Citation:

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

• Light: Science & Applications  8, Article number: 64 (2019)
• Corresponding author:
Benedict N. Murdin (b.murdin@surrey.ac.uk)
Revised: 14 May 2019
Accepted: 17 June 2019
Published online: 10 July 2019
• 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 χ(3)/n3D = 2.9 to 580 × 10-38 m5/V2 depending on the frequency, even while avoiding resonance. Using samples of a reasonable density, n3D, and thickness, L, to produce third-harmonic generation at 9 THz, a frequency that is difficult to produce with existing solid-state sources, we predict that χ(3) should exceed that of bulk InSb and χ(3)L should exceed that of graphene and resonantly enhanced quantum wells.
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• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

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

• 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
• ###### Corresponding author: Benedict N. Murdin, b.murdin@surrey.ac.uk

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 χ(3)/n3D = 2.9 to 580 × 10-38 m5/V2 depending on the frequency, even while avoiding resonance. Using samples of a reasonable density, n3D, and thickness, L, to produce third-harmonic generation at 9 THz, a frequency that is difficult to produce with existing solid-state sources, we predict that χ(3) should exceed that of bulk InSb and χ(3)L should exceed that of graphene and resonantly enhanced quantum wells.

• Reference (45)

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