Error Rates in Deterministic Ion Implantation for Qubit Arrays

Benedict Murdin; N Cassidy; D Cox; R Webb; Richard Curry

doi:10.1002/pssb.202000615

Error Rates in Deterministic Ion Implantation for Qubit Arrays

Benedict Murdin, N Cassidy, D Cox, R Webb, Richard Curry

EEE - Academic & Research

Research output: Contribution to journal › Article › peer-review

Abstract

We investigate the theoretical error rates in deterministic ion implantation, when using an ion beam governed by a Poisson point process with a detector that counts the impacts. We conclude that if the error rates are small, then for spots with nominally one implanted ion the probability of failure to implant the correct number is approximately κ/λ + η(bar) + λ/2 for a synchronous (i.e. pulsed) system or K/L + η(bar) + Lt_s for an asynchronous (i.e. continuous beam) system, where η(bar) is the probability that the detector misses an ion impact, and L(K) and λ(κ) are the numbers of ions (dark counts) per unit time and per pulse respectively. t_s is the system reaction time for an asynchronous system. This approximation allows easy identification of the greatest need for engineering effort. We examine some experimental efforts to measure these parameters and their uncertainties.

Original language	English
Article number	2000615
Journal	Physica status solidi B-basic solid state physics
Volume	258
Issue number	6
Early online date	2 Mar 2021
DOIs	https://doi.org/10.1002/pssb.202000615 https://doi.org/10.1002/pssb.202000615
Publication status	Published - 1 Jun 2021

Keywords

errors
ion implantation
single ions

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title = "Error Rates in Deterministic Ion Implantation for Qubit Arrays",

abstract = "We investigate the theoretical error rates in deterministic ion implantation, when using an ion beam governed by a Poisson point process with a detector that counts the impacts. We conclude that if the error rates are small, then for spots with nominally one implanted ion the probability of failure to implant the correct number is approximately κ/λ + η(bar) + λ/2 for a synchronous (i.e. pulsed) system or K/L + η(bar) + Lts for an asynchronous (i.e. continuous beam) system, where η(bar) is the probability that the detector misses an ion impact, and L(K) and λ(κ) are the numbers of ions (dark counts) per unit time and per pulse respectively. ts is the system reaction time for an asynchronous system. This approximation allows easy identification of the greatest need for engineering effort. We examine some experimental efforts to measure these parameters and their uncertainties.",

keywords = "errors, ion implantation, single ions",

author = "Benedict Murdin and N Cassidy and D Cox and R Webb and Richard Curry",

note = "Funding Information: The authors are grateful for support from the UK EPSRC (grant refs EP/N015215/1 SIMPLE and EP/M009564/1 ADDRFSS), and N.C. is grateful for support from Ionoptika Ltd., UK, and the EPSRC Centre for Doctoral Training in Micro‐ and Nanomaterials (grant ref EP/L016788). Funding Information: The authors are grateful for support from the UK EPSRC (grant refs EP/N015215/1 SIMPLE and EP/M009564/1 ADDRFSS), and N.C. is grateful for support from Ionoptika Ltd., UK, and the EPSRC Centre for Doctoral Training in Micro- and Nanomaterials (grant ref EP/L016788). Publisher Copyright: {\textcopyright} 2021 The Authors. physica status solidi (b) basic solid state physics published by Wiley-VCH GmbH",

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AU - Murdin, Benedict

AU - Cassidy, N

AU - Cox, D

AU - Webb, R

AU - Curry, Richard

N1 - Funding Information: The authors are grateful for support from the UK EPSRC (grant refs EP/N015215/1 SIMPLE and EP/M009564/1 ADDRFSS), and N.C. is grateful for support from Ionoptika Ltd., UK, and the EPSRC Centre for Doctoral Training in Micro‐ and Nanomaterials (grant ref EP/L016788). Funding Information: The authors are grateful for support from the UK EPSRC (grant refs EP/N015215/1 SIMPLE and EP/M009564/1 ADDRFSS), and N.C. is grateful for support from Ionoptika Ltd., UK, and the EPSRC Centre for Doctoral Training in Micro- and Nanomaterials (grant ref EP/L016788). Publisher Copyright: © 2021 The Authors. physica status solidi (b) basic solid state physics published by Wiley-VCH GmbH

PY - 2021/6/1

Y1 - 2021/6/1

N2 - We investigate the theoretical error rates in deterministic ion implantation, when using an ion beam governed by a Poisson point process with a detector that counts the impacts. We conclude that if the error rates are small, then for spots with nominally one implanted ion the probability of failure to implant the correct number is approximately κ/λ + η(bar) + λ/2 for a synchronous (i.e. pulsed) system or K/L + η(bar) + Lts for an asynchronous (i.e. continuous beam) system, where η(bar) is the probability that the detector misses an ion impact, and L(K) and λ(κ) are the numbers of ions (dark counts) per unit time and per pulse respectively. ts is the system reaction time for an asynchronous system. This approximation allows easy identification of the greatest need for engineering effort. We examine some experimental efforts to measure these parameters and their uncertainties.

AB - We investigate the theoretical error rates in deterministic ion implantation, when using an ion beam governed by a Poisson point process with a detector that counts the impacts. We conclude that if the error rates are small, then for spots with nominally one implanted ion the probability of failure to implant the correct number is approximately κ/λ + η(bar) + λ/2 for a synchronous (i.e. pulsed) system or K/L + η(bar) + Lts for an asynchronous (i.e. continuous beam) system, where η(bar) is the probability that the detector misses an ion impact, and L(K) and λ(κ) are the numbers of ions (dark counts) per unit time and per pulse respectively. ts is the system reaction time for an asynchronous system. This approximation allows easy identification of the greatest need for engineering effort. We examine some experimental efforts to measure these parameters and their uncertainties.

KW - errors

KW - ion implantation

KW - single ions

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DO - 10.1002/pssb.202000615

M3 - Article

AN - SCOPUS:85102769490

SN - 0370-1972

VL - 258

JO - Physica status solidi B-basic solid state physics

JF - Physica status solidi B-basic solid state physics

IS - 6

M1 - 2000615

ER -

Error Rates in Deterministic Ion Implantation for Qubit Arrays

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Keywords

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