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Long lifetimes of quantum-dot intersublevel transitions in the terahertz range

Abstract

Carrier relaxation is a key issue in determining the efficiency of semiconductor optoelectronic device operation. Devices incorporating semiconductor quantum dots have the potential to overcome many of the limitations of quantum-well-based devices because of the predicted long quantum-dot excited-state lifetimes. For example, the population inversion required for terahertz laser operation in quantum-well-based devices (quantum-cascade lasers1,2) is fundamentally limited by efficient scattering between the laser levels, which form a continuum in the plane of the quantum well. In this context, semiconductor quantum dots are a highly attractive alternative for terahertz devices, because of their intrinsic discrete energy levels. Here, we present the first measurements, and theoretical description, of the intersublevel carrier relaxation in quantum dots for transition energies in the few terahertz range. Long intradot relaxation times (1.5 ns) are found for level separations of 14 meV (3.4 THz), decreasing very strongly to 2 ps at 30 meV (7 THz), in very good agreement with our microscopic theory of the carrier relaxation process. Our studies pave the way for quantum-dot terahertz device development, providing the fundamental knowledge of carrier relaxation times required for optimum device design.

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Figure 1: Intersublevel transitions in quantum dots.
Figure 2: Population dynamics in quantum dots.
Figure 3: Intersublevel lifetimes in the terahertz region.

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References

  1. Faist, J. et al. Quantum cascade laser. Science 264, 553–556 (1994).

    Article  CAS  Google Scholar 

  2. Kohler, R. et al. Terahertz semiconductor-heterostructure laser. Nature 417, 156–159 (2002).

    Article  Google Scholar 

  3. Urayama, J., Norris, T. B., Singh, J. & Bhattacharya, P. Observation of phonon bottleneck in quantum dot electronic relaxation. Phys. Rev. Lett. 86, 4930–4933 (2001).

    Article  CAS  Google Scholar 

  4. Borri, P. & Langbein, W. Four-wave mixing dynamics of excitons in InGaAs self-assembled quantum dots. J. Phys. Condens. Matter 19, 295201 (2007).

    Article  Google Scholar 

  5. Botez, D. et al. Progress towards intersubband quantum-box lasers for highly efficient continuous wave operation in the mid-infrared. J. Nanophoton. 3, 031606 (2009).

    Article  Google Scholar 

  6. Murdin, B. N. et al. Direct observation of the LO phonon bottleneck in wide GaAs/AlxGa1−x As quantum wells. Phys. Rev. B 55, 5171–5176 (1997).

    Article  CAS  Google Scholar 

  7. Hartig, M. et al. Efficient intersubband scattering via carrier–carrier interaction in quantum wells. Phys. Rev. Lett. 80, 1940–1943 (1998).

    Article  CAS  Google Scholar 

  8. Wade, A. et al. Magnetic-field-assisted terahertz quantum cascade laser operating up to 225 K. Nature Photon. 3, 41–45 (2008).

    Article  Google Scholar 

  9. Sauvage, S. et al. Long polaron lifetime in InAs/GaAs self-assembled quantum dots. Phys. Rev. Lett. 88, 177402 (2002).

    Article  CAS  Google Scholar 

  10. Zibik, E. A. et al. Intraband relaxation via polaron decay in InAs self-assembled quantum dots. Phys. Rev. B 70, 161305(R) (2004).

    Article  Google Scholar 

  11. Li, X.-Q., Nakayama, H. & Arakawa, Y. Phonon bottleneck in quantum dots: Role of lifetime of the confined optical phonons. Phys. Rev. B 59, 5069–5073 (1999).

    Article  CAS  Google Scholar 

  12. Verzelen, O., Ferreira, R. & Bastard, G. Polaron lifetime and energy relaxation in semiconductor quantum dots. Phys. Rev. B 62, 4809–4812(R) (2000).

    Article  Google Scholar 

  13. Grange, T., Ferreira, R. & Bastard, G. Polaron relaxation in self-assembled quantum dots: Breakdown of the semiclassical model. Phys. Rev. B 76, 241304(R) (2007).

    Article  Google Scholar 

  14. Nabetani, Y. et al. Initial growth stage and optical properties of a three-dimensional InAs structure on GaAs. J. Appl. Phys. 76, 347–351 (1994).

    Article  CAS  Google Scholar 

  15. Stier, O. et al. Electronic and optical properties of strained quantum dots modeled by 8-band k.p theory. Phys. Rev. B 59, 5688–5701 (1999).

    Article  CAS  Google Scholar 

  16. Bester, G. et al. Pseudopotential calculation of the excitonic fine structure of million-atom self-assembled In1−xGaxAs/GaAs quantum dots. Phys. Rev. B 67, 161306 (2003).

    Article  Google Scholar 

  17. Fafard, S. et al. Manipulating the energy levels of semiconductor quantum dots. Phys. Rev. B 59, 15368–15373 (1999).

    Article  CAS  Google Scholar 

  18. Fafard, S. & Allen, C. Nì. Intermixing in quantum-dot ensembles with sharp adjustable shells. Appl. Phys. Lett. 75, 2374–2376 (1999).

    Article  CAS  Google Scholar 

  19. Zibik, E. A. et al. Effects of alloy intermixing on the lateral confinement potential in InAs/GaAs self-assembled quantum dots probed by intersublevel absorption spectroscopy. Appl. Phys. Lett. 90, 163107 (2007).

    Article  Google Scholar 

  20. Lehnert, U. et al. Proc. 29th FEL Conference, Novosibirsk, Russia (2007); available at <http://accelconf.web.cern.ch/AccelConf/f07/PAPERS/MOPPH036.PDF>.

  21. Bockelman, U. & Bastard, G. Phonon scattering and energy relaxation in two-, one-, and zero-dimensional electron gases. Phys. Rev. B 42, 8947–8951 (1990).

    Article  Google Scholar 

  22. Benisty, H., Sotomayor-Torres, C. M. & Weisbuch, C. Intrinsic mechanism for the poor luminescence properties of quantum-box systems. Phys. Rev. B 44, 10945–10948 (1991).

    Article  CAS  Google Scholar 

  23. Inoshita, T. & Sakaki, H. Density of states and phonon-induced relaxation of electrons in semiconductor quantum dots. Phys. Rev. B 56, R4355–R4358 (1997).

    Article  CAS  Google Scholar 

  24. Hameau, S. et al. Strong electron–phonon coupling regime in quantum dots: Evidence for everlasting resonant polarons. Phys. Rev. Lett. 83, 4152–4155 (1999).

    Article  CAS  Google Scholar 

  25. Carpenter, B. A. et al. Intraband magnetospectroscopy of singly and doubly charged n-type self-assembled quantum dots. Phys. Rev. B 74, 161302(R) (2006).

    Article  Google Scholar 

  26. Garcia, C. P. et al. Evidence of correlation in spin excitations of few-electron quantum dots. Phys. Rev. Lett. 95, 266806 (2005).

    Article  Google Scholar 

  27. Fujisawa, T. et al. Allowed and forbidden transitions in artificial hydrogen and helium atoms. Nature 419, 278–281 (2002).

    Article  CAS  Google Scholar 

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Acknowledgements

Financial support was provided by the UK Engineering and Physical Sciences Research Council (EPSRC). The LPA (UMR 8551) is associated with the CNRS and the Universities Paris 6 and Paris 7. The free-electron laser ‘FELBE’ is supported by the Integrating Activity on Synchrotron and Free-Electron Laser Science (IA-SFS) under the EU contract RII3-CT-2004-506008 of the 6th Framework ‘Structuring the European Research Area, Research Infrastructures Action’. We are grateful to P. Michel and the FELBE team for their dedicated support.

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Contributions

E.A.Z. and L.R.W. conceived the experiments; E.A.Z., L.R.W., B.A.C., N.E.P., D.S. and S.W. carried out the experiments; T.G., R.F. and G.B. made the theory and modelled the experiments; E.A.Z. and T.G. analysed the data; L.R.W., R.F., E.A.Z. and M.S.S. supervised the project; H.Y.L. grew the samples; T.G., E.A.Z., R.F. and L.R.W. wrote the paper with major input and edits from M.S.S. and M.H. All authors discussed the results and commented on the manuscript.

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Correspondence to R. Ferreira or L. R. Wilson.

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Zibik, E., Grange, T., Carpenter, B. et al. Long lifetimes of quantum-dot intersublevel transitions in the terahertz range. Nature Mater 8, 803–807 (2009). https://doi.org/10.1038/nmat2511

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