Mapping Strain and Composition Effects on Gesn Band Structure Using Spectroscopic Ellipsometry
Authors: Attiaoui Anis , Assali Simone , Nicolas Jérôme , Moutanabbir Oussama 
Published: February 2020

One of the most interesting research areas in silicon photonics has been the development of silicon-compatible electro-optical devices including detectors, modulators, and light sources, to name a few. IN this regard, the binary alloy Ge1-xSn
x
has been of particular importance due its bandgap directness in contrast to silicon and germanium.[1-2] As a matter of fact, great efforts have been expended in recent years towards the development of the epitaxial growth of high-quality GeSn crystals on silicon platform and their introduction in design and fabrication of optoelectronic devices.[3] This interest has been nurtured by the ability to manipulate the GeSn band structure by controlling Sn composition and strain. These two degrees of freedom provide flexibility to tune the optoelectronic properties relevant to a variety of devices. For instance, GeSn is attractive material system for photodetectors with absorption edge extending over a broad wavelength range from the short wavelength infrared (SWIR, 1.6-2 µm) to the mid-infrared (MIR, 2-5 µm). In this perspective, this work reports detailed investigations of the influence of both strain and composition on the band structure above 1 eV of GeSn ternary alloys through a spectroscopic ellipsometry study. Understanding the individual influence of each parameter is highly critical to establish and optimize the properties of GeSn device layers.
GeSn thin films investigated in this work were grown using a low-pressure Chemical Vapor Deposition (LP-CVD) at different Sn compositions in the 7-18 at.% range.[4] A graded growth process on Ge-virtual substrates was used. Figure A shows a typical example of the investigated samples. The figure exhibits a schematic representation where the bottom layer (BL- 6.3% of Sn) and the top layer (TL- 12.5% of Sn) have different Sn composition. Furthermore, High-Resolution X-Ray Diffraction (HR-XRD) was used to characterize the compressive strain present in each layer. In the sample shown in Figure A, the strain was found to be respectively equal to -0.65% and -1.503%, for the BL and TL. Next, a rotating-analyzer spectroscopic ellipsometry system measures the following parameters (Ψ and Δ) for different incidence angles from 45 to 70° as shown in Figure B. These parameters are then coupled with an optical model to allow for an accurate determination of the complex dielectric (ε=ε1+iε2) of the sample.
The developed optical model is presented in Figure A where the different constituting layers are shown: GeSn(BL/ML)/ Ge(VS)/Si. Furthermore, two additional surface layers were introduced to simulate the surface roughness as well as the presence of the native GeO2 oxide. The optical properties of the GeO2 oxide were used in their tabulated form from Reference [5]. The optical model is shown as a dashed line in Figure B, and the accuracy is measured by a very low MSE of 0.598. Consequently, the dielectric constant can be extracted. Having extracted the dielectric constant from the ellipsometry measurement, it becomes now possible to quantify the contributions from the E1, E1 + Δ1, E0’, E2, and E1’ critical points in the joint density of electronic states which they will be enhanced by computing numerical second derivatives of the already measured dielectric function. The numerical second derivative is often coupled with the Savitsky-Golay smoothing filter to reduce noise while maintaining the shape and the height of waveform peaks. The resulting lineshapes were fitted with model expressions from which the critical point energies Ej, amplitudes, broadenings Aj, and phases ϕj were determined. The model lineshapes have been well established in literature. [6]
In Figure C, a lineshape fit for the E2 critical point energy for the Bottom layer (BL) was undertaken. The accuracy of the fit was confirmed with a coefficient of determination (R2) higher than 0.97. The Levenberg-Marquardt fit gave an E2 energy of 4.06±0.20 eV for the BL, whereas for the Top layer (TL), E2 was equal to 4.10±0.30 eV. After finding the energy for each sample, it becomes possible to map the effect of strain on the bang gap energies. Based on these systematic studies, this presentation will describe the individual influence of strain and composition on the optical properties of Sn-rich GeSn semiconductors.

References:

[1] A. Attiaoui and O. Moutanabbir, J. Appl.
Phys.
116 63712 (2014)
[2] S. Gupta et al, J. Appl.
Phys.
113 073707 (2013)
[3] S. Wirth et al., Progress in Crystal Growth and Characterization of Materials 62, 1 (2016)..
[4] S. Assali, Under Review (2017)
[5] Nunley et al, J. Vac. Sci. Technol. B 34(6), 061205 (2016)
[6] P. Lautenschlager, M. Garriga, L. Vina, and M. Cardona, Phys. Rev. B 36, 4821 (1987)

Figure 1