, V. A. Odnoblyudov, Y. Fainman, S. Panyakeow, and C. W. Tu, “Self-assembled lateral Bi-quantum-dot molecule formation by gas-source molecular beam epitaxy,” J. Cryst. Growth 301–302, 735–739 (2007).
    [CrossRef]
  40. G. Springholz, M. Pinczolits, V. Holý, S. Zerlauth, I. Vávra, and G. Bauer, “Vertical and lateral ordering in self-organized quantum dot superlattices,” Physica E 9, 149–163 (2001).
    [CrossRef]
  41. A. Kergommeaux, J. Faure-Vincent, A. Pron, R. Bettignies, B. Malaman, and P. Reiss, “Surface oxidation of tin chalcogenide nanocrystals revealed by 119Sn-Mossbauer spectroscopy,” J. Am. Chem. Soc. 134, 11659–11666 (2012).
    [CrossRef]

2012 (2)

A. Layek, G. Mishra, A. Sharma, M. Spasova, S. Dhar, A. Chowdhury, and R. A. Bandyopadhyaya, “Generalized three-stage mechanism of ZnO nanoparticle formation in homogeneous liquid medium,” J. Phys. Chem. C 116, 24757–24769 (2012).
[CrossRef]

A. Kergommeaux, J. Faure-Vincent, A. Pron, R. Bettignies, B. Malaman, and P. Reiss, “Surface oxidation of tin chalcogenide nanocrystals revealed by 119Sn-Mossbauer spectroscopy,” J. Am. Chem. Soc. 134, 11659–11666 (2012).
[CrossRef]

2011 (1)

J.-S. Lee, M. V. Kovalenko, J. Huang, D. S. Chung, and D. V. Talapin, “Band-like transport, high electron mobility and high photoconductivity in all-inorganic nanocrystal arrays,” Nat. Nanotechnol. 6, 348–352 (2011).
[CrossRef]

2008 (1)

R. D. Vengrenovich, B. V. Ivans’kyi, and A. V. Moskalyuk, “Generalized Chakraverty–Wagner distribution,” Ukr. J. Phys. 53, 1101–1109 (2008).

2007 (4)

J. J. Urban, D. V. Talapin, E. V. Shevchenko, C. R. Kagan, and C. B. Murray, “Synergism in binary nanocrystal superlattices leads to enhanced p-type conductivity in self-assembled PbTe/Ag2Te thin films,” Nat. Mater. 6, 115–121 (2007).
[CrossRef]

B. S. Ong, C. Li, Y. Li, Y. Wu, and R. Loutfy, “Stable, solution-processed, high-mobility ZnO thin-film transistors,” J. Am. Chem. Soc. 129, 2750–2751 (2007).
[CrossRef]

R. D. Vengrenovich, B. V. Ivanskii, and A. V. Moskalyuk, “Generalized Lifshitz–Slyozov–Wagner distribution,” J. Exp. Theor. Phys. 131, 1040–1047 (2007).

S. Suraprapapich, Y. M. Shen, V. A. Odnoblyudov, Y. Fainman, S. Panyakeow, and C. W. Tu, “Self-assembled lateral Bi-quantum-dot molecule formation by gas-source molecular beam epitaxy,” J. Cryst. Growth 301–302, 735–739 (2007).
[CrossRef]

2006 (1)

T. Shimoda, Y. Matsuki, M. Furusawa, T. Aoki, I. Yudasaka, H. Tanaka, H. Iwasawa, D. Wang, M. Miyasaka, and Y. Takeuchi, “Solution-processed silicon films and transistors,” Nature 440, 783–786 (2006).
[CrossRef]

2005 (3)

D. V. Talapin and C. B. Murray, “PbSe nanocrystal solids for n- and p-channel thin film field-effect transistors,” Science 310, 86–89 (2005).
[CrossRef]

D. B. Mitzi, M. Copel, and S. Chey, “Low-voltage transistor employing a high- mobility spin-coated chalcogenide semiconductor,” J. Adv. Mater. 17, 1285–1289 (2005).
[CrossRef]

P. Gangopadhyay, R. Kesavamoorthy, S. Bera, P. Magudapathy, K. G. M. Nair, B. K. Panigrahi, and S. V. Narasimhan, “Optical absorption and photoluminescence spectroscopy of the growth of silver nanoparticles,” Phys. Rev. Lett. 94, 047403 (2005).
[CrossRef]

2004 (1)

R. Viswanatha, S. Sapra, S. Sen Gupta, B. Satpati, P. V. Satyam, B. N. Dev, and D. D. Sarma, “Synthesis and characterization of Mn-doped ZnO nanocrystals,” J. Phys. Chem. B 108, 6303–6310 (2004).
[CrossRef]

2003 (1)

S. Takakusagi, K. Fukui, R. Tero, F. Nariyuki, and Y. Iwasawa, “Self-limiting growth of Pt nanoparticles from MeCpPtMe3 adsorbed on TiO2110 studied by scanning tunneling microscopy,” Phys. Rev. Lett. 91, 066102 (2003).
[CrossRef]

2002 (2)

A. F. Craievich, G. Kellermann, L. C. Barbosa, and O. L. Alves, “Structure characterization and mechanism of growth of PbTe nanocrystals embedded in a silicate glass,” Phys. Rev. Lett. 89, 235503 (2002).
[CrossRef]

W. W. Yu and X. Peng, “Formation of high-quality CdS and Ooher II–VI semiconductor nanocrystals in noncoordinating solvents: tunable reactivity of monomers,” Angew. Chem., Int. Ed. Engl. 41, 2368–2371 (2002).
[CrossRef]

2001 (1)

G. Springholz, M. Pinczolits, V. Holý, S. Zerlauth, I. Vávra, and G. Bauer, “Vertical and lateral ordering in self-organized quantum dot superlattices,” Physica E 9, 149–163 (2001).
[CrossRef]

2000 (2)

J. Nanda, S. Sapra, D. D. Sarma, N. Chandrasekharan, and G. Hodes, “Size-selected zinc sulfide nanocrystallites: synthesis, structure, and optical studies,” Chem. Mater. 12, 1018–1024 (2000).
[CrossRef]

C. B. Murray, C. R. Kagan, and M. G. Bawendi, “Synthesis and characterization of monodisperse nanocrystals and close-packed nanocrystal assemblies,” Annu. Rev. Mater. Sci. 30, 545–610 (2000).
[CrossRef]

1998 (2)

X. Peng, J. Wickham, and A. P. Alivisatos, “Kinetics of II-VI and III-V colloidal semiconductor nanocrystal growth: ‘focusing’ of size distributions,” J. Am. Chem. Soc. 120, 5343–5344 (1998).
[CrossRef]

N. N. Ledentsov, V. M. Ustinov, V. A. Shchukin, P. S. Kop’ev, Z. I. Alferov, and D. Bimberg, “Quantum dot heterostructures: fabrication, properties, lasers,” Fiz. Tekh. Poluprovodn 32, 385–410 (1998).

1997 (1)

R. D. Averitt, D. Sarkar, and N. J. Halas, “General vector basis function solution of Maxwell’s equations,” Phys. Rev. Lett. 78, 4217–4220 (1997).
[CrossRef]

1994 (2)

D. Leonard, K. Pond, and P. M. Petroff, “Critical layer thickness for self-assembled InAs islands on GaAs,” Phys. Rev. B 50, 11687–11692 (1994).
[CrossRef]

J.-M. Marzin, J.-M. Gerard, A. Izrael, and D. Barrier, “Photoluminescence of single InAs quantum dots obtained by self-organized growth on GaAs,” Phys. Rev. Lett. 73, 716–719 (1994).
[CrossRef]

1993 (2)

C. Ratsch and A. Zangwill, “Equilibrium theory of the Stranski–Krastanov epitaxial morphology,” Surf. Sci. 293, 123–131 (1993).
[CrossRef]

D. Leonard, M. Krishnamurthy, C. M. Reaves, S. P. Denbaars, and P. M. Petroff, “Direct information of quantum sized dots from uniform coherent islands of InGaAs on GaAs surfaces,” Appl. Phys. Lett. 63, 3203–3205 (1993).
[CrossRef]

1990 (3)

M. L. Steigerwald and L. E. Brus, “Semiconductor crystallites: a class of large molecules,” Acc. Chem. Res. 23, 183–188 (1990).
[CrossRef]

D. E. Eaglesham and M. Cerullo, “Dislocation-free Stranski–Krastanow growth of Ge on Si (100),” Phys. Rev. Lett. 64, 1943–1946 (1990).
[CrossRef]

J.-W. Mo, D. E. Savage, B. S. Swartzentruber, and M. G. Lagally, “Kinetic pathway in Stranski–Krastanov growth of Ge on Si(001),” Phys. Rev. Lett. 65, 1020–1023 (1990).
[CrossRef]

1985 (1)

L. Goldstein, F. Glas, J. Y. Marzin, M. N. Charasse, and G. LeRoux, “Growth by molecular beam epitaxy and characterization of InAs/GaAs strained-layer superlattices,” Appl. Phys. Lett. 47, 1099–1101 (1985).
[CrossRef]

1967 (1)

B. K. Chakraverty, “Grain size distribution in thin films. I. Conservative systems,” J. Phys. Chem. Solids Suppl. 28, 2401–2412 (1967).

1961 (1)

C. Wagner, “Theorie der alterung von niderschlagen durch umlösen (Ostwald Reifung),” Zs. Electrochem. 65, 581–591 (1961).

1958 (1)

I. M. Lifshits and V. V. Slyozov, “On kinetics of diffusion decay of oversaturated solid solutions,” J. Exp. Theor. Phys. 35, 479–492 (1958).

1937 (1)

I. N. Stranski and L. Krastanov, “Theory of orientation separation of ionic crystal,” Sitzungsberichte der Akademie der Wifienschaften Wien, Mathematisch Naturwifienschaftlich Klafie, Abt. Lib. Bd. 146, 797–810 (1937).

1900 (1)

W. Ostwald, “Uber die vermeintliche isomerie des rotten und gelben quecksilberoxyds und die oberflachenspannung fester korper,” Zs. Phys. Chem. 34, 495–503 (1900).

Alferov, Z. I.

N. N. Ledentsov, V. M. Ustinov, V. A. Shchukin, P. S. Kop’ev, Z. I. Alferov, and D. Bimberg, “Quantum dot heterostructures: fabrication, properties, lasers,” Fiz. Tekh. Poluprovodn 32, 385–410 (1998).

Alivisatos, A. P.

X. Peng, J. Wickham, and A. P. Alivisatos, “Kinetics of II-VI and III-V colloidal semiconductor nanocrystal growth: ‘focusing’ of size distributions,” J. Am. Chem. Soc. 120, 5343–5344 (1998).
[CrossRef]

Alves, O. L.

A. F. Craievich, G. Kellermann, L. C. Barbosa, and O. L. Alves, “Structure characterization and mechanism of growth of PbTe nanocrystals embedded in a silicate glass,” Phys. Rev. Lett. 89, 235503 (2002).
[CrossRef]

Aoki, T.

T. Shimoda, Y. Matsuki, M. Furusawa, T. Aoki, I. Yudasaka, H. Tanaka, H. Iwasawa, D. Wang, M. Miyasaka, and Y. Takeuchi, “Solution-processed silicon films and transistors,” Nature 440, 783–786 (2006).
[CrossRef]

Averitt, R. D.

R. D. Averitt, D. Sarkar, and N. J. Halas, “General vector basis function solution of Maxwell’s equations,” Phys. Rev. Lett. 78, 4217–4220 (1997).
[CrossRef]

Bandyopadhyaya, R. A.

A. Layek, G. Mishra, A. Sharma, M. Spasova, S. Dhar, A. Chowdhury, and R. A. Bandyopadhyaya, “Generalized three-stage mechanism of ZnO nanoparticle formation in homogeneous liquid medium,” J. Phys. Chem. C 116, 24757–24769 (2012).
[CrossRef]

Barbosa, L. C.

A. F. Craievich, G. Kellermann, L. C. Barbosa, and O. L. Alves, “Structure characterization and mechanism of growth of PbTe nanocrystals embedded in a silicate glass,” Phys. Rev. Lett. 89, 235503 (2002).
[CrossRef]

Barrier, D.

J.-M. Marzin, J.-M. Gerard, A. Izrael, and D. Barrier, “Photoluminescence of single InAs quantum dots obtained by self-organized growth on GaAs,” Phys. Rev. Lett. 73, 716–719 (1994).
[CrossRef]

Bauer, G.

G. Springholz, M. Pinczolits, V. Holý, S. Zerlauth, I. Vávra, and G. Bauer, “Vertical and lateral ordering in self-organized quantum dot superlattices,” Physica E 9, 149–163 (2001).
[CrossRef]

Bawendi, M. G.

C. B. Murray, C. R. Kagan, and M. G. Bawendi, “Synthesis and characterization of monodisperse nanocrystals and close-packed nanocrystal assemblies,” Annu. Rev. Mater. Sci. 30, 545–610 (2000).
[CrossRef]

Bera, S.

P. Gangopadhyay, R. Kesavamoorthy, S. Bera, P. Magudapathy, K. G. M. Nair, B. K. Panigrahi, and S. V. Narasimhan, “Optical absorption and photoluminescence spectroscopy of the growth of silver nanoparticles,” Phys. Rev. Lett. 94, 047403 (2005).
[CrossRef]

Bettignies, R.

A. Kergommeaux, J. Faure-Vincent, A. Pron, R. Bettignies, B. Malaman, and P. Reiss, “Surface oxidation of tin chalcogenide nanocrystals revealed by 119Sn-Mossbauer spectroscopy,” J. Am. Chem. Soc. 134, 11659–11666 (2012).
[CrossRef]

Bimberg, D.

N. N. Ledentsov, V. M. Ustinov, V. A. Shchukin, P. S. Kop’ev, Z. I. Alferov, and D. Bimberg, “Quantum dot heterostructures: fabrication, properties, lasers,” Fiz. Tekh. Poluprovodn 32, 385–410 (1998).

Brus, L. E.

M. L. Steigerwald and L. E. Brus, “Semiconductor crystallites: a class of large molecules,” Acc. Chem. Res. 23, 183–188 (1990).
[CrossRef]

Cerullo, M.

D. E. Eaglesham and M. Cerullo, “Dislocation-free Stranski–Krastanow growth of Ge on Si (100),” Phys. Rev. Lett. 64, 1943–1946 (1990).
[CrossRef]

Chakraverty, B. K.

B. K. Chakraverty, “Grain size distribution in thin films. I. Conservative systems,” J. Phys. Chem. Solids Suppl. 28, 2401–2412 (1967).

Chandrasekharan, N.

J. Nanda, S. Sapra, D. D. Sarma, N. Chandrasekharan, and G. Hodes, “Size-selected zinc sulfide nanocrystallites: synthesis, structure, and optical studies,” Chem. Mater. 12, 1018–1024 (2000).
[CrossRef]

Charasse, M. N.

L. Goldstein, F. Glas, J. Y. Marzin, M. N. Charasse, and G. LeRoux, “Growth by molecular beam epitaxy and characterization of InAs/GaAs strained-layer superlattices,” Appl. Phys. Lett. 47, 1099–1101 (1985).
[CrossRef]

Chey, S.

D. B. Mitzi, M. Copel, and S. Chey, “Low-voltage transistor employing a high- mobility spin-coated chalcogenide semiconductor,” J. Adv. Mater. 17, 1285–1289 (2005).
[CrossRef]

Chowdhury, A.

A. Layek, G. Mishra, A. Sharma, M. Spasova, S. Dhar, A. Chowdhury, and R. A. Bandyopadhyaya, “Generalized three-stage mechanism of ZnO nanoparticle formation in homogeneous liquid medium,” J. Phys. Chem. C 116, 24757–24769 (2012).
[CrossRef]

Chung, D. S.

J.-S. Lee, M. V. Kovalenko, J. Huang, D. S. Chung, and D. V. Talapin, “Band-like transport, high electron mobility and high photoconductivity in all-inorganic nanocrystal arrays,” Nat. Nanotechnol. 6, 348–352 (2011).
[CrossRef]

Copel, M.

D. B. Mitzi, M. Copel, and S. Chey, “Low-voltage transistor employing a high- mobility spin-coated chalcogenide semiconductor,” J. Adv. Mater. 17, 1285–1289 (2005).
[CrossRef]

Craievich, A. F.

A. F. Craievich, G. Kellermann, L. C. Barbosa, and O. L. Alves, “Structure characterization and mechanism of growth of PbTe nanocrystals embedded in a silicate glass,” Phys. Rev. Lett. 89, 235503 (2002).
[CrossRef]

Denbaars, S. P.

D. Leonard, M. Krishnamurthy, C. M. Reaves, S. P. Denbaars, and P. M. Petroff, “Direct information of quantum sized dots from uniform coherent islands of InGaAs on GaAs surfaces,” Appl. Phys. Lett. 63, 3203–3205 (1993).
[CrossRef]

Dev, B. N.

R. Viswanatha, S. Sapra, S. Sen Gupta, B. Satpati, P. V. Satyam, B. N. Dev, and D. D. Sarma, “Synthesis and characterization of Mn-doped ZnO nanocrystals,” J. Phys. Chem. B 108, 6303–6310 (2004).
[CrossRef]

Dhar, S.

A. Layek, G. Mishra, A. Sharma, M. Spasova, S. Dhar, A. Chowdhury, and R. A. Bandyopadhyaya, “Generalized three-stage mechanism of ZnO nanoparticle formation in homogeneous liquid medium,” J. Phys. Chem. C 116, 24757–24769 (2012).
[CrossRef]

Eaglesham, D. E.

D. E. Eaglesham and M. Cerullo, “Dislocation-free Stranski–Krastanow growth of Ge on Si (100),” Phys. Rev. Lett. 64, 1943–1946 (1990).
[CrossRef]

Fainman, Y.

S. Suraprapapich, Y. M. Shen, V. A. Odnoblyudov, Y. Fainman, S. Panyakeow, and C. W. Tu, “Self-assembled lateral Bi-quantum-dot molecule formation by gas-source molecular beam epitaxy,” J. Cryst. Growth 301–302, 735–739 (2007).
[CrossRef]

Faure-Vincent, J.

A. Kergommeaux, J. Faure-Vincent, A. Pron, R. Bettignies, B. Malaman, and P. Reiss, “Surface oxidation of tin chalcogenide nanocrystals revealed by 119Sn-Mossbauer spectroscopy,” J. Am. Chem. Soc. 134, 11659–11666 (2012).
[CrossRef]

Fukui, K.

S. Takakusagi, K. Fukui, R. Tero, F. Nariyuki, and Y. Iwasawa, “Self-limiting growth of Pt nanoparticles from MeCpPtMe3 adsorbed on TiO2110 studied by scanning tunneling microscopy,” Phys. Rev. Lett. 91, 066102 (2003).
[CrossRef]

Furusawa, M.

T. Shimoda, Y. Matsuki, M. Furusawa, T. Aoki, I. Yudasaka, H. Tanaka, H. Iwasawa, D. Wang, M. Miyasaka, and Y. Takeuchi, “Solution-processed silicon films and transistors,” Nature 440, 783–786 (2006).
[CrossRef]

Gangopadhyay, P.

P. Gangopadhyay, R. Kesavamoorthy, S. Bera, P. Magudapathy, K. G. M. Nair, B. K. Panigrahi, and S. V. Narasimhan, “Optical absorption and photoluminescence spectroscopy of the growth of silver nanoparticles,” Phys. Rev. Lett. 94, 047403 (2005).
[CrossRef]

Gerard, J.-M.

J.-M. Marzin, J.-M. Gerard, A. Izrael, and D. Barrier, “Photoluminescence of single InAs quantum dots obtained by self-organized growth on GaAs,” Phys. Rev. Lett. 73, 716–719 (1994).
[CrossRef]

Glas, F.

L. Goldstein, F. Glas, J. Y. Marzin, M. N. Charasse, and G. LeRoux, “Growth by molecular beam epitaxy and characterization of InAs/GaAs strained-layer superlattices,” Appl. Phys. Lett. 47, 1099–1101 (1985).
[CrossRef]

Goldstein, L.

L. Goldstein, F. Glas, J. Y. Marzin, M. N. Charasse, and G. LeRoux, “Growth by molecular beam epitaxy and characterization of InAs/GaAs strained-layer superlattices,” Appl. Phys. Lett. 47, 1099–1101 (1985).
[CrossRef]

Halas, N. J.

R. D. Averitt, D. Sarkar, and N. J. Halas, “General vector basis function solution of Maxwell’s equations,” Phys. Rev. Lett. 78, 4217–4220 (1997).
[CrossRef]

Hartmann, U.

U. Hartmann, Faszination Nanotechnologie (Elsevier, 2006).

Hodes, G.

J. Nanda, S. Sapra, D. D. Sarma, N. Chandrasekharan, and G. Hodes, “Size-selected zinc sulfide nanocrystallites: synthesis, structure, and optical studies,” Chem. Mater. 12, 1018–1024 (2000).
[CrossRef]

Holý, V.

G. Springholz, M. Pinczolits, V. Holý, S. Zerlauth, I. Vávra, and G. Bauer, “Vertical and lateral ordering in self-organized quantum dot superlattices,” Physica E 9, 149–163 (2001).
[CrossRef]

Huang, J.

J.-S. Lee, M. V. Kovalenko, J. Huang, D. S. Chung, and D. V. Talapin, “Band-like transport, high electron mobility and high photoconductivity in all-inorganic nanocrystal arrays,” Nat. Nanotechnol. 6, 348–352 (2011).
[CrossRef]

Ivans’kyi, B. V.

R. D. Vengrenovich, B. V. Ivans’kyi, and A. V. Moskalyuk, “Generalized Chakraverty–Wagner distribution,” Ukr. J. Phys. 53, 1101–1109 (2008).

Ivanskii, B. V.

R. D. Vengrenovich, B. V. Ivanskii, and A. V. Moskalyuk, “Generalized Lifshitz–Slyozov–Wagner distribution,” J. Exp. Theor. Phys. 131, 1040–1047 (2007).

Iwasawa, H.

T. Shimoda, Y. Matsuki, M. Furusawa, T. Aoki, I. Yudasaka, H. Tanaka, H. Iwasawa, D. Wang, M. Miyasaka, and Y. Takeuchi, “Solution-processed silicon films and transistors,” Nature 440, 783–786 (2006).
[CrossRef]

Iwasawa, Y.

S. Takakusagi, K. Fukui, R. Tero, F. Nariyuki, and Y. Iwasawa, “Self-limiting growth of Pt nanoparticles from MeCpPtMe3 adsorbed on TiO2110 studied by scanning tunneling microscopy,” Phys. Rev. Lett. 91, 066102 (2003).
[CrossRef]

Izrael, A.

J.-M. Marzin, J.-M. Gerard, A. Izrael, and D. Barrier, “Photoluminescence of single InAs quantum dots obtained by self-organized growth on GaAs,” Phys. Rev. Lett. 73, 716–719 (1994).
[CrossRef]

Kagan, C. R.

J. J. Urban, D. V. Talapin, E. V. Shevchenko, C. R. Kagan, and C. B. Murray, “Synergism in binary nanocrystal superlattices leads to enhanced p-type conductivity in self-assembled PbTe/Ag2Te thin films,” Nat. Mater. 6, 115–121 (2007).
[CrossRef]

C. B. Murray, C. R. Kagan, and M. G. Bawendi, “Synthesis and characterization of monodisperse nanocrystals and close-packed nanocrystal assemblies,” Annu. Rev. Mater. Sci. 30, 545–610 (2000).
[CrossRef]

Kellermann, G.

A. F. Craievich, G. Kellermann, L. C. Barbosa, and O. L. Alves, “Structure characterization and mechanism of growth of PbTe nanocrystals embedded in a silicate glass,” Phys. Rev. Lett. 89, 235503 (2002).
[CrossRef]

Kergommeaux, A.

A. Kergommeaux, J. Faure-Vincent, A. Pron, R. Bettignies, B. Malaman, and P. Reiss, “Surface oxidation of tin chalcogenide nanocrystals revealed by 119Sn-Mossbauer spectroscopy,” J. Am. Chem. Soc. 134, 11659–11666 (2012).
[CrossRef]

Kesavamoorthy, R.

P. Gangopadhyay, R. Kesavamoorthy, S. Bera, P. Magudapathy, K. G. M. Nair, B. K. Panigrahi, and S. V. Narasimhan, “Optical absorption and photoluminescence spectroscopy of the growth of silver nanoparticles,” Phys. Rev. Lett. 94, 047403 (2005).
[CrossRef]

Kop’ev, P. S.

N. N. Ledentsov, V. M. Ustinov, V. A. Shchukin, P. S. Kop’ev, Z. I. Alferov, and D. Bimberg, “Quantum dot heterostructures: fabrication, properties, lasers,” Fiz. Tekh. Poluprovodn 32, 385–410 (1998).

Kovalenko, M. V.

J.-S. Lee, M. V. Kovalenko, J. Huang, D. S. Chung, and D. V. Talapin, “Band-like transport, high electron mobility and high photoconductivity in all-inorganic nanocrystal arrays,” Nat. Nanotechnol. 6, 348–352 (2011).
[CrossRef]

Krastanov, L.

I. N. Stranski and L. Krastanov, “Theory of orientation separation of ionic crystal,” Sitzungsberichte der Akademie der Wifienschaften Wien, Mathematisch Naturwifienschaftlich Klafie, Abt. Lib. Bd. 146, 797–810 (1937).

Krishnamurthy, M.

D. Leonard, M. Krishnamurthy, C. M. Reaves, S. P. Denbaars, and P. M. Petroff, “Direct information of quantum sized dots from uniform coherent islands of InGaAs on GaAs surfaces,” Appl. Phys. Lett. 63, 3203–3205 (1993).
[CrossRef]

Lagally, M. G.

J.-W. Mo, D. E. Savage, B. S. Swartzentruber, and M. G. Lagally, “Kinetic pathway in Stranski–Krastanov growth of Ge on Si(001),” Phys. Rev. Lett. 65, 1020–1023 (1990).
[CrossRef]

Layek, A.

A. Layek, G. Mishra, A. Sharma, M. Spasova, S. Dhar, A. Chowdhury, and R. A. Bandyopadhyaya, “Generalized three-stage mechanism of ZnO nanoparticle formation in homogeneous liquid medium,” J. Phys. Chem. C 116, 24757–24769 (2012).
[CrossRef]

Ledentsov, N. N.

N. N. Ledentsov, V. M. Ustinov, V. A. Shchukin, P. S. Kop’ev, Z. I. Alferov, and D. Bimberg, “Quantum dot heterostructures: fabrication, properties, lasers,” Fiz. Tekh. Poluprovodn 32, 385–410 (1998).

Lee, J.-S.

J.-S. Lee, M. V. Kovalenko, J. Huang, D. S. Chung, and D. V. Talapin, “Band-like transport, high electron mobility and high photoconductivity in all-inorganic nanocrystal arrays,” Nat. Nanotechnol. 6, 348–352 (2011).
[CrossRef]

Leonard, D.

D. Leonard, K. Pond, and P. M. Petroff, “Critical layer thickness for self-assembled InAs islands on GaAs,” Phys. Rev. B 50, 11687–11692 (1994).
[CrossRef]

D. Leonard, M. Krishnamurthy, C. M. Reaves, S. P. Denbaars, and P. M. Petroff, “Direct information of quantum sized dots from uniform coherent islands of InGaAs on GaAs surfaces,” Appl. Phys. Lett. 63, 3203–3205 (1993).
[CrossRef]

LeRoux, G.

L. Goldstein, F. Glas, J. Y. Marzin, M. N. Charasse, and G. LeRoux, “Growth by molecular beam epitaxy and characterization of InAs/GaAs strained-layer superlattices,” Appl. Phys. Lett. 47, 1099–1101 (1985).
[CrossRef]

Li, C.

B. S. Ong, C. Li, Y. Li, Y. Wu, and R. Loutfy, “Stable, solution-processed, high-mobility ZnO thin-film transistors,” J. Am. Chem. Soc. 129, 2750–2751 (2007).
[CrossRef]

Li, Y.

B. S. Ong, C. Li, Y. Li, Y. Wu, and R. Loutfy, “Stable, solution-processed, high-mobility ZnO thin-film transistors,” J. Am. Chem. Soc. 129, 2750–2751 (2007).
[CrossRef]

Lifshits, I. M.

I. M. Lifshits and V. V. Slyozov, “On kinetics of diffusion decay of oversaturated solid solutions,” J. Exp. Theor. Phys. 35, 479–492 (1958).

Loutfy, R.

B. S. Ong, C. Li, Y. Li, Y. Wu, and R. Loutfy, “Stable, solution-processed, high-mobility ZnO thin-film transistors,” J. Am. Chem. Soc. 129, 2750–2751 (2007).
[CrossRef]

Magudapathy, P.

P. Gangopadhyay, R. Kesavamoorthy, S. Bera, P. Magudapathy, K. G. M. Nair, B. K. Panigrahi, and S. V. Narasimhan, “Optical absorption and photoluminescence spectroscopy of the growth of silver nanoparticles,” Phys. Rev. Lett. 94, 047403 (2005).
[CrossRef]

Malaman, B.

A. Kergommeaux, J. Faure-Vincent, A. Pron, R. Bettignies, B. Malaman, and P. Reiss, “Surface oxidation of tin chalcogenide nanocrystals revealed by 119Sn-Mossbauer spectroscopy,” J. Am. Chem. Soc. 134, 11659–11666 (2012).
[CrossRef]

Marzin, J. Y.

L. Goldstein, F. Glas, J. Y. Marzin, M. N. Charasse, and G. LeRoux, “Growth by molecular beam epitaxy and characterization of InAs/GaAs strained-layer superlattices,” Appl. Phys. Lett. 47, 1099–1101 (1985).
[CrossRef]

Marzin, J.-M.

J.-M. Marzin, J.-M. Gerard, A. Izrael, and D. Barrier, “Photoluminescence of single InAs quantum dots obtained by self-organized growth on GaAs,” Phys. Rev. Lett. 73, 716–719 (1994).
[CrossRef]

Matsuki, Y.

T. Shimoda, Y. Matsuki, M. Furusawa, T. Aoki, I. Yudasaka, H. Tanaka, H. Iwasawa, D. Wang, M. Miyasaka, and Y. Takeuchi, “Solution-processed silicon films and transistors,” Nature 440, 783–786 (2006).
[CrossRef]

Mishra, G.

A. Layek, G. Mishra, A. Sharma, M. Spasova, S. Dhar, A. Chowdhury, and R. A. Bandyopadhyaya, “Generalized three-stage mechanism of ZnO nanoparticle formation in homogeneous liquid medium,” J. Phys. Chem. C 116, 24757–24769 (2012).
[CrossRef]

Mitzi, D. B.

D. B. Mitzi, M. Copel, and S. Chey, “Low-voltage transistor employing a high- mobility spin-coated chalcogenide semiconductor,” J. Adv. Mater. 17, 1285–1289 (2005).
[CrossRef]

Miyasaka, M.

T. Shimoda, Y. Matsuki, M. Furusawa, T. Aoki, I. Yudasaka, H. Tanaka, H. Iwasawa, D. Wang, M. Miyasaka, and Y. Takeuchi, “Solution-processed silicon films and transistors,” Nature 440, 783–786 (2006).
[CrossRef]

Mo, J.-W.

J.-W. Mo, D. E. Savage, B. S. Swartzentruber, and M. G. Lagally, “Kinetic pathway in Stranski–Krastanov growth of Ge on Si(001),” Phys. Rev. Lett. 65, 1020–1023 (1990).
[CrossRef]

Moskalyuk, A. V.

R. D. Vengrenovich, B. V. Ivans’kyi, and A. V. Moskalyuk, “Generalized Chakraverty–Wagner distribution,” Ukr. J. Phys. 53, 1101–1109 (2008).

R. D. Vengrenovich, B. V. Ivanskii, and A. V. Moskalyuk, “Generalized Lifshitz–Slyozov–Wagner distribution,” J. Exp. Theor. Phys. 131, 1040–1047 (2007).

Murray, C. B.

J. J. Urban, D. V. Talapin, E. V. Shevchenko, C. R. Kagan, and C. B. Murray, “Synergism in binary nanocrystal superlattices leads to enhanced p-type conductivity in self-assembled PbTe/Ag2Te thin films,” Nat. Mater. 6, 115–121 (2007).
[CrossRef]

D. V. Talapin and C. B. Murray, “PbSe nanocrystal solids for n- and p-channel thin film field-effect transistors,” Science 310, 86–89 (2005).
[CrossRef]

C. B. Murray, C. R. Kagan, and M. G. Bawendi, “Synthesis and characterization of monodisperse nanocrystals and close-packed nanocrystal assemblies,” Annu. Rev. Mater. Sci. 30, 545–610 (2000).
[CrossRef]

Nair, K. G. M.

P. Gangopadhyay, R. Kesavamoorthy, S. Bera, P. Magudapathy, K. G. M. Nair, B. K. Panigrahi, and S. V. Narasimhan, “Optical absorption and photoluminescence spectroscopy of the growth of silver nanoparticles,” Phys. Rev. Lett. 94, 047403 (2005).
[CrossRef]

Nanda, J.

J. Nanda, S. Sapra, D. D. Sarma, N. Chandrasekharan, and G. Hodes, “Size-selected zinc sulfide nanocrystallites: synthesis, structure, and optical studies,” Chem. Mater. 12, 1018–1024 (2000).
[CrossRef]

Narasimhan, S. V.

P. Gangopadhyay, R. Kesavamoorthy, S. Bera, P. Magudapathy, K. G. M. Nair, B. K. Panigrahi, and S. V. Narasimhan, “Optical absorption and photoluminescence spectroscopy of the growth of silver nanoparticles,” Phys. Rev. Lett. 94, 047403 (2005).
[CrossRef]

Nariyuki, F.

S. Takakusagi, K. Fukui, R. Tero, F. Nariyuki, and Y. Iwasawa, “Self-limiting growth of Pt nanoparticles from MeCpPtMe3 adsorbed on TiO2110 studied by scanning tunneling microscopy,” Phys. Rev. Lett. 91, 066102 (2003).
[CrossRef]

Odnoblyudov, V. A.

S. Suraprapapich, Y. M. Shen, V. A. Odnoblyudov, Y. Fainman, S. Panyakeow, and C. W. Tu, “Self-assembled lateral Bi-quantum-dot molecule formation by gas-source molecular beam epitaxy,” J. Cryst. Growth 301–302, 735–739 (2007).
[CrossRef]

Ong, B. S.

B. S. Ong, C. Li, Y. Li, Y. Wu, and R. Loutfy, “Stable, solution-processed, high-mobility ZnO thin-film transistors,” J. Am. Chem. Soc. 129, 2750–2751 (2007).
[CrossRef]

Ostwald, W.

W. Ostwald, “Uber die vermeintliche isomerie des rotten und gelben quecksilberoxyds und die oberflachenspannung fester korper,” Zs. Phys. Chem. 34, 495–503 (1900).

Panigrahi, B. K.

P. Gangopadhyay, R. Kesavamoorthy, S. Bera, P. Magudapathy, K. G. M. Nair, B. K. Panigrahi, and S. V. Narasimhan, “Optical absorption and photoluminescence spectroscopy of the growth of silver nanoparticles,” Phys. Rev. Lett. 94, 047403 (2005).
[CrossRef]

Panyakeow, S.

S. Suraprapapich, Y. M. Shen, V. A. Odnoblyudov, Y. Fainman, S. Panyakeow, and C. W. Tu, “Self-assembled lateral Bi-quantum-dot molecule formation by gas-source molecular beam epitaxy,” J. Cryst. Growth 301–302, 735–739 (2007).
[CrossRef]

Peng, X.

W. W. Yu and X. Peng, “Formation of high-quality CdS and Ooher II–VI semiconductor nanocrystals in noncoordinating solvents: tunable reactivity of monomers,” Angew. Chem., Int. Ed. Engl. 41, 2368–2371 (2002).
[CrossRef]

X. Peng, J. Wickham, and A. P. Alivisatos, “Kinetics of II-VI and III-V colloidal semiconductor nanocrystal growth: ‘focusing’ of size distributions,” J. Am. Chem. Soc. 120, 5343–5344 (1998).
[CrossRef]

Petroff, P. M.

D. Leonard, K. Pond, and P. M. Petroff, “Critical layer thickness for self-assembled InAs islands on GaAs,” Phys. Rev. B 50, 11687–11692 (1994).
[CrossRef]

D. Leonard, M. Krishnamurthy, C. M. Reaves, S. P. Denbaars, and P. M. Petroff, “Direct information of quantum sized dots from uniform coherent islands of InGaAs on GaAs surfaces,” Appl. Phys. Lett. 63, 3203–3205 (1993).
[CrossRef]

Pinczolits, M.

G. Springholz, M. Pinczolits, V. Holý, S. Zerlauth, I. Vávra, and G. Bauer, “Vertical and lateral ordering in self-organized quantum dot superlattices,” Physica E 9, 149–163 (2001).
[CrossRef]

Pond, K.

D. Leonard, K. Pond, and P. M. Petroff, “Critical layer thickness for self-assembled InAs islands on GaAs,” Phys. Rev. B 50, 11687–11692 (1994).
[CrossRef]

Pron, A.

A. Kergommeaux, J. Faure-Vincent, A. Pron, R. Bettignies, B. Malaman, and P. Reiss, “Surface oxidation of tin chalcogenide nanocrystals revealed by 119Sn-Mossbauer spectroscopy,” J. Am. Chem. Soc. 134, 11659–11666 (2012).
[CrossRef]

Ratsch, C.

C. Ratsch and A. Zangwill, “Equilibrium theory of the Stranski–Krastanov epitaxial morphology,” Surf. Sci. 293, 123–131 (1993).
[CrossRef]

Reaves, C. M.

D. Leonard, M. Krishnamurthy, C. M. Reaves, S. P. Denbaars, and P. M. Petroff, “Direct information of quantum sized dots from uniform coherent islands of InGaAs on GaAs surfaces,” Appl. Phys. Lett. 63, 3203–3205 (1993).
[CrossRef]

Reiss, P.

A. Kergommeaux, J. Faure-Vincent, A. Pron, R. Bettignies, B. Malaman, and P. Reiss, “Surface oxidation of tin chalcogenide nanocrystals revealed by 119Sn-Mossbauer spectroscopy,” J. Am. Chem. Soc. 134, 11659–11666 (2012).
[CrossRef]

Sapra, S.

R. Viswanatha, S. Sapra, S. Sen Gupta, B. Satpati, P. V. Satyam, B. N. Dev, and D. D. Sarma, “Synthesis and characterization of Mn-doped ZnO nanocrystals,” J. Phys. Chem. B 108, 6303–6310 (2004).
[CrossRef]

J. Nanda, S. Sapra, D. D. Sarma, N. Chandrasekharan, and G. Hodes, “Size-selected zinc sulfide nanocrystallites: synthesis, structure, and optical studies,” Chem. Mater. 12, 1018–1024 (2000).
[CrossRef]

Sarkar, D.

R. D. Averitt, D. Sarkar, and N. J. Halas, “General vector basis function solution of Maxwell’s equations,” Phys. Rev. Lett. 78, 4217–4220 (1997).
[CrossRef]

Sarma, D. D.

R. Viswanatha, S. Sapra, S. Sen Gupta, B. Satpati, P. V. Satyam, B. N. Dev, and D. D. Sarma, “Synthesis and characterization of Mn-doped ZnO nanocrystals,” J. Phys. Chem. B 108, 6303–6310 (2004).
[CrossRef]

J. Nanda, S. Sapra, D. D. Sarma, N. Chandrasekharan, and G. Hodes, “Size-selected zinc sulfide nanocrystallites: synthesis, structure, and optical studies,” Chem. Mater. 12, 1018–1024 (2000).
[CrossRef]

Satpati, B.

R. Viswanatha, S. Sapra, S. Sen Gupta, B. Satpati, P. V. Satyam, B. N. Dev, and D. D. Sarma, “Synthesis and characterization of Mn-doped ZnO nanocrystals,” J. Phys. Chem. B 108, 6303–6310 (2004).
[CrossRef]

Satyam, P. V.

R. Viswanatha, S. Sapra, S. Sen Gupta, B. Satpati, P. V. Satyam, B. N. Dev, and D. D. Sarma, “Synthesis and characterization of Mn-doped ZnO nanocrystals,” J. Phys. Chem. B 108, 6303–6310 (2004).
[CrossRef]

Savage, D. E.

J.-W. Mo, D. E. Savage, B. S. Swartzentruber, and M. G. Lagally, “Kinetic pathway in Stranski–Krastanov growth of Ge on Si(001),” Phys. Rev. Lett. 65, 1020–1023 (1990).
[CrossRef]

Sen Gupta, S.

R. Viswanatha, S. Sapra, S. Sen Gupta, B. Satpati, P. V. Satyam, B. N. Dev, and D. D. Sarma, “Synthesis and characterization of Mn-doped ZnO nanocrystals,” J. Phys. Chem. B 108, 6303–6310 (2004).
[CrossRef]

Sharma, A.

A. Layek, G. Mishra, A. Sharma, M. Spasova, S. Dhar, A. Chowdhury, and R. A. Bandyopadhyaya, “Generalized three-stage mechanism of ZnO nanoparticle formation in homogeneous liquid medium,” J. Phys. Chem. C 116, 24757–24769 (2012).
[CrossRef]

Shchukin, V. A.

N. N. Ledentsov, V. M. Ustinov, V. A. Shchukin, P. S. Kop’ev, Z. I. Alferov, and D. Bimberg, “Quantum dot heterostructures: fabrication, properties, lasers,” Fiz. Tekh. Poluprovodn 32, 385–410 (1998).

Shen, Y. M.

S. Suraprapapich, Y. M. Shen, V. A. Odnoblyudov, Y. Fainman, S. Panyakeow, and C. W. Tu, “Self-assembled lateral Bi-quantum-dot molecule formation by gas-source molecular beam epitaxy,” J. Cryst. Growth 301–302, 735–739 (2007).
[CrossRef]

Shevchenko, E. V.

J. J. Urban, D. V. Talapin, E. V. Shevchenko, C. R. Kagan, and C. B. Murray, “Synergism in binary nanocrystal superlattices leads to enhanced p-type conductivity in self-assembled PbTe/Ag2Te thin films,” Nat. Mater. 6, 115–121 (2007).
[CrossRef]

Shimoda, T.

T. Shimoda, Y. Matsuki, M. Furusawa, T. Aoki, I. Yudasaka, H. Tanaka, H. Iwasawa, D. Wang, M. Miyasaka, and Y. Takeuchi, “Solution-processed silicon films and transistors,” Nature 440, 783–786 (2006).
[CrossRef]

Slyozov, V. V.

I. M. Lifshits and V. V. Slyozov, “On kinetics of diffusion decay of oversaturated solid solutions,” J. Exp. Theor. Phys. 35, 479–492 (1958).

Spasova, M.

A. Layek, G. Mishra, A. Sharma, M. Spasova, S. Dhar, A. Chowdhury, and R. A. Bandyopadhyaya, “Generalized three-stage mechanism of ZnO nanoparticle formation in homogeneous liquid medium,” J. Phys. Chem. C 116, 24757–24769 (2012).
[CrossRef]

Springholz, G.

G. Springholz, M. Pinczolits, V. Holý, S. Zerlauth, I. Vávra, and G. Bauer, “Vertical and lateral ordering in self-organized quantum dot superlattices,” Physica E 9, 149–163 (2001).
[CrossRef]

Steigerwald, M. L.

M. L. Steigerwald and L. E. Brus, “Semiconductor crystallites: a class of large molecules,” Acc. Chem. Res. 23, 183–188 (1990).
[CrossRef]

Stranski, I. N.

I. N. Stranski and L. Krastanov, “Theory of orientation separation of ionic crystal,” Sitzungsberichte der Akademie der Wifienschaften Wien, Mathematisch Naturwifienschaftlich Klafie, Abt. Lib. Bd. 146, 797–810 (1937).

Suraprapapich, S.

S. Suraprapapich, Y. M. Shen, V. A. Odnoblyudov, Y. Fainman, S. Panyakeow, and C. W. Tu, “Self-assembled lateral Bi-quantum-dot molecule formation by gas-source molecular beam epitaxy,” J. Cryst. Growth 301–302, 735–739 (2007).
[CrossRef]

Swartzentruber, B. S.

J.-W. Mo, D. E. Savage, B. S. Swartzentruber, and M. G. Lagally, “Kinetic pathway in Stranski–Krastanov growth of Ge on Si(001),” Phys. Rev. Lett. 65, 1020–1023 (1990).
[CrossRef]

Takakusagi, S.

S. Takakusagi, K. Fukui, R. Tero, F. Nariyuki, and Y. Iwasawa, “Self-limiting growth of Pt nanoparticles from MeCpPtMe3 adsorbed on TiO2110 studied by scanning tunneling microscopy,” Phys. Rev. Lett. 91, 066102 (2003).
[CrossRef]

Takeuchi, Y.

T. Shimoda, Y. Matsuki, M. Furusawa, T. Aoki, I. Yudasaka, H. Tanaka, H. Iwasawa, D. Wang, M. Miyasaka, and Y. Takeuchi, “Solution-processed silicon films and transistors,” Nature 440, 783–786 (2006).
[CrossRef]

Talapin, D. V.

J.-S. Lee, M. V. Kovalenko, J. Huang, D. S. Chung, and D. V. Talapin, “Band-like transport, high electron mobility and high photoconductivity in all-inorganic nanocrystal arrays,” Nat. Nanotechnol. 6, 348–352 (2011).
[CrossRef]

J. J. Urban, D. V. Talapin, E. V. Shevchenko, C. R. Kagan, and C. B. Murray, “Synergism in binary nanocrystal superlattices leads to enhanced p-type conductivity in self-assembled PbTe/Ag2Te thin films,” Nat. Mater. 6, 115–121 (2007).
[CrossRef]

D. V. Talapin and C. B. Murray, “PbSe nanocrystal solids for n- and p-channel thin film field-effect transistors,” Science 310, 86–89 (2005).
[CrossRef]

Tanaka, H.

T. Shimoda, Y. Matsuki, M. Furusawa, T. Aoki, I. Yudasaka, H. Tanaka, H. Iwasawa, D. Wang, M. Miyasaka, and Y. Takeuchi, “Solution-processed silicon films and transistors,” Nature 440, 783–786 (2006).
[CrossRef]

Tero, R.

S. Takakusagi, K. Fukui, R. Tero, F. Nariyuki, and Y. Iwasawa, “Self-limiting growth of Pt nanoparticles from MeCpPtMe3 adsorbed on TiO2110 studied by scanning tunneling microscopy,” Phys. Rev. Lett. 91, 066102 (2003).
[CrossRef]

Tu, C. W.

S. Suraprapapich, Y. M. Shen, V. A. Odnoblyudov, Y. Fainman, S. Panyakeow, and C. W. Tu, “Self-assembled lateral Bi-quantum-dot molecule formation by gas-source molecular beam epitaxy,” J. Cryst. Growth 301–302, 735–739 (2007).
[CrossRef]

Urban, J. J.

J. J. Urban, D. V. Talapin, E. V. Shevchenko, C. R. Kagan, and C. B. Murray, “Synergism in binary nanocrystal superlattices leads to enhanced p-type conductivity in self-assembled PbTe/Ag2Te thin films,” Nat. Mater. 6, 115–121 (2007).
[CrossRef]

Ustinov, V. M.

N. N. Ledentsov, V. M. Ustinov, V. A. Shchukin, P. S. Kop’ev, Z. I. Alferov, and D. Bimberg, “Quantum dot heterostructures: fabrication, properties, lasers,” Fiz. Tekh. Poluprovodn 32, 385–410 (1998).

Vanderbilt, D.

D. Vanderbilt and L. K. Wickham, “Elastic relaxation energies of coherent germanium islands on silicon,” in Evolution of Thin Film and Surface Microstructures (Mater. Res. Soc. Symp. Proc.), C. V. Thompson, J. Y. Tsao, and D. J. Srolovitz, eds. (Materials Research Society, 1991), Vol. 202, pp. 555–560.

Vávra, I.

G. Springholz, M. Pinczolits, V. Holý, S. Zerlauth, I. Vávra, and G. Bauer, “Vertical and lateral ordering in self-organized quantum dot superlattices,” Physica E 9, 149–163 (2001).
[CrossRef]

Vengrenovich, R. D.

R. D. Vengrenovich, B. V. Ivans’kyi, and A. V. Moskalyuk, “Generalized Chakraverty–Wagner distribution,” Ukr. J. Phys. 53, 1101–1109 (2008).

R. D. Vengrenovich, B. V. Ivanskii, and A. V. Moskalyuk, “Generalized Lifshitz–Slyozov–Wagner distribution,” J. Exp. Theor. Phys. 131, 1040–1047 (2007).

Viswanatha, R.

R. Viswanatha, S. Sapra, S. Sen Gupta, B. Satpati, P. V. Satyam, B. N. Dev, and D. D. Sarma, “Synthesis and characterization of Mn-doped ZnO nanocrystals,” J. Phys. Chem. B 108, 6303–6310 (2004).
[CrossRef]

Wagner, C.

C. Wagner, “Theorie der alterung von niderschlagen durch umlösen (Ostwald Reifung),” Zs. Electrochem. 65, 581–591 (1961).

Wang, D.

T. Shimoda, Y. Matsuki, M. Furusawa, T. Aoki, I. Yudasaka, H. Tanaka, H. Iwasawa, D. Wang, M. Miyasaka, and Y. Takeuchi, “Solution-processed silicon films and transistors,” Nature 440, 783–786 (2006).
[CrossRef]

Wickham, J.

X. Peng, J. Wickham, and A. P. Alivisatos, “Kinetics of II-VI and III-V colloidal semiconductor nanocrystal growth: ‘focusing’ of size distributions,” J. Am. Chem. Soc. 120, 5343–5344 (1998).
[CrossRef]

Wickham, L. K.

D. Vanderbilt and L. K. Wickham, “Elastic relaxation energies of coherent germanium islands on silicon,” in Evolution of Thin Film and Surface Microstructures (Mater. Res. Soc. Symp. Proc.), C. V. Thompson, J. Y. Tsao, and D. J. Srolovitz, eds. (Materials Research Society, 1991), Vol. 202, pp. 555–560.

Wu, Y.

B. S. Ong, C. Li, Y. Li, Y. Wu, and R. Loutfy, “Stable, solution-processed, high-mobility ZnO thin-film transistors,” J. Am. Chem. Soc. 129, 2750–2751 (2007).
[CrossRef]

Yu, W. W.

W. W. Yu and X. Peng, “Formation of high-quality CdS and Ooher II–VI semiconductor nanocrystals in noncoordinating solvents: tunable reactivity of monomers,” Angew. Chem., Int. Ed. Engl. 41, 2368–2371 (2002).
[CrossRef]

Yudasaka, I.

T. Shimoda, Y. Matsuki, M. Furusawa, T. Aoki, I. Yudasaka, H. Tanaka, H. Iwasawa, D. Wang, M. Miyasaka, and Y. Takeuchi, “Solution-processed silicon films and transistors,” Nature 440, 783–786 (2006).
[CrossRef]

Zangwill, A.

C. Ratsch and A. Zangwill, “Equilibrium theory of the Stranski–Krastanov epitaxial morphology,” Surf. Sci. 293, 123–131 (1993).
[CrossRef]

Zerlauth, S.

G. Springholz, M. Pinczolits, V. Holý, S. Zerlauth, I. Vávra, and G. Bauer, “Vertical and lateral ordering in self-organized quantum dot superlattices,” Physica E 9, 149–163 (2001).
[CrossRef]

Acc. Chem. Res. (1)

M. L. Steigerwald and L. E. Brus, “Semiconductor crystallites: a class of large molecules,” Acc. Chem. Res. 23, 183–188 (1990).
[CrossRef]

Angew. Chem., Int. Ed. Engl. (1)

W. W. Yu and X. Peng, “Formation of high-quality CdS and Ooher II–VI semiconductor nanocrystals in noncoordinating solvents: tunable reactivity of monomers,” Angew. Chem., Int. Ed. Engl. 41, 2368–2371 (2002).
[CrossRef]

Annu. Rev. Mater. Sci. (1)

C. B. Murray, C. R. Kagan, and M. G. Bawendi, “Synthesis and characterization of monodisperse nanocrystals and close-packed nanocrystal assemblies,” Annu. Rev. Mater. Sci. 30, 545–610 (2000).
[CrossRef]

Appl. Phys. Lett. (2)

L. Goldstein, F. Glas, J. Y. Marzin, M. N. Charasse, and G. LeRoux, “Growth by molecular beam epitaxy and characterization of InAs/GaAs strained-layer superlattices,” Appl. Phys. Lett. 47, 1099–1101 (1985).
[CrossRef]

D. Leonard, M. Krishnamurthy, C. M. Reaves, S. P. Denbaars, and P. M. Petroff, “Direct information of quantum sized dots from uniform coherent islands of InGaAs on GaAs surfaces,” Appl. Phys. Lett. 63, 3203–3205 (1993).
[CrossRef]

Chem. Mater. (1)

J. Nanda, S. Sapra, D. D. Sarma, N. Chandrasekharan, and G. Hodes, “Size-selected zinc sulfide nanocrystallites: synthesis, structure, and optical studies,” Chem. Mater. 12, 1018–1024 (2000).
[CrossRef]

Fiz. Tekh. Poluprovodn (1)

N. N. Ledentsov, V. M. Ustinov, V. A. Shchukin, P. S. Kop’ev, Z. I. Alferov, and D. Bimberg, “Quantum dot heterostructures: fabrication, properties, lasers,” Fiz. Tekh. Poluprovodn 32, 385–410 (1998).

J. Adv. Mater. (1)

D. B. Mitzi, M. Copel, and S. Chey, “Low-voltage transistor employing a high- mobility spin-coated chalcogenide semiconductor,” J. Adv. Mater. 17, 1285–1289 (2005).
[CrossRef]

J. Am. Chem. Soc. (3)

B. S. Ong, C. Li, Y. Li, Y. Wu, and R. Loutfy, “Stable, solution-processed, high-mobility ZnO thin-film transistors,” J. Am. Chem. Soc. 129, 2750–2751 (2007).
[CrossRef]

X. Peng, J. Wickham, and A. P. Alivisatos, “Kinetics of II-VI and III-V colloidal semiconductor nanocrystal growth: ‘focusing’ of size distributions,” J. Am. Chem. Soc. 120, 5343–5344 (1998).
[CrossRef]

A. Kergommeaux, J. Faure-Vincent, A. Pron, R. Bettignies, B. Malaman, and P. Reiss, “Surface oxidation of tin chalcogenide nanocrystals revealed by 119Sn-Mossbauer spectroscopy,” J. Am. Chem. Soc. 134, 11659–11666 (2012).
[CrossRef]

J. Cryst. Growth (1)

S. Suraprapapich, Y. M. Shen, V. A. Odnoblyudov, Y. Fainman, S. Panyakeow, and C. W. Tu, “Self-assembled lateral Bi-quantum-dot molecule formation by gas-source molecular beam epitaxy,” J. Cryst. Growth 301–302, 735–739 (2007).
[CrossRef]

J. Exp. Theor. Phys. (2)

R. D. Vengrenovich, B. V. Ivanskii, and A. V. Moskalyuk, “Generalized Lifshitz–Slyozov–Wagner distribution,” J. Exp. Theor. Phys. 131, 1040–1047 (2007).

I. M. Lifshits and V. V. Slyozov, “On kinetics of diffusion decay of oversaturated solid solutions,” J. Exp. Theor. Phys. 35, 479–492 (1958).

J. Phys. Chem. B (1)

R. Viswanatha, S. Sapra, S. Sen Gupta, B. Satpati, P. V. Satyam, B. N. Dev, and D. D. Sarma, “Synthesis and characterization of Mn-doped ZnO nanocrystals,” J. Phys. Chem. B 108, 6303–6310 (2004).
[CrossRef]

J. Phys. Chem. C (1)

A. Layek, G. Mishra, A. Sharma, M. Spasova, S. Dhar, A. Chowdhury, and R. A. Bandyopadhyaya, “Generalized three-stage mechanism of ZnO nanoparticle formation in homogeneous liquid medium,” J. Phys. Chem. C 116, 24757–24769 (2012).
[CrossRef]

J. Phys. Chem. Solids Suppl. (1)

B. K. Chakraverty, “Grain size distribution in thin films. I. Conservative systems,” J. Phys. Chem. Solids Suppl. 28, 2401–2412 (1967).

Nat. Mater. (1)

J. J. Urban, D. V. Talapin, E. V. Shevchenko, C. R. Kagan, and C. B. Murray, “Synergism in binary nanocrystal superlattices leads to enhanced p-type conductivity in self-assembled PbTe/Ag2Te thin films,” Nat. Mater. 6, 115–121 (2007).
[CrossRef]

Nat. Nanotechnol. (1)

J.-S. Lee, M. V. Kovalenko, J. Huang, D. S. Chung, and D. V. Talapin, “Band-like transport, high electron mobility and high photoconductivity in all-inorganic nanocrystal arrays,” Nat. Nanotechnol. 6, 348–352 (2011).
[CrossRef]

Nature (1)

T. Shimoda, Y. Matsuki, M. Furusawa, T. Aoki, I. Yudasaka, H. Tanaka, H. Iwasawa, D. Wang, M. Miyasaka, and Y. Takeuchi, “Solution-processed silicon films and transistors,” Nature 440, 783–786 (2006).
[CrossRef]

Phys. Rev. B (1)

D. Leonard, K. Pond, and P. M. Petroff, “Critical layer thickness for self-assembled InAs islands on GaAs,” Phys. Rev. B 50, 11687–11692 (1994).
[CrossRef]

Phys. Rev. Lett. (7)

J.-M. Marzin, J.-M. Gerard, A. Izrael, and D. Barrier, “Photoluminescence of single InAs quantum dots obtained by self-organized growth on GaAs,” Phys. Rev. Lett. 73, 716–719 (1994).
[CrossRef]

D. E. Eaglesham and M. Cerullo, “Dislocation-free Stranski–Krastanow growth of Ge on Si (100),” Phys. Rev. Lett. 64, 1943–1946 (1990).
[CrossRef]

J.-W. Mo, D. E. Savage, B. S. Swartzentruber, and M. G. Lagally, “Kinetic pathway in Stranski–Krastanov growth of Ge on Si(001),” Phys. Rev. Lett. 65, 1020–1023 (1990).
[CrossRef]

P. Gangopadhyay, R. Kesavamoorthy, S. Bera, P. Magudapathy, K. G. M. Nair, B. K. Panigrahi, and S. V. Narasimhan, “Optical absorption and photoluminescence spectroscopy of the growth of silver nanoparticles,” Phys. Rev. Lett. 94, 047403 (2005).
[CrossRef]

S. Takakusagi, K. Fukui, R. Tero, F. Nariyuki, and Y. Iwasawa, “Self-limiting growth of Pt nanoparticles from MeCpPtMe3 adsorbed on TiO2110 studied by scanning tunneling microscopy,” Phys. Rev. Lett. 91, 066102 (2003).
[CrossRef]

A. F. Craievich, G. Kellermann, L. C. Barbosa, and O. L. Alves, “Structure characterization and mechanism of growth of PbTe nanocrystals embedded in a silicate glass,” Phys. Rev. Lett. 89, 235503 (2002).
[CrossRef]

R. D. Averitt, D. Sarkar, and N. J. Halas, “General vector basis function solution of Maxwell’s equations,” Phys. Rev. Lett. 78, 4217–4220 (1997).
[CrossRef]

Physica E (1)

G. Springholz, M. Pinczolits, V. Holý, S. Zerlauth, I. Vávra, and G. Bauer, “Vertical and lateral ordering in self-organized quantum dot superlattices,” Physica E 9, 149–163 (2001).
[CrossRef]

Science (1)

D. V. Talapin and C. B. Murray, “PbSe nanocrystal solids for n- and p-channel thin film field-effect transistors,” Science 310, 86–89 (2005).
[CrossRef]

Sitzungsberichte der Akademie der Wifienschaften Wien, Mathematisch Naturwifienschaftlich Klafie, Abt. Lib. Bd. (1)

I. N. Stranski and L. Krastanov, “Theory of orientation separation of ionic crystal,” Sitzungsberichte der Akademie der Wifienschaften Wien, Mathematisch Naturwifienschaftlich Klafie, Abt. Lib. Bd. 146, 797–810 (1937).

Surf. Sci. (1)

C. Ratsch and A. Zangwill, “Equilibrium theory of the Stranski–Krastanov epitaxial morphology,” Surf. Sci. 293, 123–131 (1993).
[CrossRef]

Ukr. J. Phys. (1)

R. D. Vengrenovich, B. V. Ivans’kyi, and A. V. Moskalyuk, “Generalized Chakraverty–Wagner distribution,” Ukr. J. Phys. 53, 1101–1109 (2008).

Zs. Electrochem. (1)

C. Wagner, “Theorie der alterung von niderschlagen durch umlösen (Ostwald Reifung),” Zs. Electrochem. 65, 581–591 (1961).

Zs. Phys. Chem. (1)

W. Ostwald, “Uber die vermeintliche isomerie des rotten und gelben quecksilberoxyds und die oberflachenspannung fester korper,” Zs. Phys. Chem. 34, 495–503 (1900).

Other (6)

L. A. Kosyachenko, ed., Solar Cells: Thin-Film Technologies (InTech, 2011), p. 456.

L. A. Kosyachenko, ed., Solar Cells: Silicon Wafer-Based Technologies (InTech, 2011), p. 364.

L. A. Kosyachenko, ed., Solar Cells: New Aspects and Solutions Edited (InTech, 2011), p. 512.

L. A. Kosyachenko, ed., Solar Cells: Dye-Sensitized Devices (InTech, 2011), p. 492.

D. Vanderbilt and L. K. Wickham, “Elastic relaxation energies of coherent germanium islands on silicon,” in Evolution of Thin Film and Surface Microstructures (Mater. Res. Soc. Symp. Proc.), C. V. Thompson, J. Y. Tsao, and D. J. Srolovitz, eds. (Materials Research Society, 1991), Vol. 202, pp. 555–560.

U. Hartmann, Faszination Nanotechnologie (Elsevier, 2006).

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Figures (5)

Fig. 1.
Fig. 1.

Generalized Chakraverty–Wagner distribution computed for the set of magnitudes of the parameter x(0x1) (fragment a); the same dependences normalized by their maxima (fragment b).

Fig. 2.
Fig. 2.

Generalized Lifshitz–Slyozov–Wagner distribution (GLSWD) computed for the set of magnitudes of the parameter x(0x1) (fragment a); the same dependences normalized by their maxima (fragment b).

Fig. 3.
Fig. 3.

Comparison of the theoretical dependence, Eq. (13), with the experimental histograms for InAs/GaAs(001) QDs obtained by applying the molecular-beam epitaxy technique at 500°C.

Fig. 4.
Fig. 4.

Comparison of the theoretical dependence, Eq. (13), with the experimental histograms for PbSe QDs at buffer layer PbTe(111) obtained by applying the molecular-beam epitaxy technique at a substrate temperature of 360°C.

Fig. 5.
Fig. 5.

Comparison of the theoretical dependence, Eq. (16), with the experimentally obtained histograms for SnS NCs synthesized from oversaturated solutions by applying the colloid chemistry technique.

Equations (22)

Equations on this page are rendered with MathJax. Learn more.

j=ji+jS,
jS=2πDSlnl(CCr),
ji=4πr2α2(θ)sin2θβ(CCr),
ddt(43πr3sin3θα1(θ))=jυm,
α1(θ)=(23cosθ+cos2θ/4)
drdt=A*r3(1xxr2rg2+1)(rrk1),
jijs=1xxA*=σCυm2DS2kTsin4θα2(θ)α12(θ)lnl,
drdt=B*r(x1x·rg2r2+1)(rrk1),
B*=σCυm2βkTsin2θα22(θ)α1(θ).
f(r,t)t+t[f(r,t)r˙]=0,
r˙drdt,f(r,t)=φ(rg)g(u),
Φ=43πα1(θ)1sin3θ0rgr3f(r,t)dr.
φ(rg)=Qrg4,
Q=Φ43πα1(θ)1sin3θ01u3g(u)du.
f(r,t)=1rg4Q·g(u)=1rg4g(u),
g(u)=Q·g(u)
g(u)=u3(u2+2ux2+2x2+x)D/2(1u)B×exp(FDx22x2+xx4arctgu+x22x2+xx4)exp(C1u),
B=32x4+16x3+48x2+13x+5AC=12x2+3x+3AD=80x4+40x3+15x2+x+2AF=32x6+16x5+54x4+34x3+8x2AA=16x4+8x3+9x2+2x+1.
g(u)=u(1u)5exp(31u).
g(u)=u3exp(12(1u))exp(162arctgu+12)(1u)19/6(u2+2u+3)23/12.
g(u)=u2(1u)B(u+x2+x)Dexp(C1u),
{B=2x4+4x3+12x2+10x+5F,D=4x4+8x3+6x2+2x+1F,C=3x2+3x+3F,F=x4+2x3+3x2+2x+1.

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