Optimization of Si/SiGe Heterostructures for Large and Robust Valley Splitting in Silicon Qubits

Abstract: The notoriously low and fluctuating valley splitting is one of the key challenges for electron spin qubits in silicon (Si), limiting the scalability of Si-based quantum processors. In silicon-germanium (SiGe) heterostructures, the problem can be addressed by the design of the epitaxial layer stack. Several heuristic strategies have been proposed to enhance the energy gap between the two nearly degenerate valley states in strained Si/SiGe quantum wells (QWs), e.g., sharp Si/SiGe interfaces, Ge spikes or oscillating Ge concentrations within the QW. In this work, we develop a systematic variational optimization approach to compute optimal Ge concentration profiles that boost selected properties of the intervalley coupling matrix element. Our free-shape optimization approach is augmented by a number of technological constraints to ensure feasibility of the resulting epitaxial profiles. The method is based on an effective-mass-type envelope-function theory accounting for the effects of strain and compositional alloy disorder. Various previously proposed heterostructure designs are recovered as special cases of the constrained optimization problem. Our main result is a novel heterostructure design we refer to as the "modulated wiggle well," which provides a large deterministic enhancement of the valley splitting along with a reliable suppression of the disorder-induced volatility. In addition, our new design offers a wide-range tunability of the valley splitting ranging from about 200 $μ$eV to above 1 meV controlled by the vertical electric field, which offers new perspectives to engineer switchable qubits with on-demand adjustable valley splitting.