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 1 Institute for Physics of Microstructures, Russian Academy of Sciences, Nizhny Novgorod, Russian Federation 2 Institute of Planetary Research, Germany Aerospace Center, Berlin, Germany 3 Institute of Crystal Growth, Berlin, Germany Supported by RAS, RFBR (Russia), DFG (Germany) IPM RAS IKZ Кремниевые лазеры для терагерцового диапазона (Silicon lasers for terahertz domain)

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

1s(A 1 ) 1s(T 2 ) 1s(E ) - P AsSbBi 2p 0 2s 2p ± 10 meV 1s(T 2 :  8) 1s(T 2 :  7 ) Conduction Band Group V Donors in Silicon

+ ~1/r ~  (r) Состояния мелких доноров в кремнии {0, 0, 0, 0, 1,-1} = {0, 0, 1,-1, 0, 0} = {1,-1, 0, 0, 0, 0} = T2 T2 {1, 1,-1,-1, 0, 0} = {1, 1, 1, 1,-2,-2} = E {1, 1, 1, 1, 1, 1} = A1A1

Principle state lifetimes PAs Pump-probe~30 ps~20 ps FWHM Si N ~26 ps NTD, 1,2х10 14 cm -3 FWHM Si 28 ~80 ps 2p ± state (A 1, E) Exp. PAs Pump-probe~30 ps~50 ps FWHM Si N ~32 ps NTD, 1,2х10 14 cm -3 ~30 ps 7х10 14 cm -3 FWHM Si 28 ~160 ps 2p 0 state (A 1, E) Theory PAsSb 2р 0 (ps) А1А Е T2T р ± (ps)

Layout of the experiment

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

Si:P experiment (10,6 µm TEA CO 2 laser excitation) P donor THz output vs. pump intensity under different stress.

Sb donor THz output vs. pump intensity and compressive stress. Si:Sb experiment (10,6 µm TEA CO2 laser excitation) 200kW/cm 2 correspond quant/cm 2 s.

Si:Sb Under Q-switch CO 2 laser pump Least value of threshold intensity ~150W/cm 2

Si:As experiment (10,6 µm TEA CO 2 laser excitation) As donor THz output vs. stress under several pump intensity. 200kW/cm 2 correspond quant/cm 2 s. As donor THz output vs. pump intensity under different stress

Least value of threshold intensity ~300W/cm 2 Si:As Under Q-switch CO 2 laser pump

Si:Bi experiment (10,6 µm TEA CO 2 laser excitation) Bi donor THz output vs. stress under several pump intensity. 200kW/cm 2 correspond quant/cm 2 s. Sb donor THz output vs. pump intensity under different stress. Intensity, a.u.

Energy levels of donors in stressed Si As Sb 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 K 111 K 010 qNqN qfqf qgqg e e [100] [010] [001] e Brillouin zone vector of reciprocal lattice; normal process; umklapp-process f -type; umklapp-process g -type;

0 2p 0 1s(E) 1s(T 2 ) 1s(A 1 ) 1s(B 2 ) 1s(B 1 ) 1s(E) 1s(A 1 ) 21∙10 9 c ∙10 10 c ∙10 10 c ∙10 9 c -1 2p 0 (А 1 +В 2 ) Si:Sb Stress (0.6 kbar) Laser state relaxation rates 0 2p 0 1s(E) 1s(T 2 ) 1s(A 1 ) 1s(B 2 ) 1s(B 1 ) 1s(E) 1s(A 1 ) 29∙10 9 c -1 7∙10 10 c ∙10 10 c ∙10 9 c -1 2p 0 (А 1 +В 2 ) Si:P Stress (0.6 kbar) intra 2p± = 2.15 ∙10 10 c -1 intra 2p0 = 2 ∙10 9 c -1

0 2p 0 1s(E) 1s(T 2 ) 1s(A 1 ) 1s(B 2 ) 1s(B 1 ) 1s(E) 1s(A 1 ) 2.6∙ ∙ ∙10 9 2p 0 (А 1 +В 2 ) Stress (2.5 kbar) 2p± 2s 15∙ ∙10 9 intra 2p± = 2.15 ∙10 10 c -1 intra 2p0 = 2 ∙10 9 c p 0 1s(E) 1s(T 2 ) 1s(A 1 ) 1s(B 2 ) 1s(B 1 ) 1s(E) 1s(A 1 ) 5.5∙10 9 2∙ ∙10 9 2p 0 (А 1 +В 2 ) Stress (1.8 kbar) 2p± 2s 3∙10 11 E E Si:As Si:Bi Laser state relaxation rates, s -1 intra 2p± = 2.15 ∙10 10 c -1 intra 2p0 = 2 ∙10 9 c -1

Влияние деформации на эффективность накачки рабочих состояний (Pump efficiency of the laser states depending on stress) СО 2 Релаксация на фононах THg СО 2 Релаксация на фононах THg emission

Population, gain, absorption Si:Sb Donor gain & D- - center absorption Population of 2p 0 states and D- center concentration in unstressed (red lines) & stressed silicon (blue lines) Blue lines correspond to valley shift 5 meV (0.6 kbar)

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 2p 0 one as well as emission frequency for As and Bi donors; - lasing of P and Sb donors is based on the 2p 0 – 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.

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

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.

1кбар соответствует 8.5 мэВ Si:P 1s(E) 1s(T 2 ) 1s(A 1 ) TA-f 8.4∙10 9 c -1 TA-f 12.4∙10 9 c -1 LA-g 0.3∙10 9 c -1 LA-g c -1 TA-g 7∙10 10 c -1 TA-g 3.6∙10 10 c -1 2p02p0 Si:P Темп внутридолинных переходов: 2р 0 - 1s 2.1∙10 9 с ∙10 10 c -1 7∙10 10 c ∙10 10 c -1

1 kbar yields 8.5 meV valley shift for [100] stress Si:Sb 1s(E) 1s(T 2 ) 1s(A 1 ) TA-f ~10 8 c -1 TA-f 14.2∙10 9 c -1 LA-g 2.6∙10 9 c -1 LA-g 1.75∙10 9 c -1 TA-g 4.6∙10 10 c -1 TA-g 3.8∙10 10 c -1 2p 0 Si:Sb Intra valley scattering rate : 2р 0 - 1s 2.1∙10 9 с ∙10 10 c ∙10 10 c ∙10 10 c -1

Si:As LA-f 0.79∙10 10 c -1 1s(E) 1s(T 2 ) 1s(A 1 ) TA-f 12.2∙10 9 c -1 LA-g 0.63∙10 9 c -1 LA-g 0.7∙10 9 c -1 TA-f 2.7∙10 10 c -1 TA-f 1.6∙10 10 c -1 2p 0 2s 2p ± LA-g 5∙10 10 c -1 LA-g 3.3∙10 10 c -1 TA-f 1.46 ∙10 9 c -1 LA-f 0.98∙10 9 c -1 LA-f 2.7∙10 10 c -1 LA-g 6∙10 9 c -1 LA-g 6∙10 9 c -1 Intra valley scattering rates: 2р 0 - 1s 2.1∙10 9 с -1 2s - 1s 5.2∙10 9 c -1 2p± - 1s 0.1 ∙10 9 c -1 2p± - 2p ∙10 9 c -1 2p± - 2s 8.9 ∙10 9 c ∙10 10 c ∙10 10 c ∙10 10 c -1 5∙10 10 c -1

Relaxation of the lower laser level f- and g-phonon scattering rates in As donor under stress Relaxation of 2р(+/-) and 2р 0 states

1s(T 2 :Г 7 ) 1s(T 2 :Г 8 ) 1s(A 1 ) TA-f 5.2∙10 9 c -1 LA-g ~ 10 8 c -1 LA-g 2∙10 9 c -1 LA-f 4.7∙10 9 c -1 TA-f 6∙10 9 c -1 2p 0 2s 2p ± LA-g 0.53∙10 9 c -1 LA-g 0.4∙10 9 c -1 TA-f 1.4∙10 10 c -1 TO-f ~3.2∙10 11 c -1 1s(E) LA-g 3.7∙10 9 c -1 Si:Bi

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

Relaxation 1s(B 2 ) state in Bi donor under stressed silicon