Statistical Structure of Charge Disorder in Si/SiGe Quantum Dots

TL;DR

This work addresses device-to-device variability in Si/SiGe double quantum dots arising from electrostatic disorder at the oxide interface. By combining finite-element simulations with a predictive multivariate model, the authors show that disorder-induced fluctuations concentrate along a small number of principal axes, enabling a three-mode disorder space that captures over 90% of the variance. Principal Component Analysis reveals physically interpretable modes corresponding to symmetric squeezing, asymmetric detuning, and a common vertical-field shift, and a three-gate control scheme can effectively compensate these modes while plunger-only control cannot. The results yield a practical framework for disorder-aware controllability, improve data-driven tuning strategies, and underscore the importance of barrier gate control for scalable spin-qubit operation in Si/SiGe devices.

Abstract

Properties of quantum dot based spin qubits have significant inter-device variability due to unavoidable presence of various types of disorder in semiconductor nanostructures. A significant source of this variability is charge disorder at the semiconductor-oxide interface, which causes unpredictable, yet, as we show here, correlated fluctuations in such essential properties of quantum dots like their mutual tunnel couplings, and electronic confinement energies. This study presents a systematic approach to characterize and mitigate the effects of such disorder. We utilize finite element modeling of a Si/SiGe double quantum dot to generate a large statistical ensemble of devices, simulating the impact of trapped interface charges. This work results in a predictive statistical model capable of generating realistic artificial data for training machine learning algorithms. By applying Principal Component Analysis to this dataset, we identify the dominant modes through which disorder affects the multi-dimensional parameter space of the device. Our findings show that the parameter variations are not arbitrary, but are concentrated along a few principal axes, i.e. there are significant correlations between many properties of the devices. We finally compare that against control modes generated by sweeping the gate voltages, revealing limitations of the plunger-only control. This work provides a framework for enhancing the controllability and operational yield of spin qubit devices, by systematically addressing the nature of electrostatic disorder that leads to statistical correlations in properties of double quantum dots.

Figures (11)

• Figure 1: Device Model and Experimental Regime. (a)-(c) schematic diagrams of double-well potential along three axes used to present relevant DQD parameters (d) Schematic of the simulated Si/SiGe DQD device structure showing the gate layout and trapped charges. Example distribution of the disorder potential generated solely by defects, shown with all gates turned off. e) side view of DQD device (f) Extracted plunger gate lever arm $\alpha$, confirming agreement with typical experimental values.
• Figure 2: Estimated yields of 76% and 20% are obtained for (a) $\rho = 5 \times 10^{9}$ cm$^{-2}$ and (b) $\rho = 5 \times 10^{10}$ cm$^{-2}$, respectively. The results are obtained under constraints of a plunger gate correction below 20 mV, orbital energies above 1 meV in both dots, and tunnel gaps ranging between $10$ and $250$$\mu$eV. The histograms in the top and right panels show the distributions of tunnel coupling and detuning correction, respectively. The dark (light) gray shading indicates the number of samples that fall inside (outside) the success box. The overlay step histogram showing the entire distribution, including all the data points.
• Figure 3: Marginal distributions of the key DQD parameters as function of charge density $\rho$. The corresponding ensemble-averaged value of each DQD parameter are summarized in Table \ref{['tab:avg_parameters']}. The vertical dashed line represents the defect-free DQD parameters, serving as a reference for a device where the gates are set to $V_{L/R} = 0.35 \, \text{V}$ and $V_B = -0.1 \, \text{V}$.
• Figure 4: Fluctuations in the tunnel coupling $t_c$ as a function of interdot distance $d$ for two charge densities: (a) $\rho = 5 \times 10^{10}\,\mathrm{cm}^{-2}$ and (b) $\rho = 5 \times 10^{9}\,\mathrm{cm}^{-2}$. (c) Joint conditional density $P(d,h_B \mid 2t_c =\mathrm{value})$ for three values of $t_c$. The results indicate that variations in $t_c$ are primarily driven by fluctuations in $d$, which is positively correlated with $h_B$.
• Figure 5: Model validation via synthetic sampling. A scatter plot matrix showing pairwise correlations between key DQD parameters. Comparison of (i) a multivariate normal model (red) and (ii) a reduced principal-component model using the first three components (yellow) against the reference dataset from full simulations (blue). The diagonal cells show overlays of the three 1D marginals, demonstrating close agreement with the original data. All three data (original and reconstructed) are obtained for density $\rho = 5 \times 10^{10}$ cm$^{-2}$.