Germanium Quantum Wells for Non-Linear Integrated Photonics
Authors: Barzaghi Andrea , Falcone Virginia , Calcaterra Stefano , Giani Raffaele , Ballabio Andrea , Isella Giovanni , Chrastina Daniel , Ortolani Michele , Virgilio Michele , Frigerio Jacopo 
Published: November 2022

In recent years, mid-infrared integrated photonics has raised an increasing interest due to the envisioned applications in molecular sensing, environmental monitoring and security. The Silicon-on-insulator (SOI) based technology, operating at wavelengths λ < 3.2 μm has already reached a significant technology readiness level. By leveraging the maturity of the SOI technology and taking advantage of the high index contrast between Si and SiO2 many functionalities such as low loss waveguiding, modulation and frequency comb generation have already been demonstrated. However, the wavelength range is limited by the absorption of the SiO2 layer. Many material platforms, such as III-V semiconductors, halides and chalcogenides are under investigation to fill this gap. Of particular interest is the Ge-rich SiGe-on-Si material platform, thanks to its compatibility to already existing foundry processes and its wide transparency at the wavelengths of interest. Nevertheless, key functionalities such as wavelength conversion, photodetection and high-speed modulation are still missing.
A viable way to achieve such advanced functionalities is the exploitation of intersubband transitions (ISBTs) in hole-doped Ge/SiGe quantum wells (QWs). In particular, ISBTs in can be leveraged to engineer an artificial second-order optical nonlinearity in group IV materials, where it is normally absent for symmetry reasons. In this work, we exploit ISBTs in asymmetric coupled Ge/SiGe (ACQWs) (see Fig.1) to achieve highly efficient second harmonic generation at mid-infrared frequencies. The ACQW has been designed with an advanced semi-empirical first neighbor sp3d5s*
tight-binding model, which has been used to calculate the second-order nonlinear susceptibility χ(2) (see fig 1b).
The ACQW has been then grown by Low-Energy Plasma-Enhanced Chemical Vapor Deposition (LEPECVD) and structurally characterized by x-ray diffraction (XRD) and high-resolution scanning transmission electron microscopy (STEM) . For the optical measurements, samples were cut in a 2 mm single-pass surface-plasmon waveguide with the side facets shaped to 70° with respect to the growth plane and the top facet close to the ACQWs region coated by a Ti/Au layer. Then the samples (cooled at 10 K) have been pumped with a CW quantum cascade laser emitting at λ =10.3 μm. The light coming out from the samples have been then filtered and collected by an MCT detector. The second harmonic emission has been recorded as a function of the input power (see fig. 1c) and a c(2) = 6x104 pm/V has been extracted from the measurement, a two orders of magnitude improvement with respect to the best nonlinear crystals.
Finally, the possibility to integrate ACQWs in waveguides has been theoretically investigated. Since artificial nonlinearities based on ISBTs involve real quantum states, as opposite to the virtual quantum states employed in standard nonlinear crystals, significative optical absorption at the pump and at the second harmonic wavelengths must be considered. Therefore, the length of the ACQW waveguide must be carefully designed in order to limit the optical losses. By solving the coupled wave equations with optical absorption at the pump and second harmonic wavelengths, we show that high conversion efficiencies around ≈ 10% can be achieved with waveguide integrated ACQWs for an optimal waveguide length of a ≈200 μm.
The integration scheme, shown in fig 2a, consists in a stack of ACQW integrated in a waveguide containing a periodic corrugation, which is necessary to achieve quasi-phase matching between the pump and the second harmonic. Input and output coupling of the light is achieved through adiabatic tapers by integrating the ACQW stack on a Si0.3Ge0.7 waveguide, where the light is injected and from which it is collected and measured. The pump and the second harmonic mode are fairly overlapped in the ACQW region, as shown in fig 2b and 2c, where the distribution of the first TM mode has been simulated using the Lumerical software package.
In conclusion, Ge/SiGe ACQW are very promising to expand the functionalities available in MIR integrated photonic circuits, especially in the important spectral region up to 10 μm. In particular, the experimental data obtained from the material characterization, as well as the preliminary studies of waveguide integration show that Ge/SiGe ACQW has the potential to realize highly efficient integrated wavelength converters.
Acknowledgments: This work has been supported by Fondazione Cariplo, grant n° 2020-4427.

Figure 1