The critical role of substrate disorder in valley splitting in Si quantum wells

Abstract

Atomic-scale disorder at the top interface of a Si quantum well is known to suppress the valley splitting. Such disorder may be inherited from the underlying substrate and relaxed buffer growth, but can also arise at the top quantum well interface due to the random SiGe alloy. Here, we perform activation energy (transport) measurements in the quantum Hall regime to determine the source of the disorder affecting the valley splitting. We consider three Si/SiGe heterostructures with nominally identical substrates but different barriers at the top of the quantum well, including two samples with pure-Ge interfaces. For all three samples, we observe a surprisingly strong and universal dependence of the valley splitting on the electron density (Ev∼n 2.7 ) over the entire experimental range (Ev=30-200 µeV). We interpret these results via tight binding theory, arguing that the underlying valley physics is determined mainly by disorder arising from the substrate and relaxed buffer growth. arXiv:1804.01914v2 [cond-mat.mes-hall]

Effect of Quantum Hall Edge Strips on Valley Splitting in Silicon Quantum Wells

“…Under similar experimental conditions we measure a g factor ≈1.8, close to the expected value of 2 [32]. This observation suggests that the measured quantum Hall gaps are not enhanced by electron-electron interactions [29] and that they represent the single particle valley splitting relevant for silicon qubits. The conventional theory of valley splitting in a silicon quantum well predicts that E v depends on the penetration of the electron wave function into the quantum well barrier, with E v ∝ E z [25].…”

“…This penetration is proportional to E z and the two-dimensional electron density [25] n ¼ ϵE z =e, which is easily measured in a Hall bar geometry. However, valley splitting in Si/SiGe 2DEGs is usually probed by activation energy measurements in the quantum Hall regime [26][27][28][29]. In this regime, drawing the correct relationship between valley splitting and electric field is challenging since the presence of quantum Hall edge states adds complexity to the electrostatics of the system compared to the simple electrostatics of an infinite 2DEG.…”

Semiconductor quantum computation

“…Therefore, a reproducible and controllable valley splitting in silicon is on demand. Till now, several researches have been performed on valley splitting in silicon [162,[164][165][166][167][168]. As a whole, the valley splitting in quantum dots based on silicon MOS and SOI are in the range of 300-800 μeV and 610-880 μeV, respectively, and can be easily controlled by electric field [162,167].…”

Crystalline materials for quantum computing: Semiconductor heterostructures and topological insulators exemplars

“…31 The current major challenge with Si/SiGe is the lower valley splitting (50 to 200 µeV), [32][33][34][35] compared to Si-MOS, due to the atomistic imperfection and chemical disorder at the epitaxial Si/SiGe interface. However, first steps are being taken to improve the heterostructures by incorporating more complex Ge concentration profiles 36 for increased the valley splitting.…”