Short-Range Scattering Sources of Two-Dimensional Hole Gases in Undoped Ge/Gesi Heterostructures
Authors: Su Yi-Hsin , Chuang Yen , Liu Chia-You , Lu Tzu-Ming , Li Jiun-Yun 
Published: February 2020

Germanium has recently gained attention due to its potential for spintronic applications [1]. While most prior studies were done on modulation-doped Ge/GeSi heterostructures, there have been few reports on the mobility-limiting mechanisms in undoped structures. In this work, we investigate the electrostatics and magneto-transport of two-dimensional hole gases in undoped Ge/Ge1-xSix heterostructures with different Si fractions. The quantum transport data were correlated with material properties, such as dislocation densities and oxygen concentrations.
The undoped Ge/Ge1-xSix heterostructures (x = 0.18, 0.28, 0.36) were grown by chemical vapor deposition. The growth details can be found in our prior work [2]. Transmission electron microscopy (TEM), secondary ion mass spectroscopy (SIMS), and reciprocal space mapping (RSM) were used to characterize the layer thicknesses, the dislocation densities, the strain distributions, and the impurity concentrations in the Ge/GeSi heterostructures. Enhancement-mode Hall bar devices were fabricated for low-temperature (4 K and 0.3 K) mobility measurements [2].

The hole density was modulated by gating. By increasing the Si fraction of the GeSi barrier, the saturation density increases due to a larger valence band offset [2,3]. For each device, the mobility increases with density, showing the dominance of carrier screening, while the mobility decreases with the Si fraction. For the power dependence of mobility versus density (μ=nα), α is 0.20 ~ 0.43 for all devices in the density regime of 8 x 1010 to 4 x 1011 cm-2. This indicates that the remote impurity scattering at the oxide interface, (α =1.5) is unlikely the dominant scattering source.

Planar-view TEM were performed to characterize threading and misfit dislocations. For the Ge/GexSi1-x heterostructures with x = 0.18 and x = 0.28, threading dislocations were ~ 4.9 x 108 cm-2 and ~ 7.7 x 108 cm-2, respectively. For all Ge/GeSi heterostructures, the thickness of the strained Ge quantum well is ~ 20 nm, slightly larger than the critical thicknesses. Therefore, misfit dislocations are expected to impact the mobility as the crystal is fully or partially relaxed.

Oxygen impurities could also be important scattering sources. The oxygen level increases with the Si fraction of the GeSi barrier (Fig. 1(a)), which could be attributed to a stronger bonding between Si-O over Ge-O [4]. The expected mobility limited by ionized oxygen would be ~100 times lower than the experimental data, which indicates that structural defects and strain inhomogeneity induced by neutral oxygen precipitates could be the more dominant scattering sources than charged impurities [5].
Finally, Dingle-ratio analysis was performed to characterize the mobility mechanisms [6]. The Dingle ratios are small (5 ~ 14) (Fig. 1(b)), indicating that the short-range (large-angle) scattering dominates. As the Si fraction increases, the Dingle ratio decreases, showing that the short-range scattering is stronger. This result suggests that both the oxygen impurities and the dislocations are the most important scattering sources.

In summary, the scattering mechanisms in undoped Ge/GeSi heterostructures were investigated. Weak density-mobility dependence and small Dingle ratios suggest that the dominant scattering sources are dislocations and oxygen impurities.

Acknowledgements

This work at National Taiwan University has been support by the Ministry of Science and Technology (107-2622-8-002-018- and 107-2112-M-002-014-). This work at Sandia National Laboratories has been supported by the Division of Materials Sciences and Engineering, Office of Basic Energy Sciences, U.S. Department of Energy (DOE). This work was performed, in part, at the Center for Integrated Nanotechnologies, a U.S. DOE, Office of Basic Energy Sciences, user facility. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525.

Figure 1