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Exciton-to-plasma Mott crossover in silicon

  • Regular Article - Optical Phenomena and Photonics
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Abstract

Excitonic Mott transition is a many-body crossover phenomenon where, even at zero temperature, a gas of excitons is expected to spontaneously ionize as its density or pressure is increased. Although this ionization due to the disappearance of the bound states from the energy spectra has long been predicted and continues to be studied, compelling demonstrations have been missing and the exact mechanism remains controversial. We revisit the phenomenon for silicon and report a number of striking features. The low temperature photoluminescence spectrum, around a certain crossover density shows a decrease in the emission intensity with increase in the excitation power. The photoluminescence efficiency (emission per incident photon) decreases by more than an order of magnitude building up to the Mott crossover, after which it becomes almost constant. This drastic loss in the oscillator strength is accompanied onset of a strong broadening of the excitonic peak. A comparison of this low temperature excitation power-dependent behavior of the photoluminescence emission with its temperature dependent change rules out the observations being explained by just the laser-induced heating of the sample.

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Data Availibility Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The data that support the findings of this study are available on reasonable request from the corresponding author].

Notes

  1. For a silicon sample mounted in the vacuum in a cold finger-based cryostat, temperatures below 20 K are sometimes unattainable due to differential heating of the sample with respect to the cold finger [38]. Unless the sample is immersed in liquid helium, the possibility of observing the electron-hole drops is eliminated [27, 29]. Many recent measurements on the Mott crossover have been deliberately performed at higher temperatures to avoid the electron-hole drop formation [23].

References

  1. L. Canham, Introductory lecture: origins and applications of efficient visible photoluminescence from silicon-based nanostructures. Faraday Discuss. 222, 10 (2020). https://doi.org/10.1039/d0fd00018c

    Article  ADS  CAS  PubMed  Google Scholar 

  2. T. Niewelt, B. Steinhauser, A. Richter, B. Veith-Wolf, A. Fell, B. Hammann, N.E. Grant, L. Black, J. Tan, A. Youssef, J.D. Murphy, J. Schmidt, M.C. Schubert, S.W. Glunz, Reassessment of the intrinsic bulk recombination in crystalline silicon. Solar Energy Mater. Solar Cells 235, 111467 (2022). https://doi.org/10.1016/j.solmat.2021.111467

    Article  CAS  Google Scholar 

  3. J.R. Haynes, M. Lax, W.F. Flood, Analysis of intrinsic recombination radiation from silicon and germanium. J. Phys. Chem. Solids 8, 392 (1959)

    Article  ADS  CAS  Google Scholar 

  4. M. Khoury, M. Abbarchi, A bright future for silicon in quantum technologies. J. Appl. Phys. 131, 200901 (2022). https://doi.org/10.1063/5.0093822

    Article  ADS  CAS  Google Scholar 

  5. H.T. Nguyen, S.C. Baker-Finch, D. Macdonald, Temperature dependence of the radiative recombination coefficient in crystalline silicon from spectral photoluminescence. Appl. Phys. Lett. 104, 112105 (2014). https://doi.org/10.1063/1.4869295

    Article  ADS  CAS  Google Scholar 

  6. E. Wigner, H.B. Huntington, On the possibility of a metallic modification of hydrogen. J. Chem. Phys. 3, 764 (1935). https://doi.org/10.1063/1.1749590

    Article  ADS  CAS  Google Scholar 

  7. D.S. Kothari, The theory of pressure-ionization and its applications. Proc. R. Soc. Lond. Ser. A 165, 486 (1938). https://doi.org/10.1098/rspa.1938.0073

    Article  ADS  CAS  Google Scholar 

  8. W. Ebeling, V.E. Fortov, V. Filinov, Quantum Statistics of Dense Gases and Nonideal Plasmas (Springer, Cham, 2017). https://doi.org/10.1007/978-3-319-66637-2

    Book  Google Scholar 

  9. N.F. Mott, Metal-insulator transition. Rev. Mod. Phys. 40, 677 (1968). https://doi.org/10.1103/RevModPhys.40.677

    Article  ADS  CAS  Google Scholar 

  10. H.Y. Geng, Public debate on metallic hydrogen to boost high pressure research. Matter Radiat. Extrem. 2, 275 (2017). https://doi.org/10.1016/j.mre.2017.10.001

    Article  Google Scholar 

  11. M. Kira, S.W. Koch, Many-body correlations and excitonic effects in semiconductor spectroscopy. Prog. Quant. Electron. 30, 155 (2006). https://doi.org/10.1016/j.pquantelec.2006.12.002

    Article  ADS  Google Scholar 

  12. K.W. Böer, U.W. Pohl, Semiconductor Physics (Springer, Cham, 2018). https://doi.org/10.1007/978-3-319-69150-3

    Book  Google Scholar 

  13. I. Pelant, J. Valenta, Luminescence Spectroscopy of Semiconductors, Luminescence Spectroscopy of Semiconductors (Oxford University Press, Oxford, 2012). https://doi.org/10.1093/acprof:oso/9780199588336.001.0001

    Book  Google Scholar 

  14. H. Kalt, C.F. Klingshirn, Semiconductor Optics 1: Linear Optical Properties of Semiconductors (Springer, Cham, 2019). https://doi.org/10.1007/978-3-030-24152-0

    Book  Google Scholar 

  15. G. Manzke, D. Semkat, H. Stolz, Mott transition of excitons in GaAs-GaAlAs quantum wells. New J. Phys. 14, 095002 (2012). https://doi.org/10.1088/1367-2630/14/9/095002

    Article  ADS  CAS  Google Scholar 

  16. G.B. Norris, K.K. Bajaj, Exciton-plasma Mott transition in Si. Phys. Rev. B 26, 6706 (1982). https://doi.org/10.1103/PhysRevB.26.6706

    Article  ADS  CAS  Google Scholar 

  17. K. Asano, T. Yoshioka, Exciton-Mott physics in two-dimensional electron-hole systems: phase diagram and single-particle spectra. J. Phys. Soc. Jpn. 83, 084702 (2014). https://doi.org/10.7566/JPSJ.83.084702

    Article  ADS  CAS  Google Scholar 

  18. C.W. Lai, J. Zoch, A.C. Gossard, D.S. Chemla, Phase diagram of degenerate exciton systems. Science 303, 503 (2004). https://doi.org/10.1126/science.1092691

    Article  ADS  CAS  PubMed  Google Scholar 

  19. D. Semkat, F. Richter, D. Kremp, G. Manzke, W.-D. Kraeft, K. Henneberger, Ionization equilibrium in an excited semiconductor: Mott transition versus Bose-Einstein condensation. Phys. Rev. B 80, 155201 (2009). https://doi.org/10.1103/PhysRevB.80.155201

    Article  ADS  CAS  Google Scholar 

  20. E. Baldini, T. Palmieri, A. Dominguez, A. Rubio, M. Chergui, Giant exciton Mott density in anatase TiO\(_2\). Phys. Rev. Lett. 125, 116403 (2020). https://doi.org/10.1103/PhysRevLett.125.116403

    Article  ADS  CAS  PubMed  Google Scholar 

  21. C. Jeffries, L. Keldysh, Electron-Hole Droplets in Semiconductors (North-Holland Publishing Company, Amsterdam, 1983)

    Google Scholar 

  22. A. Amo, M.D. Martìn, L. Viña, A.I. Toropov, K.S. Zhuravlev, Photoluminescence dynamics in GaAs along an optically induced Mott transition. J. Appl. Phys. 101, 081717 (2007). https://doi.org/10.1063/1.2722786

    Article  ADS  CAS  Google Scholar 

  23. T. Suzuki, R. Shimano, Exciton Mott transition in Si revealed by terahertz spectroscopy. Phys. Rev. Lett. 109, 04642 (2012). https://doi.org/10.1103/PhysRevLett.109.046402

    Article  CAS  Google Scholar 

  24. F. Sekiguchi, R. Shimano, Excitonic correlation in the Mott crossover regime in Ge. Phys. Rev. B 91, 155202 (2015). https://doi.org/10.1103/PhysRevB.91.155202

    Article  ADS  CAS  Google Scholar 

  25. A. Schleife, C. Rödl, F. Fuchs, K. Hannewald, F. Bechstedt, Optical absorption in degenerately doped semiconductors: Mott transition or Mahan excitons? Phys. Rev. Lett. 107, 236405 (2011). https://doi.org/10.1103/PhysRevLett.107.236405

    Article  ADS  CAS  PubMed  Google Scholar 

  26. Y. Hayamizu, M. Yoshita, Y. Takahashi, H. Akiyama, C.Z. Ning, L.N. Pfeiffer, K.W. West, Biexciton Gain and the Mott Transition in GaAs Quantum Wires. Phys. Rev. Lett. 99, 167403 (2007). https://doi.org/10.1103/PhysRevLett.99.167403

    Article  ADS  CAS  PubMed  Google Scholar 

  27. J. Shah, M. Combescot, A.H. Dayem, Investigation of exciton-plasma Mott transition in Si. Phys. Rev. Lett. 38, 1497 (1977). https://doi.org/10.1103/PhysRevLett.38.1497

    Article  ADS  CAS  Google Scholar 

  28. P. Grivickas, V. Grivickas, J. Linnros, Excitonic absorption above the Mott transition in Si. Phys. Rev. Lett. 91, 246401 (2003). https://doi.org/10.1103/PhysRevLett.91.246401

    Article  ADS  CAS  PubMed  Google Scholar 

  29. A.F. Dite, V.G. Lysenko, V.B. Timofeev, The kinetics of recombination radiation and the temperature of the electron-hole plasma in silicon. Phys. Stat. Sol. (b) 66, 53 (1974). https://doi.org/10.1002/pssb.2220660104

    Article  ADS  CAS  Google Scholar 

  30. L. Kappei, J. Szczytko, F. Morier-Genoud, B. Deveaud, Direct observation of the Mott transition in an optically excited semiconductor quantum well. Phys. Rev. Lett. 94, 147403 (2005). https://doi.org/10.1103/PhysRevLett.94.147403

    Article  ADS  CAS  PubMed  Google Scholar 

  31. M. Shahmohammadi, G. Jacopin, G. Rossbach, J. Levrat, E. Feltin, J.-F. Carlin, J.-D. Ganiére, R. Butté, N. Grandjean, B. Deveaud, Biexcitonic molecules survive excitons at the Mott transition Nat. Comm. 5, Article number: 5251 (2014). https://www.nature.com/articles/ncomms6251

  32. F. Chiaruttini, T. Guillet, C. Brimont, D. Scalbert, S. Cronenberger, B. Jouault, P. Lefebvre, B. Damilano, M. Vladimirova, Complexity of the dipolar exciton Mott transition in GaN/(AlGa)N nanostructures. Phys. Rev. B 103, 045308 (2021). https://doi.org/10.1103/PhysRevB.103.045308

    Article  ADS  CAS  Google Scholar 

  33. F. Sekiguchi, T. Mochizuki, C. Kim, H. Akiyama, L.N. Pfeiffer, K.W. West, R. Shimano, Anomalous metal phase emergent on the verge of an exciton Mott transition. Phys. Rev. Lett. 118, 067401 (2017). https://doi.org/10.1103/PhysRevLett.118.067401

    Article  ADS  PubMed  Google Scholar 

  34. Y. Murotani, C. Kim, H. Akiyama, L.N. Pfeiffer, K.W. West, R. Shimano, Light-driven electron-hole Bardeen-Cooper-Schrieffer-like state in bulk GaAs. Phys. Rev. Lett. 123, 197401 (2019). https://doi.org/10.1103/PhysRevLett.123.197401

    Article  ADS  CAS  PubMed  Google Scholar 

  35. G. Rossbach, J. Levrat, G. Jacopin, M. Shahmohammadi, J.-F. Carlin, J.-D. Ganiére, R. Butté, B. Deveaud, N. Grandjean, High-temperature Mott transition in wide-band-gap semiconductor quantum wells. Phys. Rev. B 90, 201308(R) (2014). https://doi.org/10.1103/PhysRevB.90.201308

    Article  ADS  CAS  Google Scholar 

  36. D. Guerci, M. Capone, M. Fabrizio, Exciton Mott transition revisited. Phys. Rev. Mater. 3, 054605 (2019). https://doi.org/10.1103/PhysRevMaterials.3.054605

    Article  CAS  Google Scholar 

  37. R. Zimmermann, Many-Particle Theory of Highly Excited Semiconductors (Teubner, Leipzig, 1988)

    Google Scholar 

  38. P.J. Dean, J.R. Haynes, W.F. Flood, New radiative recombination processes involving neutral donors and acceptors in silicon and germanium. Phys. Rev. 161, 711 (1967). https://doi.org/10.1103/PhysRev.161.711

    Article  ADS  CAS  Google Scholar 

  39. W.S. Yoo, K. Kang, G. Murai, M. Yoshimotob, Temperature dependence of photoluminescence spectra from crystalline silicon. ECS J. Solid State Sci. Technol. 4, 456 (2015). https://doi.org/10.1149/2.0251512jss

    Article  CAS  Google Scholar 

  40. G.G. MacFarlane, T.P. Mclean, J.E. Quarrington, V. Roberts, Fine structure in the absorption-edge spectrum of Si. Phys. Rev. 111, 1245 (1958). https://doi.org/10.1103/PhysRev.108.1377

  41. F.A. Johnson, Lattice absorption bands in silicon. Proc. Phys. Soc. 73, 265 (1958). https://doi.org/10.1088/0370-1328/73/2/315

    Article  ADS  Google Scholar 

  42. M. Lax, in Proceedings of the International Conference on Semiconductor Physics, Exeter 14, 395 (1962)

  43. W.P. Dumke, Two-phonon indirect transitions and lattice scattering in Si. Phys. Rev. 118, 938 (1960). https://doi.org/10.1103/PhysRev.118.938

    Article  ADS  CAS  Google Scholar 

  44. R.B. Hammond, D.L. Smith, T.C. McGill, Temperature dependence of silicon luminescence due to splitting of the indirect ground state. Phys. Rev. 35, 1535 (1975). https://doi.org/10.1103/PhysRevLett.35.1535

    Article  ADS  CAS  Google Scholar 

  45. R.J. Elliot, Intensity of optical absorption by excitons. Phys. Rev. 108, 1384 (1957). https://doi.org/10.1103/PhysRev.108.1384

    Article  ADS  Google Scholar 

  46. A. Forchel, B. Laurlch, J. Wagner, W. Schmid, T.L. Reinecke, Systematics of electron-hole liquid condensation from studies of silicon with varying uniaxial stress. Phys. Rev. B. 25, 2730 (1982). https://doi.org/10.1103/PhysRevB.25.2730

    Article  ADS  CAS  Google Scholar 

  47. D.W. Snoke, J.D. Crawford, Hysteresis in the Mott transition between plasma and insulating gas. Phys. Rev. E 52, 5796 (1995). https://doi.org/10.1103/PhysRevE.52.5796

    Article  ADS  CAS  Google Scholar 

  48. F. Sekiguchi, R. Shimano, Rate equation analysis of the dynamics of first-order exciton Mott transition. J. Phys. Soc. Jpn. 86, 103702 (2017). https://doi.org/10.7566/JPSJ.86.103702

    Article  ADS  Google Scholar 

  49. R.K. Pathria, P.D. Beale, Statistical Mechanics, 3rd edn. (Elsevier, New York, 2011)

    Google Scholar 

  50. M.A. Green, Improved value for the silicon free exciton binding energy. AIP Adv. 3, 112104 (2013). https://doi.org/10.1063/1.4828730

    Article  ADS  CAS  Google Scholar 

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Acknowledgements

Bhavtosh Bansal thanks the Science and Engineering Research Board, Department of Science and Technology, Government of India, for the Core Research Grant (No. CRG/2018/003282 and CRG/2022/008662). Basabendra Roy thanks Council of Scientific and Industrial Research (CSIR), India for financial support.

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  1. Indian Institute of Science Education and Research Kolkata, Mohanpur, Nadia, West Bengal, 741246, India

    Basabendra Roy & Bhavtosh Bansal

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BB conceived of the study and guided the research work. The experiments were done by BR. Both authors discussed the results and wrote the manuscript.

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The Supplementary Material discusses the temperature dependence of the photoluminescence spectra. (146 KB)

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Roy, B., Bansal, B. Exciton-to-plasma Mott crossover in silicon. Eur. Phys. J. D 78, 24 (2024). https://doi.org/10.1140/epjd/s10053-024-00814-w

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