Electric dipole spin resonance is studied theoretically at a shallow donor formed in a nanowire with spin-orbit coupling in a magnetic field. Such system may represent a donor-based qubit. The single discrete energy level of the donor is accompanied by the set of continuum states, which provide a non-trivial interplay for the picture of electric dipole spin resonance driven by an external monochromatic field. Strongly nonlinear dependencies of spin flip time as well as of the coordinate mean values on the electric field amplitude are observed, demonstrating the significance of coupling to the continuum for spin-based qubits manipulation in nanostructures.
Defects in crystals are leading candidates for photon-based quantum technologies, but progress in developing practical devices critically depends on improving defect optical and spin properties. Motivated by this need, we study a new defect qubit candidate, the shallow donor in ZnO. We demonstrate all-optical control of the electron spin state of the donor qubits and measure the spin coherence properties. We find a longitudinal relaxation time T$_1$ exceeding 100 ms, an inhomogeneous dephasing time T$_2^*$ of $17\pm2$ ns, and a Hahn spin-echo time T$_2$ of $50\pm13$ $μ$s. The magnitude of T$_2…
Electronic and nuclear spins of shallow donors in Silicon are attractive candidates for qubits in quantum computer proposals. Shallow donor exchange gates are frequently invoked to preform two-qubit operations in such proposals. We study shallow donor electron properties in Si within the Kohn-Luttinger envelope function approach, incorporating the full Bloch states of the six band edges of Si conduction band, obtained from {\it ab initio} calculations within the density-functional and pseudopotential frameworks. Inter-valley interference between the conduction-band-edge states of Si leads to o…
We present a complete theoretical treatment of Stark effects in doped silicon, whose predictions are supported by experimental measurements. A multi-valley effective mass theory, dealing non-perturbatively with valley-orbit interactions induced by a donor-dependent central cell potential, allows us to obtain a very reliable picture of the donor wave function within a relatively simple framework. Variational optimization of the 1s donor binding energies calculated with a new trial wave function, in a pseudopotential with two fitting parameters, allows an accurate match of the experimentally det…
In a recent paper Hao et al. [Phys. Rev. B 80, 035329 (2009)] reported variational calculations of energy spectrum for shallow hydrogenic donor in the structure of semiconductor/insulator/metal with a new type of trial wave function. They also performed calculations for semiconductor/insulator system and found that their method gives energy values lower than those obtained by MacMillen and Landman [Phys. Rev. B 29, 4524 (1984)]. As follows from these results MacMillen and Landman have got much larger errors in energy values than they expected. However we confirm that the theoretical approach s…
We study the low-temperature dynamics of a shallow donor, e.g., $^{31}$P, impurity electron spin in silicon, interacting with the bath of nuclear spins of the $^{29}$Si isotope. For small applied magnetic fields, the electron spin relaxation is controlled by the steady state distribution of the nuclear spins. We calculate the relaxation times $T_1$ and $T_2$ as functions of the external magnetic field, and conclude that nuclear spins play an important role in the donor electron spin decoherence in Si:P at low magnetic fields.
We carry out a detailed investigation of neutral ($D^0$) and charged ($D^-$) impurity states of hydrogen-like donors in spherical semiconductor quantum dots. The investigation is carried out within the effective mass theory (EMT). We take recourse to local density approximation (LDA) and the Harbola-Sahni (HS) schemes for treating many-body effects. We experiment with a variety of confining potentials: square, harmonic and triangular. We observe that the donor level undergoes shallow to deep transition as the dot radius ($R$) is reduced. On further reduction of the dot radius it becomes shallo…
The ground state energy and the extend of the wavefunction of a negatively charged donor (D-) located near a semiconductor-metal or a semiconductor-dielectric interface is obtained. We apply the effective mass approximation and use a variational two-electron wavefunction that takes into account the influence of all image charges that arise due to the presence of the interface, as well as the correlation between the two electrons bound to the donor. For a semiconductor-metal interface, the D- binding energy is enhanced for donor positions d>1.5a_B (a_B is the effective Bohr radius) due to the a…
Proposed silicon-based quantum-computer architectures have attracted attention because of their promise for scalability and their potential for synergetically utilizing the available resources associated with the existing Si technology infrastructure. Electronic and nuclear spins of shallow donors (e.g. phosphorus) in Si are ideally suited candidates for qubits in such proposals, where shallow donor exchange gates are frequently invoked to perform two-qubit operations. An important potential problem in this context is that intervalley interference originating from the degeneracy in the Si cond…
The binding energy of a negatively charged hydrogenic impurity with on- and off-center position in a spherical Gaussian quantum dot was calculated with the configuration interaction method. Our calculations show that $E_b$ is always positive for on-center impurities with a maximum near to the radius for one-electron stability of the potential well $R_c$. For off-center positions the binding energy can assume negative values within a range of the quantum dot radius, thus indicating the instability of the system.
Proposed silicon-based quantum-computer architectures have attracted attention because of their promise for scalability and their potential for synergetically utilizing the available resources associated with the existing Si technology infrastructure. Electronic and nuclear spins of shallow donors (e.g. phosphorus) in Si are ideal candidates for qubits in such proposals because of their long spin coherence times due to their limited interactions with their environments. For these spin qubits, shallow donor exchange gates are frequently invoked to perform two-qubit operations. We discuss in thi…
Germanium is a widely used material for electronic and optoelectronic devices and recently it has become an important material for spintronics and quantum computing applications. Donor spins in silicon have been shown to support very long coherence times ($T_{2}$) when the host material is isotopically enriched to remove any magnetic nuclei. Germanium also has non-magnetic isotopes so it is expected to support long $T_{2}$s while offering some new properties. Compared to Si, Ge has a strong spin-orbit coupling, large electron wavefunction, high mobility, and highly anisotropic conduction band …
In this work we investigate electron-impurity binding energy in GaN/HfO$_2$ quantum wells. The calculation considers simultaneously all energy contributions caused by the dielectric mismatch: (i) image self-energy (i.e., interaction between electron and its image charge), (ii) the direct Coulomb interaction between the electron-impurity and (iii) the interactions among electron and impurity image charges. The theoretical model account for the solution of the time-dependent Schrödinger equation and the results shows how the magnitude of the electron-impurity binding energy depends on the positi…
Density functional theory calculations are used to show that it is possible to dope semiconducting transition metal dichalcogenides (TMD) such as MoS$_2$ and WS$_2$ with electrons and/or holes either by chemical substitution or by adsorption on the sulfur layer. Notably, the activation energies of Lithium and Phosphorus, a shallow donor and a shallow acceptor, respectively, are smaller than 0.1 eV. Substitutional halogens are also proposed as alternative donors adequate for different temperature regimes. All dopants proposed result in very little lattice relaxation and, hence, are expected to …
Selenium impurities in silicon are deep double donors and their optical and electronic properties have been recently investigated due to their application for infrared detection. However, a singly-ionised selenium donor (Se$^{+}$) possesses an electron spin which makes it a potential candidate as a silicon-based spin qubit, with significant potential advantages compared to the more commonly studied group V donors. Here we study the electron spin relaxation ($T_1$) and coherence ($T_2$) times of Se$^{+}$ in isotopically purified 28-silicon, and find them to be up to two orders of magnitude long…
Donor states in Si nanodevices can be strongly modified by nearby insulating barriers and metallic gates. We report here experimental results indicating a strong reduction in the charging energy of isolated As dopants in Si FinFETs relative to the bulk value. By studying the problem of two electrons bound to a shallow donor within the effective mass approach, we find that the measured small charging energy may be due to a combined effect of the insulator screening and the proximity of metallic gates.
We have studied the properties of Si, Ge shallow donors and Fe, Mg deep acceptors in $β$-Ga2O3 through temperature dependent van der Pauw and Hall effect measurements of samples grown by a variety of methods, including edge-defined film-fed (EFG), Czochralski (CZ), molecular beam epitaxy (MBE), and low pressure chemical vapor deposition (LPCVD). Through simultaneous, self-consistent fitting of the temperature dependent carrier density and mobility, we are able to accurately estimate the donor energy of Si and Ge to be 30 meV in $β$-Ga2O3. Additionally, we show that our measured Hall effect dat…
We have investigated the conductance of long quantum wires formed in GaAs/AlGaAs heterostructures. Using realistic fluctuation potentials from donor layers we have simulated numerically the conductance of four different kinds of wires. While ideal wires show perfect quantization, potential fluctuations from random donors may give rise to strong conductance oscillations and degradation of the quantization plateaux. Statistically there is always the possibility of having large fluctuations in a sample that may effectively act as a microconstriction. We therefore introduce microconstrictions in t…
Silicon-based quantum-computer architectures have attracted attention because of their promise for scalability and their potential for synergetically utilizing the available resources associated with the existing Si technology infrastructure. Electronic and nuclear spins of shallow donors (e.g. phosphorus) in Si are ideal candidates for qubits in such proposals due to the relatively long spin coherence times. For these spin qubits, donor electron charge manipulation by external gates is a key ingredient for control and read-out of single-qubit operations, while shallow donor exchange gates are…
We investigate theoretically donor-based charge qubit operation driven by external electric fields. The basic physics of the problem is presented by considering a single electron bound to a shallow-donor pair in GaAs: This system is closely related to the homopolar molecular ion H_2^+. In the case of Si, heteropolar configurations such as PSb^+ pairs are also considered. For both homopolar and heteropolar pairs, the multivalley conduction band structure of Si leads to short-period oscillations of the tunnel-coupling strength as a function of the inter-donor relative position. However, for any …
We measure a large valley-orbit splitting for shallow isolated phosphorus donors in a silicon gated nanowire. This splitting is close to the bulk value and well above previous reports in silicon nanostructures. It was determined using a double dopant transport spectroscopy which eliminates artifacts induced by the environment. Quantitative simulations taking into account the position of the donors with respect to the Si/SiO$_2$ interface and electric field in the wire show that the values found are consistent with the device geometry.
We study spin polarization in a split-gate quantum wire focussing on the effect of a realistic smooth potential due to remote donors. Electron interaction and spin effects are included within the density functional theory in the local spin density approximation. We find that depending on the electron density, the spin polarization exhibits qualitatively different features. For the case of relatively high electron density, when the Fermi energy $E_{F}$ exceeds a characteristic strength of a long-range impurity potential $V_{donors}$, the density spin polarization inside the wire is practically …
We analyze the valley composition of one electron bound to a shallow donor close to a Si/barrier interface as a function of an applied electric field. A full six-valley effective mass model Hamiltonian is adopted. For low fields, the electron ground state is essentially confined at the donor. At high fields the ground state is such that the electron is drawn to the interface, leaving the donor practically ionized. Valley splitting at the interface occurs due to the valley-orbit coupling, V_vo^I = |V_vo^I| e^{i theta}. At intermediate electric fields, close to a characteristic shuttling field, …
We report on a dynamic photoconductive gain effect in quantum wires which are lithographically fabricated in an AlGaAs/GaAs quantum well via a shallow-etch technique. The effect allows resolving the one-dimensional subbands of the quantum wires as maxima in the photoresponse across the quantum wires. We interpret the results by optically induced holes in the valence band of the quantum well which shift the chemical potential of the quantum wire. The non-linear current-voltage characteristics of the quantum wires also allow detecting the photoresponse effect of excess charge carriers in the con…
Atomically precise placement of dopants in Si permits creating substitutional P nanowires by design. High-resolution images show that these wires are few atoms wide with some positioning disorder with respect to the substitutional Si structure sites. Disorder is expected to lead to electronic localization in one-dimensional (1D) - like structures. Experiments, however, report good transport properties in quasi-1D P nanoribbons. We investigate theoretically their electronic properties using an effective single-particle approach based on a linear combination of donor orbitals (LCDO), with a basi…
A dipolar gate alternative to the exchange gate based Kane quantum computer is proposed where the qubits are electron spins of shallow group V donors in silicon. Residual exchange coupling is treated as gate error amenable to quantum error correction, removing the stringent requirements on donor positioning characteristic of all silicon exchange-based implementations [B. Koiller et al., Phys. Rev. Lett. 88, 027903 (2002)]. Contrary to common speculation, such a scheme is scalable with no overhead in gating time even though it is based on long-range dipolar inter-qubit coupling.
This work studies the effect of temperature on the binding energy of a shallow hydrogenic impurity located on the axis of a cylindrical semiconductor GaAs Al_x Ga_{1-x} As quantum well wire. The results show that the binding energy at a low temperature of 100 K is increased by about 11% over that associated with nearly room temperature, $300 K$, and is also increased by about 23% over that associated with temperature of 500 K.
A doping series of AlAs (001) quantum wells with Si delta-modulation doping on both sides reveals different dark and post-illumination saturation densities, as well as temperature dependent photoconductivity. The lower dark two-dimensional electron density saturation is explained assuming deep binding energy of Delta_DK = 65.2 meV for Si-donors in the dark. Persistent photoconductivity (PPC) is observed upon illumination, with higher saturation density indicating shallow post-illumination donor binding energy. The photoconductivity is thermally activated, with 4 K illumination requiring post-i…
Radio-frequency dispersive read-out can provide a useful probe to nano-scale structures such as nano-wire devices, especially when the implementation of charge sensing is not straightforward. Here we demonstrate dispersive `gate-only' read-out of phosphor donors in a silicon nano-scale transistor. The technique enables access to states that are only tunnel-coupled to one contact, which is not easily achievable by other methods. This allows us to locate individual randomly placed donors in the device channel. Furthermore, the setup is naturally compatible with high bandwidth access to the probe…
We present a unified approach for calculating the properties of shallow donors inside or outside heterostructure quantum wells. The method allows us to obtain not only the binding energies of all localized states of any symmetry, but also the energy width of the resonant states which may appear when a localized state becomes degenerate with the continuous quantum well subbands. The approach is non-variational, and we are therefore also able to evaluate the wave functions. This is used to calculate the optical absorption spectrum, which is strongly non-isotropic due to the selection rules. The …
We propose qubits based on shallow donor electron spins in germanium. Spin-orbit interaction for donor spins in germanium is in many orders of magnitude stronger than in silicon. In a uniform bulk material it leads to very short spin lifetimes. However the lifetime increases dramatically when the donor is placed into a quasi-2D phononic crystal and the energy of the Zeeman splitting is tuned to lie within a phonon bandgap. In this situation single phonon processes are suppressed by energy conservation. The remaining two-phonon decay channel is very slow. The Zeeman splitting within the gap can…
Electrical detection of spins is an essential tool in understanding the dynamics of spins in semiconductor devices, providing valuable insights for applications ranging from optoelectronics and spintronics to quantum information processing. For electron spins bound to shallow donors in silicon, bulk electrically-detected magnetic resonance has relied on coupling to spin readout partners such as paramagnetic defects or conduction electrons which fundamentally limits spin coherence times. Here we demonstrate electrical detection of phosphorus donor electron spin resonance by transport through a …
We report the results of an experiment investigating coherence and correlation effects in a system of coupled donors. Two donors are strongly coupled to two leads in a parallel configuration within a nano-wire field effect transistor. By applying a magnetic field we observe interference between two donor-induced Kondo channels, which depends on the Aharonov-Bohm phase picked up by electrons traversing the structure. This results in a non-monotonic conductance as a function of magnetic field and clearly demonstrates that donors can be coupled through a many-body state in a coherent manner. We p…
Impurity spins in crystal matrices are promising components in quantum technologies, particularly if they can maintain their spin properties when close to surfaces and material interfaces. Here, we investigate an attractive candidate for microwave-domain applications, the spins of group-VI Impurity spins in crystal matrices are promising components in quantum technologies, particularly if they can maintain their spin properties when close to surfaces and material interfaces. Here, we investigate an attractive candidate for microwave-domain applications, the spins of group-VI $^{125}$Te$^+$ don…
Control of hyperfine interactions is a fundamental requirement for quantum computing architecture schemes based on shallow donors in silicon. However, at present, there is lacking an atomistic approach including critical effects of central-cell corrections and non-static screening of the donor potential capable of describing the hyperfine interaction in the presence of both strain and electric fields in realistically sized devices. We establish and apply a theoretical framework, based on atomistic tight-binding theory, to quantitatively determine the strain and electric field dependent hyperfi…
We consider charge qubits based on shallow donor electron states in silicon and coupled quantum dots in GaAs. Specifically, we study the feasibility of P$_2^+$ charge qubits in Si, focusing on single qubit properties in terms of tunnel coupling between the two phosphorus donors and qubit decoherence caused by electron-phonon interaction. By taking into consideration the multi-valley structure of the Si conduction band, we show that inter-valley quantum interference has important consequences for single-qubit operations of P$_2^+$ charge qubits. In particular, the valley interference leads to a…
Semiconductor devices continue to press into the nanoscale regime, and new applications have emerged for which the quantum properties of dopant atoms act as the functional part of the device, underscoring the necessity to probe the quantum structure of small numbers of dopant atoms in semiconductors[1-3]. Although dopant properties are well-understood with respect to bulk semiconductors, new questions arise in nanosystems. For example, the quantum energy levels of dopants will be affected by the proximity of nanometer-scale electrodes. Moreover, because shallow donors and acceptors are analogo…
We report on a photoconductive gain in semiconductor quantum wires which are lithographically defined in an AlGaAs/GaAs quantum well via a shallow-etch technique. The effect allows resolving the one-dimensional subbands of the quantum wires as maxima in the photoresponse across the quantum wires. We interpret the results by optically induced holes in the valence band of the quantum well which shift the one-dimensional subbands of the quantum wire. Here we demonstrate that the effect persists up to a temperature of about 17 Kelvin.
We consider spin-lattice relaxation processes for electrons trapped in lateral Si quantum dots in a $[001]$ inversion layer. Such dots are characterized by strong confinement in the direction perpendicular to the surface and much weaker confinement in the lateral direction. The spin relaxation is assumed to be due to the modulation of electron $g$-factor by the phonon-induced strain, as was shown previously for the shallow donors. The results clearly indicate that the specific valley structure of the ground electron state in Si quantum dots causes strong anisotropy for both the one-phonon and …
The electronic conduction of a novel, three-terminal molecular architecture, analogous to a heterojunction bipolar transistor is studied. In this architecture, two diode arms consisting of donor-acceptor molecular wires fuse through a ring, while a gate modulating wire is a π-conjugated wire. The calculated results show the enhancement or depletion mode of a transistor by applying a gate field along the positive or negative direction. A small gate field is required to switch on the current in the proposed architecture. The changes in the electronic conduction can be attributed to the intrinsic…
We calculate the electronic structure for a modulation doped and gated T-shaped quantum wire using density functional theory. We calculate the bandgap renormalization as a function of the density of conduction band electrons, induced by the donor layer and/or the gate, for the translationally invariant wire, incorporating all growth and geometric properties of the structure completely. We show that most of the bandgap renormalization arises from exchange-correlation effects, but that a small shift also results from the difference of wave function evolution between electrons and holes. We calcu…
We study the structural, optical, and transport properties of sidewall quantum wires on GaAs(001) substrates. The QWRs are grown by molecular beam epitaxy (MBE) on GaAs(001) substrates prepatterned with shallow ridges. They form as a consequence of material accumulation on the sidewalls of the ridges during the overgrowth of a quantum well (QW) on the patterned surface. The QWRs are approximately 200 nm-wide and have emission energies red-shifted by 27meV with respect to the surrounding QW. Spatially resolved spectroscopic photoluminencence studies indicate that the QW thickness reduces around…
A novel breakdown (BD) mechanism of shallow impurity under the electric field at low temperatures is suggested for n-GaAs samples with the donor concentrations $N_D=10^{14} ÷10^{16}cm^{-3}$ and the compensation degree $K=\frac{N_A}{N_D}=0.3 ÷0.8$ with acceptors of concentration N_A in the external magnetic fields up to H=6.5~T. Diagnosis of the BD mechanism was performed by SI Zeeman and cyclotron resonance photoelectric spectroscopy methods in the wide interval of the electric field including the BD region too. The obtained results reveal that the BD electric field $\mathcal{E}_{BD}$ does not…
A shallow potential well in a near-perfect quantum wire will bind a single-electron and behave like a quantum dot, giving rise to spin-dependent resonances of propagating electrons due to Coulomb repulsion and Pauli blocking. It is shown how this may be used to generate full entanglement between static and flying spin-qubits near resonance in a two-electron system via singlet or triplet spin-filtering. In a quantum wire with many electrons, the same pairwise scattering may be used to explain conductance, thermopower and shot-noise anomalies, provided the temperature/energy scale is sufficientl…
We report on electron spin resonance (ESR) measurements of phosphorus donors localized in a 200 square micron area below the inductive wire of a lumped element superconducting resonator. By combining quantum limited parametric amplification with a low impedance microwave resonator design we are able to detect around 20000 spins with a signal-to-noise ratio (SNR) of 1 in a single shot. The 150 Hz coupling strength between the resonator field and individual spins is significantly larger than the 1 - 10 Hz coupling rates obtained with typical coplanar waveguide resonator designs. Due to the large…
