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V.N. Shastin 1 , R.Kh. Zhukavin 1 , K.A. Kovalevsky 1 , V.V. Tsyplenkov 1 ,

IPM RAS. Кремниевые лазеры для терагерцового диапазона (Silicon lasers for terahertz domain). V.N. Shastin 1 , R.Kh. Zhukavin 1 , K.A. Kovalevsky 1 , V.V. Tsyplenkov 1 , S.G. Pavlov 2 , H.-W. Hübers 2 . N.V. Abrosimov 3 , H. Riemann 3.

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V.N. Shastin 1 , R.Kh. Zhukavin 1 , K.A. Kovalevsky 1 , V.V. Tsyplenkov 1 ,

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  1. IPM RAS Кремниевые лазеры для терагерцового диапазона (Silicon lasers for terahertzdomain) V.N. Shastin1, R.Kh. Zhukavin1, K.A. Kovalevsky1, V.V.Tsyplenkov1, S.G. Pavlov2, H.-W. Hübers2. N.V. Abrosimov3, H. Riemann 3 1Institute for Physics of Microstructures, Russian Academy of Sciences, Nizhny Novgorod, Russian Federation 2Institute of Planetary Research, Germany Aerospace Center, Berlin, Germany 3Institute of Crystal Growth, Berlin, Germany Supported by RAS, RFBR (Russia), DFG (Germany) IKZ

  2. Contents: Unstressed silicon Experimental results Donor state relaxation rates Stressed silicon Experimental results Donor state relaxation rates

  3. Group V Donors in Silicon Conduction Band 2p± 2s 10 meV 2p0 As Sb Bi P 1s(E) 1s(T2) 1s(T2:8) 1s(T2:7) 1s(A1) -

  4. + ~(r) ~1/r Состояния мелких доноров в кремнии = {1, 1, 1, 1, 1, 1} A1 = {1, 1, 1, 1,-2,-2} E = {1, 1,-1,-1, 0, 0} = {1,-1, 0, 0, 0, 0} = T2 {0, 0, 1,-1, 0, 0} = {0, 0, 0, 0, 1,-1}

  5. Principle state lifetimes 2p± state (A1, E) 2p0 state (A1, E)

  6. Layout of the experiment

  7. TEA CO2 laser excitation, unstressed silicon (Family of experimental data) Operating temperature Emission spectra: Donors concentration:1·1015 - 5· 1015 cm-3 Threshold intensity:10-100 kW/cm2 Small signal gain: 0.1-0.2 cm-1 THz Quantum efficiency: Exp.? Theory: up to 10% 2×3×7 mm3

  8. Si:Pexperiment(10,6 µm TEA CO2 laser excitation) P donorTHz output vs. pump intensity under different stress.

  9. Si:Sbexperiment(10,6 µm TEA CO2 laser excitation) Sb donor THz output vs. pump intensity and compressive stress. 200kW/cm2 correspond 1025quant/cm2s.

  10. Si:Sb Under Q-switch CO2 laser pump Least value of threshold intensity ~150W/cm2

  11. 220 Si:As experiment(10,6 µm TEA CO2 laser excitation) 170 0 1 2 As donorTHz output vs. pump intensity under different stress. As donorTHz output vs. stress under several pump intensity. 200kW/cm2 correspond 1025quant/cm2s.

  12. Si:As Under Q-switch CO2 laser pump Least value of threshold intensity ~300W/cm2

  13. Si:Biexperiment(10,6 µm TEA CO2 laser excitation) Intensity, a.u. Bi donorTHz output vs. stress under several pump intensity. 200kW/cm2 correspond 1025quant/cm2s. Sb donorTHz output vs. pump intensity under different stress.

  14. [001] [010] e e [100] qg qf K010 K111 qN e Brillouinzone vector of reciprocal lattice; normal process; umklapp-processf-type; umklapp-processg-type; X-valley splitting under uniaxial stress X. The stress removes sixfold degeneracy and, as a result, the energy difference ΔE appears between different groups of valleys. Intervalley phonon scattering of electrons in Si Energy levels of donors in stressed Si As Sb

  15. Si:Sb Laser state relaxation rates 2p0(А1+В2) 2p0 1s(B1) 1s(E) 1s(A1) 21∙109c-1 6.8∙109c-1 1s(E) 1s(T2) 1s(B2) Si:P 2.1∙1010 c-1 1s(A1) 4.6∙1010 c-1 Stress (0.6 kbar) 1s(A1) 0 2p0(А1+В2) 2p0 intra2p± = 2.15 ∙1010 c-1 intra2p0= 2 ∙109 c-1 1s(B1) 1s(E) 1s(A1) 29∙109c-1 9.2∙109c-1 1s(E) 1s(T2) 1s(B2) 4.4∙1010 c-1 1s(A1) 7∙1010 c-1 1s(A1) Stress (0.6 kbar) 0

  16. Si:As E Laser state relaxation rates, s-1 14∙109 2p± 2s 2p0(А1+В2) 15∙109 2p0 1s(B1) 1s(E) 1s(A1) 4.2∙109 1s(E) 1s(T2) 1s(B2) Si:Bi 3.5∙1010 2.6∙1010 1s(A1) E 1s(A1) Stress (2.5 kbar) 0 2p± 2s 2p0(А1+В2) 2p0 1s(B1) 1s(E) 1s(A1) intra2p± = 2.15 ∙1010 c-1 intra2p0= 2 ∙109 c-1 intra2p± = 2.15 ∙1010 c-1 intra2p0= 2 ∙109 c-1 8.5∙109 3∙1011 1s(E) 1s(T2) 1s(B2) 5.5∙109 2∙109 1s(A1) 1s(A1) 0 Stress (1.8 kbar)

  17. Релаксация на фононах СО2 THg emission Релаксация на фононах THg emission СО2 THg Влияние деформации на эффективность накачкирабочих состояний (Pump efficiency of the laser states depending on stress)

  18. Population, gain, absorption Si:Sb Donor gain & D--centerabsorption Population of 2p0 states and D- center concentration in unstressed (red lines) & stressed silicon (blue lines) Blue lines correspond to valley shift 5 meV (0.6 kbar)

  19. Summary The axial compressive stress of silicon crystal applied along [100] crystallographic orientation: From the experiment - increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors; - changes the 2p±- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors; - lasing of P and Sb donors is based on the 2p0 – 1s(T2) transitions & laser line does not depend on stress. From the theoretical treatment - f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys; - valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states ; - D-center THz absorption block lasing of donors in silicon under photo-ionizing excitation & can be eliminated by axial deformation of the host crystal.

  20. Current study & Further development 1) Spin-orbit interaction & laser frequencies Si:Sb, Si:Bi 2) Group-V donor lasing from isotope enriched silicon 28Si 3) Low T donor relaxation in stressed silicon (exp. study) 4) Donor/acceptor lasing from low dimensional Si/SiGe structures 5) CW operation

  21. D- binding energy vs. compression L.E.Oliveira, L.M.Falicov, Phys.Rev.B 33,6990,(1986)-solid curve; D.M. Larsen, Phys.Rev. B 23,5521 (1981) –dashed curve.

  22. Si:P 2p0 TA-f 8.4∙109 c-1 TA-f 12.4∙109 c-1 LA-g 0.3∙109 c-1 LA-g 5.75109 c-1 1s(E) 1s(T2) TA-g 7∙1010 c-1 TA-g 3.6∙1010 c-1 1s(A1) Si:P 2.6∙1010 c-1 3.6∙1010 c-1 7∙1010 c-1 Темп внутридолинных переходов: 2р0-1s2.1∙109 с-1 1кбар соответствует 8.5 мэВ

  23. Si:Sb 2p0 TA-f ~108 c-1 TA-f 14.2∙109 c-1 LA-g 2.6∙109 c-1 LA-g 1.75∙109 c-1 1s(E) 1s(T2) TA-g 4.6∙1010 c-1 TA-g 3.8∙1010 c-1 1s(A1) Si:Sb 1.8∙1010 c-1 3.8∙1010 c-1 4.6∙1010 c-1 Intra valley scattering rate : 2р0-1s2.1∙109 с-1 1 kbar yields 8.5 meV valley shift for [100] stress

  24. 2p± 2s 2p0 TA-f 1.46 ∙109 c-1 TA-f 12.2∙109 c-1 LA-g 0.63∙109 c-1 LA-g 0.7∙109 c-1 LA-g 6∙109c-1 LA-g 6∙109 c-1 LA-f 0.79∙1010 c-1 1s(E) 1s(T2) TA-f 2.7∙1010 c-1 TA-f 1.6∙1010 c-1 LA-g 5∙1010 c-1 LA-g 3.3∙1010 c-1 LA-f 0.98∙109 c-1 LA-f 2.7∙1010 c-1 1s(A1) Si:As 2.7∙1010 c-1 1.6∙1010 c-1 5∙1010 c-1 7.7∙1010 c-1 Intra valley scattering rates: 2р0-1s2.1∙109 с-1 2s - 1s 5.2∙109 c-1 2p± - 1s 0.1 ∙109 c-1 2p± - 2p014.4∙109 c-1 2p± - 2s8.9 ∙109 c-1

  25. f- and g-phonon scattering rates in As donor under stress Relaxation of 2р(+/-) and 2р0 states Relaxation of the lower laser level

  26. 2p± 2s 2p0 TA-f 1.4∙1010 c-1 TA-f 5.2∙109 c-1 LA-g ~ 108 c-1 LA-g 2∙109 c-1 LA-g 3.7∙109 c-1 1s(E) 1s(T2:Г7) 1s(T2:Г8) LA-f 4.7∙109 c-1 TA-f 6∙109 c-1 LA-g 0.53∙109 c-1 LA-g 0.4∙109 c-1 TO-f ~3.2∙1011 c-1 1s(A1) Si:Bi

  27. f- and g-phonon scattering rates in Bi donor under stress

  28. Relaxation 1s(B2) state in Bi donor under stressed silicon

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