Atomic-scale disorder at the interface of silicon-germanium quantum wells has long presented a major obstacle to building stable quantum bits. Researchers at the Institute of Semiconductors, Chinese Academy of Sciences, and Ningxia University report that CMOS-compatible uniaxial strain can substantially enhance valley splitting, effectively shielding it from the effects of this interface disorder. Atomistic pseudopotential calculations demonstrate that this strain linearly restores valley splitting while maintaining a narrow distribution of disorder-induced variations. These findings establish a route to improve gate uniformity in silicon-based spin qubits, potentially enabling scalable quantum processors.

Silicon Quantum Wells for Scalable Spin Qubits

Uniaxial strain introduces a new coupling channel between bulk valleys in adjacent Brillouin zones through a small momentum transfer, markedly reducing the susceptibility of valley splitting to interfacial disorder in silicon-germanium quantum wells. This coupling mechanism, revealed through calculations, offers a pathway to stabilize a critical property for scalable quantum computing. Achieving substantial and controllable valley splitting in Si/SiGe quantum wells has proven difficult, despite various material design strategies. Yang Liu and Gang Wang contributed equally to this work, affiliated with the State Key Laboratory of Semiconductor Physics and Chip Technologies and Ningxia University, respectively.

Valley Splitting Challenges from Interface Disorder

Calculations reveal that even a small amount of shear strain, just 0.2 percent, can stabilize valley splitting in silicon-germanium quantum wells, preventing further suppression caused by atomic-scale disorder at the interface. This level of stabilization is important for practical spin qubit applications, where consistent and predictable qubit behavior is essential. While computationally designed “magic” Si/Ge atomic-layer stacks were predicted to yield a giant valley splitting of 8.7 meV, and simplified superlattice barriers could produce 3.7 meV, these values are significantly diminished by interfacial alloy disorder.

The research highlights that such disorder inevitably destroys the large valley splitting predicted for many proposed quantum well designs. Because this inter-BZ coupling is entirely induced by shear strain, the analysis reveals the atomistic origin of the robustness of shear strain-enhanced valley splitting against both interfacial steps and alloy disorder in silicon quantum wells. The reduced momentum transfer makes it less susceptible to cancellation by fluctuations in interface positions.

Atomistic Pseudopotential Calculations of Valley Splitting

Atomistic pseudopotential calculations reveal that uniaxial strain linearly restores valley splitting diminished by atomic-scale disorder, a step toward stable silicon-based quantum bits. The ability to predictably control these variations is important for creating qubits with consistent performance characteristics. The research details a microscopic theoretical model incorporating shear strain into existing valley splitting frameworks, illuminating the underlying mechanisms at play.

To confirm the model’s accuracy, atomistic simulations were performed on ideal silicon-germanium quantum wells with varying thicknesses and under both positive and negative electric fields. These simulations focused on the influence of quantum well thickness and electric field direction on the relative phase angle and the overall trend of valley splitting under shear strain. Analysis of the oscillatory behavior of the relative phase angle as a function of interface position under a positive electric field further supports the model’s validity.

“We demonstrate through atomistic semi-empirical pseudopotential calculations that uniaxial strain can substantially enhance the immunity of valley splitting to interfacial disorder,” the paper states. The simulations confirm that this mechanism stabilizes valley splitting even with significant interface imperfections, offering a pathway to scalable quantum processors.

Uniaxial Strain Restores Suppressed Valley Splitting

CMOS-compatible uniaxial strain can effectively restore valley splitting in silicon-germanium quantum wells to beyond 0.2 meV, a threshold important for spin qubit operation, even with unavoidable atomic-scale disorder at the interface. This restoration is achieved with a remarkable reduction in variability induced by that disorder, a longstanding challenge in creating stable quantum bits.

The mechanism behind this effect involves a linear relationship between applied strain and the restoration of valley splitting, with a large enhancement rate maintained while keeping disorder-induced variations within a narrow distribution. This asymmetric enhancement stems from the opposing effects of tensile and compressive strain on the confinement energy of valley states within the silicon quantum well.

Compressive strain enhances valley splitting at a higher rate than tensile strain, as illustrated in supplementary figures detailing the energy landscape. The team’s analysis demonstrates that strain-restored valley splitting exhibits a suppressed variation ratio directly attributable to atomic disorder. The results demonstrate that this approach can effectively restore valley splitting, offering a pathway toward scalable silicon electron spin qubits and improved gate uniformity.

Strain-Induced Coupling Between Bulk Valleys

Uniaxial strain establishes a new interaction pathway between valleys in adjacent Brillouin zones, facilitating a degree of control over valley splitting previously hampered by atomic-scale imperfections. The mechanism, detailed through atomistic pseudopotential calculations, activates an inter-band coupling channel involving the Δ₁ and Δ₂’ bands, effectively mediating interaction between valleys. The ability to counteract interface disorder is particularly significant because the sharp spatial variation introduces high-momentum Fourier components that couple the ±k₀ valleys, creating valley splitting.

The Hamiltonian describing the silicon-germanium quantum well includes a confinement potential and an external electric field added to the bulk silicon Hamiltonian. This approach provides a practical pathway toward robust spin qubit implementation and addresses the uniform challenge in scaling up to fault-tolerant quantum computing.

Enhanced Immunity to Disorder via Uniaxial Strain

This restoration isn’t merely a recovery of lost signal, but a demonstrable reduction in the variability of that signal, a critical factor for reliable quantum computation. Applying 2% can push valley splitting beyond the 0.2 meV threshold necessary for spin qubit operation, while simultaneously minimizing fluctuations caused by alloy randomness. The theoretical model extends established frameworks for valley splitting by incorporating the strain tensor, revealing how shear strain reshapes valley coupling to resist atomic disorder.

In bulk silicon, the conduction-band minimum lies along specific directions, and quantum confinement lifts the degeneracy of these valleys. However, the team’s work shows that shear strain introduces a coupling that is resilient against atomic-scale disorder, effectively decoupling the valley splitting from the interface roughness. “This critical distinction indicates that while interface roughness has long been regarded as the primary obstacle to achieving high and uniform valley splitting, shear strain provides a pathway that circumvents this limitation,” the researchers explain.

Implications for Uniformity in Silicon Qubit Devices

Atomistic pseudopotential calculations demonstrate that a 0.2% shear strain is sufficient to stabilize valley splitting for spin qubit applications, preventing further suppression from atomic-scale disorder at the silicon-germanium interface. The calculations reveal that this coupling is distinct from previous observations, as it remains resilient even with significant interface roughness, a long-standing obstacle to stable valley splitting.

The restored valley splitting, achieved through strain, exhibits a suppressed variation ratio, indicating a more predictable and consistent quantum state. The ability to predictably control valley splitting through strain offers a significant advantage over material design strategies that have historically struggled with uniformity.

👉 More information
🗞 Robust valley splitting against interface atomic disorder towards scalable silicon quantum computing: Computational design
✍️ Yang Liu, Gang Wang, Shan Guan, Jun-Wei Luo and Shu-Shen Li
🧠 DOI: http://link.aps.org/doi/10.1103/f66n-c6sm

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