Silicon lasers for terahertz domain V N Shastin

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 1 Institute IPM RAS 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 IKZ Supported by RAS, RFBR (Russia), DFG (Germany)

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

Group V Donors in Silicon 2 p± 2 s 2 p 0 1 s(E) 1 s(T 2) 1 s(A 1) - P As Sb 10 me. V Conduction Band Bi 1 s(T 2: 8) 1 s(T 2: 7)

Principle state lifetimes 2 p± state (A 1, E) 2 p 0 state (A 1, E) P As Pump-probe ~30 ps ~50 ps FWHM Si. N ~32 ps ~30 ps Exp. FWHM Si 28 7 х1014 NTD, 1, 2 х1014 cm-3 2 р± (ps) As Pump-probe ~30 ps ~20 ps FWHM Si. N ~26 ps NTD, 1, 2 х1014 cm-3 FWHM Si 28 ~160 ps Theory 2 р0 (ps) P P As Sb А 1 40 50 50 Е 32 56 50 T 2 37 62 54 52 47 52 ~80 ps

Layout of the experiment

TEA CO 2 laser excitation, unstressed silicon (Family of experimental data) Operating temperature Emission spectra: Donors concentration: 1·1015 - 5· 1015 cm-3 Threshold intensity: 10 -100 k. W/cm 2 Small signal gain: 0. 1 -0. 2 cm-1 Quantum efficiency: Exp. ? Theory: up to 10% THz 2× 3× 7 mm 3

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

Si: Sb experiment (10, 6 µm TEA CO 2 laser excitation) Sb donor THz output vs. pump intensity and compressive stress. 200 k. W/cm 2 correspond 1025 quant/cm 2 s.

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

220 Si: As experiment (10, 6 µm TEA CO 2 laser excitation) As donor THz output vs. stress under several pump intensity. 200 k. W/cm 2 correspond 1025 quant/cm 2 s. 170 0 1 2 As donor THz output vs. pump intensity under different stress.

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

(10, 6 µm TEA CO 2 laser excitation) Bi donor THz output vs. stress under several pump intensity. 200 k. W/cm 2 correspond 1025 quant/cm 2 s. Intensity, a. u. Si: Bi experiment Sb donor THz output vs. pump intensity under different stress.

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 [001] [010] e [100] qf Energy levels of donors in stressed Si As Sb K 111 e qg K 010 q. N e Brillouin zone vector of reciprocal lattice; normal process; umklapp-process f -type; umklapp-process g -type;

Si: Sb Laser state relaxation rates 2 p 0(А 1+В 2) 2 p 0 21∙ 109 c-1 6. 8∙ 109 c-1 1 s(E) 1 s(T 2) 4. 6∙ 1010 c-1 1 s(A 1) intra 2 p± = 2. 15 2 p 0= 2 1 s(B 2) 2. 1∙ 1010 c-1 1 s(A 1) Si: P Stress (0. 6 kbar) 0 intra 1 s(B 1) 1 s(E) 1 s(A 1) ∙ 1010 ∙ 109 c-1 2 p 0(А 1+В 2) 2 p 0 29∙ 109 c-1 9. 2∙ 109 c-1 1 s(E) 1 s(T 2) 4. 4∙ 1010 c-1 7∙ 1010 c-1 1 s(A 1) 0 Stress (0. 6 kbar) 1 s(B 1) 1 s(E) 1 s(A 1) 1 s(B 2) 1 s(A 1)

Si: As E 14∙ 109 15∙ 109 2 p 0 1 s(B 1) 1 s(E) 1 s(A 1) 4. 2∙ 109 1 s(E) 1 s(T 2) 2. 6∙ 1010 1 s(A 1) ∙ 1010 E Stress (2. 5 kbar) =2. 15 ∙ 10 c-1 2 p 0= Si: Bi 1 s(A 1) 9 -1 intra 2 p 0= 2 ∙ 10 c 9 1 s(B 2) 3. 5∙ 1010 0 intra = intra 2 p± Laser state relaxation rates, s-1 2 p± 2 s 2 p 0(А 1+В 2) c-110 2 ∙ 10 c-1 2 p± 2 s 2 p 0(А 1+В 2) 2 p 0 3∙ 1011 8. 5∙ 109 1 s(E) 1 s(T 2) 1 s(B 1) 1 s(E) 1 s(A 1) 1 s(B 2) 5. 5∙ 109 2∙ 109 1 s(A 1) 0 Stress (1. 8 kbar)

Population, gain, absorption Si: Sb Population of 2 p 0 states and D- center concentration in unstressed (red lines) & stressed silicon (blue lines) Donor gain & D--center absorption Blue lines correspond to valley shift 5 me. V (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 2 p±- upper laser state for the 2 p 0 one as well as emission frequency for As and Bi donors; - lasing of P and Sb donors is based on the 2 p 0 – 1 s(T 2) transitions & laser line does not depend on stress. From 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/Si. Ge 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.

Si: P 2. 6∙ 1010 c-1 TA-f 8. 4∙ 109 c-1 2 p 0 TA-f LA-g 12. 4∙ 109 c-1 0. 3∙ 109 c-1 LA-g 5. 75109 c-1 1 s(E) 3. 6∙ 1010 c-1 7∙ 1010 c-1 TA-g 3. 6∙ 1010 c-1 1 s(T 2) 1 s(A 1) Темп внутридолинных переходов: 2 р0 - 1 s 2. 1∙ 109 с-1 1 кбар соответствует 8. 5 мэ. В

Si: Sb 1. 8∙ 1010 c-1 TA-f ~108 c-1 2 p 0 TA-f LA-g 14. 2∙ 109 c-1 2. 6∙ 109 c-1 LA-g 1. 75∙ 109 c-1 1 s(E) 3. 8∙ 1010 c-1 4. 6∙ 1010 c-1 1 s(T 2) TA-g 4. 6∙ 1010 c-1 TA-g 3. 8∙ 1010 c-1 1 s(A 1) Intra valley scattering rate : 2 р0 - 1 s 2. 1∙ 109 с-1 1 kbar yields 8. 5 me. V valley shift for [100] stress

Si: As 2 p± 2. 7∙ 1010 c-1 2 s 2 p 0 1. 6∙ 1010 c-1 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∙ 109 c-1 LA-f 0. 79∙ 1010 c-1 1 s(E) 5∙ 1010 c-1 7. 7∙ 1010 c-1 1 s(T 2) 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 1 s(A 1) Intra valley scattering rates: 2 р0 - 1 s 2. 1∙ 109 с-1 2 s - 1 s 5. 2∙ 109 c-1 2 p± - 1 s 0. 1 ∙ 109 c-1 2 p± - 2 p 0 14. 4 ∙ 109 c-1 2 p± - 2 s 8. 9 ∙ 109 c-1

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

Si: Bi 2 p± 2 s 2 p 0 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 1 s(E) 1 s(T 2: Г 7) LA-f 4. 7∙ 109 c-1 TA-f 6∙ 109 c-1 LA-g 0. 53∙ 109 c-1 1 s(T 2: Г 8) LA-g 0. 4∙ 109 c-1 TO-f ~3. 2∙ 1011 c-1 1 s(A 1)

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

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