Optimization of Si/SiGe heterostructures for large and robust valley splitting in silicon qubits
Authors
- Thayil, Abel
- Ermoneit, Lasse
ORCID: 0009-0006-0329-0164 - Schreiber, Lars R.
- Koprucki, Thomas
ORCID: 0000-0001-6235-9412 - Kantner, Markus
ORCID: 0000-0003-4576-3135
2020 Mathematics Subject Classification
- 35Q40 35Q81 35Q93 65K10 49M41 81Q37 81V65
Keywords
- Spin-qubits, quantum computers, quantum dots, semiconductor heterostructures, valleytronics, random alloy fluctuations, perturbation theory, PDE constrained optimization, shape optimization
DOI
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), emphe.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 emphmodulated 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 controlled by the vertical electric field, which offers new perspectives to engineer switchable qubits with on-demand adjustable valley splitting.
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