Epitaxy of Group-IV Semiconductors for Quantum Electronics
Authors: Hartmann Jean-Michel , Bernier Nicolas , Pierre Francois , Barnes Jean-Paul , Mazzocchi Vincent , Krawczyk Julia , Lima Gabriel , Kiyooka Elyjah , De Franceschi Silvano 
Published: September 2023

Epitaxy of group-IV semiconductors is a key enabler for quantum devices. Low temperature epitaxy can be used to deposit Si:B layers with boron concentrations so high that they are superconductive (ECS Transactions 98(5), 203 (2020)). Tensily strained Si layers sandwiched between relaxed Si0.7Ge0.3 layers behave as quantum wells for electrons, enabling electron spin quantum bit (qubit) fabrication. Purified 28Si without deleterious 29Si isotopes (with a nuclear spin) are ideal as the core of fully-depleted, multiple gate transistors for qubits. Compressively-strained Ge layers sandwiched between relaxed Si0.2Ge0.8 layers can confine a two-dimensional hole gas (2DHG) offering an emerging pathway to hole-spin qubits.
In the following, we will focus on the latter two subjects. We will show how we succeeded in growing 28Si layers with the following concentrations: 28Si isotopes > 99,992%, 29Si isotopes < 0.006% and 30Si isotopes < 0.002% (Journal of Crystal Growth 509, 1 (2019)). Such values can instructively be compared to those in natural Si: 28Si: 92.223%, 29Si: 4.678% and 30Si: 3.092%. The availability and cost of isotopically enriched 28SiH4 is a major difficulty, however. We thus quantified the impact of growth temperature and HCl mass-flow on the Si growth rate. At high temperature, above 850°C, we reached a silane supply limited regime with a good decomposition efficiency, high growth rates (> 100 nm min.-1 for the SiH4 mass-flow selected) and almost no impact of the HCl flow. There was otherwise, below 850°C, a H- and Cl-surface desorption limited regime, with a lesser decomposition efficiency and Si growth rates which dropped as the temperature decreased and/or the HCl mass-flow increased. Thick 28Si layers should be grown at high temperature, while low temperature epitaxy should be limited to the deposition of thin 28Si layers on top of SiGe sacrificial layers (28SOI fabrication with a bonding-etch back approach) or the thickening of SOI substrates (to avoid elastic or plastic relaxation/dewetting).
We otherwise fabricated c-Ge/SiGe heterostructures for hole spin qubits. We first grew at 850°C, 20 Torr and with a SiH2Cl2 + GeH4 chemistry, SiGe virtual substrates (VS), with a gradual ramping-up of the Ge concentration (to confine misfit dislocations) and a capping with 3 µm thick constant composition layers. Reciprocal Space Maps around the (004) and (224) X-Ray Diffraction (XRD) orders gave us the Ge concentration in those SiGe caps (73.8% and 78.7%) and their macroscopic degrees of strain relaxation (102.0 and 102.5%). The surface cross-hatch, e.g. the regular array of undulations with a 1-2 µm spatial wavelength because of a periodic strain field in VS, was suppressed using Chemical Mechanical Polishing (CMP). We then grew on top of the polished SiGe VS, at 500°C, 20 Torr and with a SiH2Cl2 + GeH4 chemistry, {100 nm thick SiGe 74% or 79% / 16 nm thick compressively-strained Ge / variable thickness SiGe 74% or 79% overlayer / Si 2nm cap} stacks. The parameter that changed was the SiGe overlayer, with 22, 33, 44 or 55 nm thicknesses probed.
Compared to polished surfaces, a slight surface roughening was observed for the SiGe stacks, larger for the SiGe 74%/c-Ge than for 79%/c-Ge stacks. Thicker SiGe overlayers yielded smoother surfaces. We ascribe these surface undulations, with a ~ 100 nm wavelength, to an elastic relaxation of the compressive strain in the c-Ge layers. XRD showed that those stacks were pseudomorphic, with the same in-plane lattice parameter for the c-Ge layers than that of the SiGe VS underneath. Energy Dispersive X-ray spectroscopy (EDX) mapping of the whole structure showed that the Ge grading was rather linear with, as intended, a 10% Ge/µm grading. Cross-sectional Transmission Electron Microscopy (TEM) showed the presence of numerous misfit dislocations in the graded layer and none in the thick Si0.21Ge0.79 / c-Ge stack on top. A slight Ge concentration increase, by a few %, was measured by EDX at the CMP location, with a perfect crystallinity in the stack grown on top. The 16 nm thick c-Ge layer itself was perfectly monocrystalline, with a 1-2 bi-atomic layer roughness at c-Ge/SiGe interfaces, no in-plane deformation compared to the surrounding SiGe and an out-of-plane deformation of 1.5% from Precession Electron Diffraction.
Magnetotransport measurements in Hall-bar devices were performed at 4.2 K to assess the electrical properties of the 2DHG in the grown SiGe/c-Ge heterostructures. At low magnetic field, a hole mobility of 1.2 x 105 cm2 V-1 s-1 was obtained for a hole density of n2DHG = 3.7x1011 cm-2 in the c-Ge/SiGe 79% 55nm sample, whereas quantum Hall effect plateaus and Shubnikov-De-Haas oscillations were observed at higher fields.

Figure 1