In this paper, we propose a method for resonant optical excitation of ortho states of two-electron donors in silicon, direct transitions to which from the ground state are extremely suppressed in case of a weak spin-orbit coupling. Excitation is proposed to be carried out using the points of anti-crossing of ortho and para states under conditions of uniaxial stress of the crystal. In these points the states cannot be unambiguously assigned to any group of states with a certain spin, as a result of which the optical transition becomes allowed. The structure of the energy levels of two-electron impurities is such that the excitation of such state almost unambiguously leads to the population of the underlying ortho-type state, which is expected to be very long-lived in the case of weak spin-orbit coupling. In the present work, theoretical estimates of the cross sections for optical transitions in the vicinity of the level anticrossing point as a function of strain for strong and weak spin-orbit coupling are made.

Using adiabatic and one-electron approximations, the rate of multiphonon relaxation of the 1s(T2) triplet of neutral magnesium donors in silicon is estimated. The dominant scattering processes associated with interaction with LO and LA phonons are taken into account. According to calculations, the rate of multiphonon relaxation at zero temperature is of the order of 1011 s–1.

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.

Silicon doped with neutral helium-like magnesium donors is studied theoretically as an active medium in the THz frequency range. The inversion mechanism in Si:Mg under optical excitation does not have the necessary efficiency due to the presence of fast relaxation processes. On the contrary, the mechanism of stimulated Raman scattering (SRS) is less sensitive to relaxation times and allows the lasing spectrum to be tuned. An important feature of doubly charged donors is the presence of two Stokes shifts in the system, which significantly expands the range of laser frequencies. Calculations show that the combined use of uniaxial crystal strain and excitation quantum energy tuned in the range of 95‒105 meV (23‒25.5 THz) will make it possible to obtain Raman lasing in the frequency band of 7‒33 meV (~1.5‒8 THz).

In this paper, we propose a method for resonant optical excitation of ortho states of two-electron donors in silicon, direct transitions to which from the ground state are extremely suppressed in case of a weak spin-orbit coupling. Excitation is proposed to be carried out using the points of anti-crossing of ortho and para states under conditions of uniaxial stress of the crystal. In these points the states cannot be unambiguously assigned to any group of states with a certain spin, as a result of which the optical transition becomes allowed. The structure of the energy levels of two-electron impurities is such that the excitation of such state almost unambiguously leads to the population of the underlying ortho-type state, which is expected to be very long-lived in the case of weak spin-orbit coupling. In the present work, theoretical estimates of the cross sections for optical transitions in the vicinity of the level anticrossing point as a function of strain for strong and weak spin-orbit coupling are made.

The wave functions of electrons localized at P, As, and Sb shallow donors in Ge are calculated in the envelope function approximation taking into account valley–orbit coupling induced by the short-range donor potential. An approach is proposed that makes it possible to include intervalley mixing into the equation for the multicomponent envelope function. The effects of valley–orbit coupling are calculated using perturbation theory and the single-valley “bare” functions are determined by the Ritz method. The parameters of the short-range part of the potential and the coefficient of intervalley mixing are found for each donor individually and yield the best agreement with the measured energies of the singlet and triplet states. The envelope functions of the 1s(A1) and 1s(T2) states are calculated. The parameters of the valley–orbit interaction for each donor are obtained. It is shown how the functions of the 2s, 2p0, 2p±, and 3p0 excited states should be modified to remain orthogonal to the singlet and triplet functions in the framework of a more rigorous multivalley model.

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.

The role of intervalley processes in electron–phonon interaction for the relaxation of excited shallow arsenic donors in germanium is analyzed. The rates of intracenter intervalley transitions with the emission of TA phonons in germanium are calculated depending on the uniaxial compression stress along the {111} crystallographic direction. It is shown that the intervalley transitions to the donor ground state with the emission of phonons can play a significant role in the relaxation of excited impurities only upon uniaxial stress of the crystal, since there are no exact resonances between the impurity transitions and intervalley phonons at zero stress. There are also transitions from highly excited states lying in a narrow band of energies (~0.5 meV) near the very bottom of the conduction band to the first excited state 1 s (3) (Γ 5 ) (in stressed Ge to 1 s (3) (Γ 3 ). The average rate of these transitions is estimated as 0.3 × 10 9 s –1 .

A theoretical study was made of the conditions for observing the photon echo effect in a germanium crystal doped with shallow donors. A numerical calculation of the medium polarization excited by a sequence of two optical pulses at a frequency close to the impurity transition frequency has been made. The effect of excitation pulse parameters, such as the pulse duration, the inhomogeneous broadening of impurity transitions and the relaxation rate of population and coherence in the system on the echo is considered. The key aspect in the experimental implementation of the effect is the control of the crystal temperature under photoexcitation, since the rate of coherence relaxation in the system strongly depends on the temperature of the crystal lattice. Keywords: germanium, shallow donors, coherent effects, photon echo.

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.

A theoretical study was made of the conditions for observing the photon echo effect in a germanium crystal doped with shallow donors. A numerical calculation of the medium polarization excited by a sequence of two optical pulses at a frequency close to the impurity transition frequency has been made. The effect of excitation pulse parameters, such as the pulse duration, the inhomogeneous broadening of impurity transitions and the relaxation rate of population and coherence in the system on the echo is considered. The key aspect in the experimental implementation of the effect is the control of the crystal temperature under photoexcitation, since the rate of coherence relaxation in the system strongly depends on the temperature of the crystal lattice.

In the framework of the envelope function approximation, the wave functions of electrons localized at shallow donors P, As, Sb in Ge are calculated taking into account the valley-orbit coupling caused by the donor short-range potential. It is proposed an approach that makes it possible to include inter-valley mixing in the equation for a multi-component envelope function. The calculation of the effects of the valley-orbit interaction was carried out according to the perturbation theory, while the "bare" single-valley functions were found using the Ritz method. The parameters of the short-range part of the potential and the coefficient of inter-valley mixing were found individually for each donor, making it possible to obtain the best agreement with the results of experimental measurements of the energies of the singlet and triplet states. The envelope functions of the 1s(A1) and 1s(T2) states are calculated. The parameters of the valley-orbit interaction are found for each donor. It is also shown how the functions of the excited 2s, 2p0, 2p±, 3p0 states should be modified in order to remain orthogonal to the singlet and triplet functions within the framework of a more rigorous multivalley model.

The role of the intervalley processes of electron-phonon interaction in the relaxation of excited shallow arsenic donors in germanium is analyzed. The rates of intracenter inter-valley transitions with emission of TA phonons in ger-manium are calculated in dependence on the uniaxial compression stress along {111} crystallographic direction. It is shown that inter-valley transitions to the ground state of the donor with emission of phonons can play a significant role in the relaxation of excited impurities only upon uniaxial stress of the crystal, since at zero stress, there are no exact resonances between impurity transitions and intervalley phonons. There are also transitions from highly excited states lying in a narrow band of energies (~ 0.5 meV) under very bottom of the conduction band to the first excited state 1s(3)(Г5) (in stressed germanium crystal to 1s(3)(Г3) state). The average rate of these transitions is estimated at 0.3×109 s-1.

The wave functions of low-lying 1s (A1), 2s, 2p0, 2p±, and 3p0 states of P, As, and Sb shallow donor centers in germanium are calculated in the scope of the envelope-function approximation taking into account the short-range impurity potential. The latter is constructed individually for each impurity allowing for the spatial permittivity dispersion and the difference between the ion cores of germanium and the impurity center. The envelope-function equation is solved using the Ritz variational method; herewith, the selected test functions of orbitally nondegenerate s states are characterized by two spatial scales. The first scale, on the order of the donor effective Bohr radius, corresponds to the long-range part of the potential, and the second scale, which is smaller by an order of magnitude, simulates the electron response to the short-range part of the donor potential. The electron density in the donor ground state is shifted to the nucleus, which is due to allowance made for the attracting “central cell” potential. The envelope functions of p states are in turn constructed so that they are orthogonal to envelopes in the ground states for each impurity centers and are different for various donors in contrast with previous works.

The results of experimental and theoretical investigations of terahertz-emission-spectrum tuning by means of uniaxial stress of a silicon crystal doped with shallow bismuth donors are presented for the case of intracenter optical excitation. The frequency tuning of two emission lines of the bismuth donor is shown for the case of uniaxial strain along the [001] crystallographic direction. The cross sections of stimulated Raman scattering for uniaxially stressed bismuth-doped silicon are calculated.

The relaxation rates of arsenic donor states in germanium upon interaction with acoustic phonons are analyzed depending on uniaxial crystal compression deformation along [110] direction at low temperatures (<10 K). It is shown that the formation of the inverse population of donor levels, which depends on the crystal-deformation magnitude, occurs under optical excitation, which gives us grounds to assume the possibility of the effect of stimulated radiation in the THz frequency range at intracenter transitions of shallow arsenic donors under their optical excitation. It is shown that uniaxial deformation can lead to switching of the laser transition and, consequently, to a variation in the stimulated-radiation frequency.

Experimental investigations of the relaxation times in germanium doped by shallow arsenic donors at low temperatures have been performed with use of pump-probe technique. The dedicated setup utilizes terahertz radiation from the NovoFEL free electron laser. Relaxation times of several excited states have been measured. The values of measured lifetimes fall into nanosecond range. Experimental results are compared with theoretical calculations which take into account acoustic phonon assisted relaxation.

The results of investigations of relaxation processes of donor bound electrons in the germanium doped by arsenic at cryogenic temperatures are presented. The lifetimes of p-type excited states of a donor were measured by pump-probe technique utilizing THz radiation from free-electron laser NovoFEL. The uniaxial stress along [111] axis was applied to the crystal to modify the energy spectrum of the impurity and intervalley relaxation processes. The analysis of experimental for p-type excited states allows to get the upper limit for the relaxation time of lowest 1s excited state. The comparison of obtained experimental results with the theoretical estimates for the interaction with TA phonons indicates on the enhancement of the interaction with the phonons having wavenumbers corresponding to the flat part of the dispersion.

The dynamics of the formation and decay of coherent states of shallow impurity centers in crystalline germanium resonantly excited by a pair of laser pulses, following one another with a time delay is analyzed theoretically. The required laser-radiation power, the upper limit on the lattice temperature, and the allowed inhomogeneous broadening of the impurity lines making possible the observation of Ramsey interference in this system are estimated.