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

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

Light Sci Appl. 2019 Jul 10:8:64. doi: 10.1038/s41377-019-0174-6. eCollection 2019.

Authors

Nguyen H Le¹, Grigory V Lanskii², Gabriel Aeppli^{3

4

5}, Benedict N Murdin¹

Affiliations

¹ 1Advanced Technology Institute and SEPNet, University of Surrey, Guildford, GU2 7XH UK.
² 2Institute of Monitoring of Climatic and Ecological Systems SB RAS, 10/3 Academical Ave., Tomsk, 634055 Russia.
³ 3Laboratory for Solid State Physics, ETH Zurich, Zurich, CH-8093 Switzerland.
⁴ 4Institut de Physique, EPF Lausanne, Lausanne, CH-1015 Switzerland.
⁵ 5Paul Scherrer Institut, Villigen, PSI CH-5232 Switzerland.

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⁾/n _3D = 2.9 to 580 × 10^-38 m⁵/V² depending on the frequency, even while avoiding resonance. Using samples of a reasonable density, n _3D, 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.

Keywords: Nonlinear optics; Silicon photonics; Terahertz optics.