Abstract

We study electrically tunable self-assembled InAs quantum dot molecules through photoluminescence (PL) and time-resolved PL measurements. For the model we assume quantum dots with cylindrical symmetry, for which the confinement potentials have been modeled as narrow quantum wells in the growth and in-plane directions matched to parabolic potentials. We focus on the hole scattering rates by bulk acoustic phonons, as these rates are the leading contribution for the neutral indirect exciton relaxation rate when the electron localizes primarily on one dot. The hole–phonon scattering structure factor for acoustic phonons is found to contain a phase relationship between the phonon wave and the hole wave function, which can be tuned by an external electric field. The phase relationship leads to interference effects and tunable oscillatory relaxation rates of indirect excitons, in agreement with experiments.

© 2012 Optical Society of America

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  1. U. Bockelmann and G. Bastard, “Phonon scattering and energy relaxation in two-, one-, and zero-dimensional electron gases,” Phys. Rev. B 42, 8947–8951 (1990).
    [CrossRef]
  2. B. Ohnesorge, M. Albrecht, J. Oshinowo, A. Forchel, and Y. Arakawa, “Rapid carrier relaxation in self-assembled InxGa1−xAs/GaAs quantum dots,” Phys. Rev. B 54, 11532–11538(1996).
    [CrossRef]
  3. P. Borri, W. Langbein, U. Woggon, M. Schwab, M. Bayer, S. Fafard, Z. Wasilewski, and P. Hawrylak, “Exciton dephasing in quantum dot molecules,” Phys. Rev. Lett. 91, 267401 (2003).
    [CrossRef]
  4. J. I. Climente, A. Bertoni, G. Goldoni, and E. Molinari, “Phonon-induced electron relaxation in weakly confined single and coupled quantum dots,” Phys. Rev. B 74, 035313 (2006).
    [CrossRef]
  5. J. I. Climente, A. Bertoni, G. Goldoni, and E. Molinari, “Directionality of acoustic-phonon emission in weakly confined semiconductor quantum dots,” Phys. Rev. B 75, 245330 (2007).
    [CrossRef]
  6. J. E. Rolon, “Coherent exciton phenomena in quantum dot molecules,” Ph.D. thesis (Ohio University, 2011).
  7. K. C. Wijesundara, J. E. Rolon, S. E. Ulloa, A. S. Bracker, D. Gammon, and E. A. Stinaff, “Tunable exciton relaxation in vertically coupled semiconductor InAs quantum dots,” Phys. Rev. B 84, 081404(R) (2011).
    [CrossRef]
  8. E. A. Stinaff, M. Scheibner, A. S. Bracker, I. V. Ponomarev, V. L. Korenev, M. E. Ware, M. F. Doty, T. L. Reinecke, and D. Gammon, Science 311, 636–639 (2006).
    [CrossRef]
  9. A. O. Govorov, “Spin-Förster transfer in optically excited quantum dots,” Phys. Rev. B 71, 155323 (2005).
    [CrossRef]
  10. A. Nazir, B. W. Lovett, S. D. Barrett, J. H. Reina, and G. A. D. Briggs, “Anticrossings in Förster coupled quantum dots,” Phys. Rev. B 71, 045334 (2005).
    [CrossRef]
  11. S. M. Reimann and M. Manninen, “Electronic structure of quantum dots,” Rev. Mod. Phys. 74, 1283–1342(2002).
    [CrossRef]
  12. A. S. Bracker, M. Scheibner, M. F. Doty, E. A. Stinaff, I. V. Ponomarev, J. C. Kim, L. J. Whitman, T. L. Reinecke, and D. Gammon, “Engineering electron and hole tunneling with asymmetric InAs quantum dot molecules,” Appl. Phys. Lett. 89, 233110 (2006).
    [CrossRef]
  13. V. F. Gantmakher and Y. B. Levinson, Carrier Scattering in Metals and Semiconductors, Modern Problems in Condensed Matter Sciences (Elsevier Science, 1987).
  14. V. Mlinar, M. Bozkurt, J. M. Ulloa, M. Ediger, G. Bester, A. Badolato, P. M. Koenraad, R. J. Warburton, and A. Zunger, “Structure of quantum dots as seen by excitonic spectroscopy versus structural characterization: using theory to close the loop,” Phys. Rev. B. 80, 165425 (2009).
    [CrossRef]
  15. E. L. Ivchenko and G. E. Pikus, Superlattices and Other Heterostructures (Springer, 1995).

2011 (1)

K. C. Wijesundara, J. E. Rolon, S. E. Ulloa, A. S. Bracker, D. Gammon, and E. A. Stinaff, “Tunable exciton relaxation in vertically coupled semiconductor InAs quantum dots,” Phys. Rev. B 84, 081404(R) (2011).
[CrossRef]

2009 (1)

V. Mlinar, M. Bozkurt, J. M. Ulloa, M. Ediger, G. Bester, A. Badolato, P. M. Koenraad, R. J. Warburton, and A. Zunger, “Structure of quantum dots as seen by excitonic spectroscopy versus structural characterization: using theory to close the loop,” Phys. Rev. B. 80, 165425 (2009).
[CrossRef]

2007 (1)

J. I. Climente, A. Bertoni, G. Goldoni, and E. Molinari, “Directionality of acoustic-phonon emission in weakly confined semiconductor quantum dots,” Phys. Rev. B 75, 245330 (2007).
[CrossRef]

2006 (3)

A. S. Bracker, M. Scheibner, M. F. Doty, E. A. Stinaff, I. V. Ponomarev, J. C. Kim, L. J. Whitman, T. L. Reinecke, and D. Gammon, “Engineering electron and hole tunneling with asymmetric InAs quantum dot molecules,” Appl. Phys. Lett. 89, 233110 (2006).
[CrossRef]

E. A. Stinaff, M. Scheibner, A. S. Bracker, I. V. Ponomarev, V. L. Korenev, M. E. Ware, M. F. Doty, T. L. Reinecke, and D. Gammon, Science 311, 636–639 (2006).
[CrossRef]

J. I. Climente, A. Bertoni, G. Goldoni, and E. Molinari, “Phonon-induced electron relaxation in weakly confined single and coupled quantum dots,” Phys. Rev. B 74, 035313 (2006).
[CrossRef]

2005 (2)

A. O. Govorov, “Spin-Förster transfer in optically excited quantum dots,” Phys. Rev. B 71, 155323 (2005).
[CrossRef]

A. Nazir, B. W. Lovett, S. D. Barrett, J. H. Reina, and G. A. D. Briggs, “Anticrossings in Förster coupled quantum dots,” Phys. Rev. B 71, 045334 (2005).
[CrossRef]

2003 (1)

P. Borri, W. Langbein, U. Woggon, M. Schwab, M. Bayer, S. Fafard, Z. Wasilewski, and P. Hawrylak, “Exciton dephasing in quantum dot molecules,” Phys. Rev. Lett. 91, 267401 (2003).
[CrossRef]

2002 (1)

S. M. Reimann and M. Manninen, “Electronic structure of quantum dots,” Rev. Mod. Phys. 74, 1283–1342(2002).
[CrossRef]

1996 (1)

B. Ohnesorge, M. Albrecht, J. Oshinowo, A. Forchel, and Y. Arakawa, “Rapid carrier relaxation in self-assembled InxGa1−xAs/GaAs quantum dots,” Phys. Rev. B 54, 11532–11538(1996).
[CrossRef]

1990 (1)

U. Bockelmann and G. Bastard, “Phonon scattering and energy relaxation in two-, one-, and zero-dimensional electron gases,” Phys. Rev. B 42, 8947–8951 (1990).
[CrossRef]

Albrecht, M.

B. Ohnesorge, M. Albrecht, J. Oshinowo, A. Forchel, and Y. Arakawa, “Rapid carrier relaxation in self-assembled InxGa1−xAs/GaAs quantum dots,” Phys. Rev. B 54, 11532–11538(1996).
[CrossRef]

Arakawa, Y.

B. Ohnesorge, M. Albrecht, J. Oshinowo, A. Forchel, and Y. Arakawa, “Rapid carrier relaxation in self-assembled InxGa1−xAs/GaAs quantum dots,” Phys. Rev. B 54, 11532–11538(1996).
[CrossRef]

Badolato, A.

V. Mlinar, M. Bozkurt, J. M. Ulloa, M. Ediger, G. Bester, A. Badolato, P. M. Koenraad, R. J. Warburton, and A. Zunger, “Structure of quantum dots as seen by excitonic spectroscopy versus structural characterization: using theory to close the loop,” Phys. Rev. B. 80, 165425 (2009).
[CrossRef]

Barrett, S. D.

A. Nazir, B. W. Lovett, S. D. Barrett, J. H. Reina, and G. A. D. Briggs, “Anticrossings in Förster coupled quantum dots,” Phys. Rev. B 71, 045334 (2005).
[CrossRef]

Bastard, G.

U. Bockelmann and G. Bastard, “Phonon scattering and energy relaxation in two-, one-, and zero-dimensional electron gases,” Phys. Rev. B 42, 8947–8951 (1990).
[CrossRef]

Bayer, M.

P. Borri, W. Langbein, U. Woggon, M. Schwab, M. Bayer, S. Fafard, Z. Wasilewski, and P. Hawrylak, “Exciton dephasing in quantum dot molecules,” Phys. Rev. Lett. 91, 267401 (2003).
[CrossRef]

Bertoni, A.

J. I. Climente, A. Bertoni, G. Goldoni, and E. Molinari, “Directionality of acoustic-phonon emission in weakly confined semiconductor quantum dots,” Phys. Rev. B 75, 245330 (2007).
[CrossRef]

J. I. Climente, A. Bertoni, G. Goldoni, and E. Molinari, “Phonon-induced electron relaxation in weakly confined single and coupled quantum dots,” Phys. Rev. B 74, 035313 (2006).
[CrossRef]

Bester, G.

V. Mlinar, M. Bozkurt, J. M. Ulloa, M. Ediger, G. Bester, A. Badolato, P. M. Koenraad, R. J. Warburton, and A. Zunger, “Structure of quantum dots as seen by excitonic spectroscopy versus structural characterization: using theory to close the loop,” Phys. Rev. B. 80, 165425 (2009).
[CrossRef]

Bockelmann, U.

U. Bockelmann and G. Bastard, “Phonon scattering and energy relaxation in two-, one-, and zero-dimensional electron gases,” Phys. Rev. B 42, 8947–8951 (1990).
[CrossRef]

Borri, P.

P. Borri, W. Langbein, U. Woggon, M. Schwab, M. Bayer, S. Fafard, Z. Wasilewski, and P. Hawrylak, “Exciton dephasing in quantum dot molecules,” Phys. Rev. Lett. 91, 267401 (2003).
[CrossRef]

Bozkurt, M.

V. Mlinar, M. Bozkurt, J. M. Ulloa, M. Ediger, G. Bester, A. Badolato, P. M. Koenraad, R. J. Warburton, and A. Zunger, “Structure of quantum dots as seen by excitonic spectroscopy versus structural characterization: using theory to close the loop,” Phys. Rev. B. 80, 165425 (2009).
[CrossRef]

Bracker, A. S.

K. C. Wijesundara, J. E. Rolon, S. E. Ulloa, A. S. Bracker, D. Gammon, and E. A. Stinaff, “Tunable exciton relaxation in vertically coupled semiconductor InAs quantum dots,” Phys. Rev. B 84, 081404(R) (2011).
[CrossRef]

E. A. Stinaff, M. Scheibner, A. S. Bracker, I. V. Ponomarev, V. L. Korenev, M. E. Ware, M. F. Doty, T. L. Reinecke, and D. Gammon, Science 311, 636–639 (2006).
[CrossRef]

A. S. Bracker, M. Scheibner, M. F. Doty, E. A. Stinaff, I. V. Ponomarev, J. C. Kim, L. J. Whitman, T. L. Reinecke, and D. Gammon, “Engineering electron and hole tunneling with asymmetric InAs quantum dot molecules,” Appl. Phys. Lett. 89, 233110 (2006).
[CrossRef]

Briggs, G. A. D.

A. Nazir, B. W. Lovett, S. D. Barrett, J. H. Reina, and G. A. D. Briggs, “Anticrossings in Förster coupled quantum dots,” Phys. Rev. B 71, 045334 (2005).
[CrossRef]

Climente, J. I.

J. I. Climente, A. Bertoni, G. Goldoni, and E. Molinari, “Directionality of acoustic-phonon emission in weakly confined semiconductor quantum dots,” Phys. Rev. B 75, 245330 (2007).
[CrossRef]

J. I. Climente, A. Bertoni, G. Goldoni, and E. Molinari, “Phonon-induced electron relaxation in weakly confined single and coupled quantum dots,” Phys. Rev. B 74, 035313 (2006).
[CrossRef]

Doty, M. F.

A. S. Bracker, M. Scheibner, M. F. Doty, E. A. Stinaff, I. V. Ponomarev, J. C. Kim, L. J. Whitman, T. L. Reinecke, and D. Gammon, “Engineering electron and hole tunneling with asymmetric InAs quantum dot molecules,” Appl. Phys. Lett. 89, 233110 (2006).
[CrossRef]

E. A. Stinaff, M. Scheibner, A. S. Bracker, I. V. Ponomarev, V. L. Korenev, M. E. Ware, M. F. Doty, T. L. Reinecke, and D. Gammon, Science 311, 636–639 (2006).
[CrossRef]

Ediger, M.

V. Mlinar, M. Bozkurt, J. M. Ulloa, M. Ediger, G. Bester, A. Badolato, P. M. Koenraad, R. J. Warburton, and A. Zunger, “Structure of quantum dots as seen by excitonic spectroscopy versus structural characterization: using theory to close the loop,” Phys. Rev. B. 80, 165425 (2009).
[CrossRef]

Fafard, S.

P. Borri, W. Langbein, U. Woggon, M. Schwab, M. Bayer, S. Fafard, Z. Wasilewski, and P. Hawrylak, “Exciton dephasing in quantum dot molecules,” Phys. Rev. Lett. 91, 267401 (2003).
[CrossRef]

Forchel, A.

B. Ohnesorge, M. Albrecht, J. Oshinowo, A. Forchel, and Y. Arakawa, “Rapid carrier relaxation in self-assembled InxGa1−xAs/GaAs quantum dots,” Phys. Rev. B 54, 11532–11538(1996).
[CrossRef]

Gammon, D.

K. C. Wijesundara, J. E. Rolon, S. E. Ulloa, A. S. Bracker, D. Gammon, and E. A. Stinaff, “Tunable exciton relaxation in vertically coupled semiconductor InAs quantum dots,” Phys. Rev. B 84, 081404(R) (2011).
[CrossRef]

A. S. Bracker, M. Scheibner, M. F. Doty, E. A. Stinaff, I. V. Ponomarev, J. C. Kim, L. J. Whitman, T. L. Reinecke, and D. Gammon, “Engineering electron and hole tunneling with asymmetric InAs quantum dot molecules,” Appl. Phys. Lett. 89, 233110 (2006).
[CrossRef]

E. A. Stinaff, M. Scheibner, A. S. Bracker, I. V. Ponomarev, V. L. Korenev, M. E. Ware, M. F. Doty, T. L. Reinecke, and D. Gammon, Science 311, 636–639 (2006).
[CrossRef]

Gantmakher, V. F.

V. F. Gantmakher and Y. B. Levinson, Carrier Scattering in Metals and Semiconductors, Modern Problems in Condensed Matter Sciences (Elsevier Science, 1987).

Goldoni, G.

J. I. Climente, A. Bertoni, G. Goldoni, and E. Molinari, “Directionality of acoustic-phonon emission in weakly confined semiconductor quantum dots,” Phys. Rev. B 75, 245330 (2007).
[CrossRef]

J. I. Climente, A. Bertoni, G. Goldoni, and E. Molinari, “Phonon-induced electron relaxation in weakly confined single and coupled quantum dots,” Phys. Rev. B 74, 035313 (2006).
[CrossRef]

Govorov, A. O.

A. O. Govorov, “Spin-Förster transfer in optically excited quantum dots,” Phys. Rev. B 71, 155323 (2005).
[CrossRef]

Hawrylak, P.

P. Borri, W. Langbein, U. Woggon, M. Schwab, M. Bayer, S. Fafard, Z. Wasilewski, and P. Hawrylak, “Exciton dephasing in quantum dot molecules,” Phys. Rev. Lett. 91, 267401 (2003).
[CrossRef]

Ivchenko, E. L.

E. L. Ivchenko and G. E. Pikus, Superlattices and Other Heterostructures (Springer, 1995).

Kim, J. C.

A. S. Bracker, M. Scheibner, M. F. Doty, E. A. Stinaff, I. V. Ponomarev, J. C. Kim, L. J. Whitman, T. L. Reinecke, and D. Gammon, “Engineering electron and hole tunneling with asymmetric InAs quantum dot molecules,” Appl. Phys. Lett. 89, 233110 (2006).
[CrossRef]

Koenraad, P. M.

V. Mlinar, M. Bozkurt, J. M. Ulloa, M. Ediger, G. Bester, A. Badolato, P. M. Koenraad, R. J. Warburton, and A. Zunger, “Structure of quantum dots as seen by excitonic spectroscopy versus structural characterization: using theory to close the loop,” Phys. Rev. B. 80, 165425 (2009).
[CrossRef]

Korenev, V. L.

E. A. Stinaff, M. Scheibner, A. S. Bracker, I. V. Ponomarev, V. L. Korenev, M. E. Ware, M. F. Doty, T. L. Reinecke, and D. Gammon, Science 311, 636–639 (2006).
[CrossRef]

Langbein, W.

P. Borri, W. Langbein, U. Woggon, M. Schwab, M. Bayer, S. Fafard, Z. Wasilewski, and P. Hawrylak, “Exciton dephasing in quantum dot molecules,” Phys. Rev. Lett. 91, 267401 (2003).
[CrossRef]

Levinson, Y. B.

V. F. Gantmakher and Y. B. Levinson, Carrier Scattering in Metals and Semiconductors, Modern Problems in Condensed Matter Sciences (Elsevier Science, 1987).

Lovett, B. W.

A. Nazir, B. W. Lovett, S. D. Barrett, J. H. Reina, and G. A. D. Briggs, “Anticrossings in Förster coupled quantum dots,” Phys. Rev. B 71, 045334 (2005).
[CrossRef]

Manninen, M.

S. M. Reimann and M. Manninen, “Electronic structure of quantum dots,” Rev. Mod. Phys. 74, 1283–1342(2002).
[CrossRef]

Mlinar, V.

V. Mlinar, M. Bozkurt, J. M. Ulloa, M. Ediger, G. Bester, A. Badolato, P. M. Koenraad, R. J. Warburton, and A. Zunger, “Structure of quantum dots as seen by excitonic spectroscopy versus structural characterization: using theory to close the loop,” Phys. Rev. B. 80, 165425 (2009).
[CrossRef]

Molinari, E.

J. I. Climente, A. Bertoni, G. Goldoni, and E. Molinari, “Directionality of acoustic-phonon emission in weakly confined semiconductor quantum dots,” Phys. Rev. B 75, 245330 (2007).
[CrossRef]

J. I. Climente, A. Bertoni, G. Goldoni, and E. Molinari, “Phonon-induced electron relaxation in weakly confined single and coupled quantum dots,” Phys. Rev. B 74, 035313 (2006).
[CrossRef]

Nazir, A.

A. Nazir, B. W. Lovett, S. D. Barrett, J. H. Reina, and G. A. D. Briggs, “Anticrossings in Förster coupled quantum dots,” Phys. Rev. B 71, 045334 (2005).
[CrossRef]

Ohnesorge, B.

B. Ohnesorge, M. Albrecht, J. Oshinowo, A. Forchel, and Y. Arakawa, “Rapid carrier relaxation in self-assembled InxGa1−xAs/GaAs quantum dots,” Phys. Rev. B 54, 11532–11538(1996).
[CrossRef]

Oshinowo, J.

B. Ohnesorge, M. Albrecht, J. Oshinowo, A. Forchel, and Y. Arakawa, “Rapid carrier relaxation in self-assembled InxGa1−xAs/GaAs quantum dots,” Phys. Rev. B 54, 11532–11538(1996).
[CrossRef]

Pikus, G. E.

E. L. Ivchenko and G. E. Pikus, Superlattices and Other Heterostructures (Springer, 1995).

Ponomarev, I. V.

A. S. Bracker, M. Scheibner, M. F. Doty, E. A. Stinaff, I. V. Ponomarev, J. C. Kim, L. J. Whitman, T. L. Reinecke, and D. Gammon, “Engineering electron and hole tunneling with asymmetric InAs quantum dot molecules,” Appl. Phys. Lett. 89, 233110 (2006).
[CrossRef]

E. A. Stinaff, M. Scheibner, A. S. Bracker, I. V. Ponomarev, V. L. Korenev, M. E. Ware, M. F. Doty, T. L. Reinecke, and D. Gammon, Science 311, 636–639 (2006).
[CrossRef]

Reimann, S. M.

S. M. Reimann and M. Manninen, “Electronic structure of quantum dots,” Rev. Mod. Phys. 74, 1283–1342(2002).
[CrossRef]

Reina, J. H.

A. Nazir, B. W. Lovett, S. D. Barrett, J. H. Reina, and G. A. D. Briggs, “Anticrossings in Förster coupled quantum dots,” Phys. Rev. B 71, 045334 (2005).
[CrossRef]

Reinecke, T. L.

E. A. Stinaff, M. Scheibner, A. S. Bracker, I. V. Ponomarev, V. L. Korenev, M. E. Ware, M. F. Doty, T. L. Reinecke, and D. Gammon, Science 311, 636–639 (2006).
[CrossRef]

A. S. Bracker, M. Scheibner, M. F. Doty, E. A. Stinaff, I. V. Ponomarev, J. C. Kim, L. J. Whitman, T. L. Reinecke, and D. Gammon, “Engineering electron and hole tunneling with asymmetric InAs quantum dot molecules,” Appl. Phys. Lett. 89, 233110 (2006).
[CrossRef]

Rolon, J. E.

K. C. Wijesundara, J. E. Rolon, S. E. Ulloa, A. S. Bracker, D. Gammon, and E. A. Stinaff, “Tunable exciton relaxation in vertically coupled semiconductor InAs quantum dots,” Phys. Rev. B 84, 081404(R) (2011).
[CrossRef]

J. E. Rolon, “Coherent exciton phenomena in quantum dot molecules,” Ph.D. thesis (Ohio University, 2011).

Scheibner, M.

E. A. Stinaff, M. Scheibner, A. S. Bracker, I. V. Ponomarev, V. L. Korenev, M. E. Ware, M. F. Doty, T. L. Reinecke, and D. Gammon, Science 311, 636–639 (2006).
[CrossRef]

A. S. Bracker, M. Scheibner, M. F. Doty, E. A. Stinaff, I. V. Ponomarev, J. C. Kim, L. J. Whitman, T. L. Reinecke, and D. Gammon, “Engineering electron and hole tunneling with asymmetric InAs quantum dot molecules,” Appl. Phys. Lett. 89, 233110 (2006).
[CrossRef]

Schwab, M.

P. Borri, W. Langbein, U. Woggon, M. Schwab, M. Bayer, S. Fafard, Z. Wasilewski, and P. Hawrylak, “Exciton dephasing in quantum dot molecules,” Phys. Rev. Lett. 91, 267401 (2003).
[CrossRef]

Stinaff, E. A.

K. C. Wijesundara, J. E. Rolon, S. E. Ulloa, A. S. Bracker, D. Gammon, and E. A. Stinaff, “Tunable exciton relaxation in vertically coupled semiconductor InAs quantum dots,” Phys. Rev. B 84, 081404(R) (2011).
[CrossRef]

E. A. Stinaff, M. Scheibner, A. S. Bracker, I. V. Ponomarev, V. L. Korenev, M. E. Ware, M. F. Doty, T. L. Reinecke, and D. Gammon, Science 311, 636–639 (2006).
[CrossRef]

A. S. Bracker, M. Scheibner, M. F. Doty, E. A. Stinaff, I. V. Ponomarev, J. C. Kim, L. J. Whitman, T. L. Reinecke, and D. Gammon, “Engineering electron and hole tunneling with asymmetric InAs quantum dot molecules,” Appl. Phys. Lett. 89, 233110 (2006).
[CrossRef]

Ulloa, J. M.

V. Mlinar, M. Bozkurt, J. M. Ulloa, M. Ediger, G. Bester, A. Badolato, P. M. Koenraad, R. J. Warburton, and A. Zunger, “Structure of quantum dots as seen by excitonic spectroscopy versus structural characterization: using theory to close the loop,” Phys. Rev. B. 80, 165425 (2009).
[CrossRef]

Ulloa, S. E.

K. C. Wijesundara, J. E. Rolon, S. E. Ulloa, A. S. Bracker, D. Gammon, and E. A. Stinaff, “Tunable exciton relaxation in vertically coupled semiconductor InAs quantum dots,” Phys. Rev. B 84, 081404(R) (2011).
[CrossRef]

Warburton, R. J.

V. Mlinar, M. Bozkurt, J. M. Ulloa, M. Ediger, G. Bester, A. Badolato, P. M. Koenraad, R. J. Warburton, and A. Zunger, “Structure of quantum dots as seen by excitonic spectroscopy versus structural characterization: using theory to close the loop,” Phys. Rev. B. 80, 165425 (2009).
[CrossRef]

Ware, M. E.

E. A. Stinaff, M. Scheibner, A. S. Bracker, I. V. Ponomarev, V. L. Korenev, M. E. Ware, M. F. Doty, T. L. Reinecke, and D. Gammon, Science 311, 636–639 (2006).
[CrossRef]

Wasilewski, Z.

P. Borri, W. Langbein, U. Woggon, M. Schwab, M. Bayer, S. Fafard, Z. Wasilewski, and P. Hawrylak, “Exciton dephasing in quantum dot molecules,” Phys. Rev. Lett. 91, 267401 (2003).
[CrossRef]

Whitman, L. J.

A. S. Bracker, M. Scheibner, M. F. Doty, E. A. Stinaff, I. V. Ponomarev, J. C. Kim, L. J. Whitman, T. L. Reinecke, and D. Gammon, “Engineering electron and hole tunneling with asymmetric InAs quantum dot molecules,” Appl. Phys. Lett. 89, 233110 (2006).
[CrossRef]

Wijesundara, K. C.

K. C. Wijesundara, J. E. Rolon, S. E. Ulloa, A. S. Bracker, D. Gammon, and E. A. Stinaff, “Tunable exciton relaxation in vertically coupled semiconductor InAs quantum dots,” Phys. Rev. B 84, 081404(R) (2011).
[CrossRef]

Woggon, U.

P. Borri, W. Langbein, U. Woggon, M. Schwab, M. Bayer, S. Fafard, Z. Wasilewski, and P. Hawrylak, “Exciton dephasing in quantum dot molecules,” Phys. Rev. Lett. 91, 267401 (2003).
[CrossRef]

Zunger, A.

V. Mlinar, M. Bozkurt, J. M. Ulloa, M. Ediger, G. Bester, A. Badolato, P. M. Koenraad, R. J. Warburton, and A. Zunger, “Structure of quantum dots as seen by excitonic spectroscopy versus structural characterization: using theory to close the loop,” Phys. Rev. B. 80, 165425 (2009).
[CrossRef]

Appl. Phys. Lett. (1)

A. S. Bracker, M. Scheibner, M. F. Doty, E. A. Stinaff, I. V. Ponomarev, J. C. Kim, L. J. Whitman, T. L. Reinecke, and D. Gammon, “Engineering electron and hole tunneling with asymmetric InAs quantum dot molecules,” Appl. Phys. Lett. 89, 233110 (2006).
[CrossRef]

Phys. Rev. B (7)

U. Bockelmann and G. Bastard, “Phonon scattering and energy relaxation in two-, one-, and zero-dimensional electron gases,” Phys. Rev. B 42, 8947–8951 (1990).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

(a) PL spectra as a function of energy separation between the indirect and direct exciton due to applied electric field relative to the exciton anticrossing. (b) Indirect exciton lifetime relative to the exciton energy separation along with a polynomial fit to guide the eye. (c) Measured indirect exciton normalized intensity. (d) Indirect to direct exciton intensity ratio extracted from decay rates corresponding to nonresonant excitation.

Fig. 2.
Fig. 2.

(a) Biexponential behavior of the direct exciton lifetime resulting from resonant excitation at the indirect exciton energy. (b) Rates extracted for indirect, direct, and nonradiative contribution using the biexponential data.

Fig. 3.
Fig. 3.

Model schematics. (a) InAs QDM consisting of two QDs (bottom, B, and top, T) with cylindrical symmetry separated by a distance d = d ˜ + ( h B + h T ) / 2 from their centers, having widths l B and l T , respectively; here d ˜ is the sharp edge GaAs barrier width (not shown). (b) Parabolic potentials are matched to the square well confinement potential band edges, V e ( h ) . The lowest energy eigenstates correspond to the Gaussian ground state of the harmonic oscillator problem.

Fig. 4.
Fig. 4.

Structure factor as function of in-plane q , axial q z phonon wave vectors, and different polar angles θ , for fixed applied electric field F = 0 and interdot distance d = 7 nm . The structure factor exhibits prominent resonances mostly along the q z d axis, and these resonances shift towards higher values of q z d for increasing θ . For the range of energies used in the experiment of Fig. 1, phonons emitted closely to the z axis contribute the most to the relaxation rate. See numerical values in Table 1.

Fig. 5.
Fig. 5.

Structure factor contour plot as function of energy separation and phonon axial wave vector, for fixed d = 7 nm . The dotted purple line indicates the phonon wave vector dispersion as a function of energy separation. The relaxation rates are strictly nonzero for allowed phonon wave vectors satisfying Eq. (40), in other words, only at the intersection points between the purple line and the contour points. Resonances are prominent at q z d = π and q z d = 3 π , which correspond to an energy separation of Δ E = 2.6 meV and Δ E = 6.2 meV , respectively. See numerical values in Table 1.

Fig. 6.
Fig. 6.

Theoretical fit to phonon rates along with structure factor characteristics and experimentally extracted exciton relaxation rates. (a) Sum of the deformation potential and piezoelectric channels of the indirect state gives rise to the theoretical total phonon-mediated relaxation rate ( γ p , theory ), shown as the green (solid) line. (b) Extracted rates for exciton states and nonradiative relaxation channels [phonon ( γ p ), trion ( γ t )] and a clear agreement with γ p and γ p , theory is established.

Tables (1)

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Table 1. Parameters Used in Calculations

Equations (48)

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d N I d t = R I N I γ p N I κ N I + G , d N D d t = R D N D + γ p N I κ N D + G ,
I I I D = 1 + κ / R D 1 + ( κ + 2 γ p ) / R I ,
H e ( h ) ϕ e ( h ) ( r ) = [ 2 2 m e ( h ) * 2 + V e ( h ) ( r ) ] ϕ e ( h ) ( r ) ,
V ( r ) = 1 2 m e ( h ) * ω e ( h ) 2 r 2 + 1 2 m e ( h ) * ω e ( h ) z 2 z 2 ,
r 2 = r 2 + z 2 .
ϕ e ( h ) ( r ) = ψ e ( h ) x ( x ) ψ e ( h ) y ( y ) ψ e ( h ) z ( z ) ,
ψ n ( x ) = ( 1 n ! 2 n d x π 1 2 ) 1 2 H n ( x d x ) e x 2 2 d x 2 ,
ϕ e ( h ) ( r ) = ( 1 π 3 2 d 2 d ) 1 2 exp ( r 2 2 d 2 z 2 2 d 2 ) ,
ϕ B ( r ) = ϕ h ( r ) ,
ϕ T ( r ) = ϕ h ( r d k ^ ) ,
ϕ B ( T ) ( r ) = exp ( r 2 2 d B ( T ) 2 ) d B ( T ) π ,
ϕ B ( z ) = exp ( z 2 2 d B 2 ) d B π ,
ϕ T ( z ) = exp ( ( z d ) 2 2 d T 2 ) d T π ,
X h B h T e B e T = ( a 11 a 12 a 21 a 22 ) ( ψ h T ψ h B ) ( b 11 b 12 a 21 a 22 ) ( ψ e T ψ e B ) ,
ψ e ( h ) B ( T ) = ϕ B ( T ) ( r ) ϕ e ( h ) B ( T ) ( z ) ,
H ^ h = ( ϵ h t h t h ϵ h + Δ S ( F ) ) ,
H ^ e = ( ϵ e t e t e ϵ e + Δ E 0 Δ S ( F ) ) ,
E h ± = ϵ h + 1 2 ( Δ S ( F ) ± Δ S 2 ( F ) + 4 t h 2 ) ,
( a 11 a 12 ) = 1 A + h ( ( Δ S ( F ) + Δ E h ) / t h 2 ) ,
( a 21 a 22 ) = 1 A h ( ( Δ S ( F ) Δ E h ) / t h 2 ) ,
Δ E h = Δ S 2 ( F ) + 4 t h 2
A ± h = ( 4 + ( Δ E h ± Δ S ( F ) ) 2 / t h 2 ) 1 2 ,
H ^ h ( e ) p h = ν q M ν e ( h ) ( q ) ( b ^ e i q · r + b ^ e i q · r ) ,
τ i f 1 = 2 π ν q | Ψ f | W ν | Ψ i | 2 δ ( E f E i ± E q ) ,
γ p h = 2 π ν q | M ν h ( q ) | 2 | Ψ | e i q · r | Ψ + | 2 δ ( Δ E h c s | q | ) .
I B B = a 11 a 21 e d B 2 q 2 4 e d B 2 q z 2 4 ,
I T T = a 22 a 12 e d T 2 q 2 4 e d T 2 q z 2 4 e i q z d ,
I B T + I T T = 2 ( a 22 a 11 + a 21 a 12 ) f B T e D B T 2 q 2 2 × e D B T 2 q z 2 4 e i q z d 2 ,
q 2 = q x 2 + q y 2 ,
D B T = d B d T d B 2 + d T 2 ,
D B T = d B d T d B 2 + d T 2 ,
f B T = d B d T d B 2 + d T 2 d B d T d B 2 + d T 2 exp ( d 2 4 D B T 2 ) .
| Ψ | e i q · r | Ψ + | 2 = | I B B | 2 + | I T T | 2 + | I B T | 2 + 2 ( I B B I T T * ) + 2 ( I B B I B T * ) + 2 ( I T T I B T * ) .
| I B B | 2 = | a 11 a 21 | 2 e q 2 2 ( d B 2 sin 2 θ + d B 2 cos 2 θ ) ,
| I T T | 2 = | a 12 a 22 | 2 e q 2 2 ( d T 2 sin 2 θ + d T 2 cos 2 θ ) ,
| I B T | 2 = 4 | a 11 a 22 + a 21 a 12 | 2 f B T 2 e q 2 ( D B T 2 sin 2 θ + D B T 2 2 cos 2 θ ) ,
2 ( I B B I T T * ) = 2 a 11 a 21 a 12 a 22 e 1 4 q 2 ( ( d B 2 + d T 2 ) sin 2 θ + ( d B 2 + d T 2 ) cos 2 θ ) cos ( q d cos θ ) ,
2 ( I B B I B T * ) = 4 a 11 a 12 ( a 11 a 22 + a 21 a 12 ) f B T e 1 2 q 2 ( ( d B 2 2 + D B T ) sin 2 θ + ( d B 2 + D B T 2 2 ) cos 2 θ ) × cos ( q d 2 cos θ ) ,
2 ( I T T I B T * ) = 4 a 12 a 22 ( a 11 a 22 + a 21 a 12 ) f B T e 1 2 q 2 ( ( d T 2 2 + D B T ) sin 2 θ + ( d T 2 + D B T 2 2 ) cos 2 θ ) × cos ( q d 2 cos θ ) .
q = Δ E h c s q = q sin θ q z = q cos θ .
| M ν = L A D P h ( q ) | 2 = D h 2 2 ρ c L A Ω c q ,
| M ν = L A P Z h ( q ) | 2 = 32 e 2 π 2 e 14 , v 2 ( 3 q x q y q z ) 2 ϵ 2 ρ c L A Ω c q 7 ,
| M ν = T A P Z h ( q ) | 2 = 32 e 2 π 2 e 14 , v 2 ϵ 2 ρ c L A Ω c | q x 2 q y 2 + q y 2 q z 2 + q z 2 q x 2 q 5 ( 3 q x q y q z ) 2 q 7 | .
γ p h = γ ν = LA DP + γ ν = LA PZ + γ ν = TA PZ ,
γ p h LA DP = D 2 q 3 4 π c LA 2 d 0 π d θ sin θ | Ψ | e i q · r | Ψ + | 2 ,
γ p h LA PZ = 18 π e 2 e 14 , v 2 c LA 2 ϵ 2 d q 0 π d θ sin 5 θ cos 2 θ | Ψ | e i q · r | Ψ + | 2 ,
γ p h TA PZ = 8 π e 2 e 14 , v 2 4 c TA 2 ϵ 2 d q 0 π d θ ( sin 5 θ + 8 sin 3 θ cos 2 θ 9 sin 5 θ cos 2 θ ) × | Ψ | e i q · r | Ψ + | 2 .
R I = ϵ 1 2 E 10 01 3 O X I 2 μ B 2 3 π ϵ 0 c 3 ,

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