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For more info see http://www.lyx.org/ \lyxformat 345 \begin_document \begin_header \textclass book \begin_preamble \renewcommand{\vec}[1]{\mathbf{#1}} % vectors are bold \numberwithin{equation}{chapter} \usepackage{graphicx} \usepackage{amsfonts} \usepackage{amssymb} \usepackage[small,compact]{titlesec} % compress section headings %\usepackage{bibspacing} % compress bibliography spacing \let\oldbib\thebibliography \renewcommand{\thebibliography}[1]{% \oldbib{#1}% \setlength{\itemsep}{-4pt}% } % Compress lists \let\oldenumerate=\enumerate \def\enumerate{\oldenumerate% \setlength{\itemsep}{0pt}\setlength{\parsep}{0pt}}% \usepackage[avantgarde]{quotchap} \renewcommand{\maketitle}{ \thispagestyle{empty} \begin{center} \includegraphics[scale=0.4]{images/unimelb.png}\\ \vfill \resizebox{\textwidth}{!}{\huge \@title}\\ \vspace{1cm} {\Large \@author}\\ \vspace{3cm} {\rmfamily \@date}\\ \vspace{2cm} {\rmfamily School of Physics}\\ {\rmfamily The University of Melbourne}\\ \vspace{5cm} \end{center} \clearpage \setcounter{page}{1} } \end_preamble \options openany \use_default_options true \begin_modules theorems-ams \end_modules \language english \inputencoding auto \font_roman times \font_sans helvet \font_typewriter default \font_default_family default \font_sc false \font_osf false \font_sf_scale 100 \font_tt_scale 100 \graphics default \paperfontsize 12 \spacing single \use_hyperref true \pdf_bookmarks true \pdf_bookmarksnumbered false \pdf_bookmarksopen false \pdf_bookmarksopenlevel 1 \pdf_breaklinks false \pdf_pdfborder false \pdf_colorlinks false \pdf_backref false \pdf_pdfusetitle true \papersize a4paper \use_geometry true \use_amsmath 1 \use_esint 1 \cite_engine basic \use_bibtopic false \paperorientation portrait \leftmargin 2cm \topmargin 2cm \rightmargin 2cm \bottommargin 2cm \headheight 0.5cm \headsep 0.5cm \footskip 0.5cm \columnsep 1cm \secnumdepth 1 \tocdepth 2 \paragraph_separation indent \defskip medskip \quotes_language english \papercolumns 1 \papersides 2 \paperpagestyle headings \tracking_changes false \output_changes false \author "" \author "" \end_header \begin_body \begin_layout Standard \begin_inset Note Note status open \begin_layout Plain Layout - write a little more about the technical details of the colutron implant and fix up the schematic \end_layout \begin_layout Plain Layout - improve the introduction to chapter 2 along the lines of David's suggestions \end_layout \begin_layout Plain Layout - do a final pass for coherence and linkage \end_layout \begin_layout Plain Layout - write the abstract and remaining frontmatter \end_layout \begin_layout Plain Layout - references fixing up -- remove et. al.'s , journal abbreviations \end_layout \end_inset \end_layout \begin_layout Title The Problem of Coherent Transport in the Solid State \end_layout \begin_layout Author Jonathan Newnham \begin_inset Newline newline \end_inset \begin_inset space ~ \end_inset \begin_inset Newline newline \end_inset Supervisors: D. N. Jamieson and P. Spizziri \end_layout \begin_layout Standard \begin_inset ERT status open \begin_layout Plain Layout \backslash pagenumbering{roman} \end_layout \end_inset \end_layout \begin_layout Section* Abstract \end_layout \begin_layout Standard [[ This will be a lot like the introduction to Chapter 2, with a bit of setup for Chapter 4.]] \end_layout \begin_layout Standard \begin_inset Note Note status collapsed \begin_layout Plain Layout Proposals for the Quantum Internet of the mid 21st century with revolutionary capabilities for information storage, processing and commuication are now emerging. These architectures require quantum memory, coherent quantum transport, and readout of quantum states. Here we look at the practical issues associated with the fabrication of these components using the techniques available early 21st century based on promising lines of investigation laid down over the past decade. \end_layout \begin_layout Plain Layout In particular we look at models for coherent transport using nanowires and nanoscale mosfets, insertion and activation of single donors into nanoscale devices and ... \end_layout \begin_layout Plain Layout present a pile of experiments on electrically detected magnetic resonance measurements of the quantized energy levels in these devices. \end_layout \begin_layout Plain Layout from a practical point of view towards how they could be fabricated using the technology of the early 21st century. \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset Newpage clearpage \end_inset \end_layout \begin_layout Section* Acknowledgements \end_layout \begin_layout Description David \begin_inset space ~ \end_inset Jamieson \end_layout \begin_layout Description Paul \begin_inset space ~ \end_inset Spizziri \end_layout \begin_layout Description Wayne \begin_inset space ~ \end_inset Hutchison \end_layout \begin_layout Description Andrew \begin_inset space ~ \end_inset Alves for request and feedback on cantilever aperture simulations and for providing experimental data \end_layout \begin_layout Description Laurens \begin_inset space ~ \end_inset van \begin_inset space ~ \end_inset Beverens \end_layout \begin_layout Description Samuel \begin_inset space ~ \end_inset Thompson for an excellent labview controller for the I-V measurements and information on the AFSiD samples \end_layout \begin_layout Description Felix \begin_inset space ~ \end_inset Hoehne \begin_inset space ~ \end_inset and \begin_inset space ~ \end_inset Martin \begin_inset space ~ \end_inset Brandt \end_layout \begin_layout Description Stephen \begin_inset space ~ \end_inset Gregory \begin_inset Note Note status open \begin_layout Plain Layout XXX: spelling? \end_layout \end_inset for the use of and much assistance with the EPP wire-bonder \end_layout \begin_layout Section* Statement of Contribution and Originality \end_layout \begin_layout Standard Chapter 1 is an original review. Of Chapter 2, the simulation development was my own work; nanowire growth was performed by Laurens van Beverens at UC Berkeley; nanowire preparation, implantation and initial measurements I performed with Paul Spizziri; low-tempe rature I-Vs were performed by Wayne Hutchinson at UNSW@ADFA; and the EDMR measurements were performed by Felix Hoehne and W. Hutchinson at the Walter Schottky Institut in M \begin_inset ERT status open \begin_layout Plain Layout \backslash " \end_layout \end_inset unchen, Germany. To the best of my knowledge, the particular laser annealing process described here (as an application of Cui et. al.'s Raman temperature measurement method) was conceived entirely by P. Spizziri. \end_layout \begin_layout Standard \begin_inset CommandInset toc LatexCommand tableofcontents \end_inset \end_layout \begin_layout Standard \begin_inset CommandInset nomencl_print LatexCommand printnomenclature \end_inset \end_layout \begin_layout Standard \begin_inset CommandInset nomenclature LatexCommand nomenclature symbol "nm" description "Nanometers: $10^{-9}$ m. 1 nm is comparable to the size of a water molecule." \end_inset \begin_inset CommandInset nomenclature LatexCommand nomenclature prefix "um" symbol "$\\mu$m" description "micrometers: $10^{-6}$ m. A human hair is usually between 20-200 $\\mu$m." \end_inset \begin_inset CommandInset nomenclature LatexCommand nomenclature symbol "WSI" description "The Walter Schottky Institut" \end_inset \end_layout \begin_layout Standard \begin_inset Newpage clearpage \end_inset \end_layout \begin_layout Standard \begin_inset ERT status open \begin_layout Plain Layout \backslash pagenumbering{arabic} \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset ERT status open \begin_layout Plain Layout \backslash setcounter{page}{1} \end_layout \end_inset \end_layout \begin_layout Chapter Review of Coherent Transport \begin_inset OptArg status open \begin_layout Plain Layout Review \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset CommandInset label LatexCommand label name "cha:review" \end_inset \end_layout \begin_layout Standard \begin_inset Note Note status collapsed \begin_layout Plain Layout General (historical) introduction for any scientist. \series bold VERY IMPORTANT CHAPTER. \end_layout \end_inset \end_layout \begin_layout Standard Quantum computing holds many promising applications in science and industry. In this first chapter review we discuss the historial context, delve into more recent developments in solid-state systems, and outline the next experimen tal steps required in the development of solid-state coherent transport. \end_layout \begin_layout Standard In 1982 Paul Benioff proposed \begin_inset CommandInset citation LatexCommand cite key "benioff1982quantum" \end_inset the first recognisable theoretical framework for a quantum computer. That same year, Feynman discussed the impossibility of simulating quantum systems with classical computers \begin_inset CommandInset citation LatexCommand cite key "feynman1982simulating" \end_inset . Feynman also pushed the idea of controlled manipulation of coherent quantum states in a 1986 book \begin_inset CommandInset citation LatexCommand cite key "feynman1986quantum" \end_inset . Deutsch \begin_inset CommandInset citation LatexCommand cite key "Deutsch1992" \end_inset showed that a quantum computer could be exponentially faster than a classical computer. \begin_inset Note Note status collapsed \begin_layout Plain Layout for a certain obscure class of problems: those that rely on computing a large fraction of possible states of the system but only measuring global properties of the resultant states through interference between them all. \end_layout \end_inset \end_layout \begin_layout Standard Quantum computing remained a niche interest until 1994, when Shor proposed his factorization algorithm \begin_inset Foot status collapsed \begin_layout Plain Layout \begin_inset CommandInset citation LatexCommand cite key "shor1999polynomial" \end_inset is the original article; an excellent \begin_inset Quotes eld \end_inset man on the street \begin_inset Quotes erd \end_inset explanation is \begin_inset CommandInset citation LatexCommand cite key "Aaronson2007" \end_inset \end_layout \end_inset . This sparked widespread interest as it could be applied to break the public-key cryptography algorithm RSA, used almost ubiquitously for communication security by businesses, banks, militaries and the ssh and https protocols. Shor's algorithm for factorizing large numbers was exponentially faster than anything a modern classical computer could achieve. Widespread interest was aroused. \end_layout \begin_layout Standard In 1998, Bruce Kane followed up on Seth Lloyd's more feasible theoretical construction \begin_inset CommandInset citation LatexCommand cite key "lloyd1993potentially" \end_inset \begin_inset Foot status collapsed \begin_layout Plain Layout which contains the first published mention of the word \begin_inset Quotes eld \end_inset qubit \begin_inset Quotes erd \end_inset \end_layout \end_inset \begin_inset Note Note status open \begin_layout Plain Layout XXX earlier? \end_layout \end_inset with a concrete architecture based on the spin- \begin_inset Formula $\frac{1}{2}$ \end_inset nucleus of phosphorus embedded in a \begin_inset Quotes eld \end_inset spinless \begin_inset Quotes erd \end_inset solid silicon-28 matrix and controlled with classical electrical gates \begin_inset CommandInset citation LatexCommand cite key "kane1998silicon" \end_inset . Other architectures based on (among others) photons, trapped ions and supercond uctors followed \begin_inset CommandInset citation LatexCommand cite key "Milburn1999,roadmap" \end_inset . \end_layout \begin_layout Standard Harking back to Feynman's original predictions, Lanyon et. al. have recently used a photonic quantum computer to perform a simple quantum chemistry calculation: calculating the energy levels of atomic hydrogen \begin_inset CommandInset citation LatexCommand cite key "lanyon2010towards" \end_inset . This problem is well known and has been performed on modern classical computers , but the scalability of quantum computing promises much more complex simulation s and determinations of molecular properties well out of reach of any current or future classical supercomputer. A new understanding of chemistry and biology would likely result, having widespread applications in materials processing, medicine, drug design and biological and chemical engineering. \end_layout \begin_layout Standard No past or future classical computer can fully simulate a quantum system with more than about 50 interacting two-level systems. This corresponds to about \begin_inset Formula $2^{50}=10^{15}$ \end_inset different interactions that must be stored in memory and recalculated at each time step. A quantum computer, however, could potentially perform such a simulation using just 50 qubits. This is a very good reason to build a quantum computer. \end_layout \begin_layout Standard Coherently controlled quantum devices also have important applications as sensors. SQUID \begin_inset CommandInset nomenclature LatexCommand nomenclature symbol "SQUIDs" description "Superconducting Quantum Interference Devices" \end_inset s form the basis for the definitions and accurate measurement of voltage and magnetic field, and diamond and trapped ion quantum devices have been proposed for use in sensing applications \begin_inset CommandInset citation LatexCommand cite key "degen2008scanning,morton_bang-bang_2006" \end_inset . \begin_inset Note Note status open \begin_layout Plain Layout CITE igor? \end_layout \end_inset \end_layout \begin_layout Subsubsection Structure of this document \end_layout \begin_layout Standard Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:outline" \end_inset shows a rough outline of the fundamental capabilites of a quantum computer. In the remainder of this Chapter, we begin with a review of progress in fabricating various possible architectures. We then refine our focus and explore different options for implementing one of these capabilities, coherent transport, in solid state systems. \end_layout \begin_layout Standard Chapter 2 then discusses recent work aimed at building a solid foundation for a coherent transport proof-of-principle, and the fabrication of precursors to coherent transport devices. Chapter 3 then discusses some recent measurements on these potential precursor devices. \end_layout \begin_layout Standard \begin_inset Float figure placement H wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Graphics filename images/outline.svg lyxscale 25 width 80text% \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout The primary components of a quantum computer and the foundations required to build them. The highlighted line represents coherent transport of information. \begin_inset CommandInset label LatexCommand label name "fig:outline" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Standard \end_layout \begin_layout Standard \begin_inset Note Note status collapsed \begin_layout Plain Layout Foundation papers/classics: ?Divincenzo?, ?Lloyd1990 Nature Designer Hamiltonian s? \end_layout \end_inset \end_layout \begin_layout Section Potential Architectures \begin_inset Note Note status collapsed \begin_layout Plain Layout (for those with a more immediate interest in current progress) \end_layout \end_inset \end_layout \begin_layout Standard Since the proposal by Kane, various architectures have been proposed as ways to build a quantum computer. \begin_inset CommandInset citation LatexCommand cite key "roadmap" \end_inset is a comprehensive review. Normally the \begin_inset Quotes eld \end_inset Divincenzo Criteria \begin_inset Quotes erd \end_inset \begin_inset CommandInset citation LatexCommand cite key "divincenzo2001physical" \end_inset are used to quantify the progress using various architectures, however we choose the following, more subjective approach as it is more relevant to experiments. Some of the most important tradeoffs involved in choice of architecture are: \end_layout \begin_layout Enumerate \noindent coherence time (how long you have to perform computations before your qubits decohere). This should also take into consideration the interaction and transport times between qubits. \end_layout \begin_layout Enumerate \noindent scalability (a device must scale to at least 50 qubits to be really useful) \end_layout \begin_layout Enumerate \noindent transport ease (how easy it is to transport qubits on demand with currently known methods) \end_layout \begin_layout Enumerate \noindent interaction ease (how easy it is to coherently interact two qubits) \end_layout \begin_layout Enumerate \noindent manipulation ease (how easy it is to set/read a single qubit on demand without interfering with the others) \end_layout \begin_layout Enumerate \noindent manufacturability (how easy it is to make) \end_layout \begin_layout Standard \begin_inset Float table wide false sideways false status open \begin_layout Plain Layout \lang british \begin_inset ERT status open \begin_layout Plain Layout \backslash resizebox{ \backslash textwidth}{!}{ \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout Architecture \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Coherence \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Scalability \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Transport \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Interact \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Manipulation \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Manufacture \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Kane type \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 9 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 9 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 1 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 3 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 4 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 2 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout NMR liquid \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 3 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 1 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 1 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 8? \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 8 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 9 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Photonic \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 3 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 3 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 9 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 4 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 9 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 8 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout GaAs QDs \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 2 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 8 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 5 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 7 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 9 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 8 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout P in Si - \begin_inset Formula $\mbox{e}^{-}$ \end_inset spin \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 7 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 9 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 3 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 3 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 7 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 3 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Ion Traps \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 9 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 6 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 8 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 6 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 9 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 7 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Superconductors \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 5 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 7 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 3 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 5 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 8 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 6 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Diamond NV \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 8 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 7 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 5 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 3 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 7 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 6 \end_layout \end_inset \end_inset \end_layout \begin_layout Plain Layout \begin_inset ERT status open \begin_layout Plain Layout } \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout Architecture advantages and disadvantages. Each property is given a critical assessment by the author on a scale of 1-9 (9 being the best) \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Paragraph Kane \end_layout \begin_layout Standard A Kane-type quantum computer \begin_inset CommandInset citation LatexCommand cite key "kane1998silicon" \end_inset is a solid-state device consisting of phosphorus atoms in a silicon lattice, and using the nuclear spin of the phosphorus atom as the qubit (Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:Si:P-interaction-zone" \end_inset ). Manipulation and readout is performed using metallic wires on the surface of the silicon. It's very hard to interact with this qubit as the nucleus is deeply buried in a sea of electrons. Transport is also difficult as the state must be transferred coherently to an electron spin, that electron must be coherently transported through the silicon lattice, and then the state must be transferred back to a different nucleus. Both of these problems are solved by the ion trap method (below), which removes the supporting silicon lattice completely. One attraction of this architecture is that many of the processing steps (such as gate fabrication and crystalline-silicon growth) are well understood by the conventional semiconductor manufacturing industry. Another attraction is that the system should have reasonably long coherence times, especially if no-net-nuclear-spin Si-28 is used for the supporting lattice. \end_layout \begin_layout Standard The problem of charge traps in the oxide stealing the electron from donor atoms may need to be solved by using something other than the conventional silicon dioxide to separate the gates. Kane suggests SiGe. \end_layout \begin_layout Standard Recent progress has demonstrated coherent control of (bulk) P nuclear spins via the unpaired electron \begin_inset CommandInset citation LatexCommand cite key "morton2008solid" \end_inset . A recent variation \begin_inset CommandInset citation LatexCommand cite key "morton2009silicon" \end_inset on the original proposal simplifies some aspects of this architecture by only requiring localised readout of a 2D array (and having entanglement generated globally). \end_layout \begin_layout Standard A theoretical treatment of nuclear spin coherence decay via spin-orbit coupling and phonon emission is given in \begin_inset CommandInset citation LatexCommand cite key "Hasegawa1960" \end_inset . \end_layout \begin_layout Paragraph NMR Liquid \end_layout \begin_layout Standard \noun on Nuclear Magnetic Resonance \noun default was first performed in 1940s. In this approach, molecules with several interacting nuclear spins are affected by global fields. Different \begin_inset Quotes eld \end_inset qubits \begin_inset Quotes erd \end_inset are addressed by tuning the resonating microwave field frequency or magnetic field strength. \end_layout \begin_layout Standard Such qubits were demonstrated by IBM \begin_inset CommandInset citation LatexCommand cite key "chuang1998experimental,vandersypen2001experimental" \end_inset , who arguably performed Shor's algorithm to factorize the number 15, with some questions as to whether there was any coherent entanglement. This method is not scalable past a few qubits due to the method of addressing individual qubits. Recently, solid-state NMR quantum computers have been investigated. Due to the lack of molecular drift (changing magnetic field and thus precession frequency), this is more scalable, although the addressing problem still has no proposed solution \begin_inset CommandInset citation LatexCommand cite key "roadmap" \end_inset . \end_layout \begin_layout Paragraph Photonic \end_layout \begin_layout Standard A photonic quantum computer uses the direction of polarization of a photon as a qubit. Systems involve firing a light pulse through a set of lenses. This architecture has scalability problems; experiments seem to have topped out at about 11 qubits due to difficulties generating and reliably detecting many entangled photons. Recent reviews are \begin_inset CommandInset citation LatexCommand cite key "kok2007linear,o2007optical" \end_inset . This architecture has important applications in provably-secure quantum communication and long-range coherent transport. Coupling of photons to other quantum-mechanical systems is a growing field (see § \begin_inset CommandInset ref LatexCommand ref reference "sec:coupling" \end_inset ). The original paper is \begin_inset CommandInset citation LatexCommand cite key "knill2001scheme" \end_inset . Beautiful results have recently been demonstrated with optical memories at ANU \begin_inset CommandInset nomenclature LatexCommand nomenclature symbol "ANU" description "Australian National University" \end_inset \begin_inset CommandInset citation LatexCommand cite key "Hosseini2009" \end_inset and similarly \begin_inset CommandInset citation LatexCommand cite key "H'etet2008" \end_inset , temporarily storing photons coherently in excited states of a crystal. \end_layout \begin_layout Paragraph P in Si: electron spin \end_layout \begin_layout Standard This architecture is similar to the Kane proposal but stores the spin on the phosphorus atom's valence electron instead of the nucleus \begin_inset CommandInset citation LatexCommand cite key "vrijen2000electron,Hill2005" \end_inset . A P-31 atom replaces a silicon atom 20nm from the surface in a Si-28 crystal. All the Si-28 electrons are paired up, and Si-28 has no net nuclear spin so this is a very clean environment for the spin-1/2 P nucleus and its extra electron. The valence electron on the P atom is then controlled with metallic wires ( \noun on gates \noun default ) on the surface of the crystal (Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:Si:P-interaction-zone" \end_inset ). One of the advantages of this architecture is that the gate fabrication process is highly mature thanks to the silicon chip industry, and 20nm gates are regularly produced in bulk. \end_layout \begin_layout Standard Major hurdles for this architecture include manufacturability (positioning single phosphorus atoms is hard \begin_inset CommandInset citation LatexCommand cite key "schenkel2003formation" \end_inset ) and transport \begin_inset CommandInset citation LatexCommand cite key "hollenberg2006two" \end_inset . Two competing methods for fabrication are ion implantation \begin_inset CommandInset citation LatexCommand cite key "schenkel2003formation" \end_inset and the bottom-up approach \begin_inset CommandInset citation LatexCommand cite key "ruess2007narrow" \end_inset (more on these later). \begin_inset CommandInset citation LatexCommand cite key "clark2008solid" \end_inset is a recent review. \end_layout \begin_layout Standard A recent advance by the Australian Center for Quantum Computing Technology demonstrated single-shot readout of electron spins and found electron-spin coherence times ( \begin_inset Formula $T_{1}$ \end_inset ) of about 6s \begin_inset CommandInset citation LatexCommand cite key "morello2010single" \end_inset . This is a convicing demonstration of the Readout component of Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:outline" \end_inset . \end_layout \begin_layout Standard \begin_inset Float figure wide false sideways false status collapsed \begin_layout Plain Layout \noindent \align center \begin_inset Graphics filename images/sip.pdf width 30text% \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout Si:P interaction zone (courtesy David Jamieson). \begin_inset CommandInset label LatexCommand label name "fig:Si:P-interaction-zone" \end_inset \end_layout \end_inset \end_layout \begin_layout Plain Layout \end_layout \end_inset \end_layout \begin_layout Paragraph GaAs Quantum Dots \end_layout \begin_layout Standard Similar to the P in Si system, a quantum dot confines electrons using electrical ly charged gates instead of the potential well of a phosphorus atom. In gallium arsenide, the large sea of nuclear spins (~ \begin_inset Formula $10^{6}$ \end_inset in interaction range) near the dot limits coherence times to a few microseconds. A quantum dot constructed in a no-nuclear-spin material may mitigate this problem \begin_inset CommandInset citation LatexCommand cite key "angus2007gate,hu2007ge" \end_inset . Coupled qubits in this architecture have been demonstrated \begin_inset CommandInset citation LatexCommand cite key "petta2005coherent" \end_inset but the possibility of coherent transport remains an open question. \end_layout \begin_layout Paragraph Ion trap \end_layout \begin_layout Standard In this architecture, ions (spin qubits) float in vacuum above a 2D network of electrical gates which control the ions \begin_inset CommandInset citation LatexCommand cite key "kielpinski2002architecture" \end_inset . This approach looks very promising in the short term. Ion traps transporting several qubits have been demonstrated by NIST Maryland \begin_inset CommandInset citation LatexCommand cite key "blakestad2009high" \end_inset , together with repeated gate operations \begin_inset CommandInset citation LatexCommand cite key "home2009complete" \end_inset . Coherence times are measured in hours because there is very little for the ions to interact with. The current hurdle is heating of the ions by the trapping lasers or gates; this may be mitigated using magnetic gates \begin_inset CommandInset citation LatexCommand cite key "ospelkaus2008trapped" \end_inset . This architecture is technologically expensive, requiring atomic cooling and high vacuum. \end_layout \begin_layout Paragraph Superconductors \end_layout \begin_layout Standard \noun on Superconducting Quantum Interference Devices \noun default ( \noun on SQUIDs \noun default ) are small superconducting rings. For quantum computing, they store a qubit as the charge, phase of a current orbiting in the ring, or quantized magnetic flux through the ring. Coherence is more difficult in these systems because of additional energy levels above or below the two states used as qubit states \begin_inset CommandInset citation LatexCommand cite key "zhou2002quantum" \end_inset . A recent review is available \begin_inset CommandInset citation LatexCommand cite key "clarke2008superconducting" \end_inset . \begin_inset Note Note status open \begin_layout Plain Layout XXX Recent articles \end_layout \end_inset \end_layout \begin_layout Paragraph Diamond \end_layout \begin_layout Standard The most popular diamond system uses the free electron in a nitrogen vacancy (NV) defect in a diamond crystal as the qubit. \begin_inset Note Note status collapsed \begin_layout Plain Layout There are rumours that coherence times of about 1 second at \emph on room temperature \emph default have been demonstrated in high-purity C-12 diamond. \end_layout \end_inset The best published coherence time for this system is 2ms \begin_inset CommandInset citation LatexCommand cite key "ladd2010quantum" \end_inset . Proposals use optical transport and readout, which can cause difficulty if qubits are close together due to difficulty focusing lasers to address individual NV \begin_inset CommandInset nomenclature LatexCommand nomenclature symbol "NV" description "Nitrogen Vacancy, a defect involving a nitrogen atom in the diamond crystal lattice" \end_inset centres. Manipulation is performed optically. This system is promising, but novel manufacturing techniques are required, delaying progress \begin_inset CommandInset citation LatexCommand cite key "greentree2006critical" \end_inset . NV centres can also be used on their own as sensitive localised magnetic field detectors \begin_inset CommandInset citation LatexCommand cite key "gaebel2006room" \end_inset . Exploiting the magnetic dipole interaction between nearby (10nm) NV centres faces similar problems to the Si:P system \begin_inset CommandInset citation LatexCommand cite key "neumann2010quantum" \end_inset . \end_layout \begin_layout Standard \begin_inset Note Note status open \begin_layout Plain Layout Cite \begin_inset CommandInset citation LatexCommand cite key "wrachtrup2001quantum" \end_inset ? \end_layout \end_inset \end_layout \begin_layout Paragraph Other \end_layout \begin_layout Standard There are many other exotic architecture proposals. They include trapping an electron between a donor and the image charge of a donor in the nearby oxide \begin_inset CommandInset citation LatexCommand cite key "calderon2009quantum" \end_inset , or using fullerenes \begin_inset CommandInset citation LatexCommand cite key "morton2005high,morton_bang-bang_2006" \end_inset . Many more are given in a more comprehensive review of current progress \begin_inset CommandInset citation LatexCommand cite key "roadmap" \end_inset . \end_layout \begin_layout Standard A more recent review focusing on solid-state systems is \begin_inset CommandInset citation LatexCommand cite key "ladd2010quantum" \end_inset . Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:Coherence-times" \end_inset shows a summary of the coherence times for various solid-state systems. \end_layout \begin_layout Standard \begin_inset Float figure placement h wide false sideways false status collapsed \begin_layout Plain Layout \noindent \align center \begin_inset Graphics filename images/solid-state-coherence-times-summary.png lyxscale 50 width 70text% \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout Coherence times of various solid-state systems. \begin_inset Formula $T_{1}$ \end_inset is the decay time for the system to relax into its ground state; \begin_inset Formula $T_{2}$ \end_inset is the time for two coherent states at different energy levels to build up a large phase difference so that they are effectively incoherent. Image by John Morton and Jessica van Donkelaar. \begin_inset CommandInset label LatexCommand label name "fig:Coherence-times" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset Note Note status collapsed \begin_layout Plain Layout Sanker's room temp short-channel device from Science. \end_layout \end_inset \end_layout \begin_layout Section Coherent Transport \end_layout \begin_layout Standard As we stated in the introduction, one of the necessary components of a quantum computer is the ability to transport qubits from one place to another. From here on, we will focus on electron-spin systems due to their extreme scalability and relative feasability in other areas. Several methods for qubit transport in electron-spin-based architectures have been proposed. Which method is the most technologically viable remains to be seen. \end_layout \begin_layout Subsection CTAP \end_layout \begin_layout Standard \noun on Coherent Transport by Adiabatic Passage \noun default is a possibility for solid-state coherent transport \begin_inset CommandInset citation LatexCommand cite key "CTAP" \end_inset . In the simplest version of CTAP (Figure \begin_inset CommandInset ref LatexCommand ref reference "fig:CTAP" \end_inset ), there are three donors, two of which are ionised by gates. Barrier gates control the tunneling rate between adjacent donors. To move the electron from one end of the chain to the other, the barrier at the end of the chain is lowered and then raised. While this barrier is being raised, the other barrier between the first two donors is lowered, and to complete the sequence the start barrier is raised. This counter-intuitive pulse sequence ideally results in no population of the electron on the intermediate atom at any point. \end_layout \begin_layout Standard \begin_inset Float figure wide false sideways false status collapsed \begin_layout Plain Layout \noindent \align center \begin_inset Graphics filename images/CTAP.pdf width 70text% \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout CTAP, from \begin_inset CommandInset citation LatexCommand cite key "CTAP" \end_inset . The left-hand graph shows the voltage applied to the barrier gates during the transport process. The right-hand graphs show the potential and energy levels at several points during the process. This non-intuitive process involves lowering the second barrier (by increasing the voltage on the second gate) before the first. \begin_inset CommandInset label LatexCommand label name "fig:CTAP" \end_inset \end_layout \end_inset \end_layout \begin_layout Plain Layout \end_layout \end_inset \end_layout \begin_layout Standard Using a simple electric field gradient to push the valence electron along a chain of ionised donors is also discussed in \begin_inset CommandInset citation LatexCommand cite key "CTAP" \end_inset , and shown to have a lower fidelity. This may be a useful precursor study to perform, in particular to ensure that the electrons are available in a real device and can be moved around. \end_layout \begin_layout Standard CTAP scalability is discussed in \begin_inset CommandInset citation LatexCommand cite key "greentree2008spatial" \end_inset . A recent study \begin_inset CommandInset citation LatexCommand cite key "Rahman2009" \end_inset using the NEMO 3D tight-binding simulation toolkit \begin_inset CommandInset citation LatexCommand cite key "ahmed2009multimillion" \end_inset shows that the scheme is extremely sensitive to the exact position of each donor. Tuning the protocol's gate voltages allows high fidelity transport for donor position variation of several lattice spacings or a few nanometres. \end_layout \begin_layout Standard \noun on Heteronuclear CTAP \noun default involves using a larger atom in the intermediate position. It may be easier to use a different atom for the central potential-well if that atom has a lower electron affinity and hence requires less accurate positioning \begin_inset CommandInset citation LatexCommand cite key "jong2009coherent" \end_inset . \end_layout \begin_layout Subsection Spin Bus \end_layout \begin_layout Standard \begin_inset FormulaMacro \newcommand{\ket}[1]{|#1\rangle} {|#1\rangle} \end_inset \end_layout \begin_layout Standard In its simplest form, a \noun on spin bus \noun default \begin_inset CommandInset citation LatexCommand cite key "li2005quantum,mehring2006spin,friesen2007efficient" \end_inset consists of an antiferromagnetic Ising-model chain of spins \begin_inset Foot status open \begin_layout Plain Layout i.e. spins prefer to antialign, up-down-up... or down-up-down... \end_layout \end_inset , tightly coupled to their neighbours but nothing else. At low enough temperatures, a bus with an odd number of sites \begin_inset Formula $N$ \end_inset has two possible states: an extra spin-up or an extra spin-down. This allows treatment of the bus as an effective single spin. \end_layout \begin_layout Standard To transfer spins, the bus is then coupled to the destination site, allowed to equilibriate, and then decoupled. It is then coupled to the source site, allowed to equilibriate and decoupled. This has the effect of transferring the spin at the source site to the destination site with high probability. This non-intuitive coupling order is reminiscent of CTAP. \end_layout \begin_layout Standard Spin buses more than several hundred sites long (perhaps 1-10 \begin_inset Formula $\mu$ \end_inset m in solid state devices) are probably not practical due to long equilibrating times, donor diffusion and unintended coupling with parasitic sites. No spin bus has been demonstrated to date. A simple constraint on the temperature required for antiferromagnetic behaviour is derived in \begin_inset CommandInset citation LatexCommand cite key "chaves2009model" \end_inset . \end_layout \begin_layout Standard A potentially more useful application of such a device is the generation of highly entangled states between many sites. This is because it is quite straightforward to couple many sites to the bus at once. An example is the procedure for generating a \begin_inset Formula $W_{n}$ \end_inset state, \begin_inset Formula $\ket{00\ldots001}+\ket{00\ldots010}+\cdots+\ket{10\ldots000}$ \end_inset , given in \begin_inset CommandInset citation LatexCommand cite key "friesen2007efficient" \end_inset . \end_layout \begin_layout Subsection Photonic Coupling and The Flying Qubit \begin_inset CommandInset label LatexCommand label name "sec:coupling" \end_inset \end_layout \begin_layout Standard In the long term, it will be very important to be able to transport quantum information long distances. Divincenzo calls such transport \noun on flying qubits \noun default . Almost all proposed flying qubits use photons as the information carrier. Theoretical models of how to couple a quantum dot to a photon have been published \begin_inset CommandInset citation LatexCommand cite key "clark_quantum_2007" \end_inset , and preliminary work towards experimental demonstration has shown that quantum dots can absorb \begin_inset CommandInset citation LatexCommand cite key "shields2000" \end_inset and emit \begin_inset CommandInset citation LatexCommand cite key "dewhurst_slow-light-enhanced_2010" \end_inset single photons (in a directionally controlled way). \end_layout \begin_layout Standard Optical coupling between single-electron quantum dots has been demonstrated \begin_inset CommandInset citation LatexCommand cite key "yamamoto_optically_2009" \end_inset . Yamamoto's group has also demonstrated control over the quantum state of a single quantum dot using optical techniques \begin_inset CommandInset citation LatexCommand cite key "press_complete_2008" \end_inset . Abanto's architecture \begin_inset CommandInset citation LatexCommand cite key "abanto2010quantum" \end_inset results in much-needed leeway for solid state qubit donor placement by placing the donors in or between optical cavities and coupling them using cavity modes (resonant, bound photons) instead of Coulomb interactions. This looks very promising and will hopefully be demonstrated quite soon. \end_layout \begin_layout Standard It is also possible to couple photons to excitons (electron-hole pairs) \begin_inset CommandInset citation LatexCommand cite key "Hudson2007,stevenson_semiconductor_2006" \end_inset . The question of how to coherently couple such excitons to solid-state qubits remains open. \end_layout \begin_layout Standard Projects to demonstrate long-range quantum entanglement have been successful between islands 144km apart \begin_inset CommandInset citation LatexCommand cite key "ursin2006free" \end_inset and are plans are afoot to do it via a satellite \begin_inset CommandInset citation LatexCommand cite key "ursin2009space" \end_inset . \end_layout \begin_layout Standard \begin_inset Note Note status open \begin_layout Subsection Ensemble Systems \end_layout \begin_layout Plain Layout Coupling to waveguides? \begin_inset Note Note status open \begin_layout Plain Layout Oxford group. \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Subsection Blue Sky options \end_layout \begin_layout Standard \begin_inset Note Note status collapsed \begin_layout Plain Layout It would be fun to emulate the ion trap guys. I don't know how this is possible, because the point of the ion trap stuff is that they basically get rid of the silicon lattice so they can move the qubits around easily. \end_layout \begin_layout Plain Layout Perhaps we can harness the spin Hall effect? \end_layout \begin_layout Plain Layout Kondo effect? \end_layout \begin_layout Plain Layout Spin waves? \end_layout \end_inset \end_layout \begin_layout Standard Coherent electron transport in carbon nanotubes has been demonstrated \begin_inset CommandInset citation LatexCommand cite key "Tsukagoshi1999" \end_inset . It may be possible to perform this kind of \noun on ballistic transport \noun default in the Si:P system. This would likely require atomically precise donor placement. \end_layout \begin_layout Standard It has recently been shown that photosynthesis involves coherent transport \begin_inset CommandInset citation LatexCommand cite key "Engel2007photosynth" \end_inset . Engel et. al. observed \begin_inset Quotes eld \end_inset remarkably long-lived \begin_inset Quotes erd \end_inset coherent states in FMO bacteriochlorophyll complexes at 77K. Perhaps if we understand this mechanism then we can do it on chip, maybe even by using actual chlorophyll molecules. Self-assembly processes could potentially be essential to future mass productio n. \end_layout \begin_layout Section Deterministic fabrication \end_layout \begin_layout Standard In order to experimentally demonstrate some of the above coherent transport options, it is necessary to be able to accurately position donors. This section discusses techniques for doing so. \end_layout \begin_layout Subsection Donor ion positioning \end_layout \begin_layout Standard There are two main strategies for donor ion placement: \begin_inset Quotes eld \end_inset top-down \begin_inset Quotes erd \end_inset and \begin_inset Quotes eld \end_inset bottom-up \begin_inset Quotes erd \end_inset . The bottom up process involves placing atoms on a silicon surface and then growing more silicon around them; top down involves implanting ions into a clean silicon lattice by ion implantation. \end_layout \begin_layout Standard Ion implantation is less accurate; for 20 \begin_inset space ~ \end_inset nm depth, ions will straggle up/down and sideways an average of 8nm compared with about 1 \begin_inset space ~ \end_inset nm for bottom-up. \begin_inset Note Note status open \begin_layout Plain Layout NEED IMAGE. \end_layout \end_inset The bottom-up approach currently involves a considerable effort to make a single device (and so is likely less scalable in the long term) and the epitaxially grown silicon lattice above the donors may be less crystalline. \end_layout \begin_layout Standard \begin_inset Note Note status collapsed \begin_layout Plain Layout The bottom-up process involves removing a few hydrogen atoms from the surface of a hydrogen-terminated atomically-flat silicon crystal and then adsorbing phosphene gas (PH \begin_inset Formula $_{3}$ \end_inset ). Several hydrogen atoms must be removed for this to work, so exactly which site the P atom goes to is difficult to control. It's a beautiful process potentially with sub-nanometre accuracy. \end_layout \end_inset \end_layout \begin_layout Standard Outlines of the bottom-up process are given in \begin_inset CommandInset citation LatexCommand cite key "oberbeck2002encapsulation,Schofield2003" \end_inset . The AFM step, involving removing a few hydrogen atoms from the surface of a silicon crystal, is discussed in \begin_inset CommandInset citation LatexCommand cite key "Hallam2007" \end_inset . A more accurate technique aiming for single-atom positioning using an STM tip is discussed in the letter \begin_inset CommandInset citation LatexCommand cite key "ruess2004toward" \end_inset and the article \begin_inset CommandInset citation LatexCommand cite key "ruess2007narrow" \end_inset . This has recently resulted in the successful positioning of a single ion to within 1 \begin_inset space ~ \end_inset nm (3 lattice spacings). \end_layout \begin_layout Standard The semiconductor industry has been using ion implantation to fabricate electronic devices since the 1950s. More recently, more accurate methods of implanting a counted number of ions have been demonstrated \begin_inset CommandInset citation LatexCommand cite key "shinada2005enhancing" \end_inset , down to exceptionally low energies of about 10 keV \begin_inset CommandInset citation LatexCommand cite key "jamieson2005" \end_inset . The counting can be done by collecting secondary electrons emitted when the ion impacts the surface \begin_inset CommandInset citation LatexCommand cite key "schenkel2003solid,shinada2008reliable" \end_inset , or by collecting the induced charge from the substrate after the impact \begin_inset CommandInset citation LatexCommand cite key "jamieson2005" \end_inset . It is quite difficult to focus a low-energy ion beam to below the micron range. Instead of relying on fine focus, the step and repeat system \begin_inset CommandInset citation LatexCommand cite key "Orwa2009" \end_inset , a masking process relying on a mobile secondary mask \begin_inset CommandInset citation LatexCommand cite key "meijer2008towards" \end_inset , will allow 20 \begin_inset space ~ \end_inset nm resolution of donor placement. \end_layout \begin_layout Section Si:P system measurements \end_layout \begin_layout Standard \begin_inset CommandInset label LatexCommand label name "sec:measurements" \end_inset \end_layout \begin_layout Standard When making devices at the nanoscale, it is sometimes more difficult to figure out exactly what has been made than it was to make it in the first place. This section discusses measurements that help identify these systems, and provide data for theoretical models. \end_layout \begin_layout Subsection Embedded nanowires \end_layout \begin_layout Standard In two papers \begin_inset CommandInset citation LatexCommand cite key "iwano1994carrier,iwano1998hopping" \end_inset , Iwano et. al. implant 100 keV Ga into doped Si using a focused ion beam. The resulting wires are less than 100nm wide and about 50 \begin_inset Formula $\mu$ \end_inset m long, and were measured down to 4.2 K. The conduction model is not fully explained in these papers. Iwano refers to it as the \begin_inset Quotes eld \end_inset Hopping model \begin_inset Quotes erd \end_inset but makes many assumptions without careful study. Most of the samples were annealed at 600--690 \begin_inset Formula $^{\circ}$ \end_inset C and measurements show reduced conduction indicative of lattice defects. \end_layout \begin_layout Standard \begin_inset Note Note status open \begin_layout Plain Layout Is this next paragraph necessary? \end_layout \end_inset \end_layout \begin_layout Standard Conductance measurements on 8nm wide monolayer-thick P in Si wires are performed in \begin_inset CommandInset citation LatexCommand cite key "Ruess2008atomic" \end_inset . Rue \begin_inset ERT status open \begin_layout Plain Layout \backslash ss \end_layout \end_inset \begin_inset space ~ \end_inset finds Ohmic conduction (1 in 4 atoms in the wire is a P atom) with the resistanc e heavily dependent on temperature. In the range 1--10 Kelvin, the resistance is also heavily dependent on the applied magnetic field ( \noun on magnetoresistance \noun default ). They found several different conduction mechanisms were necessary to fit the measured data. Above 10K no magnetic field dependence was observed. At 4 K, increased magnetic field increased the resistance (positive magnetoresi stance), consistent with the 1D \noun on variable-range-hopping \noun default (VRH) model \begin_inset CommandInset citation LatexCommand cite key "azbel1991variable" \end_inset . This semi-classical model is based on conduction electrons tunneling between nearby phosphorus ions. It ignores non-localised effects of fully quantum-mechanical models such as Cooper pairing or ballistic transport. Positive magnetoresistance is consistent with the magnetic field perpendicular to the conduction plane squeezing the electron wave-function and hence reducing the tunneling rates and increasing resistance. At 1 K, Rue \begin_inset ERT status open \begin_layout Plain Layout \backslash ss \end_layout \end_inset \begin_inset space ~ \end_inset found a negative magnetorestance for small magnetic fields (0-1 Tesla), which is not well explained. \end_layout \begin_layout Standard No EDMR studies of narrow implanted wires have been done. Such a study on the Si:P system would provide vital information about the availability of electrons on donors close to the oxide interface and their potential usefulness in future quantum computing devices. \begin_inset Note Note status open \begin_layout Plain Layout XXX David -- More comments on usefulness \end_layout \end_inset \end_layout \begin_layout Standard Shin et. al. have made a SET so small (2 \begin_inset space ~ \end_inset nm channel) that it works at room temperature \begin_inset CommandInset citation LatexCommand cite key "shin2010enhanced" \end_inset . They claim to be able to do this reliably. This is a much easier method of fabricating quantum dots in silicon than positioning single ions. Coherence times for this system will probably be quite low because the oxide contains many noisy spins and is very close (1 \begin_inset space ~ \end_inset nm) to the electron. \end_layout \begin_layout Standard \begin_inset Note Note status open \begin_layout Plain Layout During a brief discussion with Andy Martin about the Mott transition he mentioned superfluidity/conductivity as possibly being related. \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset Note Note status open \begin_layout Plain Layout Cite Shinada, McCamey? \end_layout \end_inset \end_layout \begin_layout Subsection ESR \end_layout \begin_layout Standard The standard technique for detecting the species and electronic environment of certain donor atoms is through ESR. These techniques allow unambiguous identification of paramagnetic impurities by allowing measurement of their energy levels, which act much like a \begin_inset Quotes eld \end_inset fingerprint \begin_inset Quotes erd \end_inset for identifying donors. Such identification is important to be sure that the fabrication process has not resulted in other impurities such as crystal defects which will disrupt the electronic landscape of a quantum computer. These techniques will also allow us to ensure that the implanted donors are electrically active and that the phosphorus atom has an electron at home to be used as a qubit. \end_layout \begin_layout Standard \emph on \noun on ESR \begin_inset CommandInset nomenclature LatexCommand nomenclature symbol "ESR" description "Electron Spin Resonance, also known as Electron Paramagnetic Resonance (EPR)" \end_inset \emph default \noun default ( \noun on electron spin resonance \noun default ) is very similar to the older technique of NMR ( \noun on Nuclear magnetic resonance \noun default ) \begin_inset CommandInset nomenclature LatexCommand nomenclature symbol "NMR" description "Nuclear magnetic resonance" \end_inset \begin_inset CommandInset citation LatexCommand cite key "weil2007electron" \end_inset . A static magnetic field and a microwave field are applied to a sample. At a certain ratio of frequency to magnetic field, the sample will absorb more energy from the microwave field. An electron is in a bound state around an atom and in an applied magnetic field will have its energy levels split by the \noun on hyperfine splitting \noun default or \emph on \noun on Zeeman effect \emph default \noun default (Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:Hyperfine-levels" \end_inset ), where a spin-down electron will have less energy than a spin-up electron due to alignment or anti-alignment with the magnetic field. The electron is allowed to transition between these states (flipping its spin), but only by absorbing or emitting a photon (or phonon) of the correct energy. If the material is allowed to relax in the magnetic field, there will tend to be considerably more electrons in the lower ( \emph on \noun on ground \emph default \noun default ) state than the upper excited state. The electron will thus tend to absorb photons of the correct energy from the applied microwave field, flipping it into its higher-energy state before it relaxes back down to its ground state via spontaneous emission of a phonon or photon (with a characteristic timescale of \begin_inset Formula $T_{1}$ \end_inset ). If the microwave field is of the wrong frequency, the ground-state electrons will not absorb as many photons. There is thus a certain set of frequencies at which the spins get flipped frequently, the sample is less magnetised and more photons get absorbed. These are the \emph on \noun on resonant frequencies \emph default \noun default , and from this we can work out the energy levels and thus identify the donor. The energy level information also sometimes allows us to deduce information about the local environment of the electron we are interacting with. \end_layout \begin_layout Standard Due to various experimental systems being designed to operate in different ranges of magnetic field and at different microwave frequencies, a common method of representing spectra is needed. For this, the \noun on g-factor \noun default is used, defined by \end_layout \begin_layout Standard \begin_inset Formula \[ \hbar\omega=g\mu_{\mbox{B}}B\] \end_inset where \begin_inset Formula $\omega=2\pi f$ \end_inset is the microwave frequency, \begin_inset Formula $B$ \end_inset the magnetic field strength and \begin_inset Formula $\mu_{\mbox{B}}$ \end_inset the Bohr magneton. The g-factor for a free electron is ~2.00232. \end_layout \begin_layout Standard \begin_inset Formula \[ \] \end_inset \end_layout \begin_layout Standard \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \noindent \align center \begin_inset Graphics filename images/spin-splitting-energy-levels.eps width 50col% \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout \begin_inset CommandInset label LatexCommand label name "fig:Hyperfine-levels" \end_inset \end_layout \end_inset \end_layout \end_inset \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \noindent \align center \begin_inset Graphics filename images/edmr.pdf width 40text% \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout \begin_inset CommandInset label LatexCommand label name "fig:EDMR" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout (a) Hyperfine levels and the first-order transitions for a spin- \begin_inset Formula $\frac{1}{2}$ \end_inset nucleus ( \begin_inset Formula $l$ \end_inset ) and electron ( \begin_inset Formula $s$ \end_inset ), after \begin_inset CommandInset citation LatexCommand cite key "kittel1996introduction" \end_inset . (b) A band structure outline of the EDMR mechanism. A donor impurity such as a phosphorus atom (P) sits just below the conduction band. A recombination centre (A) sits between the donor and the valence band and provides a recombination pathway for the donor. However, if the P and A electron spins are aligned (not shown), the Pauli exclusion principle prevents the second electron from decaying from P to A and the recombination pathway is blocked. \begin_inset Note Note status open \begin_layout Plain Layout Sample spectrum? \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Plain Layout \end_layout \end_inset \end_layout \begin_layout Subsection EDMR \begin_inset CommandInset label LatexCommand label name "sub:EDMR-theory" \end_inset \end_layout \begin_layout Standard \emph on \noun on EDMR \begin_inset CommandInset nomenclature LatexCommand nomenclature symbol "EDMR" description "Electrically-detected magnetic resonance" \end_inset \emph default \noun default ( \emph on \noun on electrically detected magnetic resonance \emph default \noun default ) is a more sensitive method of detecting the ESR condition, and so can be used to detect a smaller number of donor atoms. To perform EDMR, a recombination centre is used to modifiy the number of charge carriers, depending on the ESR condition \begin_inset CommandInset citation LatexCommand cite key "boehme2003theory" \end_inset . This results in a change in the conductance of the sample which can be directly measured. \end_layout \begin_layout Standard An outline of the EDMR mechanism is shown in Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:EDMR" \end_inset . To perform a pulsed EDMR experiment, the system is first initialised by placing it in a magnetic field and allowing it to relax. This orients the spins of the donor and recombination centre electrons in the direction of the magnetic field (B). As we are interested in probing the P donor, we apply a microwave pulse ( \begin_inset Formula $\gamma$ \end_inset ) at a phosphorus resonant frequency ( \begin_inset Formula $\omega_{1}$ \end_inset or \begin_inset Formula $\omega_{2}$ \end_inset of Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:Hyperfine-levels" \end_inset ) and observe that with more recombination, there will be fewer conduction electrons in the conduction band and a corresponding increase in the resistance , which can be directly measured. \end_layout \begin_layout Standard EDMR has been demonstrated on a single electron from a quantum dot \begin_inset CommandInset citation LatexCommand cite key "elzerman_single-shot_2004" \end_inset . It has not yet been done on a single implanted phosphorus donor, although measurements of less than 100 donors \begin_inset CommandInset citation LatexCommand cite key "mccamey2006electrically,mccamey2007thesis" \end_inset and theoretical analyses \begin_inset CommandInset citation LatexCommand cite key "Hoehne2010" \end_inset of such a measurement have been published, relying on the \begin_inset Formula $P_{b}$ \end_inset interface defect found at the interface between the bulk silicon and the silicon dioxide surface coating to act as the recombination centre. \end_layout \begin_layout Standard The EDMR signal is normally enhanced using above-bandgap light to excite many carriers and hence make the recombination more pronounced \begin_inset CommandInset citation LatexCommand cite key "bayerl1997electrically" \end_inset . This also suggests the technique of \noun on optically-detected magnetic resonance \noun default in which the luminescence of transitioning electrons is measured. Finally, spatially-resolved detection is possible by localising the optical carrier excitation \begin_inset CommandInset citation LatexCommand cite key "bayerl1997electrically" \end_inset with a focused laser or conduction current with a scanning probe. \end_layout \begin_layout Standard We will return to the extremely sensitive technique of EDMR in Chapter \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "cha:characterization" \end_inset . \end_layout \begin_layout Section Summary \end_layout \begin_layout Standard There are several methods for performing coherent transport in the solid state. It remains to be seen which transport mechanism can be physically implemented using state-of-the-art technology. Having explored several possible approaches to implementing coherent transport, in the next chapter we dive into an experimental program designed to build some of the required knowledge and devices for testing these ideas. \end_layout \begin_layout Standard \begin_inset Note Note status open \begin_layout Subsubsection Coulomb Blockade and Density of States \end_layout \begin_layout Plain Layout \begin_inset CommandInset citation LatexCommand cite key "lansbergen2008gate" \end_inset (Sven Rogge) found an arsenic atom in the channel of their finfet and measured coulomb blockade. \end_layout \begin_layout Plain Layout \begin_inset CommandInset citation LatexCommand cite key "mottonen2009probe" \end_inset Discusses the density of states in the leads when measuring devices. \end_layout \begin_layout Plain Layout There's a paper by Nai Shyan Lai that I should cite here about spin-dependent transport, but I can't find it. \end_layout \begin_layout Plain Layout \begin_inset CommandInset citation LatexCommand cite key "tan2009transport" \end_inset NEED TO READ THIS PAPER. \end_layout \begin_layout Plain Layout \begin_inset CommandInset citation LatexCommand cite key "Morello2009" \end_inset NEED TO READ THIS PAPER. \end_layout \begin_layout Plain Layout \begin_inset CommandInset citation LatexCommand cite key "pierre2010single" \end_inset dopants in a finfet channel. \end_layout \end_inset \end_layout \begin_layout Chapter Fabrication of nanostructured devices \begin_inset OptArg status open \begin_layout Plain Layout Fabrication of nanostructured devices \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset CommandInset label LatexCommand label name "cha:fab" \end_inset \end_layout \begin_layout Standard \begin_inset Note Note status collapsed \begin_layout Plain Layout \begin_inset CommandInset citation LatexCommand cite key "iwano1994carrier" \end_inset used a FIB to implant Gallium (p-type) wires in n-type Si. Discusses I-V and magnetoresistance measurements and temperature dependence, showing one-dimensional variable range hopping, nearest-neighbour hopping and more general VRH conduction. \begin_inset CommandInset citation LatexCommand cite key "iwano1998hopping" \end_inset refines the theoretical discussion. \end_layout \begin_layout Plain Layout \begin_inset CommandInset citation LatexCommand cite key "chen2008thermal" \end_inset discusses the thermal conductivity of 30nm Si nanowires and finds a linear temperature dependence at low temperatures, related to phonon-boundary collisions being very frequency-dependent. \end_layout \begin_layout Plain Layout \begin_inset CommandInset citation LatexCommand cite key "cui2000doping" \end_inset perform conductivity measurements on silicon nanowires, but have no way of measuring the absolute density of dopants as these are incorporated during growth. The electronic band structure of this type of measurement is analysed. \end_layout \begin_layout Plain Layout Negative magnetoresistance is the result of strongly-overlapping electron wavefunction, but also usually implies that \begin_inset Formula $\rho$ \end_inset is independent of temperature. \begin_inset CommandInset citation LatexCommand cite key "toyozawa_theory_1962" \end_inset . \end_layout \end_inset \end_layout \begin_layout Standard As new fabrication methods allow us to make smaller and smaller devices, the dominant effects governing electrical conduction are substituted for other, less well understood effects. This is relevant for all the types of nanowires discussed in the introduction: ballistic transport in carbon nanotubes, adiabatic spin transport in the Spin Bus, coherent wavefunctions in superconductors, and so on. However, it is of particular importance in the Si:P system as the trend in miniaturization of conventional silicon transistors finally approaches fundamental physical limits. \end_layout \begin_layout Standard In the limiting case, a single-atom nanowire -- a device consisting of a single atom in a narrow channel -- allows us to read out the quantum signature of an single atom in a nanowire. Some knowledge has recently been gained on arsenic in silicon \begin_inset CommandInset citation LatexCommand cite key "lansbergen2008gate,pierre2010single" \end_inset , but this is a less than ideal system, as arsenic does not fit neatly into the silicon lattice and has the further complication of a nuclear spin that allows four basic electron-spin-coupled energy levels. There is currently a pressing need for more information on the Si:P system, particularly in the domain of time-resolved measurement to measure the \begin_inset Formula $T_{2}$ \end_inset coherence time of the system. Doped nanowires would also serve as excellent model systems for doping with 1-D arrays of donors using a system such as step-and-repeat. \end_layout \begin_layout Standard In this Chapter, we implement a method for the fabrication of extremely narrow doped channels. Along the way, simulations evaluating the distribution of implanted ions is studied, as well as a method of deterministic ion implantation. Chapter \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "cha:characterization" \end_inset then takes these fabricated devices and introduces one of the techniques of quantum measurement. \end_layout \begin_layout Standard \begin_inset Note Note status open \begin_layout Plain Layout Introduction to chapter 2: \end_layout \begin_layout Plain Layout - Look at introduction to michelle simmons paper on nanowires for introduce chapter 2 \end_layout \begin_layout Plain Layout - Refer to introduction. Nanowires: carbon nanotubes, spin bus... \end_layout \begin_layout Plain Layout - Limiting case of nanowire: single atom in channel -- can read out quantum signature of atom in that sort of nanowire. Channel of FET. sven rogge. \end_layout \begin_layout Plain Layout Reuss: \end_layout \begin_layout Plain Layout As silicon devices continue to shrink in size, electrical conduction is governed not only by the exact dopant distribution but also by the environment the dopants are embedded in. This places high demands for the ability to fabricate devices with atomic precision regarding dopant positioning, precise interface control,1 and minimal defect generation. \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset Note Note status open \begin_layout Plain Layout Would be good to have a few more words of context: Nanowires as proxies of the channel in nano-mosfets, linear confinement for coherent transport, model systems for doping with 1D arrays of donors, ... \end_layout \begin_layout Plain Layout XXX David... need some help here... \end_layout \end_inset \end_layout \begin_layout Section Fabrication of silicon nanodevices \begin_inset OptArg status open \begin_layout Plain Layout Fabrication \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset CommandInset label LatexCommand label name "sec:fab" \end_inset \end_layout \begin_layout Standard This section describes how silicon nanowires were prepared for the major measurements in Chapter \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "cha:characterization" \end_inset . This method was found to be a simple and viable approach to constructing narrow-channel devices. \end_layout \begin_layout Subsection Nanowire growth \end_layout \begin_layout Standard The first step to performing narrow-channel EDMR is to make the narrow channel. Fortunately for us, some silicon nanowires were already available, having been grown using the chemical vapor deposition \begin_inset CommandInset nomenclature LatexCommand nomenclature symbol "CVD" description "Chemical Vapor Deposition" \end_inset self-assembly method by Laurens van Beverens at UC Berkeley in 2007. Some boron was incorporated during the growth of these nanowires. A review of several nanowire fabrication methods including the CVD method is available \begin_inset CommandInset citation LatexCommand cite key "Banerjee2002" \end_inset . Our nanowires were cylindrical and single-crystal (a major benefit of the self-assembly growth process), with diameters of 60 \begin_inset space ~ \end_inset nm and lengths up to more than 10 \begin_inset space ~ \end_inset \begin_inset Formula $\mu$ \end_inset m. They were provided in acetone solution. \end_layout \begin_layout Subsection Preparation for measurement: electrical connection \end_layout \begin_layout Standard Once we had the narrow channels, the next step was to make electrical connection. To do this, a small amount of the nanowire solution was dabbed onto a chip with thermally-evaporated gold contacts (as in Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:Microscope H14-1" \end_inset ), and allowed to dry. This resulted in nanowires being scattered over the surface. We then headed over to the FEI Nova dual-beam (SEM \begin_inset CommandInset nomenclature LatexCommand nomenclature symbol "SEM" description "Scanning Electron Microscope, a very high resolution microscope that uses electrons instead of light" \end_inset and focused ion) system \begin_inset CommandInset nomenclature LatexCommand nomenclature symbol "FIB" description "Focused Ion Beam" \end_inset (Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:The-FIB" \end_inset ) at Bio21 to deposit platinum from likely-looking wires to the gold contacts on the surface of the chip. \end_layout \begin_layout Standard \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Graphics filename images/fib.jpg width 25col% \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout \begin_inset Quotes eld \end_inset The FIB \begin_inset Quotes erd \end_inset at Bio21. \begin_inset CommandInset label LatexCommand label name "fig:The-FIB" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Standard We are not the first to perform this type of process; in 2000, Chung et. al. \begin_inset CommandInset citation LatexCommand cite key "chung2000silicon" \end_inset used EBL and e-beam evaporation to deposit Au/Ti or Al contacts onto 15--35 \begin_inset space ~ \end_inset nm Si wires. Marzi et. al. \begin_inset CommandInset citation LatexCommand cite key "marzi2004probing" \end_inset in 2004 were among the first to use the FIB process, wiring up freestanding 70nm platinum nanowires. They found 330 \begin_inset Formula $\Omega$ \end_inset contact resistance. In 2005, Nam et. al. deposited platinum to connect to GaN nanowires using a gallium beam (the normal ion species used in FIBs) \begin_inset CommandInset citation LatexCommand cite key "nam2005focused" \end_inset . The Li Battery SiNW \begin_inset CommandInset nomenclature LatexCommand nomenclature symbol "SiNW" description "Silicon nanowire" \end_inset team \begin_inset CommandInset citation LatexCommand cite key "chan2007high" \end_inset wired up silicon nanowires using EBL and FIB deposition. They used 500nm high Pt contacts (look in the supplementary material for that article). They removed the native oxide beforehand using an HF \begin_inset CommandInset nomenclature LatexCommand nomenclature symbol "HF" description "Hydrogen Fluoride" \end_inset etch. All of these methods resulted in a satisfactory electrical connection to the nanowire. \end_layout \begin_layout Standard To begin making electrical connection, we placed the chip inside the SEM vacuum chamber and pumped down the vacuum. After locating a likely-looking nanowire, we measured its diameter (to \begin_inset Formula $\pm5$ \end_inset \family roman \series medium \shape up \size normal \emph off \bar no \noun off \color none \begin_inset space ~ \end_inset nm \family default \series default \shape default \size default \emph default \bar default \noun default \color inherit ). The nanowires we chose to wire up were all about 60 \begin_inset space ~ \end_inset nm in diameter, and looked extremely straight under the SEM. There were many narrower wires (down to 10nm) also visible, but these tended to disappear during exposure to the electron beam. \end_layout \begin_layout Standard Once we had found a suitable wire, we began the deposition process. The first step was to remove the native oxide on the ends of the wire using the reactive-ion-etching functionality. This involves injecting gaseous XeF \begin_inset Formula $_{3}$ \end_inset over the sample and focusing the electron beam onto the surface. Where XeF \begin_inset Formula $_{3}$ \end_inset is close to the surface, the e-beam cracks the occasional XeF \begin_inset Formula $_{3}$ \end_inset molecule, part of which then reacts with the silicon or oxygen in the oxide we wish to remove. In this way, the surface is etched away without any damage to the underlying crystal, although the crystal itself will be etched if the process were allowed to continue. We set the etch to a nominal 2 \begin_inset Formula $\mu$ \end_inset m depth (a few seconds for about a 1 \begin_inset Formula $\mu$ \end_inset m \begin_inset Formula $^{2}$ \end_inset area). As we were using the e-beam and not the ion beam, the \emph on actual \emph default depth of the etch was less than the diameter of the nanowires, as we could still see them in the etched region after etching. This etching step is necessary as the naturally-formed oxide on the surface of the nanowire would otherwise block electrical connection to the underlying silicon. \end_layout \begin_layout Standard Having exposed a suitable silicon surface, the next step was to deposit the platinum contact. This is performed in a similar way to the etching, except that a different gas is used. Molecules of this gas, [(CH \begin_inset Formula $_{3}$ \end_inset ) \begin_inset Formula $_{3}$ \end_inset CH \begin_inset Formula $_{3}$ \end_inset C \begin_inset Formula $_{5}$ \end_inset H \begin_inset Formula $_{4}$ \end_inset Pt], rest briefly on the surface of the material, where the electron beam cracks the molecule, briefly freeing a platinum atom which then sticks to the surface. Platinum then builds up on the surface where the electron beam is focused. Some of the platinum also incorporates slightly into the silicon, forming a platinum silicide which provides excellent electrical conductivity with a minimal Schottky barrier \begin_inset Foot status collapsed \begin_layout Plain Layout Normally, a metal-silicon interface forms a simple diode and has a noticible voltage drop. We did not observe noticible voltage drops in any of our measurements. \end_layout \end_inset . Using this functionality, we wrote contacts from the ends of the wires to the much larger gold pads on the chip. The deposition software was normally instructed to deposit 5 \begin_inset Formula $\mu$ \end_inset m of platinum (using a 6.3 nA @ 5 kV beam) but the software is calibrated for ion-beam deposition and e-beam deposition of platinum is very slow, so it is likely that less than 300 \begin_inset space ~ \end_inset nm was deposited. \end_layout \begin_layout Standard Having made electrical connection to the gold contacts, we are then able to connect the nanowire to test equipment by landing point-probe needles on the gold contacts by hand or by attaching the chip to a carrier and wire-bonding to even larger (about 2 \begin_inset space ~ \end_inset mm \begin_inset Formula $^{2}$ \end_inset ) pads on the carrier. \end_layout \begin_layout Subsection I-V Characterisation \end_layout \begin_layout Standard \begin_inset CommandInset nomenclature LatexCommand nomenclature symbol "I-V" description "Electrical measurement of current as a function of voltage." \end_inset \end_layout \begin_layout Standard \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Graphics filename images/Resistances.svg lyxscale 20 width 48text% groupId 2 \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout The room-temperature resistances of all nanowires that made it as far as reasonable measurement. \begin_inset CommandInset label LatexCommand label name "fig:The-resistances" \end_inset \end_layout \end_inset \end_layout \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset Float figure wide false sideways false status collapsed \begin_layout Plain Layout \align center \begin_inset Graphics filename images/resistance-B14-3.png lyxscale 20 width 48text% groupId 2 \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout A typical resistance curve. This particular curve is for the B14-3 nanowire. The dotted line is a linear fit with a resistance of 2.15M \begin_inset Formula $\Omega$ \end_inset . The scan was traced in both directions several times, which is not visible because the result is very repeatable. \begin_inset CommandInset label LatexCommand label name "fig:A-typical-resistance" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout Nanowire measured resistance. \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Standard Once the electrical connection was available, we brought the device to the AFM \begin_inset CommandInset nomenclature LatexCommand nomenclature symbol "AFM" description "Atomic Force Microscopy" \end_inset lab in the MARC \begin_inset CommandInset nomenclature LatexCommand nomenclature symbol "MARC" description "Microanalytical Research Centre" \end_inset clean room for initial testing. To find out if the process had worked, we performed room-temperature I-Vs, using a Keithley 487 picoammeter / voltage source controlled by a Labview program. Scans were run in 0.01 V increments with 300ms acquisition time for each data point. The nanowires were typically extremely ohmic at up to \begin_inset Formula $\pm0.1$ \end_inset V, as shown in Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:A-typical-resistance" \end_inset . A plot of the various lengths and resistances we measured is given in Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:The-resistances" \end_inset . No change was observed (at room temperature) by varying the incident light on the sample, indicating that any boron acceptors in the sample were completel y thermally activated as usual. The next section discusses how we used these initial measurements to determine the amount of boron in the wires. \end_layout \begin_layout Subsection Resistivity and doping density \end_layout \begin_layout Standard As will be discussed shortly, the B14-1 wire of Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:The-resistances" \end_inset is an outlier. The remaining samples are clumped reasonably linearly; This is expected, as classical theory tells us that constant-diameter wires should have their resistance proportional to their length. Using this fit, we can determine the conductivity of the wires and thus carrier concentrations. \end_layout \begin_layout Standard Classically, the resistivity of a cylinder of constant thickness is \begin_inset Formula \begin{equation} R=\rho\frac{l}{A}\end{equation} \end_inset where \begin_inset Formula $l$ \end_inset is the length, \begin_inset Formula $A$ \end_inset cross-sectional area and \begin_inset Formula $\rho$ \end_inset the intrinsic resistivity of the material. For the longest wire, B14-2, this works out to be \begin_inset Formula $\rho=2\times10^{-1}\,\Omega\cdot\mbox{cm}$ \end_inset , with large error margins of perhaps an order of magnitude (the other wires are within an order of magnitude of this value). This corresponds \begin_inset CommandInset citation LatexCommand cite key "carrierdensity" \end_inset to a p-type (boron doping) carrier density of \begin_inset Formula $1\times10^{17}\mbox{ cm}^{-3}$ \end_inset , a high but reasonable concentration of donors. The carrier density corresponds quite closely to the dopant density at room temperature because almost all of the donors are thermally activated. Now knowing the amount of boron in our nanowires, the next section briefly returns to the anomalous B14-1. \end_layout \begin_layout Subsection Avalanche breakdown \end_layout \begin_layout Standard One important measurement was a melting-current measurement we performed on one of the first wires (B14-1). The measured I-V curve is shown in Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:Avalanche-breakdown" \end_inset . This nanowire was 1.7 \begin_inset Formula $\mu$ \end_inset m long. The breakdown voltage for pure silicon is about \begin_inset Formula $3\times10^{7}$ \end_inset V/m, giving a breakdown voltage for this wire of about 51 V. However, the wire melted at one end with an applied bias of only 10 V. The bias applied in the other direction revealed some non-linear behaviour but did not cause any damage. The I-V curve with positive bias looks reminiscent of avalanche breakdown, a process in which electrons which are accelerated by the strong electric field build up enough energy to free electron-hole pairs at their next collision, resulting in a multiplication effect whereby the newly freed electrons become additional carriers. The result is that at a certain voltage, the current suddenly becomes much larger. The region of the sample with the highest resistance (the part where the most electron-lattice collisions occur) has the most electrons impacting it, and the region becomes heated and further damaged. This heating eventually led our nanowire to melt (Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:Avalanche-breakdown-1" \end_inset ). \end_layout \begin_layout Standard This conclusively shows that the nanowire itself was conducting current, and not carrier leakage or extraneous platinum deposited on the surface on and around the wire. It also indicates that the electrical connection at the melted end of the nanowire was probably high-resistance, which would explain why the nanowire is an outlier in Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:The-resistances" \end_inset . \end_layout \begin_layout Standard \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \begin_inset Float figure wide false sideways false status collapsed \begin_layout Plain Layout \align center \begin_inset Graphics filename images/High Bias damage.txt.png lyxscale 20 width 48text% groupId 2 \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout I-V curve of one of the first nanowires measured. This scan was taken from left to right over a period of about 20 seconds. The dotted line shows a linear fit with a resistance of 26 M \begin_inset Formula $\Omega$ \end_inset . \begin_inset CommandInset label LatexCommand label name "fig:Avalanche-breakdown" \end_inset \end_layout \end_inset \end_layout \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset Float figure wide false sideways false status collapsed \begin_layout Plain Layout \align center \begin_inset Graphics filename images/B14 wire 1 01_012.jpeg lyxscale 20 width 48text% groupId 2 \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout The nanowire after the I-V measurement. \begin_inset CommandInset label LatexCommand label name "fig:Avalanche-breakdown-1" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout A nano-fuse. \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Standard Having fully characterized the fabricated devices, we now move on to controlled modification of their properties. \end_layout \begin_layout Section Ion implantation \end_layout \begin_layout Standard In order to introduce controlled amounts of phosphorus into our devices, we performed ion implantation using the MARC Colutron (Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:The-MARC-colutron." \end_inset ). This section discusses the workings of the colutron and a typical implantation run. \end_layout \begin_layout Standard Implants were performed at 14 keV. A typical mass spectrum (before filtering) is shown in Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:colutron schematic" \end_inset . This shows the peaks in current corresponding to several species of ion in the source. Comparison with previous experiments and knowledge of the source allow us to identify the peaks and so set the mass filter to the correct ion (by adjusting the magnetic field component of the velocity filter). Our implantations used the 0.6 \begin_inset space ~ \end_inset mm diameter beam-defining aperture. Implant fluences were calculated to yield a doping level of \begin_inset Formula $10^{17}\mbox{ ions/cm}^{3}$ \end_inset as this is below the semimetallic density but still provides many ions in the channel for measurement. \end_layout \begin_layout Standard \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Graphics filename images/photos-small/colutron-5.JPG lyxscale 10 width 48text% \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout A photograph of the colutron. The foreground shows the sample chamber (grey cylinder) and sample holder (beige frame). The ion source is at the far end. \end_layout \end_inset \end_layout \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Graphics filename images/colutron.svg lyxscale 20 width 48text% groupId 2 \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout A schematic of the MARC colutron. \begin_inset Note Note status open \begin_layout Plain Layout XXX Redraw. \end_layout \end_inset \begin_inset CommandInset label LatexCommand label name "fig:colutron schematic" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout The MARC colutron. \begin_inset CommandInset label LatexCommand label name "fig:The-MARC-colutron." \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset Note Note status collapsed \begin_layout Subsection Fabrication timeline \end_layout \begin_layout Plain Layout Unsuccessful attempts that were later successful are not noted. \end_layout \begin_layout Description 2010-03-12 Platinum e-beam deposition and I-V curves of B14-1 nanowire \end_layout \begin_layout Description 2010-03-15 Implant on Colutron \end_layout \begin_layout Description 2010-03-17 Raman anneal at Bio21 and I-V measurement \end_layout \begin_layout Description 2010-03-23 B14-1 wire melted -- back to SEM for a look \end_layout \begin_layout Description 2010-05-19 H14 nanowire wired up (e-beam) \end_layout \begin_layout Description 2010-06-10 F14 wired up (e-beam) \end_layout \begin_layout Description 2010-06-28 F14 I-Vs \end_layout \begin_layout Description 2010-07-02 F14 wires found damaged - gold etched? Looks like electric shock. \end_layout \begin_layout Description 2010-07-02 Implanted AFSiD and H14 blank sent to Wayne for EDMR, low temp. measurements \end_layout \begin_layout Description 2010-07-28 Masks prepared for high-freq carrier \end_layout \begin_layout Description 2010-08-20 TEM of gate on N2D1 device (AFSiD device returned for re-wirebonding) \end_layout \begin_layout Description 2010-08-25 Second attempt at high-freq carrier deposition successful \end_layout \begin_layout Description 2010-08-25 e-beam 2 nanowires on H6 chip (wires dirty/cleaned?), 1 test on J8 (wires dirty) and 1 on high-freq carrier. \end_layout \begin_layout Description 2010-08-26 Colutron implant of H6 nanowires. I-Vs show no conduction (no measurement before implant). \end_layout \begin_layout Description 2010-08-27 aggressive cleaning removes some of the pad on the high-freq nanowire \end_layout \begin_layout Description 2010-08-31 Anneal H6, still no conduction \end_layout \begin_layout Description 2010-09-01 LBL process demonstrated; no success making contact to any of three attempted nanowires, even after 15min 400 degree bake in N2 (using RTA). \end_layout \begin_layout Description 2010-09-02 AFSiD and H14 re-bonded and sent back to Wayne for WSI EDMR \end_layout \begin_layout Description 2010-09-09 B14 SEM four new wires (2-5), one with gate (5) \end_layout \begin_layout Plain Layout \end_layout \end_inset \end_layout \begin_layout Subsection Effect of ion implantation on nanowires \end_layout \begin_layout Standard Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:I-V implant" \end_inset shows I-V curves of a nanowire before and after the phosphorus implantation. This particular implant was performed with a 55 \begin_inset space ~ \end_inset pA beam current and 600 \begin_inset space ~ \end_inset \begin_inset Formula $\mu$ \end_inset m beam area for 2.5 \begin_inset Formula $\pm0.3$ \end_inset \begin_inset space ~ \end_inset s, resulting in \begin_inset Formula $150\pm30$ \end_inset ions entering the channel. The slight increase in the resistance is consistent with the interpretation that some lattice damage has occurred, as is expected during ion implantation. The occasional zero-current behaviour near zero voltage is attributed to the gentle connection to the surface contacts on the point-probe station. A later anneal (see § \begin_inset CommandInset ref LatexCommand ref reference "sec:donor-activiation" \end_inset ) resulted in significantly increased conductivity consistent with the interpret ation of phosphorus donors becoming activated (and being more numerous than the already-present boron acceptors, resulting in an overall n-type material). \end_layout \begin_layout Standard \align center \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Graphics filename images/H14-1 I-V -implant.svg lyxscale 50 width 48text% groupId 2-largescreen \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout The I-V curve of the as-provided nanowire, H14-1, before and after phosphorus implant. Resistances are 97.8 k \begin_inset Formula $\Omega$ \end_inset and 102.4 k \begin_inset Formula $\Omega$ \end_inset respectively. \begin_inset CommandInset label LatexCommand label name "fig:I-V implant" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Standard Having now fabricated phosphorus-doped nanowires, we digress into a discussion aimed at understanding the exact distribution of the phosphorus in these (and potentially other) devices. We will return to the nanowires in § \begin_inset CommandInset ref LatexCommand ref reference "sec:donor-activiation" \end_inset . \end_layout \begin_layout Section Simulations of the ion implantation process \begin_inset OptArg status open \begin_layout Plain Layout Simulations of ion implantation \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset Note Note status collapsed \begin_layout Subsubsection Timeline \end_layout \begin_layout Description 2009-11-00 Developed first GEANT4 simulation, of cantilever aperture for Andrew and Jess \end_layout \begin_layout Description 2010-02-00 Simulated aluminium oxide mask (tunnels) with electrons for Paul and Jinghua \end_layout \begin_layout Description 2010-03-00 Masked diamond simulation (revised 2010-05) for Julius and Steven \end_layout \begin_layout Description 2010-06-00 Added platinum narrowing ability to cantilever simulation \end_layout \begin_layout Description 2010-08-14 SiN aperture simulation for Andrew's paper \end_layout \begin_layout Description 2010-09-00 Simulation of aluminium oxide mask with ions (He-4 @ 0.5, 1, 2MeV and P-31 @ 14 keV) \end_layout \begin_layout Description 2010-10-00 Simulation of ion implant distribution in cylindrical nanowire. \end_layout \end_inset \end_layout \begin_layout Standard As a further step towards the technological understanding required to fabricate quantum devices, a solid understanding of the ion implantation process is required. This section presents a foundational study on the ion implantation technique. In order to understand the distribution of ions resulting from ion implantation and the suitability of the top-down fabrication process, we develop \begin_inset Note Note status collapsed \begin_layout Plain Layout XXX Tense \end_layout \end_inset several simulations of various implantation scenarios and masking approaches. This section describes some of these simulations and analyses the result. Notes describing the development process (based on GEANT4's TestEm7 example) are available \begin_inset CommandInset citation LatexCommand cite key "geant4-dev-notes" \end_inset . \end_layout \begin_layout Standard GEANT4's simulation ability was found to be extremely useful; several other simulations of ion implantation were performed and are described in Appendix \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "cha:further-simulations" \end_inset . Apart from being pivotal material for several papers, this work also provides further validation of the somewhat unconventional approach of using GEANT4 to simulate low energy ion implantation. \end_layout \begin_layout Subsection Step And Repeat \end_layout \begin_layout Standard One of the important processes for positioning ions is the step-and-repeat process. This subsection describes some simulations that were performed to quantify its accuracy. \end_layout \begin_layout Standard The step-and-repeat process of controlled single-ion implantation is illustrated in Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:The-Step-and-repeat" \end_inset . In this process, a PMMA \begin_inset CommandInset nomenclature LatexCommand nomenclature symbol "PMMA" description "Poly(methyl methacrylate), also known as acrylic, plexiglas and perspex, is a hard, transparent plastic." \end_inset mask is defined on the silicon surface using EBL \begin_inset CommandInset nomenclature LatexCommand nomenclature symbol "EBL" description "Electron Beam Lithography. An electron beam is used to expose photoresist which is then chemically dissolved to form a mask." \end_inset . A secondary mask, the cantilever, is then sequentially positioned above each hole and allows us to implant into each hole in the PMMA mask separately. \begin_inset Note Note status collapsed \begin_layout Plain Layout Don't repeat yourself: Ions can be detected by collecting and measuring the current from secondary electrons that are scattered as the ion travels through the silicon substrate \begin_inset CommandInset citation LatexCommand cite key "shinada1999influence,schenkel2002single" \end_inset . \end_layout \end_inset The accuracy of the ion implantation process is essential for the demonstration of CTAP \begin_inset CommandInset nomenclature LatexCommand nomenclature symbol "CTAP" description "Coherent Transport by Adiabatic Passage" \end_inset (as poorly-placed ions will interact too weakly or strongly with one another). One particular concern is the scattering of ions from the secondary mask into incorrect holes in the primary mask, which would appear as \begin_inset Quotes eld \end_inset correct \begin_inset Quotes erd \end_inset implants as the detection system has no way of measuring the location of the ion, only its presence. \end_layout \begin_layout Standard \begin_inset Float figure wide false sideways false status collapsed \begin_layout Plain Layout \align center \begin_inset Graphics filename images/ICONN2010 Abstract Figure 1.svg lyxscale 50 width 48text% \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout The Step and Repeat process. The dotted red lines indicate the tracks of implanted ions. \begin_inset CommandInset label LatexCommand label name "fig:The-Step-and-repeat" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Subsubsection Modelling and simulation \end_layout \begin_layout Standard To determine the potential number of incorrect implants as a result of using the secondary mask, I used the particle-physics toolkit \noun on GEANT4 \noun default \begin_inset CommandInset citation LatexCommand cite key "Geant4" \end_inset to simulate ion trajectories, as in \begin_inset CommandInset citation LatexCommand cite key "gorelick" \end_inset . Mendenhall's recent screened nuclear scattering improvements for low-energy ions \begin_inset CommandInset citation LatexCommand cite key "Mendenhall2005" \end_inset were essential to the accuracy of the simulation. \end_layout \begin_layout Standard The \noun on SRIM \noun default ion implantation program \begin_inset CommandInset citation LatexCommand cite key "SRIM" \end_inset is also widely used. It can only handle layers of material, not complicated geometry, and so was not appropriate for this problem. Both GEANT4 and SRIM are probably inaccurate at ion energies below 1 \begin_inset space ~ \end_inset keV, because in this regime the effects of molecular bonds become important. Both packages treat nuclei as independent, and also do not take into account crystal structure, meaning that effects such as channeling are not observed in the simulations. SRIM is much easier to use, as GEANT4 requires the user to write a C++ program. Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:SRIM-compare" \end_inset gives a comparison between GEANT4 and SRIM, and shows that even at this very low energy, the toolkits agree reasonably well. Since SRIM has been extensively validated, this gives confidence that GEANT4's simulations are reasonable. \end_layout \begin_layout Standard \begin_inset Float figure wide false sideways false status collapsed \begin_layout Plain Layout \align center \begin_inset Graphics filename images/Geant vs SRIM Range.svg lyxscale 20 width 48text% groupId 2 \end_inset \begin_inset Graphics filename images/Geant vs. SRIM RadialRange.svg lyxscale 20 width 48text% groupId 2 \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout Ion implantation simulation toolkits comparison: SRIM and GEANT4 implanting into silicon. \begin_inset CommandInset label LatexCommand label name "fig:SRIM-compare" \end_inset \end_layout \end_inset \end_layout \begin_layout Plain Layout \end_layout \end_inset \end_layout \begin_layout Standard In order to characterise the secondary mask aperture, the pelletron at MARC was used to irradiate the aperture with 500 keV He-4 with the aperture at various angles to the beam. The resulting experimental spectrum is shown in Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:The-Step-and-repeat Results" \end_inset b and c. Simulations with GEANT4 were eventually able to match this data (also shown) by adjusting the shape of the aperture in the simulation. \end_layout \begin_layout Standard Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:The-Step-and-repeat Results" \end_inset a shows the resulting shape of the aperture. Several ion tracks from the simulation are overlaid on the figure. \end_layout \begin_layout Standard The simulation was then run for a different ion species and energy, namely 14 keV P-31. A second simulation with a different aperture (Aperture 2) produced similar results. This was somewhat surprising as it was thought that the second half of the cantilever would catch many of the ions scattered by the chokepoint near the top end of the aperture. Aperture 2 was much thinner and its narrowest point was near the end, and so was thought to be a less optimal design. It turns out that both apertures are approximately equivalent at small angles. \end_layout \begin_layout Standard Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:The-Step-and-repeat Results" \end_inset d summarises these results. For the 14 keV implants, more than 96% of the ions transmitted through the aperture are unscattered, indicating that the step-and-repeat process is a feasible method for deterministically implanting multiple ions. \end_layout \begin_layout Standard \begin_inset Float figure wide false sideways false status collapsed \begin_layout Plain Layout \align center \begin_inset Graphics filename images/G4Aperture -montage.png lyxscale 25 width 100text% \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout Cantilever simulation and comparison to experimental data (tracks are simulated 500keV He-4 ions). \series bold a) \series default A visualisation of the simulation. This is Aperture 1. \series bold b) \series default A comparison with experimental and simulated 500keV He-4 ions, at various aperture rotations. \series bold c) \series default A detailed comparison for aperture rotation 0. (inset) Aperture 2. \series bold d) \series default Final performance of the simulated apertures for various ions. \begin_inset CommandInset label LatexCommand label name "fig:The-Step-and-repeat Results" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Standard Having now found excellent tools for analysing ion distributions as a result of implantation, we return to fabrication issues in the next section. \end_layout \begin_layout Standard \begin_inset Note Note status open \begin_layout Subsection Ion distribution in nanowires \end_layout \begin_layout Plain Layout To understand the distribution of ions in our implanted silicon nanowires, a similar simulation was performed. XXX Discussion \end_layout \begin_layout Plain Layout XXX: Screenshot of simulation \end_layout \begin_layout Plain Layout XXX: Graph of ion density cross-section \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset Newpage clearpage \end_inset \end_layout \begin_layout Section Donor activation \end_layout \begin_layout Standard \begin_inset CommandInset label LatexCommand label name "sec:donor-activiation" \end_inset \end_layout \begin_layout Standard One of the side-effects of the implantation process is that it creates a significant amount of damage to the crystal lattice. This is undesirable as it both prevents smooth electrical conduction and often renders donors ineffective as they are not fully incorporated into the lattice. The lattice damage can be repaired with an anneal (heating) step, which this section discusses. \end_layout \begin_layout Standard The standard method of annealing in commercial silicon processing is with an incandescent heater. We found it easier to perform the anneal in another way. We are able to simultaneously heat and measure the temperature of a sample using a standard Raman spectrometer/laser combination following the technique of Cui, Amtmann, Ristein and Ley \begin_inset CommandInset citation LatexCommand cite key "cui1998noncontact" \end_inset . In this process (the physics of which are outlined below), the laser is focused on the sample and heats it. A small part of the beam is Raman scattered, and the Raman system collects and analyses this light and produces a spectrum. This spectrum allows us to determine the temperature of the sample in the manner explained below. Depending on the magnification used, the laser is focused down to a spot as small as 1 \begin_inset Formula $\mu$ \end_inset m in diameter. \end_layout \begin_layout Standard The major advantage of this method is that it is a very targetted heating process. This allows us to avoid having to remove the fragile aluminium wire bonds which are sometimes present as we would have to for a more typical oven-type thermal annealing process. \end_layout \begin_layout Subsection Raman spectroscopy \end_layout \begin_layout Standard Photons impinging on a crystal can be scattered in two main ways. The most obvious, \noun on Rayleigh scattering \noun default , results from elastic collisions with the material and the photons are reflected with an unchanged frequency. The other way involves the complication of a lattice phonon participating in the interaction, resulting in a \noun on Raman shift \noun default in the wavelength of the scattered photon. \begin_inset CommandInset citation LatexCommand cite key "raman1928new,smith2005modern" \end_inset The Raman shift is normally given in terms of the initial and final wavelengths as \end_layout \begin_layout Standard \begin_inset Formula \begin{equation} \Omega=\frac{1}{\lambda_{\mbox{laser}}}-\frac{1}{\lambda}\end{equation} \end_inset \end_layout \begin_layout Standard Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:Raman" \end_inset shows the transitions involved in a Raman measurement. Transitions which move to a slightly higher-energy vibrational state ( \begin_inset Formula $m\to n$ \end_inset ) are referred to as \noun on Stokes \noun default -shifted photons, and these photons have slightly-increased energy and thus a positive Raman shift. Transitions where the photon loses some energy to the vibrational state are referred to as \noun on anti-Stokes \noun default transitions. \end_layout \begin_layout Standard Because Raman scattering is relatively rare (often, only one in \begin_inset Formula $10^{8}$ \end_inset photons will be scattered in this way), careful filtering of the reflected light must be employed to remove the Rayleigh-scattered laser light that would otherwise swamp and damage the detector. In our Raman systems this is done with optical notch or edge filters. \end_layout \begin_layout Standard \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Graphics filename images/raman-basics.svg \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout Diagram of the transitions involved in Rayleigh and Raman scattering, from \begin_inset CommandInset citation LatexCommand cite key "smith2005modern" \end_inset . \begin_inset CommandInset label LatexCommand label name "fig:Raman" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Subsection Raman spectroscopic temperature measurement: Stokes / Anti-Stokes Ratio \end_layout \begin_layout Standard At very low temperatures, the Stokes signal is much stronger than the anti-Stoke s signal, because most bonds are in the lower-energy initial state. As the temperature increases, molecules become thermally excited into the higher-energy vibrational states. The ratio of molecular bonds in different energy levels can be calculated from the usual Boltzmann distribution: \end_layout \begin_layout Standard \begin_inset Formula \begin{equation} \frac{N_{n}}{N_{m}}=\frac{g_{n}}{g_{m}}\exp\mbox{\ensuremath{\left[\frac{-\left(E_{n}-E_{m}\right)}{kT}\right]}}\label{eq:boltzmann}\end{equation} \end_inset where \begin_inset Formula $N$ \end_inset is the number of molecules or bonds in a certain state, \begin_inset Formula $g$ \end_inset is the degeneracy of that state, \begin_inset Formula $E$ \end_inset is the energy level of that state, \begin_inset Formula $k=1.38\times10^{-23}\mbox{ JK}^{-1}$ \end_inset is the Boltzmann constant and \begin_inset Formula $T$ \end_inset is the temperature. \end_layout \begin_layout Standard Due to the different cross-sections between phonon and photon interactions of differing frequencies, the observed intensity ratio takes the form \end_layout \begin_layout Standard \begin_inset Formula \begin{equation} \frac{I_{\mbox{AS}}}{I_{\mbox{S}}}=\left(\frac{\omega_{l}+\omega_{p}}{\omega_{l}-\omega_{p}}\right)^{4}\gamma e^{\left(\hbar\omega_{p}/kT\right)}\label{eq:stokes-anti-stokes}\end{equation} \end_inset where \begin_inset Formula $\omega_{(l,p)}$ \end_inset is the angular frequency of the (photon, phonon) and \begin_inset Formula $\gamma$ \end_inset allows for a difference in the detection efficiencies of the two photons. At high temperatures, \begin_inset Formula $\gamma$ \end_inset begins to vary with temperature. Cui et. al. suggest that this may be due to sample reflectivity, transmission or refraction changing at higher temperatures. Despite the Stokes/Anti-Stokes ratio being a common method of determining temperature from Raman spectra, the variation of \begin_inset Formula $\gamma$ \end_inset and the requirement of accurately measuring the intensity of both the Stokes and the anti-Stokes peaks makes this method unsuitable for our purposes. \end_layout \begin_layout Subsection Raman spectroscopic temperature measurement: Stokes shift \end_layout \begin_layout Standard A second method of measuring temperature, that proposed in \begin_inset CommandInset citation LatexCommand cite key "cui1998noncontact" \end_inset , relies on small shifts in the position of the Stokes peak as a result of temperature changes. A change in temperature shifts the Stokes peak due to the anharmonicity of the lattice potentials, which allows phonons in the usual harmonic basis to interact. This interaction causes shifts in the vibrational energy levels with temperatur e. \begin_inset Note Note status collapsed \begin_layout Plain Layout The usual Morse potential employed to discuss lattice phonons is here replaced with the simpler \end_layout \begin_layout Plain Layout \begin_inset Formula \begin{equation} U(x)=cx^{2}-gx^{3}-fx^{4}\end{equation} \end_inset \end_layout \begin_layout Plain Layout where \begin_inset Formula $g>0$ \end_inset represents the asymmetry of the mutual repulsion of the atoms and \begin_inset Formula $f>0$ \end_inset represents the softening of the vibrations at large amplitudes. \end_layout \end_inset For the silicon system, the 3rd order anharmonic component has more effect than the 4th, and the net result is a shift downwards in energy levels as temperature increases, resulting in a smaller Raman shift. \begin_inset CommandInset citation LatexCommand cite key "hart1970temperature,kittel1996introduction,balkanski1983anharmonic" \end_inset . \end_layout \begin_layout Standard Cui proposes the empirical formula \end_layout \begin_layout Standard \begin_inset Formula \begin{equation} \Omega(T)=\Omega_{0}-\frac{C}{e^{[D(hc\Omega_{0}/kT)]}-1}\end{equation} \end_inset to describe the Raman shift as a function of temperature, where \begin_inset Formula $\Omega_{0}$ \end_inset is the Raman shift at 0 K. This is a completely empirical formula that has been found to work better than theoretically-based results, and gives an accuracy of about \begin_inset Formula $\pm$ \end_inset 8 K. It also does not require the anti-Stokes peak and so it is easier to analyse and still works on Raman systems that employ an edge filter. \end_layout \begin_layout Standard Cui finds \begin_inset Formula $\Omega_{0}=524$ \end_inset cm \begin_inset Formula $^{-1}$ \end_inset , \begin_inset Formula $C=10.53$ \end_inset cm \begin_inset Formula $^{-1}$ \end_inset and \begin_inset Formula $D=0.587$ \end_inset for Si. A calibration performed by Paul Spizziri on the MARC system found best fit values of \begin_inset Formula $C=10.7$ \end_inset \begin_inset Formula $ $ \end_inset cm \begin_inset Formula $^{-1}$ \end_inset and \begin_inset Formula $D=0.59$ \end_inset . \end_layout \begin_layout Subsection Our annealing process \end_layout \begin_layout Standard The Raman system at Bio21 employs an edge filter to remove the laser light. This also removes the entirety of the anti-Stokes signal and so the Stokes/anti -Stokes ratio approach to temperature measurement is not available. The Raman system in the MARC cleanroom employs a notch filter, so the above type of measurement is possible; however it is less desirable as it is prone to interference and other negative effects. \end_layout \begin_layout Standard Using the above theory, we are able to anneal our samples. The laser on the Raman system in the MARC cleanroom (Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:Raman photo marc" \end_inset ) (which is a Renishaw RM 1000 Raman/luminescence system, we used the 514 \begin_inset space ~ \end_inset nm Argon-ion laser) on full power for 10s heated the sample to 900 K. The Raman laser (Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:Raman photo bio21" \end_inset ) at Bio21 is more powerful, getting up to 1200 K in a cold nitrogen atmosphere. \end_layout \begin_layout Standard Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:Raman nanowire forest blank" \end_inset shows spectra demonstrating the technique. The blank silicon signal is almost perfectly fit by a single mixed Gaussian/Lor entzian. The other data set in this image (black squares) is for a forest of nanowires grown on the surface of a silicon wafer. It clearly shows a second peak where the nanowires have heated up in the effect described above. The second peak is centred on 504 cm \begin_inset Formula $^{-1}$ \end_inset which corresponds to a temperature of 1200 K. \end_layout \begin_layout Standard Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:Raman-spectrum-anneael" \end_inset shows a typical single-nanowire spectrum. This particular spectrum was acquired over a 10s scan using 10mW laser power and the 50x lens. Some discolouration of the platinum contacts was noted and so the usual 30 s anneal was not performed. \end_layout \begin_layout Standard \begin_inset Float figure wide false sideways false status collapsed \begin_layout Plain Layout \align center \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Graphics filename images/raman-spectra-paul.svg lyxscale 20 width 48text% groupId 2 \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout A Raman spectra of a forest of nanowires, a fit, and a spectrum for blank silicon. \begin_inset CommandInset label LatexCommand label name "fig:Raman nanowire forest blank" \end_inset Data and fit provided by P. \begin_inset space ~ \end_inset Spizziri. \end_layout \end_inset \end_layout \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Graphics filename images/raman-laserAnneal-H14-1.svg lyxscale 20 width 48text% groupId 2 \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout Raman spectrum recorded during laser annealing exposure. \begin_inset CommandInset label LatexCommand label name "fig:Raman-spectrum-anneael" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Plain Layout \align center \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Graphics filename images/photos-small/raman-2.JPG lyxscale 10 width 40text% \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout The Raman spectrometer at MARC. \begin_inset CommandInset label LatexCommand label name "fig:Raman photo marc" \end_inset \end_layout \end_inset \end_layout \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Graphics filename images/photos-small/bio21-raman.jpg lyxscale 10 width 40text% \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout The Raman spectrometer at Bio21. \begin_inset CommandInset label LatexCommand label name "fig:Raman photo bio21" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout Various Raman spectra \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Standard This spectrum is well understood. The main peak at 520.32 \begin_inset Formula $\pm0.05$ \end_inset cm \begin_inset Formula $^{-1}$ \end_inset is the well-known signal from the bulk silicon below the silicon dioxide (which the laser penetrates as the oxide is only a few hundred \begin_inset space ~ \end_inset nm thick), as in Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:Raman nanowire forest blank" \end_inset . The laser does not heat this material significantly as it is not thermally isolated. A second, much smaller peak from the nanowire itself is centered at 510 \begin_inset Formula $\pm3$ \end_inset cm \begin_inset Formula $^{-1}$ \end_inset and is attributed to the nanowire itself. At room temperature the crystalline nanowire would be expected to give the same signal as the bulk silicon; the shift of \begin_inset Formula $10$ \end_inset cm \begin_inset Formula $^{-1}$ \end_inset is attributed to heating of the wire. \end_layout \begin_layout Standard These fits are mixed Gaussian and Lorentzian because the actual signal is Lorentzian but the instrument response is Gaussian. \end_layout \begin_layout Standard The annealing process was successful for our purposes. Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:I-V anneal" \end_inset shows I-V curves of before and after an annealling step. The conduction of the wire has clearly increased (162 k \begin_inset Formula $\Omega$ \end_inset changed to 82 k \begin_inset Formula $\Omega$ \end_inset ) \begin_inset Formula $ $ \end_inset , consistent with the interpretation that at least some of the newly added donors have been successfully activated by the annealing process. Ideally the anneal would have gone to higher temperatures (a 5 s anneal at 900 \begin_inset Formula $^{\circ}$ \end_inset C is a typical cycle that removes almost all lattice damage and activates most donors), but we did not want to risk damaging the platinum contacts as this had caused problems in the past. \end_layout \begin_layout Standard \align center \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Graphics filename images/H14-1 I-V -anneal.svg lyxscale 50 width 48text% groupId 2-largescreen \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout I-V curves of H14-1 after mounting (162 k \begin_inset Formula $\Omega$ \end_inset ) and anneal (82.8 k \begin_inset Formula $\Omega$ \end_inset ). \begin_inset CommandInset label LatexCommand label name "fig:I-V anneal" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Section AFSiD consortium devices \end_layout \begin_layout Standard As an alternative device structure, we also experiment with devices fabricated using more traditional processing steps on silicon wafers. These are provided from Europe by the AFSiD consortium \begin_inset CommandInset citation LatexCommand cite key "afsid" \end_inset . Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:A-typical-AFSiD" \end_inset shows one of the devices that we implanted. These devices are fabricated as silicon-on-insulator \begin_inset CommandInset nomenclature LatexCommand nomenclature symbol "SOI" description "Silicon-on-insulator" \end_inset devices, and the gates which are later grown over the top are grown polysilicon. The SOI structure is created by implanting a silicon wafer with oxygen. The gate is intended to have a gap in it where it crosses the channel to allow ion implantation into the channel; in this batch of devices, there was no such gap (Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:Afsid-TEM-2" \end_inset ) This last pair of TEM images clearly shows the 5 \begin_inset space ~ \end_inset nm gate oxide (light blue), crystalline channel (green), and polysilicon top gate (red). The very thin gate oxide makes these devices extremely sensitive to static charge, as a voltage difference between the gate and channel easily causes breakdown of the oxide and shorts out the gate. \end_layout \begin_layout Standard These devices make an excellent alternative structure to the crystalline nanowires previously discussed. The channel acts as a nanowire on its own, and the additional gate required by field-effect-transistors (FET) is potentially extremely useful in EDMR measurements as electrical gating can then be used in place of optical gating. FETs are an extremely important component of the Readout section of the architecture of Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:outline" \end_inset and additional characterization of their behaviour at the nanoscale is also valuable. \end_layout \begin_layout Standard \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \begin_inset Graphics filename images/p1.jpeg lyxscale 20 width 48text% groupId 2 \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout A top-down SEM image of an AFSiD device. This device was cut up for TEM analysis along the dotted line. The channel is below the small depression in the gate. \end_layout \end_inset \end_layout \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \begin_inset Graphics filename images/p1_002-both.jpg lyxscale 20 width 48text% groupId 2 \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout (top) An SEM false-color view through the side of the device, showing the source, drain, gate (red) and oxide (grey) around the layer. The (blue) material on the surface is deposited platinum as part of the sample extraction process. The thick oxide layer below the devices is also visible, the silicon substrate below that (green). (bottom) A TEM image of the same region. The polysilicon of the gate (red) is clearly identifiable by the characteristic interference pattern. \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Plain Layout \align center \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \begin_inset Graphics filename images/afsid_both.jpg lyxscale 20 width 80text% \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout A TEM image taken on the other axis (on a similar device from the same batch), along the gate (along the line between source and drain). Red indicates the polysilicon gate; light blue is the high-quality 5 \begin_inset space ~ \end_inset nm oxide grown between channel and gate; green is crystalline silicon. The thick layer of oxide underneath the channel is grey. \begin_inset CommandInset label LatexCommand label name "fig:Afsid-TEM-2" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout A typical AFSiD device. \begin_inset CommandInset label LatexCommand label name "fig:A-typical-AFSiD" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Standard One of the important processing steps for our purposes is the doping of the source/drain and gates to make them good conductors. These gates were doped by implanting a heavy dose of arsenic with the sensitive regions of the devices masked off. However, due to diffusion during processing steps, small amounts of arsenic are still present in the channel itself, as kinetic monte-carlo dynamics simulations of the ion implantation process in these devices showed \begin_inset CommandInset citation LatexCommand cite key "pierre2010single" \end_inset . This will be important when we come to interpreting the EDMR spectrum of these devices in § \begin_inset CommandInset ref LatexCommand ref reference "sec:edmr-result" \end_inset . \end_layout \begin_layout Section Summary \end_layout \begin_layout Standard \begin_inset Note Note status open \begin_layout Plain Layout XXX probably needs a bit more here. \end_layout \end_inset \end_layout \begin_layout Standard Having successfully fabricated suitable nanoscale quantum devices, we now turn to the crucial probing of the quantum degrees of freedom of the Si:P system. \end_layout \begin_layout Chapter Transport Measurement and characterization \begin_inset OptArg status collapsed \begin_layout Plain Layout Characterization \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset Note Note status open \begin_layout Plain Layout Be upfront -- this is the frontier everything else enables crucial probing quantum degrees of freedom \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset CommandInset label LatexCommand label name "cha:characterization" \end_inset \end_layout \begin_layout Standard This chapter describes the measurements performed on the nanowires, and discusses the theory necessary to understand the results. \end_layout \begin_layout Standard \begin_inset CommandInset citation LatexCommand cite key "read1992first" \end_inset found that effective-mass theory is valid for wires with diameter larger than 2.3 \begin_inset space ~ \end_inset nm, and hence 1-D quantum confinement effects are most noticable in wires with this diameter or less. As our wires are about twenty times larger than this, we believe conduction through the wires will be effectively classical at room temperature. This is what we observed in the room temperature I-V curves discussed in Section \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "sec:fab" \end_inset . \end_layout \begin_layout Standard \end_layout \begin_layout Section Low temperature I-V \end_layout \begin_layout Standard At low temperatures, however, the conductance measurement can be a very different story. In AlGaAs devices operating on two-dimensional electron gases held against the crystal interface, electric-potential-defined wires showing quantized conductance at 1 K can be made from physical gates as far apart as 500 \begin_inset space ~ \end_inset nm \begin_inset CommandInset citation LatexCommand cite key "kane1998quantized" \end_inset . The actual width of the wire in this case is difficult to determine but this shows some chance of such quantized conductance in these nanowires. Typical currents for such quantized measurements are of the order of 1nA, and the conductance is quantized in units of \begin_inset Formula $2e^{2}/h$ \end_inset , which corresponds to about 13 k \begin_inset Formula $\Omega$ \end_inset . As such, one would expect to see steps in the current as the voltage was increased as additional conduction bands become available. \end_layout \begin_layout Standard Low temperature measurements can also be extremely sensitive. Two measurements of current perturbations caused by single ions in semiconducto r channels and giving significant amounts of information have been performed \begin_inset CommandInset citation LatexCommand cite key "lansbergen2008gate,pierre2010single" \end_inset . These high-impact papers analyse the I-V measurements at various magnetic fields resulting from single arsenic dopant atoms. Such measurements on phosphorus dopants (the critical Si:P system) remain unperformed as of this writing. As we are implanting practically identical devices made on the same production line with phosphorus, they would be suitable for such a measurement, and would go a long way towards a definitive determination of the suitability of the Si:P system in terms of the Memory component of Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:outline" \end_inset . \begin_inset Note Note status collapsed \begin_layout Plain Layout move some of this to introduction? mention coulomb diamonds etc? \end_layout \end_inset \end_layout \begin_layout Standard This type of measurement works best on highly-crystalline samples free of defects and dopants, and also works better for samples shorter than 500 \begin_inset space ~ \end_inset nm. Such measurements also require electrical gating to ensure measureable currents are occupying the allowed conduction bands. The most interesting experiments compare a completely clear channel to one with one or two specifically placed impurities \begin_inset CommandInset citation LatexCommand cite key "johnson2010drain,lansbergen2008gate" \end_inset . \end_layout \begin_layout Standard W. Hutchinson kindly performed two low-temperature (4.2K) I-V measurements in a helium dip, before and after we implanted the nanowire with phosphorus. The measurements are shown in Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:H14-1-nanowire" \end_inset . The measurement did not show any evidence of quantized conductance because it was optically gated (thus exciting carriers into otherwise forbidden conduction bands). Our nanowire devices were not successfully fabricated with electronic gates. Low temperature measurements on implanted AFSiD devices have not yet been performed due to difficulty implanting ions through the gate into the channel. \end_layout \begin_layout Standard \begin_inset Float figure wide false sideways false status collapsed \begin_layout Plain Layout \align center \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \begin_inset Graphics filename images/low-temp-resistance.svg lyxscale 20 width 48text% groupId 2 \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout Low-temperature (4.2K) I-V curves taken by W. Hutchinson of the H14-1 nanowire. \end_layout \end_inset \end_layout \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \begin_inset Graphics filename images/SEM S1 H14_019.jpeg lyxscale 20 width 48text% groupId 2 \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout An SEM of H14-1. The deposited platinum contacts providing electrical connection are clearly visible and look slightly transparent; the wire is about 850nm long. \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Plain Layout \align center \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \begin_inset Graphics filename images/Microscope H14-1.JPG lyxscale 10 width 48text% \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout An optical microscope photo of H14-1. The platinum contacts are clearly visible. The test short between an adjacent contact (top of image) has corroded. \begin_inset CommandInset label LatexCommand label name "fig:Microscope H14-1" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout H14-1 nanowire initial characterisation. \begin_inset CommandInset label LatexCommand label name "fig:H14-1-nanowire" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Section EDMR \end_layout \begin_layout Standard \begin_inset CommandInset label LatexCommand label name "sec:edmr-result" \end_inset \end_layout \begin_layout Standard As was described in § \begin_inset CommandInset ref LatexCommand ref reference "sub:EDMR-theory" \end_inset , EDMR is a sensitive technique for probing the electrical environment of very small numbers of loosely-bound electrons in a conduction channel. Here we demonstrate proof-of-principle EDMR on a \begin_inset Quotes eld \end_inset blank \begin_inset Quotes erd \end_inset device. \end_layout \begin_layout Subsection Experimental Details \end_layout \begin_layout Standard The experimental setup for an EDMR measurement is shown in Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:EDMR-setup" \end_inset . The sample is placed in a resonant cavity that vastly improves the quality (amplitude and frequency-sharpness) of the applied microwave field. An external magnet provides the bulk of the magnetic field, and modulation coils allow the field to be scanned in the region of interest. A voltage is applied across the sample, with the drain going to a high-quality opamp (the current pre-amplifier in the diagram). This isolates the sample from the lock-in amplifier and signal output. The lock-in amplifier increases the fidelity of the measurement and results in the observed signal being the derivative of the change in current as the external magnetic field is scanned. How this works is explained in \begin_inset CommandInset citation LatexCommand cite after "p. 69" key "hubl2007thesis" \end_inset . A lamp shining on the sample provides optical carrier excitation. \end_layout \begin_layout Standard The WSI measurements are performed using a 3.5 \begin_inset space ~ \end_inset T magnet and a microwave cavity resonant at 96 \begin_inset space ~ \end_inset GHz. An illustration of the instrument is given in Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:EDMR-setup" \end_inset . \end_layout \begin_layout Standard \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Graphics filename images/edmr/WSI_McCamey.jpg lyxscale 50 width 80col% \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout The experimental setup for EDMR at WSI (from D. McCamey's thesis \begin_inset CommandInset citation LatexCommand cite key "mccamey2007thesis" \end_inset \begin_inset Note Note status open \begin_layout Plain Layout XXX Replace \end_layout \end_inset ). \begin_inset CommandInset label LatexCommand label name "fig:EDMR-setup" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Subsection Results and discussion \end_layout \begin_layout Standard The expected advantage of confined-channel measurement for EDMR is that the surface interface is always nearby. This is useful because the P \begin_inset Formula $_{\mbox{b}}$ \end_inset interface defects so important to the recombination process \begin_inset CommandInset citation LatexCommand cite after "p. 75" key "hubl2007thesis" \end_inset only form on this interface. As a result, we expect the EDMR signal to be very strong compared to the more common 2DEG-in-bulk approach. \end_layout \begin_layout Standard The first EDMR spectrum we obtained was on an AFSiD device. The spectrum with fits is shown in Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:EDMR-afsid-fit" \end_inset . The device had in the end not been implanted with phosphorus because the gate was too thick and shielded the channel, as later TEM data showed (Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:Afsid-TEM-2" \end_inset ). However, a considerable P \begin_inset Formula $_{\mbox{b}}$ \end_inset signal and peaks corresponding to exchange-coupled (very high density, greater than \begin_inset Formula $10^{18}\,\mbox{cm}^{-3}$ \end_inset ) arsenic were visible. This is likely due to the very high density of arsenic in the source and drain of this device. No hyperfine peaks are visible in this spectrum (Arsenic has a nuclear spin of \begin_inset Formula $3/2$ \end_inset and so its EDMR signature contains four hyperfine peaks in a straightforward extension of \begin_inset CommandInset ref LatexCommand ref reference "fig:Hyperfine-levels" \end_inset ). \end_layout \begin_layout Standard Given that we are quite confident there are low amounts of As in the channel, as found by earlier studies on similar devices from the same factory \begin_inset CommandInset citation LatexCommand cite key "lansbergen2008gate,pierre2010single" \end_inset , the lack of hyperfine peaks suggests that this EDMR measurement was not sensitive enough to detect the As dopants in the channel. Further increases in the sensitivity of this technique may be required to perform this measurement on phosphorus donors in the channel. This is still a good result, however, because this demonstrates that the channel is EDMR active and we are seeing the expected and required P \begin_inset Formula $_{\mbox{b}}$ \end_inset signals from the interface defects that will in the future allow us to probe P donors. \end_layout \begin_layout Standard \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Graphics filename images/EDMR-afsid.svg lyxscale 50 width 60col% \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout The fitted EDMR spectrum of an AFSiD device. The red and green lines are fits to P \begin_inset Formula $_{\mbox{b}}$ \end_inset resonances with g-factors of \begin_inset Formula $g_{\perp}=2.0081$ \end_inset and \begin_inset Formula $g_{\parallel}=2.00185$ \end_inset respectively \begin_inset CommandInset citation LatexCommand cite key "hubl2007thesis" \end_inset . The remaining blue fit is a resonance attributed to exchange-coupled arsenic. \begin_inset CommandInset label LatexCommand label name "fig:EDMR-afsid-fit" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Standard Further work including obtaining an EDMR spectrum of the H14-1 nanowire is in progress, and EDMR of P-implanted AFSiD devices is also planned. \end_layout \begin_layout Section Summary \end_layout \begin_layout Standard The results presented here demonstrate that EDMR of a confined-channel device is possible. Low temperature measurements of the nanowires fabricated in Chapter \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "cha:fab" \end_inset show that post-implant wires have increased conduction, consistent with the interpretation of added donors overcoming the background B doping and increasing the channel conductance. More accurate low-temperature measurements would likely show very interesting results. This means that those nanowires are primed for an EDMR measurement. \end_layout \begin_layout Standard An EDMR measurement of the AFSiD device did not show the expected hyperfine peaks of As in the channel, but did show extremely strong signals from the leads. This suggests that the current technique is not sensitive enough to detect the small numbers of ions within the channel. \begin_inset Note Note status open \begin_layout Plain Layout and casts doubt on earlier measurements? \end_layout \end_inset \end_layout \begin_layout Chapter Closing Material \begin_inset OptArg status open \begin_layout Plain Layout Closing material \end_layout \end_inset \end_layout \begin_layout Section Summary \end_layout \begin_layout Standard Chapter \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "cha:review" \end_inset provided an overview of current progress towards manufacturing a quantum computer. Particularly of interest in the short term are the recent demonstration of readout of quantum states in the Si:P system \begin_inset Note Note status open \begin_layout Plain Layout XXX as well as SUPERCONDUCTOR \end_layout \end_inset as well as Abanto's theoretical proposal for coupling solid-state systems to photons using optical cavities. \end_layout \begin_layout Standard Chapter \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "cha:fab" \end_inset described the fabrication process of precursor coherent transport devices. It found that silicon nanowires are a suitable proxy for commercially fabricate d nano-MOSFET channels, and described measurements indicating successful fabrication. \end_layout \begin_layout Standard Chapter \begin_inset CommandInset ref LatexCommand ref reference "cha:characterization" \end_inset then described bleeding-edge measurements of the fabricated devices. The initial measurements indicate that the technique is feasible, and observed a strong signal from P \begin_inset Formula $_{\mbox{b}}$ \end_inset interface traps and the heavily doped arsenic leads, but did not detect stray arsenic dopants that are probably in the channel, suggesting \end_layout \begin_layout Standard This work has helped build the technological understanding required to implement the coherent transport component (Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:outline" \end_inset ) of a future quantum computer. \end_layout \begin_layout Standard \begin_inset Note Note status open \begin_layout Plain Layout XXX Overall conclusion a bit ugly? \end_layout \end_inset \end_layout \begin_layout Section Future Work \end_layout \begin_layout Subsection Low-temperature measurement \end_layout \begin_layout Standard The easiest next step in this work would be a more careful study of the resistance of these nanowires at low temperature. In particular, a very high resolution I-V curve may yet show quantized conductance features reminiscent of 2DEGs, and curves taken in strong magnetic fields would likely also show interesting features following the discussion in § \begin_inset CommandInset ref LatexCommand ref reference "sec:measurements" \end_inset . \end_layout \begin_layout Subsection Single-donor or regularly-spaced-donor EDMR \end_layout \begin_layout Standard After satisfactory EDMR is performed on a nanowire with a high density of donors, the next step would be to place equally-spaced donors, or even a single donor, in the narrow channel. It would also be interesting to investigate the effects of further narrowing of the channel, which could be done fairly easily using repeated oxidation/remo val steps. The step-and-repeat approach would be useful for this. A comparison of regular-spacing and arbitrary spacing would also likely show significant differences, even at the same average density. \end_layout \begin_layout Subsection Simulations \end_layout \begin_layout Standard During this project, I was particularly struck by the large number of requests for GEANT4 simulations I received. SRIM is widely used within the group, but GEANT4 is not, presumably because it requires a large investment of time to develop a simulation, and requires knowledge of C++. In response, I think a simple-to-use program like SRIM, but based on GEANT4 and capable of editing the geometry, would be widely used. \end_layout \begin_layout Chapter \start_of_appendix Further simulations \end_layout \begin_layout Standard \begin_inset CommandInset label LatexCommand label name "cha:further-simulations" \end_inset \end_layout \begin_layout Standard It was found that GEANT4's ability to simulate complex geometry was extremely useful to the MARC group, and I coded, ran and analysed several other types of ion implantation. Apart from being useful for several papers, this work also provides further validation of the somewhat unconventional approach of using GEANT4 to simulate low energy ion implantation. \end_layout \begin_layout Subsubsection Diamond implant with mask \end_layout \begin_layout Standard Defects in the diamond crystal lattice are of particular interest to many in the MARC group. Paolo, Julius and Babs performed an experiment where they wished to investigate how defects resulting from pelletron implantation might migrate through the lattice. They saw a considerable distribution of defects in a supposedly masked region of the sample. Later experiments with a gold mask deposited directly on the surface showed no such distribution, and so the masking process (Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:Diamond-masked-implant" \end_inset ) was questioned and I simulated it. In this process, a cleaved silicon wafer acts as the mask, and 2 MeV He-4 ions from the pelletron are angled slightly (3 degrees) in to the surface to ensure the cleaved edge next to the diamond surface is impacted (and to avoid channeling through the diamond). The resulting vacancy distribution is then measured using optical fluorescence. \end_layout \begin_layout Standard The simulations showed that the suspicions were correct; a 30 \begin_inset Formula $\mu$ \end_inset m mask spacing was found to match Paulo's experimental observations quite closely. This result has important implications for several other vacancy distribution studies that were conducted in a similar manner. Another interesting observation is the column of damage at the edge of the mask. This results from ions having to travel various distances through the mask to reach this area, as a result of the slightly angled beam. \end_layout \begin_layout Standard \begin_inset Float figure placement p wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \begin_inset Graphics filename images/diamondImplant/diagram.svg lyxscale 25 width 40text% \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout The simulation geometry and a few ion tracks. The red lines are scattered electrons. \end_layout \end_inset \end_layout \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \begin_inset Graphics filename images/diamondImplant/50um-side-zoom-10000ions-recoloured.png lyxscale 25 width 40text% \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout A side view of a 10000 ion simulation. The yellow dots are energy depositions. Most of the unmasked beam was not simulated. \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout Diamond masked implant \begin_inset CommandInset label LatexCommand label name "fig:Diamond-masked-implant" \end_inset . An ion beam (1) is directed into a silicon mask. The unmasked part of the beam and some scattered ions (2) then hit the diamond target. The relationship between the mask spacing (3) and the resulting ion distributio n is the subject of this investigation. \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset Float figure placement p wide false sideways false status open \begin_layout Plain Layout \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \begin_inset Graphics filename images/diamondImplant/100 um - z axis hist-padded.svg lyxscale 50 width 30text% groupId 3 \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout Ion distribution as a function of mask spacing. \end_layout \end_inset \end_layout \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset Float figure wide false sideways false status collapsed \begin_layout Plain Layout \begin_inset Graphics filename images/diamondImplant/dist-wide-000um spacing.png lyxscale 50 width 30text% groupId 3 \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout \end_layout \end_inset \end_layout \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset Note Note status collapsed \begin_layout Plain Layout \begin_inset Float figure wide false sideways false status collapsed \begin_layout Plain Layout \begin_inset Graphics filename images/diamondImplant/dist-wide-010um spacing.png lyxscale 50 width 30text% groupId 3 \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset Float figure wide false sideways false status collapsed \begin_layout Plain Layout \begin_inset Graphics filename images/diamondImplant/dist-wide-020um spacing.png lyxscale 50 width 30text% groupId 3 \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout \end_layout \end_inset \end_layout \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset Float figure wide false sideways false status collapsed \begin_layout Plain Layout \begin_inset Graphics filename images/diamondImplant/dist-wide-050um spacing.png lyxscale 50 width 30text% groupId 3 \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout \end_layout \end_inset \end_layout \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \end_layout \end_inset \begin_inset Float figure wide false sideways false status collapsed \begin_layout Plain Layout \begin_inset Graphics filename images/diamondImplant/dist-wide-100um spacing.png lyxscale 50 width 30text% groupId 3 \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout Diamond masked implant simulation results. Figures (b) and (c) show a side view of the ion distribution resulting from various mask spacings, with distances in \begin_inset Formula $\mu$ \end_inset m. The final resting place of the ions corresponds quite closely to the vacancy distribution, because in this type of implantation the ions mostly cause damage near the end of their range. \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Subsubsection Aluminium oxide mask \end_layout \begin_layout Standard Jinghua Fang and Paul Spizziri have made microporous aluminium oxide templates. They are investigating using these templates as a mask for ion implantation. To better understand the templates' response, I developed a program to simulate implantation through such a mask. The pores in the template are about 20 \begin_inset Formula $\mu$ \end_inset m long and 80nm in diameter, for an astonishing aspect ratio of 250:1. The pores are set closely together in a hexagonal arrangement. They are very straight and transparent to electrons, as shown by TEM \begin_inset CommandInset nomenclature LatexCommand nomenclature symbol "TEM" description "Transmission Electron Microscopy" \end_inset analysis. \end_layout \begin_layout Standard Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:Aluminium-oxide-mask" \end_inset shows some simulations of an experiment performed using high-energy (0.5-2MeV) pelletron ions for characterisation. The ions would normally only travel 1-2 \begin_inset Formula $\mu$ \end_inset m through solid material, but the pores allow the ions to travel right through the mask, even when the ions must travel through the walls of several pores. This result explained the experimental data. The extremely large range of the ions' sideways motion is illustrated in Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:Al - An-end-on-view," \end_inset . For these simulations, the initial beam was about two pores in diameter, but ions would often scatter sideways through ten or more pores. The initial direction of the ions was slightly randomized, using a Gaussian divergence of std. dev. \begin_inset Formula $1^{\circ}$ \end_inset . \end_layout \begin_layout Standard Figure \begin_inset space ~ \end_inset \begin_inset CommandInset ref LatexCommand ref reference "fig:Aluminium-oxide-mask-result" \end_inset shows the result of a simulated 14 keV phosphorus implant. This shows that higher concentrations of ions are found under the centre of the pores, which results from the beam divergence. \end_layout \begin_layout Standard \begin_inset Float figure placement p wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \begin_inset Graphics filename images/alTunnels/tracks-200nm-rndm.png lyxscale 50 height 6cm groupId 2-height \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout An end-on view, showing some pores (not all the circles are drawn), ion tracks (blue) and energy depositions (yellow). \begin_inset CommandInset label LatexCommand label name "fig:Al - An-end-on-view," \end_inset \end_layout \end_inset \end_layout \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \begin_inset Graphics filename images/alTunnels/montage.png lyxscale 50 height 6cm groupId 2-height \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout A side view of several simulations. The first shows the result for no aperture rotation, 0.5MeV He ions. The second shows the result after the template is rotated by 1 degree. The third and fourth then increase the ion energy to 1 and 2MeV respectively. The white dots down the centre show the vertical positions of the pores. \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout Aluminium oxide mask simulation screenshots. \begin_inset CommandInset label LatexCommand label name "fig:Aluminium-oxide-mask" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Graphics filename images/alTunnels/0.10deg-map.png lyxscale 50 width 50text% \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout The distribution of a low-energy phosphorus beam after transmission through a porous aluminium oxide mask rotated by \begin_inset Formula $0.1^{\circ}$ \end_inset . \begin_inset CommandInset label LatexCommand label name "fig:Aluminium-oxide-mask-result" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Standard \size small \begin_inset CommandInset bibtex LatexCommand bibtex bibfiles "thesis" options "unsrt" \end_inset \end_layout \begin_layout Standard \begin_inset Note Note status open \begin_layout Plain Layout Other potential material: \end_layout \begin_layout Plain Layout Two-terminal devices \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset Note Note status open \begin_layout Plain Layout References no more et. al. \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset Note Note status open \begin_layout Plain Layout Questions: \end_layout \begin_layout Plain Layout XQ: Paul: Diagram of Raman system?, photos cd damaged -- raman photo? \end_layout \begin_layout Plain Layout XQ: Remove some figures? \end_layout \end_inset \end_layout \end_body \end_document