The Problem of Coherent Transport in the Solid State Jonathan Newnham Supervisors: D. N. Jamieson and P. G. Spizzirri Abstract This thesis begins an investigation of confined-channel electrically-detected magnetic resonance. The fabrication process of freestanding silicon nanowires and ion-implanted state-of-the-art silicon transistor devices is discussed in detail, and simulations of the ion implantation process using the GEANT4 software toolkit are developed. 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 in the early 21st century based on promising lines of investigation laid down over the past decade. In particular, we look at models for coherent transport using nanowires and nanoscale mosfets where the insertion and activation of single donors into nanoscale devices provides a platform for quantum measurement. Chapter 1 presents a brief overview of current progress towards a fully-functional quantum computer, with a particular focus on solid-state coherent transport. Chapter 2 develops a fabrication process for quasi-1D coherent transport devices. Chapter 3 presents preliminary measurements on the quantized energy levels of these nanodevices. Acknowledgements and thanks Andrew Alves for request and feedback on cantilever aperture simulations and for providing experimental data Laurens van Beverens for his wonderful explanations of EDMR and provision of a collection of nanowires and carrier chips Stephen Gregory for the use of and much assistance with the EPP wire-bonder Felix Hoehne for his astonishing prowess with EDMR measurements Wayne Hutchison for his EDMR measurements at WSI and low temperature measurements in Canberra David Jamieson for inspirational discussions, a deep understanding, and a guiding hand throughout this project Paul Spizzirri for sharing his many insightful and useful ideas, much laboratory assistance and great times throughout this project Samuel Thompson for an excellent labview controller for the I-V measurements and information on the AFSiD samples Statement of Contribution and Originality Chapter 1 is an original review. Of the remainder, the simulation development was my own work, based on the GEANT4 toolkit; nanowire growth was performed by Laurens van Beverens at UC Berkeley; nanowire preparation, implantation and initial measurements I performed with P. Spizzirri; low-temperature I-Vs were performed by W. Hutchinson at UNSW@ADFA in Canberra; and the EDMR measurements were performed by F. Hoehne and W. Hutchinson at the Walter Schottky Institut in Munich, 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. Spizzirri. Table of Contents Abstract Acknowledgements and thanks Statement of Contribution and Originality Chapter 1 Review Structure of this document 1.1 Potential Architectures Kane NMR Liquid Photonic P in Si: electron spin GaAs Quantum Dots Ion trap Superconductors Diamond Other 1.2 Coherent Transport CTAP Spin Bus Photonic Coupling and The Flying Qubit Ensemble Systems Blue Sky options 1.3 Deterministic fabrication Donor ion positioning 1.4 Si:P system measurements Embedded nanowires ESR EDMR 1.5 Summary Coulomb Blockade and Density of States Chapter 2 Fabrication of nanostructured devices 2.1 Fabrication Nanowire growth Preparation for measurement: electrical connection I-V Characterisation Resistivity and doping density Avalanche breakdown 2.2 Ion implantation Fabrication timeline Effect of ion implantation on nanowires 2.3 Simulations of ion implantation Timeline Step And Repeat Modelling and simulation Ion distribution in nanowires 2.4 Donor activation Raman spectroscopy Raman spectroscopic temperature measurement: Stokes / Anti-Stokes Ratio Raman spectroscopic temperature measurement: Stokes shift Our annealing process 2.5 AFSiD consortium devices 2.6 Summary Chapter 3 Characterization 3.1 Low temperature I-V 3.2 EDMR Experimental Details Results and discussion 3.3 Summary Chapter 4 Closing material 4.1 Summary 4.2 Future Work Low-temperature measurement Single-donor or regularly-spaced-donor EDMR Simulations Appendix A Further simulations Diamond implant with mask Aluminium oxide mask [LaTeX Command: printnomenclature] [LaTeX Command: nomenclature][LaTeX Command: nomenclature][LaTeX Command: nomenclature] Review of Coherent Transport 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 experimental steps required in the development of solid-state coherent transport. In 1982 Paul Benioff proposed [benioff1982quantum] the first recognisable theoretical framework for a quantum computer. That same year, Feynman discussed the impossibility of simulating quantum systems with classical computers [feynman1982simulating]. Feynman also developed the concept of controlled manipulation of coherent quantum states in a 1986 book [feynman1986quantum]. Deutsch showed that a quantum computer could be exponentially faster than a classical computer [Deutsch1992]. Quantum computing remained a niche interest until 1994, when Shor proposed his factorization algorithm[footnote: [shor1999polynomial] is the original article; an excellent “man on the street” explanation is [Aaronson2007] ]. 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. In 1998, Bruce Kane followed up on Seth Lloyd's more feasible theoretical construction [lloyd1993potentially][footnote: which contains the first published mention of the word “qubit” ] with a concrete architecture based on the spin-\frac{1}{2} nucleus of phosphorus embedded in a “spinless” solid silicon-28 matrix and controlled with classical electrical gates [kane1998silicon] . Other architectures based on (among others) photons, trapped ions and superconductors followed [Milburn1999, roadmap]. 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 [lanyon2010towards]. This problem is well known and has been performed on modern classical computers, but the scalability of quantum computing promises much more complex simulations and determinations of molecular properties well beyond the 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. 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 2^{50}=10^{15} 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. Coherently controlled quantum devices also have important applications as sensors. SQUID[LaTeX Command: nomenclature]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 [degen2008scanning, morton_bang-bang_2006] . Structure of this document Figure [fig:outline] 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 these components in various possible architectures. We then refine our focus and explore different options for implementing one of these capabilities, coherent transport, in solid state systems. 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. [float Figure: [Figure 1.1: The primary components of a quantum computer and the foundations required to build them. ] ] 1.1 Potential Architectures Since the proposal by Kane, various architectures have been proposed as ways to build a quantum computer. [roadmap] is a comprehensive review. Normally the “Divincenzo Criteria” [divincenzo2001physical] are used to quantify the progress using various architectures, however we have chosen the following, more subjective approach as it is more relevant to experiments. Some of the most important tradeoffs involved in the choice of architecture are: 1. 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. 2. scalability (a device must scale to at least 50 qubits to be really useful) 3. transport ease (how easy it is to transport qubits on demand with currently known methods) 4. interaction ease (how easy it is to coherently interact two qubits) 5. manipulation ease (how easy it is to set/read a single qubit on demand without interfering with the others) 6. manufacturability (how easy it is to make) [float Table: ------------------------------------------------------------------------------------------------------------------ Architecture Coherence Scalability Transport Interact Manipulation Manufacture ------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------ Kane type 9 9 1 3 4 2 ------------------------------------------------------------------------------------------------------------------ NMR liquid 3 1 1 8? 8 9 ------------------------------------------------------------------------------------------------------------------ Photonic 3 3 9 4 9 8 ------------------------------------------------------------------------------------------------------------------ GaAs QDs 2 8 5 7 9 8 ------------------------------------------------------------------------------------------------------------------ P in Si - \mbox{e}^{-}spin 7 9 3 3 7 3 ------------------------------------------------------------------------------------------------------------------ Ion Traps 9 6 8 6 9 7 ------------------------------------------------------------------------------------------------------------------ Superconductors 5 7 3 5 8 6 ------------------------------------------------------------------------------------------------------------------ Diamond NV 8 7 5 3 7 6 ------------------------------------------------------------------------------------------------------------------ [Table 1.1: Architecture advantages and disadvantages. Each property is given a critical assessment by the author on a scale of 1-9 (9 being the best) ] ] Kane A Kane-type quantum computer [kane1998silicon] 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 [fig:Si:P-interaction-zone]). 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. The problem of charge traps in the oxide ionising donor atoms (i.e. taking the loose electron) may need to be solved by using something other than the conventional silicon dioxide to separate the gates. Kane suggests SiGe. Recent progress has demonstrated coherent control of (bulk) P nuclear spins via the unpaired electron [morton2008solid]. A recent variation [morton2009silicon] on the original proposal simplifies some aspects of this architecture by only requiring localised readout of a 2D array (and having entanglement generated globally). A theoretical treatment of nuclear spin coherence decay via spin-orbit coupling and phonon emission is given in [Hasegawa1960] . NMR Liquid Nuclear Magnetic Resonance was first performed in 1940s. In this approach, molecules with several interacting nuclear spins are affected by global fields. Different “qubits” are addressed by tuning the resonating microwave field frequency or magnetic field strength. Such qubits were demonstrated by IBM [chuang1998experimental, vandersypen2001experimental] , 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 beyond a few qubits due to the combinantion of limited bandwidth and a need to address each qubit with a different frequency. 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 problem of addressing individual bits still has no proposed solution [roadmap] . Photonic A photonic quantum computer uses the direction of polarization of a photon as a qubit. Systems involve sending a light pulse through a set of optical components (waveplates and interferometer flats). 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 can be found in [kok2007linear, o2007optical] . This architecture has important applications in provably-secure quantum communication and long-range coherent transport (the Transmission component of Figure [fig:outline]). Coupling of photons to other quantum-mechanical systems is a growing field (see §[sec:coupling]). The original work, reported by Knill, is [knill2001scheme] . Beautiful results have recently been demonstrated with optical memories at ANU[LaTeX Command: nomenclature] [Hosseini2009] and similarly [H'etet2008], temporarily storing photons coherently in excited states of a crystal. P in Si: electron spin This architecture is similar to the Kane proposal but stores the spin on the phosphorus atom's valence electron instead of the nucleus [vrijen2000electron, Hill2005]. 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 (gates) on the surface of the crystal (Figure [fig:Si:P-interaction-zone]). 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. Major hurdles for this architecture include manufacturability (positioning single phosphorus atoms is hard [schenkel2003formation] ) and transport [hollenberg2006two]. Two competing methods for fabrication are ion implantation [schenkel2003formation] and the bottom-up approach [ruess2007narrow] (more on these later). Clark et. al. provide a recent review [clark2008solid]. A recent advance by the Australian Center for Quantum Computing Technology demonstrated single-shot readout of electron spins and found electron-spin coherence times (T_{1}) of about 6s [morello2010single] . This is a convicing demonstration of the Readout component of Figure [fig:outline]. [float Figure: [Figure 1.2: Si:P interaction zone (courtesy David Jamieson). ] ] GaAs Quantum Dots Similar to the P in Si system, a quantum dot confines electrons using electrically charged gates instead of the potential well of a phosphorus atom. In gallium arsenide, the large sea of nuclear spins (~10^{6} 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 [angus2007gate, hu2007ge] . Coupled qubits in this architecture have been demonstrated [petta2005coherent] but the possibility of coherent transport remains an open question. Ion trap In this architecture, ions (spin qubits) float in vacuum above a 2D network of electrical gates which control the ions [kielpinski2002architecture] . This approach looks very promising in the short term. Ion traps transporting several qubits have been demonstrated by NIST Maryland [blakestad2009high], together with repeated gate operations [home2009complete]. 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 [ospelkaus2008trapped] . This architecture is technologically expensive, requiring atomic cooling and high vacuum. Superconductors Superconducting Quantum Interference Devices (SQUIDs) 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 [zhou2002quantum] . A recent review is available [clarke2008superconducting]. Diamond The most popular diamond system uses the free electron in a nitrogen vacancy (NV) defect in a diamond crystal as the qubit. The best published coherence time for this system is 2ms [ladd2010quantum] . Proposals use optical transport and readout, which can cause difficulty if qubits are close together due to difficulty focusing lasers to address individual NV[LaTeX Command: nomenclature] centres. Manipulation is performed optically. This system is promising, but novel manufacturing techniques are required, delaying progress [greentree2006critical]. NV centres can also be used on their own as sensitive localised magnetic field detectors [gaebel2006room]. Exploiting the magnetic dipole interaction between nearby (10nm) NV centres faces similar problems to the Si:P system [neumann2010quantum]. Other 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 [calderon2009quantum], or using fullerenes [morton2005high, morton_bang-bang_2006]. Many more are given in a more comprehensive review of current progress [roadmap] . A more recent review focusing on solid-state systems is [ladd2010quantum] . Figure [fig:Coherence-times] shows a summary of the coherence times for various solid-state systems. [float Figure: [Figure 1.3: Coherence times of various solid-state systems. T_{1} is the decay time for the system to relax into its ground state; T_{2} 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. ] ] 1.2 Coherent Transport 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. CTAP Coherent Transport by Adiabatic Passage is a possibility for solid-state coherent transport [CTAP]. In the simplest version of CTAP (Figure [fig:CTAP]), 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. [float Figure: [Figure 1.4: CTAP, from [CTAP]. 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. ] ] Using a simple electric field gradient to push the valence electron along a chain of ionised donors is also discussed in [CTAP] , 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. CTAP scalability is discussed in [greentree2008spatial]. A recent study [Rahman2009] using the NEMO 3D tight-binding simulation toolkit [ahmed2009multimillion] 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. Heteronuclear CTAP 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 [jong2009coherent] . Spin Bus [math macro] In its simplest form, a spin bus [li2005quantum, mehring2006spin, friesen2007efficient] consists of an antiferromagnetic Ising-model chain of spins[footnote: i.e. spins prefer to antialign, up-down-up... or down-up-down... ], tightly coupled to their neighbours but nothing else. At low enough temperatures, a bus with an odd number of sites N has two possible states: an extra spin-up or an extra spin-down. This allows treatment of the bus as an effective single spin. 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. Spin buses more than several hundred sites long (perhaps 1-10\mum 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 [chaves2009model]. 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 W_{n} state, \ket{00\ldots001}+\ket{00\ldots010}+\cdots+\ket{10\ldots000} , given in [friesen2007efficient]. Photonic Coupling and The Flying Qubit In the long term, it will be very important to be able to transport quantum information long distances. Divincenzo calls such transport flying qubits. 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 [clark_quantum_2007] , and preliminary work towards experimental demonstration has shown that quantum dots can absorb [shields2000] and emit [dewhurst_slow-light-enhanced_2010] single photons (in a directionally controlled way). Optical coupling between single-electron quantum dots has been demonstrated [yamamoto_optically_2009]. Yamamoto's group has also demonstrated control over the quantum state of a single quantum dot using optical techniques [press_complete_2008]. Abanto's architecture [abanto2010quantum] 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. It is also possible to couple photons to excitons (electron-hole pairs) [Hudson2007, stevenson_semiconductor_2006]. The question of how to coherently couple such excitons to solid-state qubits remains open. Projects to demonstrate long-range quantum entanglement have been successful between islands 144km apart [ursin2006free] and are plans are afoot to do it via a satellite [ursin2009space]. Blue Sky options Coherent electron transport in carbon nanotubes has been demonstrated [Tsukagoshi1999]. It may be possible to perform this kind of ballistic transport in the Si:P system. This would likely require atomically precise donor placement. It has recently been shown that photosynthesis involves coherent transport [Engel2007photosynth]. Engel et. al. observed “ remarkably long-lived” 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 production. 1.3 Deterministic fabrication 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. Donor ion positioning There are two main strategies for donor ion placement: “top-down” and “bottom-up”. 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. Ion implantation is less accurate; for 20 nm depth, ions will straggle up/down and sideways an average of 8nm compared with about 1 nm for bottom-up. 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. Outlines of the bottom-up process are given in [oberbeck2002encapsulation, Schofield2003] . The AFM step, involving removing a few hydrogen atoms from the surface of a silicon crystal, is discussed in [Hallam2007]. A more accurate technique aiming for single-atom positioning using an STM tip is discussed in the letter [ruess2004toward] and the article [ruess2007narrow]. This has recently resulted in the successful positioning of a single ion to within 1 nm (3 lattice spacings). 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 [shinada2005enhancing], down to exceptionally low energies of about 10 keV [jamieson2005]. The counting can be done by collecting secondary electrons emitted when the ion impacts the surface [schenkel2003solid, shinada2008reliable], or by collecting the induced charge from the substrate after the impact [jamieson2005]. 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 [Orwa2009], a masking process relying on a mobile secondary mask [meijer2008towards], will allow 20 nm resolution of donor placement. 1.4 Si:P system measurements 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. Embedded nanowires In two papers [iwano1994carrier, iwano1998hopping], 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 \mum 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 “ Hopping model” but makes many assumptions without careful study. Most of the samples were annealed at 600--690 ^{\circ}C and measurements show reduced conduction indicative of lattice defects. Conductance measurements on 8nm wide monolayer-thick P in Si wires are performed in [Ruess2008atomic]. Rue finds Ohmic conduction (1 in 4 atoms in the wire is a P atom) with the resistance heavily dependent on temperature. In the range 1--10 Kelvin, the resistance is also heavily dependent on the applied magnetic field (magnetoresistance). 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 magnetoresistance), consistent with the 1D variable-range-hopping (VRH) model [azbel1991variable]. 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 found a negative magnetorestance for small magnetic fields (0-1 Tesla), which is not well explained. 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. Shin et. al. have made a SET so small (2 nm channel) that it works at room temperature [shin2010enhanced]. 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 nm) to the electron. ESR 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 “fingerprint” 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. ESR[LaTeX Command: nomenclature] (electron spin resonance) is very similar to the older technique of NMR (Nuclear magnetic resonance)[LaTeX Command: nomenclature] [weil2007electron]. 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 hyperfine splitting or Zeeman effect (Figure [fig:Hyperfine-levels]), 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 (ground) 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 T_{1}). 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 resonant frequencies, 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. 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 g-factor is used, defined by \hbar\omega=g\mu_{\mbox{B}}Bwhere \omega=2\pi f is the microwave frequency, B the magnetic field strength and \mu_{\mbox{B}} the Bohr magneton. The g-factor for a free electron is ~2.00232. [float Figure: [float Figure: [Sub-Figure a: ] ] [float Figure: [Sub-Figure b: ] ] [Figure 1.5: (a) Hyperfine levels and the first-order transitions for a spin-\frac{1}{2} nucleus (l) and electron (s), after [kittel1996introduction]. (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. ] ] EDMR EDMR[LaTeX Command: nomenclature] (electrically detected magnetic resonance) 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 [boehme2003theory] . This results in a change in the conductance of the sample which can be directly measured. An outline of the EDMR mechanism is shown in Figure [fig:EDMR]. 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 (\gamma) at a phosphorus resonant frequency (\omega_{1} or \omega_{2} of Figure [fig:Hyperfine-levels]) 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. EDMR has been demonstrated on a single electron from a quantum dot [elzerman_single-shot_2004]. It has not yet been done on a single implanted phosphorus donor, although measurements of less than 100 donors [mccamey2006electrically, mccamey2007thesis] and theoretical analyses [Hoehne2010] of such a measurement have been published, relying on the P_{b} interface defect found at the interface between the bulk silicon and the silicon dioxide surface coating to act as the recombination centre. The EDMR signal is normally enhanced using above-bandgap light to excite many carriers and hence make the recombination more pronounced [bayerl1997electrically]. This also suggests the technique of optically-detected magnetic resonance in which the luminescence of transitioning electrons is measured. Finally, spatially-resolved detection is possible by localising the optical carrier excitation [bayerl1997electrically] with a focused laser or conduction current with a scanning probe. We will return to the extremely sensitive technique of EDMR in Chapter [cha:characterization]. 1.5 Summary 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. Fabrication of nanostructured devices 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. 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 [lansbergen2008gate, pierre2010single] , 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 T_{2} coherence time of the system. Doped nanowires would also serve as excellent model systems for doping with 1-D arrays of donors using a fabrication method such as step-and-repeat. 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 and a method of deterministic ion implantation are described. Chapter [cha:characterization] then takes these fabricated devices and introduces one of the techniques of quantum measurement. 2.1 Fabrication of silicon nanodevices This section describes how silicon nanowires were prepared for the major measurements in Chapter [cha:characterization]. This method was found to be a simple and viable approach to constructing narrow-channel devices. Nanowire growth 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[LaTeX Command: nomenclature] 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 [Banerjee2002]. Our nanowires were cylindrical and single-crystal (a major benefit of the self-assembly growth process), with diameters of 60 nm and lengths up to more than 10 \mu m. They were provided in acetone solution. Preparation for measurement: electrical connection 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 [fig:Microscope H14-1]), and allowed to dry. This resulted in nanowires being scattered over the surface. We then headed over to the FEI Nova dual-beam (SEM[LaTeX Command: nomenclature] and focused ion) system [LaTeX Command: nomenclature] (Figure [fig:The-FIB] ) at Bio21 to deposit platinum from likely-looking wires to the gold contacts on the surface of the chip. [float Figure: [Figure 2.1: “The FIB” at Bio21. ] ] We are not the first to perform this type of process; in 2000, Chung et. al. [chung2000silicon] used EBL and e-beam evaporation to deposit Au/Ti or Al contacts onto 15--35 nm Si wires. Marzi et. al. [marzi2004probing] in 2004 were among the first to use the FIB process, wiring up freestanding 70nm platinum nanowires. They found 330 \Omega 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) [nam2005focused]. The Li Battery SiNW[LaTeX Command: nomenclature] team [chan2007high] 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[LaTeX Command: nomenclature] etch. All of these methods resulted in a satisfactory electrical connection to the nanowire. 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 \pm5 nm). The nanowires we chose to wire up were all about 60 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. 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_{3} over the sample and focusing the electron beam onto the surface. Where XeF_{3} is close to the surface, the e-beam cracks the occasional XeF_{3} 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 \mum depth (a few seconds for about a 1 \mum^{2} area). As we were using the e-beam and not the ion beam, the actual 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. 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_{3})_{3}CH_{3}C_{5}H_{4}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[footnote: Normally, a metal-silicon interface forms a simple diode and has a noticible voltage drop. We did not observe significant voltage drops in any of our measurements. ]. 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 \mum 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 nm was deposited. 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 mm^{2} ) pads on the carrier. I-V Characterisation [LaTeX Command: nomenclature] [float Figure: [float Figure: [Sub-Figure a: The room-temperature resistances of all nanowires that made it as far as reasonable measurement. ] ] [float Figure: [Sub-Figure b: 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\Omega. The scan was traced in both directions several times, which is not visible because the result is very repeatable. ] ] [Figure 2.2: Nanowire measured resistance. ] ] Once the electrical connection was available, we brought the device to the AFM[LaTeX Command: nomenclature] lab in the MARC[LaTeX Command: nomenclature] 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 \pm0.1 V, as shown in Figure [fig:A-typical-resistance]. A plot of the various lengths and resistances we measured is given in Figure [fig:The-resistances]. No change was observed (at room temperature) by varying the incident light on the sample, indicating that any boron acceptors in the sample were completely thermally activated as usual. The next section discusses how we used these initial measurements to determine the amount of boron in the wires. Resistivity and doping density As will be discussed shortly, the B14-1 wire of Figure [fig:The-resistances] 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. Classically, the resistivity of a cylinder of constant thickness is R=\rho\frac{l}{A} where l is the length, A cross-sectional area and \rho the intrinsic resistivity of the material. For the longest wire, B14-2, this works out to be \rho=2\times10^{-1}\,\Omega\cdot\mbox{cm} , with large error margins of perhaps an order of magnitude (the other wires are within an order of magnitude of this value). This corresponds [carrierdensity] to a p-type (boron doping) carrier density of 1\times10^{17}\mbox{ cm}^{-3}, 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. Avalanche breakdown 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 [fig:Avalanche-breakdown]. This nanowire was 1.7 \mum long. The breakdown voltage for pure silicon is about 3\times10^{7} 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 [fig:Avalanche-breakdown-1] ). 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 [fig:The-resistances]. [float Figure: [float Figure: [Sub-Figure a: 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\Omega. ] ] [float Figure: [Sub-Figure b: The nanowire after the I-V measurement. ] ] [Figure 2.3: A nano-fuse. ] ] Having now gained a basic understanding of what we are starting with, we can move on in the next section to controlled modification of the nanowires' properties. 2.2 Ion implantation In order to introduce controlled amounts of phosphorus into our devices, we performed ion implantation using the MARC Colutron (Figure [fig:The-MARC-colutron.]). This section discusses the workings of the colutron and a typical implantation run. The colutron uses an electric potential to accelerate ions. The first stage is called the source; here, solid phosphorus is heated by a filament until it evaporates. A large current applied to the resulting phosphorus gas results in a plasma. Charged phosphorus ions from this plasma then find their way out of a pinhole at the end of the source chamber and are accellerated by a 14 kV potential into the beam optics. The ions travel the length of the colutron, where impurities are removed with an E\times B velocity filter, and impact the sample. Implants were performed at 14 keV. A typical mass spectrum (before filtering) is shown in Figure [fig:colutron schematic]. 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 filter to the correct ion (by adjusting the magnetic field component of the velocity filter). Our implantations used the 0.6 mm diameter beam-defining aperture. Implant fluences were calculated to yield a doping level of 10^{17}\mbox{ ions/cm}^{3} as this is below the semimetallic density but still provides many ions in the channel for measurement. [float Figure: [float Figure: [Sub-Figure a: 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. ] ] [float Figure: [Sub-Figure b: A schematic of the MARC colutron. ] ] [Figure 2.4: The MARC colutron. ] ] Effect of ion implantation on nanowires Figure [fig:I-V implant] shows I-V curves of a nanowire before and after the phosphorus implantation. This particular implant was performed with a 55 pA beam current and 600 \mum diameter aperture for 2.5\pm0.3 s, resulting in 150\pm30 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 and is not a feature of the nanowire itself. A later anneal (see Section [sec:donor-activiation]) resulted in significantly increased conductivity consistent with the interpretation of phosphorus donors becoming activated (and being more numerous than the already-present boron acceptors, resulting in an overall n-type material). [float Figure: [Figure 2.5: The I-V curve of the as-provided nanowire, H14-1, before and after phosphorus implantation. Resistances are 97.8 k\Omega and 102.4 k\Omega respectively. ] ] 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 Section [sec:donor-activiation]. 2.3 Simulations of the ion implantation process 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 several simulations of various implantation scenarios and masking approaches. This section describes some of these simulations and analyses the result. More detailed notes describing the development process (based on GEANT4's TestEm7 example) are available [geant4-dev-notes]. GEANT4's simulation ability was found to be extremely useful; several other simulations of ion implantation were performed and are described in Appendix [cha:further-simulations]. Apart from being pivotal material for several papers, this additional work also provides further validation of the somewhat unconventional approach of using GEANT4 to simulate low energy ion implantation. Step And Repeat 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. The step-and-repeat process of controlled single-ion implantation is illustrated in Figure [fig:The-Step-and-repeat]. In this process, a PMMA[LaTeX Command: nomenclature] mask is defined on the silicon surface using EBL[LaTeX Command: nomenclature]. 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. The accuracy of the ion implantation process is essential for the demonstration of CTAP[LaTeX Command: nomenclature] (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 “correct” implants as the detection system has no way of measuring the location of the ion, only its presence. [float Figure: [Figure 2.6: The Step and Repeat process. The dotted red lines indicate the tracks of implanted ions. ] ] Modelling and simulation To determine the potential number of incorrect implants as a result of using the secondary mask, I used the particle-physics toolkit GEANT4 [Geant4] to simulate ion trajectories, as in [gorelick] . Mendenhall's recent screened nuclear scattering improvements for low-energy ions [Mendenhall2005] were essential to the accuracy of the simulation. The SRIM ion implantation program [SRIM] is widely used for simulating ion implantation. 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 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 [fig:SRIM-compare] 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. [float Figure: [Figure 2.7: Ion implantation simulation toolkits comparison: SRIM and GEANT4 implanting into silicon. ] ] 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 [fig:The-Step-and-repeat Results] b and c. Simulations with GEANT4 were eventually made to match this data (also shown) by adjusting the shape of the aperture in the simulation. Figure [fig:The-Step-and-repeat Results]a shows the resulting shape of the aperture. Several ion tracks from the simulation are overlaid on the figure. 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. Figure [fig:The-Step-and-repeat Results]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. [float Figure: [Figure 2.8: Cantilever simulation and comparison to experimental data (tracks are simulated 500keV He-4 ions). a) A visualisation of the simulation. This is Aperture 1. b) A comparison with experimental and simulated 500keV He-4 ions, at various aperture rotations. c) A detailed comparison for aperture rotation 0. (inset) Aperture 2. d) Final performance of the simulated apertures for various ions. ] ] Ion distribution in nanowires To understand the distribution of ions in our implanted silicon nanowires, a fairly simple simulation was performed. The nanowire was assumed to be a 60 nm-diameter silicon tube, and 14 keV P ions were injected from the side, as in Figure [fig:sim-implant]. This simulation showed a highly non-uniform distribution, with a peak density of approximately 1.2\times10^{17} cm^{-3}. Additionally, about 13% of ions that hit the surface of the nanowire were scattered and did not stop inside it. [float Figure: [float Figure: [Sub-Figure a: A simulation of the nanowire implantation process ] ] [float Figure: [Sub-Figure b: The final simulated distribution of ions in the nanowire, for 15000 ions. The area of the bins in this plot is (1 nm)^{2}. ] ] [Figure 2.9: ] ] This simulation shows that the implantation into the nanowire resulted in a doping density remarkably close to the intended amount. The distribution is also highly non-uniform, with the likely effect that the background boron doping will be dominant on one side of the wire and the implanted phosphorus dominant on the other. Having now demonstrated excellent tools for analysing ion distributions resulting from implantation, we return to fabrication issues in the next section. 2.4 Donor activation 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 and donors activated with an anneal (heating) step, which this section discusses. The standard method of annealing in commercial silicon processing is with an incandescent heater. We found it easier to perform the anneal in a more unusual 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 [cui1998noncontact]. 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 \mum in diameter. 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. Raman spectroscopy Photons impinging on a crystal can be scattered in two main ways. The most obvious, Rayleigh scattering, results from elastic collisions with the material and the photons are reflected with an unchanged frequency[footnote: The frequency shift due to Compton scattering is quite difficult to measure at visible wavelengths ]. The other way involves the complication of a lattice phonon participating in the interaction, resulting in a Raman shift in the wavelength of the scattered photon [raman1928new, smith2005modern] . The Raman shift is normally given in terms of the initial and final wavelengths as \Omega=\frac{1}{\lambda_{\mbox{laser}}}-\frac{1}{\lambda}and the usual units are cm^{-1}. Figure [fig:Raman] shows the transitions involved in a Raman measurement. Transitions which move to a slightly higher-energy vibrational state (m\to n) are referred to as Stokes-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 anti-Stokes transitions. Because Raman scattering is relatively rare (often, only one in 10^{7} photons will be Raman scattered), 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. [float Figure: [Figure 2.10: Diagram of the transitions involved in Rayleigh and Raman scattering, from [smith2005modern]. ] ] Raman spectroscopic temperature measurement: Stokes / Anti-Stokes Ratio At very low temperatures, the Stokes signal is much stronger than the anti-Stokes 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: \frac{N_{n}}{N_{m}}=\frac{g_{n}}{g_{m}}\exp\mbox{\ensuremath{\left[\frac{-\left(E_{n}-E_{m}\right)}{kT}\right]}} where N is the number of molecules or bonds in a certain state, g is the degeneracy of that state, E is the energy level of that state, k=1.38\times10^{-23}\mbox{ JK}^{-1} is the Boltzmann constant and T is the temperature. Due to the different cross-sections between phonon and photon interactions of differing frequencies, the observed intensity ratio takes the form \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)} where \omega_{(l,p)} is the angular frequency of the (photon, phonon) and \gamma allows for a difference in the detection efficiencies of the two photons. At high temperatures, \gamma 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 \gamma and the requirement of accurately measuring the intensity of both the Stokes and the anti-Stokes peaks makes this method unsuitable for our purposes. Raman spectroscopic temperature measurement: Stokes shift A second method of measuring temperature, that proposed in [cui1998noncontact] , 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 approximated harmonic basis to interact. This interaction causes shifts in the vibrational energy levels with temperature. 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. [hart1970temperature, kittel1996introduction, balkanski1983anharmonic] . Cui proposes the empirical formula \Omega(T)=\Omega_{0}-\frac{C}{e^{[D(hc\Omega_{0}/kT)]}-1}to describe the Raman shift as a function of temperature, where \Omega_{0} is the Raman shift at 0 K. This is a completely empirical formula that has so far been found to work better than theoretically-based results, and gives an accuracy of about \pm8 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. Cui finds \Omega_{0}=524 cm^{-1}, C=10.53 cm^{-1} and D=0.587 for Si. A calibration performed by P. Spizzirri on the MARC system found best fit values of C=10.7 cm^{-1} and D=0.59. Our annealing process 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 more difficult and less accurate. Using the above theory, we are able to anneal our samples. The laser on the Raman system in the MARC cleanroom (Figure [fig:Raman photo marc] ) (which is a Renishaw RM 1000 Raman/luminescence system, we used the 514 nm Argon-ion laser) on full power for 10s heated the sample to 900 K. The Raman laser (Figure [fig:Raman photo bio21]) at Bio21 is more powerful, getting up to 1200 K in a cold nitrogen atmosphere. Figure [fig:Raman nanowire forest blank] shows spectra demonstrating the technique. The blank silicon signal is almost perfectly fit by a single mixed Gaussian/Lorentzian. 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 substrate still gives the room-temperature 520 cm^{-1} peak as it dissipates heat much more quickly and as a result does not heat up noticibly. The second peak is centred on 504 cm^{-1} which corresponds to a temperature of 1200 K. Figure [fig:Raman-spectrum-anneael] 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. [float Figure: [float Figure: [Sub-Figure a: A Raman spectra of a forest of nanowires, a fit, and a spectrum for blank silicon. Data and fit provided by P. Spizzirri. ] ] [float Figure: [Sub-Figure b: Raman spectrum recorded during laser annealing exposure. ] ] [float Figure: [Sub-Figure c: The Raman spectrometer at MARC. ] ] [Figure 2.11: Various Raman spectra ] ] This spectrum is well understood. The main peak at 520.32\pm0.05 cm^{-1} 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 nm thick), as in Figure [fig:Raman nanowire forest blank] . 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\pm3 cm^{-1} 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 10 cm^{-1} is attributed to heating of the wire. These fits are mixed Gaussian and Lorentzian because the actual signal is Lorentzian but the instrument response is Gaussian. The annealing process was successful for our purposes. Figure [fig:I-V anneal] shows I-V curves of before and after an annealling step. The conduction of the wire has clearly increased (162 k\Omega changed to 82 k\Omega), 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 ^{\circ}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. [float Figure: [Figure 2.12: I-V curves of H14-1 after mounting (162 k\Omega) and anneal (82.8 k\Omega). ] ] 2.5 AFSiD consortium devices 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 [afsid]. Figure [fig:A-typical-AFSiD] shows one of the devices that we implanted. These devices are fabricated as silicon-on-insulator [LaTeX Command: nomenclature] 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 [fig:Afsid-TEM-2] ) This last pair of TEM images clearly shows the 5 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. 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 [fig:outline] and additional characterization of their behaviour at the nanoscale is also valuable. [float Figure: [float Figure: [Sub-Figure a: 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. ] ] [float Figure: [Sub-Figure b: (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. ] ] [float Figure: [Sub-Figure c: 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 nm oxide grown between channel and gate; green is crystalline silicon. The thick layer of oxide underneath the channel is grey. ] ] [Figure 2.13: A typical AFSiD device. ] ] 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 [pierre2010single]. This will be important when we come to interpreting the EDMR spectrum of these devices in §[sec:edmr-result]. 2.6 Summary 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. Transport Measurement and characterization This chapter describes the cutting-edge measurements performed on the nanowires, and discusses the theory necessary to understand the results. Read et. al. found that effective-mass theory is valid for wires with diameter larger than 2.3 nm, and hence 1-D quantum confinement effects are most noticable in wires with this diameter or less [read1992first]. 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 [sec:fab]. 3.1 Low temperature I-V 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 nm [kane1998quantized]. 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 2e^{2}/h, which corresponds to about 13 k\Omega. As such, one would expect to see steps in the current as the voltage was increased as additional conduction bands become available. Low temperature measurements can also be extremely sensitive. Two measurements of current perturbations caused by single ions in semiconductor channels and giving significant amounts of information have been performed [lansbergen2008gate, pierre2010single] . 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 [fig:outline]. This type of measurement works best on highly-crystalline samples free of defects and dopants, and also works better for samples shorter than 500 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 [johnson2010drain, lansbergen2008gate]. 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 [fig:H14-1-nanowire] . This particular measurement did not show any evidence of quantized conductance due to its low resolution and also possibly because it was optically gated (thus exciting carriers into otherwise forbidden conduction bands). Our freestanding 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. [float Figure: [float Figure: [Sub-Figure a: Low-temperature (4.2K) I-V curves taken by W. Hutchinson of the H14-1 nanowire. ] ] [float Figure: [Sub-Figure b: 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. ] ] [float Figure: [Sub-Figure c: 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. ] ] [Figure 3.1: H14-1 nanowire initial characterisation. ] ] 3.2 EDMR As was described in §[sub:EDMR-theory], 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 “blank” device. Experimental Details The experimental setup for an EDMR measurement is shown in Figure [fig:EDMR-setup]. 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 [hubl2007thesis, p. 69]. A lamp shining on the sample provides optical carrier excitation. The WSI measurements are performed using a 3.5 T magnet and a microwave cavity resonant at 96 GHz. An illustration of the instrument is given in Figure [fig:EDMR-setup]. [float Figure: [Figure 3.2: The experimental setup for EDMR at WSI (from D. McCamey's thesis [mccamey2007thesis] ). ] ] Results and discussion The expected advantage of confined-channel measurement for EDMR is that the surface interface is always nearby. This is useful because the P_{\mbox{b}} interface defects so important to the recombination process [hubl2007thesis, p. 75] 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. The first EDMR spectrum we obtained was on an AFSiD device. The spectrum with fits is shown in Figure [fig:EDMR-afsid-fit]. 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 [fig:Afsid-TEM-2]). However, a considerable P_{\mbox{b}} signal and peaks corresponding to exchange-coupled (very high density, greater than 10^{18}\,\mbox{cm}^{-3}) 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 3/2 and so its EDMR signature contains four hyperfine peaks in a straightforward extension of [fig:Hyperfine-levels]). 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 [lansbergen2008gate, pierre2010single], 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_{\mbox{b}} signals from the interface defects that will in the future allow us to probe P donors. These results are somewhat inconsistent with earlier results that claimed probing of hundreds of donors in bulk-type devices [mccamey2007thesis] using similar instrumentation. [float Figure: [Figure 3.3: The fitted EDMR spectrum of an AFSiD device. The red and green lines are fits to P_{\mbox{b}} resonances with g-factors of g_{\perp}=2.0081 and g_{\parallel}=2.00185 respectively [hubl2007thesis]. The remaining blue fit is a resonance attributed to exchange-coupled arsenic. ] ] 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. 3.3 Summary The results presented here demonstrate that EDMR of a confined-channel device is possible. Low temperature measurements of the nanowires fabricated in Chapter [cha:fab] 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. 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. Closing Material 4.1 Summary Chapter [cha:review] 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 as well as Abanto's theoretical proposal for coupling solid-state systems to photons using optical cavities. Chapter [cha:fab] described the fabrication process of precursor coherent transport devices. It found that silicon nanowires are a suitable proxy for commercially fabricated nano-MOSFET channels, and described measurements indicating successful fabrication. Chapter[cha:characterization] 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_{\mbox{b}} interface traps and the heavily doped arsenic leads, but did not detect stray arsenic dopants that are probably in the channel, suggesting This work has helped build the technological understanding required to implement the coherent transport component (Figure [fig:outline] ) of a future quantum computer. 4.2 Future Work Low-temperature measurement 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 §[sec:measurements] . Single-donor or regularly-spaced-donor EDMR 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/removal 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. Simulations 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. Further simulations 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. Diamond implant with mask 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 [fig:Diamond-masked-implant]) 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. The simulations showed that the suspicions were correct; a 30 \mu 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. [float Figure: [float Figure: [Sub-Figure A.0.1: The simulation geometry and a few ion tracks. The red lines are scattered electrons. ] ] [float Figure: [Sub-Figure A.0.2: A side view of a 10000 ion simulation. The yellow dots are energy depositions. Most of the unmasked beam was not simulated. ] ] [Figure A.1: Diamond masked implant . 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 distribution is the subject of this investigation. ] ] [float Figure: [float Figure: [Sub-Figure A.1.1: Ion distribution as a function of mask spacing. ] ] [float Figure: [Sub-Figure A.1.2: ] ] [float Figure: [Sub-Figure A.1.3: ] ] [Figure A.2: 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 \mum. 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. ] ] Aluminium oxide mask Jinghua Fang and Paul Spizzirri 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\mum 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 [LaTeX Command: nomenclature] analysis. Figure [fig:Aluminium-oxide-mask] 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\mum 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 [fig:Al - An-end-on-view,] . 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. 1^{\circ}. Figure [fig:Aluminium-oxide-mask-result] 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. [float Figure: [float Figure: [Sub-Figure A.2.1: An end-on view, showing some pores (not all the circles are drawn), ion tracks (blue) and energy depositions (yellow). ] ] [float Figure: [Sub-Figure A.2.2: 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. ] ] [Figure A.3: Aluminium oxide mask simulation screenshots. ] ] [float Figure: [Figure A.4: The distribution of a low-energy phosphorus beam after transmission through a porous aluminium oxide mask rotated by 0.1^{\circ} . ] ] [LaTeX Command: bibtex]