Quantifying the Variation in the Number of Donors in Quantum Dots Created Using Atomic Precision Advanced Manufacturing

Abstract

Atomic-precision advanced manufacturing enables unique silicon quantum electronics built on quantum dots fabricated from small numbers of phosphorus dopants. The number of dopant atoms comprising a dot plays a central role in determining the behavior of charge and spin confined to the dots and thus overall device performance. In this work, we use both theoretical and experimental techniques to explore the combined impact of lithographic variation and stochastic kinetics on the number of P incorporations in quantum dots made using these techniques and how this variation changes as a function of the size of the dot. Using a kinetic model of PH3 dissociation augmented with novel reaction barriers, we demonstrate that for a 2 × 3 silicon dimer window the probability that no donor incorporates goes to zero, allowing for certainty in the placement of at least one donor. However, this still comes with some uncertainty in the precise number of incorporated donors (either one or two), and this variability may still impact certain applications. We also examine the impact of the size of the initial lithographic window, finding that the incorporation fraction saturates to δ-layer-like coverage as the circumference-to-area ratio decreases. We predict that this incorporation fraction depends strongly on the dosage of the precursor and that the standard deviation of the number of incorporations scales as ∼√n, as would be expected for a sequence of largely independent incorporation events. Finally, we characterize an array of 36 experimentally prepared multidonor 3 × 3 nm lithographic windows with scanning tunneling microscopy, measuring the fidelity of the lithography to the desired array and the final location of PH x fragments within these lithographic windows. We use our kinetic model to examine the expected variability due to the observed lithographic error, predicting a negligible impact on incorporation statistics. We find good agreement between our model and the inferred incorporation locations in these windows from scanning tunneling microscope measurements.

EUV-induced hydrogen desorption as a step towards large-scale silicon quantum device patterning

“…Thus, this method of photon-based hydrogen desorption lithography can potentially create metallic, large-scale contacts or interconnects to multi-layer quantum devices 14 , 41 . We expect the incorporation and activation of dopants to be similar to what has been previously demonstrated on both clean surfaces 42 , 43 and hydrogen-terminated surfaces patterned with STM 44 , 45 . The only anticipated difference lies in the density of incorporated dopants, which we predict to be slightly lower due to any incomplete desorption of hydrogen.…”

Machine Learning-Assisted Precision Manufacturing of Atom Qubits in Silicon

“…For example, it has been shown that three consecutive dimers need to be desorbed in order to facilitate incorporation of a single donor. 7 , 37 For the device shown in Figure 1 b, we estimate that ≤2 (≤1) donors can be incorporated into the lithographic opening at the left (right) qubit site with seven (five) fully desorbed dimers (see Supporting Information, S1 for a detailed discussion on the incorporation chemistry). While this method provides a quick estimation for the likely donor number, it suffers from a high error rate due to the multiple chemical pathways that can occur for the phosphine gas to dissociate before P incorporates into the surface during the incorporation anneal.…”