Optical Constants Determination of Pseudomorphic Si1-XGex Layers on Si(001), with 0<x<0.54
Authors: Nolot Emmanuel , Hartmann Jean-Michel , Hilfiker J. 
Published: February 2020

Spectroscopic ellipsometry (SE) is the technique of choice for the fast, non-destructive characterization of pseudomorphic Si1-xGex/silicon heterostructures in a manufacturing environment. Because of its small spot, SE can indeed be used on blanket wafers for epitaxial process monitoring and on patterned wafers for measurement in dedicated structures as small as 50 x 50 μm². Still, SE analysis is sometimes plagued by correlation effects, i.e. difficulties in determining the thickness and optical properties in a de-convoluted manner. A reliable alloy model that would accurately describe the optical constants of fully strained Si1-xGex material in a large range of germanium content is thus required to minimize correlation in the SE analysis of Si1-xGex/Si heterostructures. Such an alloy model must be based on a set of high-quality epitaxial films characterized with i/ an accurate spectroscopic ellipsometer in order to access to the Ψ and Δ angles over a wide spectral range and ii/ analytical techniques such as X-ray reflectometry (XRR) or high-resolution X-ray diffraction (XRD), in order to accurately gain access to the thickness of the epitaxial film and its germanium content and confirm that films are indeed fully pseudomorphic.
The pseudodielectric function <ε>=<ε1>+i<ε2> deduced from the Ψ and Δ angles (figure) contains contributions from surface over-layers (native oxide, surface roughness, airborne molecular contamination) and from the substrate, since the penetration depth is most of the time higher that the critical thickness for plastic relaxation of Si1-xGex, above which such layers are not fully pseudomorphic anymore. Pickering et al. described the impact of surface over-layers and provided ways to access the true dielectric function of the Si1-xGex alloy. The most effective approach is a SE measurement immediately after removing the sample from the growth reactor together with a modelling of the SE data with a {overlayer/Si1-xGex /substrate} system. Some micro-roughness and potentially some excess Ge segregating on the growing surface can indeed contribute to this over-layer. Supposing that it is in fact a 0.5-0.7nm thick SiO2layer will however introduce negligible errors. Other authors did not include time constraints between process and measurement and determined the thickness of the overlayer from the non-vanishing pseudoabsorption below the bandgap, resulting in oxide thickness up to 2 nm, depending on the aging of the layer.
Optical constants of strained Si1-xGex are usually available in the x = 0 - 0.35 range. This abstract describes variable-angle spectroscopic ellipsometry (VASE) measurements from 0.73 to 6.48 eV on a Woollam M2000 rotating compensator ellipsometer on a series of high-quality pseudomorphic Si1-xGex films (0<x<0.54) grown by Reduced Pressure Chemical Vapor Deposition (RP-CVD) on Si(001) substrates. XRD and XRR were used to determine the germanium content and the thickness of the Si1-xGex films, respectively. The management of the surface over-layer combined a “HF-last” wet cleaning step immediately followed by SE and XRR measurements, so as to get rid of the contributions of airborne molecular contamination and aging of the epitaxial layer. The dielectric function of each Si1-xGex film of this reference wafer set was calculated using XRR-deduced thickness as a reference and describing the over-layer as SiO2 with fixed thickness equal to 0.7nm. The Si1-xGex optical constants determined at ten compositions were interpolated for arbitrary Ge composition up to 54%. This alloy model was then tested on a large number of Si1-xGex films (evaluation wafer set) in order to demonstrate its ability to accurately characterize inline pseudomorphic Si1-xGex films over a wide range of germanium contents (0.5-1 at.% accuracy concerning the determination of the Ge content).