Temperature dependence of the band gap of 28Si:P at very low temperatures measured via time-resolved optical spectroscopy

We measure the temperature dependence of the indirect band gap of isotopically purified 28Si: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 T4 dependence which is about a factor of two less than observed in previous measurements. Such a T4 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 28Si:P absorption as a contactless, local thermometer and electric field sensor with a demonstrated time resolution of milliseconds

Low Temperature Relaxation of Donor Bound Electron Spins in 28Si:P

We measure the spin-lattice relaxation of donor bound electrons in ultrapure, isotopically enriched, phosphorus-doped 28Si:P. The optical pump-probe experiments reveal at low temperatures extremely long spin relaxation times which exceed 20 h. The 28Si:P spin relaxation rate increases linearly with temperature in the regime below 1 K and shows a distinct transition to a T9 dependence which dominates the spin relaxation between 2 and 4 K at low magnetic fields. The T7 dependence reported for natural silicon is absent. At high magnetic fields, the spin relaxation is dominated by the magnetic field dependent single phonon spin relaxation process. This process is well documented for natural silicon at finite temperatures but the 28Si:P measurements validate additionally that the bosonic phonon distribution leads at very low temperatures to a deviation from the linear temperature dependence of Γ as predicted by theory

Low Temperature Relaxation of Donor Bound Electron Spins in Si 28: P

We measure the spin-lattice relaxation of donor bound electrons in ultrapure, isotopically enriched, phosphorus-doped Si28:P. The optical pump-probe experiments reveal at low temperatures extremely long spin relaxation times which exceed 20 h. The Si28:P spin relaxation rate increases linearly with temperature in the regime below 1 K and shows a distinct transition to a T9 dependence which dominates the spin relaxation between 2 and 4 K at low magnetic fields. The T7 dependence reported for natural silicon is absent. At high magnetic fields, the spin relaxation is dominated by the magnetic field dependent single phonon spin relaxation process. This process is well documented for natural silicon at finite temperatures but the Si28:P measurements validate additionally that the bosonic phonon distribution leads at very low temperatures to a deviation from the linear temperature dependence of Γ as predicted by theory

Terahertz emission from lithium doped silicon under continuous wave interband optical excitation

We report on experimental observation and study of terahertz emission from lithium doped silicon crystals under continuous wave band-to-band optical excitation. It is shown that radiative transitions of electrons from 2P excited states of lithium donor to the 1S(A1) donor ground state prevail in the emission spectrum. The terahertz emission occurs due to capture of nonequilibrium electrons to charged donors, which in turn are generated in the crystal as a result of impurity assisted electron-hole recombination. Besides the intracentre radiative transitions the terahertz emission spectrum exhibits also features at about 12.7 and 15.27 meV, which could be related to intraexciton transitions and transitions from the continuum to the free exciton ground state

Terahertz lasers based on intracentre transitions of group V donors in uniaxially deformed silicon

This paper presents a brief overview of available experimental data on the characteristics of stimulated terahertz emission (4.9 – 6.4 THz) from optically excited neutral group V donors (phosphorus, antimony, arsenic and bismuth) in crystalline silicon subjected to uniaxial compressive strain along the [100] axis. Strain is shown to have a significant effect on the characteristics in question. Optimal strain depends on the dopant and may reduce the threshold pump intensity and improve lasing efficiency. We discuss possible mechanisms behind this effect and estimate the limiting output emission parameters

The spin-flip scattering effect in the spin transport in silicon doped with bismuth

Spin transport of conduction electrons in silicon samples doped with bismuth in the 1.1•1013 - 7.7•1015 cm-3 concentration range was studied by the Hall effect measurements. The dependence of the Hall voltage magnitude on the magnetic field is the sum of the normal and spin Hall effects. The electrons are partially polarized by an external magnetic field and are scattered by the bismuth spin-orbit potential. Spin-flip scattering results in the additional electromotive force which compensates the normal Hall effect in strong magnetic fields

Optical pumping and readout of bismuth hyperfine states in silicon for atomic clock applications

The push for a semiconductor-based quantum information technology has renewed interest in the spin states and optical transitions of shallow donors in silicon, including the donor bound exciton transitions in the near-infrared and the Rydberg, or hydrogenic, transitions in the mid-infrared. The deepest group V donor in silicon, bismuth, has a large zero-field ground state hyperfine splitting, comparable to that of rubidium, upon which the now-ubiquitous rubidium atomic clock time standard is based. Here we show that the ground state hyperfine populations of bismuth can be read out using the mid-infrared Rydberg transitions, analogous to the optical readout of the rubidium ground state populations upon which rubidium clock technology is based. We further use these transitions to demonstrate strong population pumping by resonant excitation of the bound exciton transitions, suggesting several possible approaches to a solid-state atomic clock using bismuth in silicon, or eventually in enriched 28Si

Relaxation of Coulomb States in semiconductors probed by FEL radiation

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Volumes of polytopes in spaces of constant curvature

We overview the volume calculations for polyhedra in Euclidean, spherical and hyperbolic spaces. We prove the Sforza formula for the volume of an arbitrary tetrahedron in $H^3$ and $S^3$. We also present some results, which provide a solution for Seidel problem on the volume of non-Euclidean tetrahedron. Finally, we consider a convex hyperbolic quadrilateral inscribed in a circle, horocycle or one branch of equidistant curve. This is a natural hyperbolic analog of the cyclic quadrilateral in the Euclidean plane. We find a few versions of the Brahmagupta formula for the area of such quadrilateral. We also present a formula for the area of a hyperbolic trapezoid.Comment: 22 pages, 9 figures, 58 reference

Si:P as a laboratory analogue for hydrogen on high magnetic field white dwarf stars

Laboratory spectroscopy of atomic hydrogen in a magnetic flux density of 10 5 T (1 gigagauss), the maximum observed on high-field magnetic white dwarfs, is impossible because practically available fields are about a thousand times less. In this regime, the cyclotron and binding energies become equal. Here we demonstrate Lyman series spectra for phosphorus impurities in silicon up to the equivalent field, which is scaled to 32.8 T by the effective mass and dielectric constant. The spectra reproduce the high-field theory for free hydrogen, with quadratic Zeeman splitting and strong mixing of spherical harmonics. They show the way for experiments on He and H 2 analogues, and for investigation of He 2, a bound molecule predicted under extreme field conditions