[Paper Review] The impact of stochastic incorporation on atomic-precision Si:P arrays

Jeffrey Ivie, Quinn Campbell+10 more|arXiv (Cornell University)|May 25, 2021

Quantum and electron transport phenomena53 references4 citations

TL;DR

This study investigates stochastic phosphorus (P) incorporation in atomically precise Si:P arrays fabricated via scanning tunneling microscope lithography, revealing a 63±10% probability of successful P incorporation into single-donor windows at room-temperature PH₃ dosing. A kinetic model confirms this yield and identifies annealing conditions that could achieve near-deterministic incorporation, enabling scalable quantum devices.

ABSTRACT

Scanning tunneling microscope lithography can be used to create nanoelectronic devices in which dopant atoms are precisely positioned in a Si lattice within $\sim$1 nm of a target position. This exquisite precision is promising for realizing various quantum technologies. However, a potentially impactful form of disorder is due to incorporation kinetics, in which the number of P atoms that incorporate into a single lithographic window is manifestly uncertain. We present experimental results indicating that the likelihood of incorporating into an ideally written three-dimer single-donor window is $63 \pm 10\%$ for room-temperature dosing, and corroborate these results with a model for the incorporation kinetics. Nevertheless, further analysis of this model suggests conditions that might raise the incorporation rate to near-deterministic levels. We simulate bias spectroscopy on a chain of comparable dimensions to the array in our yield study, indicating that such an experiment may help confirm the inferred incorporation rate.

Motivation & Objective

• To quantify the stochastic nature of phosphorus (P) incorporation into atomically precise Si:P donor arrays fabricated using scanning tunneling microscope (STM) lithography.
• To understand how kinetic limitations in P incorporation affect the reliability and scalability of quantum devices based on donor arrays.
• To develop a kinetic model that explains the observed incorporation yield and predicts conditions for deterministic incorporation.
• To evaluate the impact of stochastic incorporation on the performance of quantum simulators and qubits based on extended Fermi-Hubbard models.

Proposed method

• Conducted STM lithography on Si(100) 2×1 surfaces using +3.5 V bias, 6.0 nA current, 6.0 mC/cm dose, and 10 nm/s tip speed to define single-donor windows.
• Performed room-temperature PH₃ dosing at 3.0×10⁻¹⁰ Torr for 10 minutes, resulting in ~0.15 Langmuir coverage, followed by 310 °C anneal for P incorporation.
• Used Kinetic Monte Carlo (KMC) simulations with the KMClib package to model P incorporation dynamics, varying parameters such as temperature, pressure, and time.
• Calculated incorporation probability P_I(n|w) for n P atoms in w-dimer windows using 200 independent simulations per condition, with error bars derived from binomial distribution.
• Simulated bias spectroscopy on donor chains to assess detectability of incorporation outcomes and validate inferred yields.
• Applied the Meir-Wingreen formula to compute current and differential conductance in donor chains based on extended Fermi-Hubbard model parameters from multi-valley effective mass theory.

Experimental results

Research questions

• RQ1 What is the probability of successful phosphorus incorporation into a single, precisely defined three-dimer window at room-temperature PH₃ dosing?
• RQ2 How do kinetic factors such as PH₃ pressure, dosing time, and annealing temperature influence the stochasticity of P incorporation?
• RQ3 Can a kinetic model accurately reproduce the experimentally observed 63±10% incorporation yield in single-donor windows?
• RQ4 What conditions could lead to near-deterministic P incorporation, enabling scalable, reliable fabrication of Si:P quantum arrays?
• RQ5 Can bias spectroscopy measurements distinguish between different incorporation outcomes (e.g., 0, 1, or 2 P atoms) in small donor chains?

Key findings

• The experimental incorporation probability for a single, precisely defined three-dimer window is 63±10% at room-temperature PH₃ dosing.
• A kinetic model based on KMC simulations successfully reproduces the observed 63±10% incorporation yield, validating the stochastic nature of the process.
• The model predicts that increasing the PH₃ partial pressure or extending the dosing time could significantly improve incorporation yield, approaching deterministic levels.
• Annealing at 310 °C after dosing is sufficient for full P incorporation, as confirmed by prior studies and consistent with the observed yield.
• Simulations of bias spectroscopy on a chain of comparable size suggest that such measurements could experimentally confirm the inferred incorporation rate.
• The study demonstrates that placement precision alone is insufficient for reliable device fabrication; incorporation kinetics must be controlled to achieve scalable quantum technologies.