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

Nguyen H Le,Benedict N Murdin,Grigory V Lanskii,Gabriel Aeppli

doi:10.1038/s41377-019-0174-6

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.

Highlights

Multiphoton absorption requires a high intensity, and was first observed shortly after the invention of the laser using impurities in solids[1] and alkali vapor[2]
Multiphoton absorption is useful for metrology and modulators, and can be enhanced where there is nearresonance of an intermediate state as in the case of Rb3, it is essentially a loss process contributing an imaginary part to the non-linear susceptibility
THz multiphoton absorption has been shown to be very large in hydrogenic shallow impurities in semiconductors, even without intermediate state resonances[7], due to the large dielectric screening and low effective mass

Summary

Introduction

Multiphoton absorption requires a high intensity, and was first observed shortly after the invention of the laser using impurities in solids[1] and alkali vapor[2]. Multiphoton absorption is useful for metrology and modulators, and can be enhanced where there is nearresonance of an intermediate state as in the case of Rb3, it is essentially a loss process contributing an imaginary part to the non-linear susceptibility.

Results

Conclusion