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Journal of Experimental and Theoretical Physics Letters

Photon Echo in Uniaxially Stressed Germanium with Antimony Donors

R. Kh. Zhukavin, Valeria D. Kukotenko, P. A. Bushuikin, Yu. Yu. Choporova, Осинцева Наталья Дмитриевна, K. A. Kovalevsky, В.В. Цыпленков, Vasily Valerievich Gerasimov, N. Dessmann, Н.В. Абросимов, V. N. Shastin

Published Apr 1, 2026• 0 citations
Publisher

Abstract

In an n -Ge crystal uniaxially stressed along the [111] crystallographic direction, the photon echo effect has been demonstrated, and the coherence relaxation time T 2 has been estimated at ~300 ps. Nonlinear polarization leading to the effect appears due to antimony donors. Uniaxial deformation of the crystal, which is responsible for valley splitting of the donor states, significantly increases the coherence time and leads to the possibility of implementing the effect.

DOI
10.1134/s0021364026600771

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Based upon the time dependent perturbation theory for coherent radiation-semiconductor interaction, the possibility of occurrence of the phenomenon of two-pulse photon echo has been investigated analytically in a bulk direct-gap semiconductor under near resonant transition regime below the absorption edge of the crystal. The excitation intensity is chosen to be in the low-to-moderate power regime such that the photoinduced electron-hole pair density remains below the Mott transition limit and the weakly bound Wannier-Mott excitonic structure of the crystal absorption edge is manifested. The band gap renormalization effect is also taken into account. Numerical estimation of the transmitted intensity has been made for electron-hole transition to the 1s excitonic states in the bulk CdS crystal. The analytical results demonstrate the occurrence of photon echo in direct-gap semiconductors.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 28, 1999•0 citations
In an n -Ge crystal uniaxially stressed along the [111] crystallographic direction, the photon echo effect has been demonstrated, and the coherence relaxation time T 2 has been estimated at ~300 ps. Nonlinear polarization leading to the effect appears due to antimony donors. Uniaxial deformation of the crystal, which is responsible for valley splitting of the donor states, significantly increases the coherence time and leads to the possibility of implementing the effect.
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).
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 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.
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 ).
Based upon the time dependent perturbation theory for coherent radiation-semiconductor interaction, the possibility of occurrence of the phenomenon of two-pulse photon echo has been investigated analytically in a bulk direct-gap semiconductor under near resonant transition regime below the absorption edge of the crystal. The excitation intensity is chosen to be in the low-to-moderate power regime such that the photoinduced electron-hole pair density remains below the Mott transition limit and the weakly bound Wannier-Mott excitonic structure of the crystal absorption edge is manifested. The band gap renormalization effect is also taken into account. Numerical estimation of the transmitted intensity has been made for electron-hole transition to the 1s excitonic states in the bulk CdS crystal. The analytical results demonstrate the occurrence of photon echo in direct-gap semiconductors.