Infrared photoionization and intracenter cross sections as well as oscillator strengths of intracenter transitions in silicon doped with single -electron, shallow donors are determined in research -grade crystals and compared with the corresponding values calculated by various theoretical models. The float -zone grown crystals were doped with substitutional group -V, interstitial group IA lithium and lithium -oxygen complex at concentrations of 10 12 -10 17 atoms / cm 3 . The concentrations of electrically active impurity centers in the samples were determined from resistivity measurements. Experimentally integrated cross sections were obtained from low -temperature absorption spectra of impurities. For an isocoric substitutional donor, the oscillator strengths for intracenter transitions into the lowest odd -parity states were compared for two main crystal growth and doping methods: the float -zone and the Czochralski techniques. The applicability of the obtained calibration coefficients for various ranges of impurity concentrations is discussed. Recommendations are given for the optimal selection of optical transitions for quantifying the density of shallow donors in silicon along with experimental values for each shallow center. The oscillator strengths of transitions of shallow impurities were estimated for almost all observed donor transitions, including those into high excited, Rydberg -like atomic states, as well as for the intracenter transitions into several even -parity excited states.

The lithium donor centers in Si 1– x Ge x ( x = 0.0039–0.05) single crystals enriched in spinless 28 Si and 72 Ge isotopes (99.998 and 99.984%, respectively) are studied by electron spin resonance at temperatures of T = 3.5–30 K and compared with its behavior in Si crystals. It is shown that lithium center with trigonal ([111]) symmetry has a most stable configuration in bulk Si 1– x Ge x for different values of x < 5 at %. Axial symmetry is explained by the distortion of the lithium central position and their neighboring atoms. The spin relaxation rates were studied in temperature range 4–30 K and it was shown that transverse and longitudinal relaxation consist of two components with rates differ by almost an order of magnitude. Together with Raman processes for 1/T 1 , a decrease in the exponent below T 5 is observed. This behavior is explained by cross-relaxation through states of the distorted configuration of lithium, which arise due to modulation of the crystal field potential by random distribution of Ge atoms.

The solubility of impurity magnesium, which was introduced by diffusion in the temperature range of 1100-1300oC in silicon, is studied by secondary-ion mass spectrometry. It is demonstrated that, with the electrically inactive impurity component taken into account, the maximum solubility of magnesium in silicon is 1-2 orders of magnitude lower (and the diffusion coefficient is higher) than the values reported earlier. Keywords: silicon, doping, magnesium impurity, solubility.

The lithium donor centers in Si1–xGex (x = 0.0039–0.05) single crystals enriched in spinless 28Si and 72Ge isotopes (99.998 and 99.984

Experimental results on the observation of terahertz luminescence under optical excitation of silicon doped with neutral helium-like magnesium donors under photoionization conditions under uniaxial stress are presented. Possible options for creating stimulated radiation sources based on Si:Mg under optical excitation are considered. The possibility of obtaining inversion at the lowest odd level and significant gain coefficients is difficult due to the rather short relaxation time of the 2p0 level. The possibility of using an alternative inversion mechanism presupposes knowledge of relaxation routes. The mechanism of stimulated Raman scattering is theoretically considered and it is shown that terahertz stimulated radiation with optical excitation of double magnesium donors in silicon can be achieved using the mechanism of electronic-type Raman scattering.

The results of observation of Ramsey oscillations in germanium doped with arsenic donors detected by photothermal ionization of Coulomb centers are presented. To excite quantum coherent superpositions of the states at the transition 1 s (A 1 )–2 p 0 the Novosibirsk free electron laser radiation was used. The results are analyzed using a theoretical model using several key parameters of the experiment.

We measure the temperature dependence of the indirect band gap of isotopically purified ^{28}Si:P in the regime from 0.1 K to 3 K by high-resolution absorption spectroscopy of the donor bound exciton transition. The measurements increase the up-to-date precision of the temperature-dependent band gap change by more than one order of magnitude and reveal a T^{4} dependence which is about a factor of two less than observed in previous measurements. Such a T^{4} dependence is predicted by theory, but the absolute values differ between our experiment and the most up-to-date calculations by a factor of 30, corroborating that the electron-phonon interaction at low temperatures is still not correctly included into theory. What is more, the ability of such very high-precision band-gap measurements facilitates the use of time- and spatially resolved ^{28}Si:P absorption as a contactless, local thermometer and electric field sensor with a demonstrated time resolution of milliseconds.

The energy spectra of lithium-related donors in silicon are revisited by temperature-dependent infrared absorption spectroscopy. We determine the valley-orbit splitting of an interstitial isolated lithium donor and its complex with residual oxygen in float-zone grown crystals doped from the melt. Lithium-oxygen donors exhibit a temperature evolution of their absorption spectra similar to that of substitutional single-electron group-V donors, while its valley-orbit splitting is corrected upwards to +9.865(5) meV. For the lithium donor, the previously reported inverted valley-orbit splitting is not confirmed since the components of different symmetry are not spectrally resolved in our study. Instead, the chemical shift of the ground state of the donor, having a symmetry different from that of group-V donors, was corrected to a slightly larger value of 1.82(2) meV. Intracenter transitions from the split-off ground state of the Li donor exhibit an anomalous broadening. In addition, several Rydberg-like high excited states, up to 7h +/-, of lithium-related centers were determined from absorption spectra of moderately doped samples.

The performance of modular, networked quantum technologies will be strongly dependent upon the quality of their quantum light-matter interconnects. Solid-state colour centres, and in particular T centres in silicon, offer competitive technological and commercial advantages as the basis for quantum networking technologies and distributed quantum computing. These newly rediscovered silicon defects offer direct telecommunications-band photonic emission, long-lived electron and nuclear spin qubits, and proven native integration into industry-standard, CMOS-compatible, silicon-on-insulator (SOI) photonic chips at scale. Here we demonstrate further levels of integration by characterizing T centre spin ensembles in single-mode waveguides in SOI. In addition to measuring long spin T1 times, we report on the integrated centres' optical properties. We find that the narrow homogeneous linewidth of these waveguide-integrated emitters is already sufficiently low to predict the future success of remote spin-entangling protocols with only modest cavity Purcell enhancements. We show that further improvements may still be possible by measuring nearly lifetime-limited homogeneous linewidths in isotopically pure bulk crystals. In each case the measured linewidths are more than an order of magnitude lower than previously reported and further support the view that high-performance, large-scale distributed quantum technologies based upon T centres in silicon may be attainable in the near term.

Different defects in silicon crystals cause lattice distortion that may violate selection rules for certain intracenter optical transitions of hydrogen-like donor centers. Perturbations due to large concentration of substitutional donors enhance all parity-forbidden atomic transitions, but cause large concentration broadening of the transition lines, prohibiting observation of transitions at close energies. Substitutional residual carbon atoms in silicon induce, in contrast, a weak-to-moderate broadening of donor absorption lines enabling the resolution of some parity-forbidden intracenter transitions in impurity absorption spectra at moderate donor densities. Binding energies of several series of s- and d-type states were obtained by resolving of intracenter transitions terminating in these states, by low-temperature infrared absorption spectroscopy in carbon-rich and/or heavily doped silicon crystals.

Achieving high-fidelity entangling operations between qubits consistently is essential for the performance of multi-qubit systems and is a crucial factor in achieving fault-tolerant quantum processors. Solid-state platforms are particularly exposed to errors due to materials-induced variability between qubits, which leads to performance inconsistencies. Here we study the errors in a spin qubit processor, tying them to their physical origins. We leverage this knowledge to demonstrate consistent and repeatable operation with above 99% fidelity of two-qubit gates in the technologically important silicon metal-oxide-semiconductor (SiMOS) quantum dot platform. We undertake a detailed study of these operations by analysing the physical errors and fidelities in multiple devices through numerous trials and extended periods to ensure that we capture the variation and the most common error types. Physical error sources include the slow nuclear and electrical noise on single qubits and contextual noise. The identification of the noise sources can be used to maintain performance within tolerance as well as inform future device fabrication. Furthermore, we investigate the impact of qubit design, feedback systems, and robust gates on implementing scalable, high-fidelity control strategies. These results are achieved by using three different characterization methods, we measure entangling gate fidelities ranging from 96.8% to 99.8%. Our analysis tools identify the causes of qubit degradation and offer ways understand their physical mechanisms. These results highlight both the capabilities and challenges for the scaling up of silicon spin-based qubits into full-scale quantum processors.

The temperature dependence of the thermal conductivity (T) of single crystals isotopically enriched 70Ge (99.926%), 72Ge (99.980%), 74Ge (99.921%) has been measured in the temperature range 80–310K. In the studied temperature range, the thermal conductivity is determined by anharmonic processes of phonon scattering; a decrease in the thermal conductivity with increasing mass of the germanium isotope is experimentally observed.

Single-crystal 70Ge germanium with high isotopic and chemical purity has been prepared by a hydride method. Germanium isotopes have been separated by centrifugation with the use of monogermane as a starting volatile substance. Isotopically enriched polycrystalline 70Ge has been prepared by pyrolyzing 70GeH4 monogermane. A 70Ge single crystal has been grown by the Czochralski technique. The resultant material has p-type conductivity and intrinsic resistivity at room temperature. The concentration of elemental impurities is under 10–6 to 10–5 wt %. The isotopic purity of the 70Ge single crystal is 99.926 at % and it contains a record low concentration of the odd isotope 73Ge: 0.00007 at %.

A new mechanism for the excitation of impurity related terahertz radiation in semiconductors under the conditions of exciton condensation into an electron–hole liquid is reported. The interaction of impurity centers with plasmons localized on droplets of an electron–hole liquid produces ionization of the centers. The subsequent capture of nonequilibrium charge carriers by ionized impurities is followed by terahertz intracenter radiative transitions. In these processes, impurity centers play the role of antennas that convert the near electromagnetic field of plasmons on droplets of an electron–hole liquid into detected radiation. The main experiments were carried out on lithium-doped silicon crystals at helium temperatures under conditions of interband photoexcitation. A theoretical model of the excitation of impurity centers by localized plasmons is developed, which explains the main regularities observed in the experiment.

Silicon doped with boron is the most widely used material in modern microelectronic devices based on p-Si. Therefore, it is important to thoroughly understand boron’s role in the processes of defect-impurity interaction in Si both on growing the material and during operation of devices. In this work, interactions of boron with oxygen in Si are investigated by studying boron absorption intracenter transitions, which are known to be highly sensitive to the local environment. In boron-doped Si, two lines with maxima at 228 and 261.3 cm−1 were detected. The linear dependence of lines intensity on boron concentration and the quadratic on oxygen content testifies that the defect responsible for the lines can be identified as BsO2i. The observed absorption lines correspond to the transitions from the ground to the excited states of boron, which are shifted toward lower frequencies relative to the main transitions due to a deformation perturbation from neighboring oxygen atoms. The activation energy of annealing and ionization energy of defect are determined. The properties of the registered ВsO2i defect differ from the known ВsO2 associated with the light-induced degradation of solar cells by local configuration. The data obtained testify that the ВsO2i defects with different properties can be formed in Si and must be taken into account when developing Si:B-based devices because they can play an important role in charge carrier transfer and affect the electrical and optical parameters of the material.

Методом масс-спектроскопии вторичных ионов исследована растворимость в кремнии примеси магния, введенного путем диффузии в интервале температур 1100-1300oС. Показано, что с учетом электрически неактивной компоненты примеси максимальная растворимость магния в кремнии на 1-2 порядка меньше, а коэффициент диффузии выше, чем опубликованные ранее данные. Ключевые слова: кремний, легирование, примесь магния, растворимость.

Silicon spin qubits promise to leverage the extraordinary progress in silicon nanoelectronic device fabrication over the past half century to deliver large-scale quantum processors. Despite the scalability advantage of using silicon technology, realising a quantum computer with the millions of qubits required to run some of the most demanding quantum algorithms poses several outstanding challenges, including how to control many qubits simultaneously. Recently, compact 3D microwave dielectric resonators were proposed as a way to deliver the magnetic fields for spin qubit control across an entire quantum chip using only a single microwave source. Although spin resonance of individual electrons in the globally applied microwave field was demonstrated, the spins were controlled incoherently. Here we report coherent Rabi oscillations of single electron spin qubits in a planar SiMOS quantum dot device using a global magnetic field generated off-chip. The observation of coherent qubit control driven by a dielectric resonator establishes a credible pathway to achieving large-scale control in a spin-based quantum computer.

In this paper formation and annealing of boron-related defects in p-type silicon grown by the floating zone technique and subjected to electron and proton irradiation at room temperature are discussed. The defect model suggested earlier has provided fresh insight into the nature of two dominant complexes containing boron in irradiated p-Si, among them boron-divacancy complexes and interstitial boron-substitutional boron pairs. In the present work the same material is irradiated with 6 MeV electron and 8 MeV protons providing additional electrical data to test this model. Additionally new information on boron-related defects in heavily doped p-Si subjected to irradiation with 2.5 MeV electrons at 4.2 K and then subjected to isochronal anneals above room temperature is also discussed. The results obtained on proton irradiated p-Si(FZ) testify that the annealing behavior of boron-divacancy complexes appears to be complicated, in contrast to the behavior of substitutional boron-interstitial boron pairs. The defect model based on the experimental information furnished so far may be used for testing and refining computerized simulations of Non-Ionizing Energy Loss (NIEL) in irradiated silicon. Keywords: silicon, boron impurity, electron- and proton-irradiation, impurity-related complexes.

We present a quantitative study of the efficiency of degenerate THz transient four-wave mixing in germanium doped by shallow impurities using the Dutch free electron laser FELIX. We derive the third order nonlinear sheet susceptibility and find values at low temperature that exceed those of any other material and wavelength range reported to date.

Ramsey oscillations have been observed in germanium doped with shallow impurities exposed to terahertz pulses from the NovoFEL facility involving free-electron lasers in experiments performed using the standard method with the action of a sequence of two optical pulses at the frequency close to the frequency of the 1 s ( A 1 ) → 2 p 0 impurity transition. The coherent state of the ensemble of donors has been detected by measuring the photocurrent caused by the thermal ejection of electrons from the 2 p 0 state to the conduction band. The revealed effect is quite stable under experimental conditions, in particular, to the temperature regime, which allows the further improvement in artificial systems based on shallow donors in germanium.