Period Dependence of Time Response of Strained Semiconductor Superlattices XIVth International Workshop on Polarized Sources, Targets & Polarimetry Leonid G. Gerchikov Laboratory of Spin-Polarized Electron Spectroscopy Department of Experimental Physics State Polytechnic University St. Petersburg, Russia

Collaborators Department of Experimental Physics, St. Petersburg State Polytechnic University, St. Petersburg, Russia, Leonid G. Gerchikov, Yuri A. Mamaev, Yuri P.Yashin Institute of Nuclear Physics, Mainz University, Mainz, Germany, Kurt Aulenbacher, Eric J. Riehn SPES PSTP2011

Outline Introduction Pulse response measurements Theoretical approach Goals and Motivation Pulse response measurements Experimental method and results Partial electron localization Theoretical approach Kinetics of electron transport in SL Role of electron localization. Pulse response and QE. Analysis of the pulse response Comparison of theory and experiment. Determination of localization times Dependence of the response time on number of SL periods Conclusions SPES PSTP2011

Best photocathodes Sample Composition Pmax QE(max) Team SLSP16 GaAs(3.2nm)/ GaAs0.68P0.34 (3.2nm) 92% 0.5% Nagoya University, 2005 SL5-777 GaAs(1.5nm)/ In0.2Al0.23Ga0.57As(3.6nm) 91% 0.14% SPbSPU, 2005 SL7-307 Al0.4Ga0.6As(2.1nm)/ In0.19Al0.2Ga0.61As(5.4nm) 0.85% SPbSPU, 2007 SPES PSTP2011

SL In0.16Al0.2Ga0.64As(5.1nm)/Al0.36Ga0.64As(2.3nm) SPES PSTP2011

Strained-well SL Unstrained barrier ab = a0 GaAs Substrate Buffer Layer a0 - latt. const GaAs BBR Strained QW aw > a0 SL Nominal Structure Large valence band splitting due to combination of deformation and quantum confinement effects in QW SPES PSTP2011

MBE grown AlInGaAs/AlGaAs strained-well SL Composition Thickness Doping As cap GaAs QW 60 A 71018 cm-3 Be Al0.4Ga0.6As SL 21 A 31017 cm-3 Be In 0.19Al 0.2Ga 0.65As 54 A Al0.35Ga0.65As Buffer 0.3 mm 61018 cm-3 Be p-GaAs substrate Eg = 1.536 eV, valence band splitting Ehh1 - Elh1 = 87 meV, Maximal polarization Pmax= 92% at QE = 0.85% SPES PSTP2011

Pulse response experiment: Experimental method Pulse response experiment: Time resolved measurements of electron emission excited by fs-laser pulse Photoexcitation

Pulse response experiment: Experimental method Pulse response experiment: Time resolved measurements of electron emission excited by fs-laser pulse Photoexcitation Beam deflection

Pulse response experiment: Experimental method Pulse response experiment: Time resolved measurements of electron emission excited by fs-laser pulse Photoexcitation Shift of transverse profile against slit Beam deflection

Pulse response experiment: Experimental method Pulse response experiment: Time resolved measurements of electron emission excited by fs-laser pulse Polarization measurements Photoexcitation Shift of transverse profile against slit Beam deflection

Pulse response of SL Al0.2In0.16Ga0.64As(3.5nm)/ Al0.28Ga0.72As(4.0nm) 15 periods Time dependence of electron emission Evidence of partial electron localization Non-exponential decay 1 < calc < 2 1 = 4 ps 2 = 12 ps calc = 6 ps SPES PSTP2011

Electronic transport in SL Electron scattering BBR Buffer e1 Localized states Capture Detachment Photoexcitation Recombination h Tunneling between QWs Tunneling to BBR Recombination hh1 lh1 Time of electron tunneling from last QW to BBR f  exp(2b), f  200 fs Recombination time r  100 ps Time of resonant tunneling between neighbouring QWs QW = ħ/∆E  exp(b), QW  20 fs Time of ballistic motion in SL SL = ħN/∆E Momentum relaxation time p  0.1 ps; Free pass N = QW/p  5 Capture time c  2-10 ps; Detachment time d  100 ps SPES PSTP2011

Electronic transport in SL Kinetic equation  – electronic density matrix H – effective Hamiltonian of SL in tight binding approximation, describes electron tunneling within SL I{} – collision term including: collisions within each QW with phonons and impurities described in constant relaxation time , p, approximation tunneling through the last SL barrier to BBR optical pumping electron capture by localized states and reverse detachment process SPES PSTP2011

Electronic diffusion in SL bulk GaAs N – number of SL periods V = E/4 = ħ/4QW – matrix element of interwell electron transition D = 40 cm2/s – diffusion coefficient S = 107 cm/s – surface recombination velocity For SL Al0.2In0.19Ga0.61As(5.4nm)/ Al0.4Ga0.6As(2.1nm) D = 12.6 cm2/s , S = 3.5*106 cm/s SPES PSTP2011

Role of partial localization: pulse response Electron localization Double exponential decay Fast decay rate 1-1 = t-1 + c-1 Slow decay rate 2-1 = d-1( c/(t+ c)) 1 < t < 2 t - miniband transport time c - capture time d - detachment time No electron localization Single exponential decay with decay time  = t SPES PSTP2011

Role of partial localization: QE n –total electron concentration nm – concentration of miniband electrons nl – concentration of localized electrons nm < n = nm + nl Electron diffusion in SL Stationary pumping Decrease of diffusion length Bulk GaAs LD  1m Perfect SL 6-905 LD = 0.4m Real SL 6-905 LD = 0.08m Maximal QE, infinite working layer SPES PSTP2011

QE as a function of working layer thickness Role of partial localization: QE QE as a function of working layer thickness SPES PSTP2011

Time dependence of electron emission Pulse response of SL 5-998 Al0.2In0.16Ga0.64As (3.5nm)/Al0.28Ga0.72As(4.0nm) 15 periods Time dependence of electron emission Parameters t = 5.8 ps – miniband transport time, calculated parameter c = 4.5 ps – capture time, fitting parameter d = 6.0 ps – detachment time, fitting parameter  = 12 ps – total extraction time r*= 44 ps – effective recombination time LD = 0.27 m – diffusion length BSL = 0.88 - extraction probability SPES PSTP2011

Time dependence of electron emission Pulse response of SL 7-396 Al0.2In0.19Ga0.61As (5.4nm)/Al0.4Ga0.6As(2.1nm) 12 periods Time dependence of electron emission Parameters t = 4.5 ps – miniband transport time, calculated parameter c = 9.0 ps – capture time, fitting parameter d = 110 ps – detachment time, fitting parameter  = 23 ps – total extraction time r*= 15 ps – effective recombination time LD = 0.14 m – diffusion length BSL = 0.77 - extraction probability SPES PSTP2011

Time dependence of electron emission Pulse response of SL 6-905 Al0.2In0.16Ga0.64As (5.1nm)/Al0.36Ga0.64As(2.3nm) 10 periods Time dependence of electron emission Parameters t = 2.5 ps – miniband transport time, calculated parameter c = 2.1 ps – capture time, fitting parameter d = 130 ps – detachment time, fitting parameter  = 40 ps – total extraction time r*= 3.6 ps – effective recombination time LD = 0.077 m – diffusion length BSL = 0.59 - extraction probability SPES PSTP2011

Time dependence of electron emission Pulse response of SL 6-908 Al0.2In0.16Ga0.64As (5.1nm)/Al0.36Ga0.64As(2.3nm) 6 periods Time dependence of electron emission Parameters t = 1.2 ps – miniband transport time, calculated parameter c = 4.5 ps – capture time, fitting parameter d = 50 ps – detachment time, fitting parameter  = 9.4 ps – total extraction time r*= 12 ps – effective recombination time LD = 0.14 m – diffusion length BSL = 0.91 - extraction probability SPES PSTP2011

Results SPES PSTP2011 Sample Number of periods Miniband transport time, t, ps Capture time, c, ps Detachment time, d,, ps Total transport time, ps Diffusion length, periods Extraction probability, % SL 5-337 15 15.8 3.7 160 63 8 36 SL 5-998 6.0 4.5 12 88 SL 7-395 200 45 11 55 SL 7-396 9.0 110 23 18 77 SL 6-905 10 2.5 2.1 130 40 59 SL 6-908 6 1.2 50 9.4 19 91 SPES PSTP2011

Calculated response time dependence on the length of SL 6 - 905-908 SPES PSTP2011

Summary Partial electron localization leads to non-exponential decay of pulse response. Analysis of pulse response allows to determine the characteristic times of capture and detachment processes. Partial electron localization decreases considerably the diffusion length in SL Partial electron localization limits QE for thick working layer. For practical application one should employ SL photocathodes with no more than 10 – 12 periods. SPES PSTP2011

Outlook study spin polarized electron transport for various excitation energies, doping levels and SL parameters. clarify the nature of localized states. figure out how localization can be reduced in order to increase QE. SPES PSTP2011

Thanks for your attention! This work was supported by Russian Ministry of Education and Science under grant 2.1.1/2240 DFG through SFB 443 Thanks for your attention! SPES PSTP2011

p >> SL = ħN/∆E, p = 10-13 s, ∆E = 40 meV, ∆Ep /ħ = 6 Ballistic transport Tunneling resonances En = E0 − ∆E/2Cos(qnd) qn = πn/d(N+1) ∆E – width of e1 miniband N – number of QW in SL Time of resonant tunneling SL = ħN/∆E  N·exp(b) Transport time  = ħ/Γ  N·exp(2b) Γ << ∆E ,  >>  SL b b b p >> SL = ħN/∆E, p = 10-13 s, ∆E = 40 meV, ∆Ep /ħ = 6 Optimal choice: bf = b/2

Pulse response of SL Al0.2In0.19Ga0.61As (5.4nm) / Al0.4Ga0.6As(2.1nm) 12 periods Time dependence of electron emission: intensity and polarization Gradual depolarization with s = 81ps Long tail of emission current - - emission from localized states

Time dependence of electron emission Pulse response of SL 6-908 (6 periods) at different wavelength Time dependence of electron emission Emission spectra P, QE

Transport below conduction band edge

Calculations of SL’s energy spectrum and photoabsorption within 8-band Kane model Miniband spectrum: Photoabsorption coefficient: Polarization:

Photocathode with DBR Goal: considerable increase of QE at the main polarization maximum and decrease of cathode heating Method: Resonance enhancement of photoabsorption in SL integrated into optical resonance cavity Photoabsorption in the working layer: L << 1,  - photoabsorbtion coefficient, L - thickness of SL Resonant enhancement by factor 2/(1-(RDBRRGaAs) 1/2)2 Heating is reduced by factor L