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(2022)ThesisIn this thesis we investigate donor molecules as a resource for scaling-up donor-based spin qubits in silicon towards error-corrected quantum computers. We first propose a novel donor-based qubit consisting of an electron spin spread across a single donor (1P) and a two-donor molecule (2P) that is electrically driven and coupled utilising the hyperfine interaction. This qubit belongs to a class of electron spin qubits called “flopping-mode” qubits, where the electron wave function is spread over two quantum dots. Using a complete error model, we first investigate how to minimise errors and the electrical driving power in the general class of qubits by optimising the magnetic gradients across the device. We then demonstrate how the magnetic gradient on the new qubit design can be atomically engineered using the hyperfine interaction within the donor molecules. In particular we show that by controlling the orientation of the nuclear spins in the qubit we can suppress the deleterious magnetic gradient originating from the hyperfine interaction within the two-donor molecule. We predict qubit errors well below 10−3 and show that the 1P-2P flopping-mode qubit can be strongly coupled to a superconducting cavity. Finally, we outline a way to scale the proposed qubits to a larger cavity-based architecture. Following this theoretical proposal we present experimental evidence that the required engineering of 2P donor-molecules is possible, using two atomic precision devices fabricated with hydrogen-resist STM lithography. We achieve high accuracy precision patterning of two different devices that contain donor molecules to reveal the following results. First we show how to improve the fidelity of single shot electron spin readout from 83% to 94% using an optimised SET design. ESR spectra performed using adiabatic spin inversion yield precise measurements of the hyperfine interactions within the molecule. Using atomistic tight binding calculations in collaboration with the group of Professor Rahman we were able to perform metrology of the individual donor configurations within the dots. The metrology could be performed with a precision of ±0.25nm using measurements of the charging energies and improved to atomic precision using the hyperfine spectroscopy. The ESR spectra demonstrated the first observation of a Stark shift in a tightly bound donor molecule. The magnitude of the shift observed was shown to depend on the molecular orientation within the crystal and offers future strategies for hyperfine engineering for optimal qubit operation. Finally, we demonstrate the first nuclear-spin readout of a tightly-bound donor molecule, with a fidelity of 88%, and show how we can track the nuclear spin states over time. Using a hidden Markov model we extracted the nuclear transition frequencies and uncover possible evidence of a dipolar coupling between the nuclear spins.
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(2022)ThesisIn this thesis we assess the design and optimisation of critical device requirements for the realisation of three qubit parity error detection in donor spin qubits in silicon. Three key results are presented: (i) the capacitative modelling and design of triple donor dot architectures needed to realise a parity device, highlighting the need for multi-donor quantum dots (ii) optimisation of the geometry of the donor charge sensor and noise levels required for reproducible high fidelity spin readout, and (iii) understanding how the configurations of the additional donor nuclear spins in these multi-donor dots impact the electron spin resonance (ESR) spectra observed and how this will affect the operation of the parity measurement. Using electrostatic simulations of the different device geometries we show that either a 1P-2P-1P or 1P-3P-1P configuration of donors in each of the individual quantum dots is needed to achieve the required (1,1)↔(2,0) equivalent interdot charge transitions with the available gate space. Using such a higher donor number ancilla qubit, we then compared the sequence of logical gates required to perform the parity measurement using single qubit rotations and different 2-qubit gates. This analysis highlighted the need for isotopically pure silicon-28 to maintain coherence within the time frame of the measurement and stable, high fidelity single shot spin read-out. We then conducted a series of experiments of how to achieve stable, high fidelity single shot spin read out in our triple dot devices. It is known that read-out fidelity is improved by increasing the signal to noise of the charge sensor and by reducing the electron temperature. As such we investigated two triple dot device designs to investigate the interplay between these two requirements. The first design had the donor dots tunnel coupled to the single electron transistor (SET) charge sensor and the second had the donor dots capacitively coupled to an independent reservoir 50nm away from the SET charge sensor. We showed that under high bias of the SET (1mV) where we achieve a good signal to noise (1nA) of the charge sensor, electron-electron interactions within the tunnel coupled SET lead to heating of the qubits (680mK) compared with the independent reservoir qubits (170mK). Ultimately we showed that this heating limits spin read-out fidelities at high power where the signal to noise of the charge sensor is greatest. We simulated the spin readout fidelity for both designs and found the independent reservoir parity design can achieve above 99% fidelities over a greater range of SET resistances (up to 10MΩ) and tunnel rates (up to 100kHz), whereas the tunnel coupled design is limited to ≈100kΩ SET resistances with tunnel rates below 100Hz. i To further investigate the reproducibility of our SET charge sensors we then investigated the optimal tunnel barrier dimensions in a series of STM-patterned devices to achieve high fidelity single shot spin read-out. We found a simple width dependent exponential model describes the optimal tunnel barrier lengths for different lead widths. For tunnel barriers with 6±0.5nm lead widths, tunnel gap lengths of 11±0.5nm were found to give reliable SET resistances of 100KΩ optimal for providing good S/N. We then measured the charge noise in several SET devices and found that charge noise is correlated with high (> 350W) powers on the SUSI cell giving rise to an increase in pressure in the growth chamber (> 1×10−10mbar). We investigated the impact of charge noise on the ability to perform high fidelity spin readout and determined a noise threshold limit (0.03meV2) to achieve fidelities above 99%. In the final chapter we integrated an antenna on a triple dot device aiming for a 1,3,1 donor dot configuration. Using a detailed analysis of STM image height profiles, charging energies from gate-gate maps, capacitance triangulation and T1 measurements we determined that the final donor number was 0,3,2 indicating that no donor had incorporated in the lefthand dot. Despite this we were able to perform single shot spin read-out of the middle (≈92%) and right dots (92%) and confirmed the donor number of the right dot to be a 2P donor molecule using ESR resonance spectrum. We measured different hyperfine couplings of A1 = 189MHz and A2 = 83MHz to each of the donors within the dot, which under different slightly electric fields of 3.2MV/m and 3.8MV/m gave rise to a Stark shift of 41±31MHz/(MV/m). Using the ESR spectra, Stark shift measurements and tight binding simulations of the donor hyperfine Hamiltonian we are able to locate the exact configuration of the phosphorus atoms within the 2P donor molecule with the second donor being [0.5 1.5 0]a0 from the first donor. From these results we identified that a (3,2) donor configuration for the ancilla/data qubit does provide an equivalent (1,1) ↔ (2,0) interdot charge transitions with the available gate space. We then present a detailed outlook, with specific device recommendations as to how to achieve the parity measurement in donor qubits going forward.
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(2022)ThesisIn this thesis we investigate quantum tunnelling of electrons in nanoscale tunnel junctions made from STM-patterned highly phosphorus doped silicon monolayers. Whilst the devices are monolayer doped, they are encapsulated in epitaxial silicon to form atomically abrupt 3D crystalline junctions that have multiple use cases in the manipulation of spin states in silicon for quantum information. First we investigate how to control the tunnelling resistance in these simple junctions by precision engineering of the junction length with STM lithography. By patterning the hydrogen resist with the tunnel junction edges along a dimer row in the [-110] crystalline direction we achieved a lithography accuracy of ±0.38nm. This precision patterning allowed us to increase the reproducibility of tunnel junction resistances to within 5% and demonstrate the exponential scaling of tunnelling resistance with junction length L. Second we investigated the tunnelling resistance as a function of lead width. By precision patterning the hydrogen resist along the dimer row in the [110] crystalline direction we reduced the lithographic accuracy of the junction length to ±0.77nm but increased the accuracy of the lead width to ±0.38nm. We observed a four order of magnitude change in the resistance of a 15nm long junction as the lead width changed from 7 to 15nm. To understand this variability, we conducted atomistic NEMO calculations and showed that the density of the states in these heavily phosphorus doped silicon wires is very sensitive to lead width. For thinner leads, where the width, W is <7nm the variability in the density of states is 0.7x108 meV-1 compared to 3.0x108 meV-1 at W~15nm. By plotting the resistances of all junctions as a function of lead width we observed an unexpected four order-of-magnitude change in the tunnelling resistance at W∼10 nm. Whilst this this could not be understood using current modelling, we speculate that it is related to size effects of the junction where the width of the leads matches the electron mean free path. We developed two unique atomic precision patterning techniques to realise 3D epitaxial gating. The first used kinetic growth manipulation to reduce the thermal budget during growth to minimise phosphorus diffusion to 0.66nm whilst achieving surfaces with 20nm2 island sizes, suitable for precision STM lithography. The second was to use the topographic height differential of the surface between STM-patterned doped surfaces and those with no underlying phosphorus atoms. Here despite ~100nm epitaxial silicon growth it was possible to observe a 0.4nm height differential. Using these two new techniques we were able to pattern 30nm wide vertically separated 3D epitaxial gates directly above tunnel junctions of size 9nm(W) x 17nm (L) and 9nm(W) x 30nm (L) with ±5nm accuracy. For the short junction we demonstrated strong capacitive coupling (a~0.36) – three times higher than for in-plane gates and showed we could tune the tunnel junction from 0.1 MOhm to 3.1 MOhm changing the barrier height from ∼0meV to 186 meV. Since the gate was more than three times narrower than previous 3D epitaxial gates, we were able to integrate two independent gates above two tunnel junctions in series within a single device. Using this device we demonstrated classical logic with an on/off ratio of ∼1000-2000. Finally we investigated the control of single electron tunnelling between a donor quantum dot qubit and an electron reservoir using a 3D epitaxial gate. We demonstrated that the tunnel rate Γ of electrons between the qubit and reservoir can be tuned from 5Hz to 10kHz which is notable since in-plane gates have not been shown to date to tune tunnel rates. This therefore represents a new capability in Si:P quantum computing devices. We discuss how future optimisation of device design will allow control of electron tunnelling for high fidelity qubit readout and controllable exchange coupling.