Giant non-linear susceptibility of hydrogenic donors in silicon and germanium

Nguyen H. Le; Grigory V. Lanskii; Gabriel Aeppli; Benedict N. Murdin

doi:10.1038/s41377-019-0174-6

Go to Nature Website

Your Location：

Home >

Browse articles >

Giant non-linear susceptibility of hydrogenic donors in silicon and germanium

Article

- Giant non-linear susceptibility of hydrogenic donors in silicon and germanium
- Light: Science & Applications Vol. 8, Issue 4, Pages: 558-564(2019)
- Affiliations：
  
  1.Advanced Technology Institute and SEPNet, University of Surrey, Guildford GU2 7XH, UK
  2.Institute of Monitoring of Climatic and Ecological Systems SB RAS, 10/3 Academical Ave., Tomsk 634055, Russia
  3.Laboratory for Solid State Physics, ETH Zurich, Zurich CH-8093, Switzerland
  4.Institut de Physique, EPF Lausanne, Lausanne CH-1015, Switzerland
  5.Paul Scherrer Institut, Villigen, PSI CH-5232, Switzerland
- Author bio：
  
  Benedict N. Murdin (b.murdin@surrey.ac.uk)
- Funds：
- DOI：10.1038/s41377-019-0174-6
  CLC：
- Published：2019，
  
  Published Online：10 July 2019，
  
  Received：31 January 2019，
  
  Revised：14 May 2019，
  
  Accepted：17 June 2019
- Accepted：
Scan QR Code
Le, N. H. et al. Giant non-linear susceptibility of hydrogenic donors in silicon and germanium. Light: Science & Applications, 8, 558-564 (2019).
DOI：

Le, N. H. et al. Giant non-linear susceptibility of hydrogenic donors in silicon and germanium. Light: Science & Applications, 8, 558-564 (2019). DOI： 10.1038/s41377-019-0174-6.

摘要

Abstract

Implicit summation is a technique for the conversion of sums over intermediate states in multiphoton absorption and the high-order susceptibility in hydrogen into simple integrals. Here

we derive the equivalent technique for hydrogenic impurities in multi-valley semiconductors. While the absorption has useful applications

it is primarily a loss process; conversely

the non-linear susceptibility is a crucial parameter for active photonic devices. For Si:P

we predict the hyperpolarizability ranges from

(3)

= 2.9 to 580 × 10

-38

depending on the frequency

even while avoiding resonance. Using samples of a reasonable density

and thickness

to produce third-harmonic generation at 9 THz

a frequency that is difficult to produce with existing solid-state sources

we predict that

(3)

shoul

d exceed that of bulk InSb and

(3)

should exceed that of graphene and resonantly enhanced quantum wells.

关键词

Keywords

references

Kaiser, W.&Garrett, C. G. B. Two-photon excitation in CaF2: Eu2+.Phys. Rev. Lett.7, 229–231 (1961)..

Abella, I. D. Optical double-photon absorption in cesium vapor.Phys. Rev. Lett.9, 453–455 (1962)..

Saha, K. et al. Enhanced two-photon absorption in a hollow-core photonic-band-gap fiber.Phys. Rev. A83, 033833 (2011)..

Franken, P. A. et al. Generation of optical harmonics.Phys. Rev. Lett.7, 118–119 (1961)..

Ward, J. F.&New, G. H. C. Optical third harmonic generation in gases by a focused laser beam.Phys. Rev.185, 57–72 (1969)..

Miles, R.&Harris, S. Optical third-harmonic generation in alkali metal vapors.IEEE J. Quantum Electron.9, 470–484 (1973)..

Van Loon, M. A. W. et al. Giant multiphoton absorption for THz resonances in silicon hydrogenic donors.Nat. Photonics12, 179–184 (2018)..

Vampa, G. et al. Theoretical analysis of high-harmonic generation in solids.Phys. Rev. Lett.113, 073901 (2014)..

Beaulieu, S. et al. Role of excited states in high-order harmonic generation.Phys. Rev. Lett.117, 203001 (2016)..

Haworth, C. A. et al. Half-cycle cutoffs in harmonic spectra and robust carrier-envelope phase retrieval.Nat. Phys.3, 52–57 (2007)..

Gontier, Y.&Trahin, M. On the multiphoton absorption in atomic hydrogen.Phys. Lett. A36, 463–464 (1971)..

Li, J. et al. Radii of Rydberg states of isolated silicon donors.Phys. Rev. B98, 085423 (2018)..

Boyd, R. W.Nonlinear Optics. 3rd edn, 640. Academic Press, New York (2008).

Kohn, W.&Luttinger, J. M. Theory of donor states in silicon.Phys. Rev.98, 915–922 (1955)..

The Mathematica FEM code used in this paper is available at,https://github.com/lehnqt/chi3.githttps://github.com/lehnqt/chi3.git.

Mizuno, J. Use of the sturmian function for the calculation of the third harmonic generation coefficient of the hydrogen atom.J. Phys. B: At. Mol. Phys.5, 1149–1154 (1972)..

Ramdas, A. K.&Rodriguez, S. Review article: spectroscopy of the solid-state analogues of the hydrogen atom: donors and acceptors in semiconductors.Rep. Prog. Phys.44, 1297–1387 (1981)..

Murdin, B. N. et al. Si:P as a laboratory analogue for hydrogen on high magnetic field white dwarf stars.Nat. Commun.4, 1469 (2013)..

Faulkner, R. A. Higher donor excited states for prolate-spheroid conduction bands: a reevaluation of silicon and germanium.Phys. Rev.184, 713–721 (1969)..

Yuen, S. Y.&Wolff, P. A. Difference-frequency variation of the free-carrier-induced, third-order nonlinear susceptibility in n-InSb.Appl. Phys. Lett.40, 457–459 (1982)..

Susoma, J. et al. Second and third harmonic generation in few-layer gallium telluride characterized by multiphoton microscopy.Appl. Phys. Lett.108, 073103 (2016)..

Thomas, G. A. et al. Optical study of interacting donors in semiconductors.Phys. Rev. B23, 5472–5494 (1981)..

Steger, M. et al. Shallow impurity absorption spectroscopy in isotopically enriched silicon.Phys. Rev. B79, 205210 (2009)..

Greenland, P. T. et al. Coherent control of Rydberg states in silicon.Nature465, 1057–1061 (2010)..

Woodward, R. I. et al. Characterization of the second- and third-order nonlinear optical susceptibilities of monolayer MoS2 using multiphoton microscopy.2D Mater.4, 11006 (2017)..

Karvonen, L. et al. Rapid visualization of grain boundaries in monolayer MoS2 by multiphoton microscopy.Nat. Commun.8, 15714 (2017)..

Säynätjoki, A. et al. Rapid large-area multiphoton microscopy for characterization of graphene.ACS Nano7, 8441–8446 (2013)..

König-Otto, J. C. et al. Four-wave mixing in landau-quantized graphene.Nano Lett.17, 2184–2188 (2017)..

Hafez, H. A. et al. Extremely efficient terahertz high-harmonic generation in graphene by hot Dirac fermions.Nature561, 507–511 (2018)..

Sirtori, C. et al. Giant, triply resonant, third-order nonlinear susceptibility$$\chi _{3\omega }.{(3)}$$in coupled quantum wells.Phys. Rev. Lett.68, 1010–1013 (1992)..

Yildirim, H.&Aslan, B. Donor-related third-order optical nonlinearites in GaAs/AlGaAs quantum wells at the THz region.Semicond. Sci. Technol.26, 085017 (2011)..

Shen, Y. R.The Principles of Nonlinear Optics. 3rd edn, 576. Wiley-Interscience, New York, 2002.

Chick, S. et al. Metrology of complex refractive index for solids in the terahertz regime using frequency domain spectroscopy.Metrologia55, 771 (2018)..

Scalari, G. et al. Magnetically assisted quantum cascade laser emitting from 740GHz to 1.4THz.Appl. Phys. Lett.97, 081110 (2010)..

Wienold, M. et al. Frequency dependence of the maximum operating temperature for quantum-cascade lasers up to 5.4 THz.Appl. Phys. Lett.107, 202101 (2015)..

Li, L. et al. Terahertz quantum cascade lasers with>1 W output powers.Electron. Lett.50, 4309 (2014)..

Li, L. H. et al. Multi-Watt high-power THz frequency quantum cascade lasers.Electron. Lett.53, 799 (2017)..

Pfeffer, P. et al. p-type Ge cyclotron-resonance laser: Theory and experiment.Phys. Rev. B47, 4522–4531 (1993)..

Hübers, H. W., Pavlov, S. G.&Shastin, V. N. Terahertz lasers based on germanium and silicon.Semicond. Sci. Technol.20, S211–S221 (2005)..

Ohtani, K., Beck, M.&Faist, J. Double metal waveguide InGaAs/AlInAs quantum cascade lasers emitting at 24 μm.Appl. Phys. Lett.105, 121115 (2014)..

Saeedi, K. et al. Optical pumping and readout of bismuth hyperfine states in silicon for atomic clock applications.Sci. Rep.5, 10493 (2015)..

Litvinenko, K. L. et al. Coherent creation and destruction of orbital wavepackets in Si:P with electrical and optical read-out.Nat. Commun.6, 6549 (2015)..

Chick, S. et al. Coherent superpositions of three states for phosphorous donors in silicon prepared using THz radiation.Nat. Commun.8, 16038 (2017)..

Stoneham, A. M. et al. Letter to the editor: optically driven silicon-based quantum gates with potential for high-temperature operation.J. Phys.: Condens. Matter15, L447–L451 (2003)..

Bebb, H. B.&Gold, A. Multiphoton ionization of hydrogen and rare-gas atoms.Phys. Rev.143, 1–24 (1966)..

Views

Downloads

CSCD

Alert me when the article has been cited

Submit

Tools

Publicity Resources

No data

Related Author

No data

Related Institution

No data

⁰