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On the Intracenter Relaxation of Shallow Arsenic Donors in Stressed Germanium. Population Inversion under Optical Excitation

Veniamin V. Tsyplenkov, V. N. Shastin

Published Nov 7, 2018• 12 citations
Publisher

Abstract

Abstract The relaxation rates of lower excited states 1s(T), 2p0, 2s, 3p0, and 2p± of arsenic donors in a germanium crystal are calculated upon the interaction with long-wavelength acoustic phonons depending on the uniaxial stress in the crystallographic direction [111]. The populations of states under optical excitation are estimated for calculated times. It is shown theoretically that optical excitation of the medium forms an inverse population of arsenic donor levels and leads to the possibility of the implementation of a four-level laser scheme with the radiative transition between 2p states and the 1s triplet state at zero strain. The estimated value of the expected gain in the medium under optical excitation conditions by CO2 laser radiation in the medium at a donor concentration of 2 × 1015 cm–3 is ~0.35 cm–1 at a frequency of 1.98 THz if the laser transition is 2p± → 1s(T) and 1.25 THz if the laser transition is 2p0 → 1s(T).

DOI
10.1134/s1063782618120254

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Abstract The relaxation rates of lower excited states 1s(T), 2p0, 2s, 3p0, and 2p± of arsenic donors in a germanium crystal are calculated upon the interaction with long-wavelength acoustic phonons depending on the uniaxial stress in the crystallographic direction [111]. The populations of states under optical excitation are estimated for calculated times. It is shown theoretically that optical excitation of the medium forms an inverse population of arsenic donor levels and leads to the possibility of the implementation of a four-level laser scheme with the radiative transition between 2p states and the 1s triplet state at zero strain. The estimated value of the expected gain in the medium under optical excitation conditions by CO2 laser radiation in the medium at a donor concentration of 2 × 1015 cm–3 is ~0.35 cm–1 at a frequency of 1.98 THz if the laser transition is 2p± → 1s(T) and 1.25 THz if the laser transition is 2p0 → 1s(T).
AbstractThe relaxation rates of lower excited states 1 s ( T ), 2 p _0, 2 s , 3 p _0, and 2 p _± of arsenic donors in a germanium crystal are calculated upon the interaction with long-wavelength acoustic phonons depending on the uniaxial stress in the crystallographic direction [111]. The populations of states under optical excitation are estimated for calculated times. It is shown theoretically that optical excitation of the medium forms an inverse population of arsenic donor levels and leads to the possibility of the implementation of a four-level laser scheme with the radiative transition between 2 p states and the 1 s triplet state at zero strain. The estimated value of the expected gain in the medium under optical excitation conditions by CO_2 laser radiation in the medium at a donor concentration of 2 × 10^15 cm^–3 is ~0.35 cm^–1 at a frequency of 1.98 THz if the laser transition is 2 p _± → 1 s ( T ) and 1.25 THz if the laser transition is 2 p _0 → 1 s ( T ).
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.
A mechanism for the generation of population inversion and far-infrared emission in Si with shallow donors is investigated. By optically pumping a phosphorus doped Si crystal with a CO2 laser it was possible to achieve population inversion between the metastable 2p0 state and the 1s(E) and 1s(T) states. Spontaneous emission from these transitions was detected. Frequency measurements of this emission are in agreement with the expected transition frequency. Absorption measurements with a far-infrared probe laser confirm the existence of population inversion between the 2p0 state and the 1s(E) and 1s(T) states.
We present measurements of coherence times of excited states of hydrogen-like arsenic impurities in germanium (Ge:As) using a table-top 2D-TDS system. We observe coherent population transfer and decay of transitions from the 2p0 and 2p± states by fitting the detected coherent nonlinear response with the known intracenter transition frequencies. Coherences between excited electronic states that are not visible via conventional single frequency pump-probe measurements are also observed in the off-diagonal resonances in the 2D frequency-domain map.