1. Workshop on Sources of Polarized Electrons and High Brightness Electron Beams Optimization of Semiconductor Superlattice for Spin-Polarized Electron Source Leonid G. Gerchikov Laboratory of Spin-Polarized Electron Spectroscopy Department of Experimental Physics State Polytechnic University St. Petersburg, Russia

2. Collaborators Department of Experimental Physics, St. Petersburg State Polytechnic University, Russia, Yuri A. Mamaev, Yuri P.Yashin, Vitaly V. Kuz’michev, Dmitry A. Vasiliev, Leonid G. Gerchikov A.F. Ioffe Physicotechnical Institute RAS, Russia, Viktor M. Ustinov, Aleksey E. Zhukov, Vladimir S. Mikhrin, Alexey P. Vasiliev Stanford Linear Accelerator Center, Stanford, CA, USA, James E. Clendenin, Takashi Maruyama Institute of Nuclear Physics, Mainz University, Mainz, Germany, Kurt Aulenbacher, Valeri Yu. Tioukin

3. Introduction –Goals of optimization –Problems of optimization –Best photocathodes Calculations of SL parameters –Energy spectrum –Photoabsorption –Transport AlInGaAs/AlGaAs SL with strained QW –Optimized design –Results Summary&OutlookOUTLINE

4. Goals of optimization High maximal P at large QE

5. High polarization of electron emission from strained semiconductor SL at the expense of QE SL Al 0.2 In 0.155 Ga 0.65 As(5.1nm)/Al 0.36 Ga 0.64 As(2.3nm) Spectra of electron emission: Polarization P and Quantum Efficiency QE Polarization is maximal at photoabsorption threshold where QE is small. Strain relaxation does not allow to produce thick photocathode with high QE. Rise of the vacuum level increases P and decreases QE

6. To get the best PQE Large valence band splitting > 60 meV High strain splitting and offsets in valence band Effective electronic transport along SL axes High quality SL, uniform layer composition and thickensses Low doping in SL Thick working layer High NEA value Heavy doped BBR layer

7. Best photocathodes SampleCompositionP max QE(  max ) Team SLSP16GaAs(3.2nm)/ GaAs 0.68 P 0.34 (3.2nm) 92%0.5%Nagoya University, 2005 SL5-777GaAs(1.5nm)/ In 0.2 Al 0.23 Ga 0.57 As(3.6nm) 91%0.14%SPbSPU, 2005 SL7-307Al 0.4 Ga 0.6 As(2.1nm)/ In 0.19 Al 0.2 Ga 0.57 As(5.4nm) 92%0.85%SPbSPU, 2007

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

9. P&QE of electron emission P 0 - initial polarization, K t, K e – depolarization factors on stages of transport in SL and emission through BBR,  s,  t – transport and spin relaxation times in SL. R – reflection from GaAs, B – probability of electron emission through BBR.

10. Polarization spectrum Initial electron polarization P 0 Energy band spectrum Main optical transitions hh1 – e1 lh1 - e1 hh2 - e2 lh2 - e2 Maximal P 0 is determined by: Valence band splitting  E hh- lh = E hh1 - E lh1 Broadening of hole spectrum  Photoabsorption spectrum Maximal P 0 is limited by: mixture of hh and lh states due to smearing of band edge and broadening of hole spectrum caused by doping and fluctuations of layer composition Photoluminescence spectrum Initial polarization losses amount up to 15% depending on structure quality and design-  and  E hh-lh

11. Initial electron polarization P 0 Enlarge  E hh-lh to increase maximal P 0 by increase of QW deformation Large strain deformation leads to structural defects and strain relaxation Optimal combination of strain deformation and quantum confinement effect to provide maximal valence band splitting with minimal risk of strain relaxation and good transport properties

12. Electronic transport in SL I=I 0 T RI0RI0 I0I0 Ballistic electron tunneling though SL T res  exp(-  b)T f  exp(-2  b) BBR Tunneling probability T = I/I 0 Tunneling time  = ∫ |Ψ(x)|² dx/I T f << T res

13. Tunneling resonances E n = E 0 − ∆E/2Cos(q n d) q n = πn/d(N+1) ∆E – width of e1 miniband N – number of QW in SL Time of resonant tunneling  SL = ħ/∆E  exp(  b) Transport time  = ħ/Γ  exp(2  b) Γ >  SL Ballistic transport bbb Optimal choice: b f = b/2

14. Electronic diffusion in SL Kinetic equation  - electronic density matrix H – effective Hamiltonian of SL in tight binding approximation St{  } – collision term including: collisions within each QW in constant relaxation time,  p, approximation tunneling through last barrier to BBR optical pumping Stationary pumping Approximate solution N – number of QW in SL V =  E/4 – matrix element of interwell electron transition

15. Electronic diffusion in SL bulk GaAs D = 40 cm 2 /s – diffusion coefficient S = 10 7 cm/s – surface recombination velocity For SL Al 0.2 In 0.2 Ga 0.6 As(5.4nm)/ Al 0.4 Ga 0.6 As(2.1nm) D = 12 cm 2 /s, S = 3*10 6 cm/s

16. Pulse response of SL Al 0.2 In 0.16 Ga 0.64 As(3.5nm)/ Al 0.28 Ga 0.72 As(4.0nm) 15 periods Time dependence of electron emission D = 16 cm 2 /s, S = 3.4*10 6 cm/s * K. Aulenbacher et al, Mainz, 2006

17. Strained-well SL Unstrained barrier a b = a 0 GaAs Substrate Buffer Layer a 0 - latt. const GaAs BBR Strained QW a w > a 0 Strained QW a w > a 0 Unstrained barrier a b = a 0 SL Large valence band splitting due to combination of deformation and quantum confinement effects in QW

18. MBE grown AlInGaAs/AlGaAs strained-well superlattice SPTU & FTI, St.Petersburg E g = 1.536 eV, valence band splitting E hh1 - E lh1 = 87 meV, Maximal polarization P max = 92% at QE = 0.85% CompositionThicknessDoping As cap GaAs QW60 A 7  10 18 cm -3 Be Al 0.4 Ga 0.6 As SL 21 A 3  10 17 cm -3 Be In 0.19 Al 0.2 Ga 0.65 As54 A Al 0.35 Ga 0.65 AsBuffer 0.3  m6  10 18 cm -3 Be p-GaAs substrate

19. Choice of SL parameters y - In concentration in QW x - Al concentration in QW z - Al concentration in barrier a – QW width b – barrier width Al x In y Ga 1-x-y As - QWAl x Ga 1-x As - Barrier y = 0.2,  E v = 76 meV x = 0.19, E g = 1.536 eV a = 5.4 nm,  E hh-lh = 87 meV z = 0.4, U hh = 332 meV, U lh = 258 meV, U e = 234 meV, b = 2.1 nm,  E e = 31 meV

20. SL Al 0.19 In 0.2 Ga 0.61 As(5.4nm)/Al 0.4 Ga 0.6 As(2.1nm) P max = 92%, QE = 0.85%

21. SL Al 0.19 In 0.2 Ga 0.61 As(5.4nm)/Al 0.4 Ga 0.6 As(2.1nm)  = 25 meV, P 0max = 97% Polarization losses at photoabsorption – 3% transport and emission – 5%

22. 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-(R DBR R GaAs ) 1/2 ) 2 Heating is reduced by factor  L Photocathode with DBR

23. Resonant enhancement of QE Accepted for publication at Semiconductors, 2008

24. Summary & Outlook  Photocathode based on optimized AlInGaAs/AlGaAs strained-well SL demonstrates P max = 92% at QE = 0.85%.  Maximal initial photoelectron polarization P 0 = 97%. To increase P 0 the higher fabrication quality SL is needed.  Optimization of polarization losses and QE on the stage of electron transport and emission needs an additional investigations.  DBR can considerably increase QE and reduce cathode heating.

25. Thanks for your attention! This work was supported by Russian Ministry of Education and Science under grant N.P. 2.1.1.2215 in the frames of a program “Development of the High School scientific potential” Swiss National Science Foundation under grant SNSF IB7420-11111

26. SL In 0.155 Al 0.2 Ga 0.645 As(5.1nm)/Al 0.36 Ga 0.64 As(2.3nm)

27. Reproducibility

28. Polarization losses caused by mixture of hh and lh states due to smearing of band edge and broadening of hole spectrum amount 5-10% depending on structural quality,  = 10-30meV. Initial electron polarization P 0 for different values of hole spectrum broadening and smearing of absorption edge Polarization losses GaAs 0.83 P 0.17 /Al 0.1 In 0.18 Ga 0.72 As (5x4nm)x20 QE spectrum for different values valence band tails  = 10-30meV

29.  s – время спиновой релаксации, при T=300K, N a =4*10 17 cm -3  s = 7*10 -11 s  ext – время выхода электронов из СР в область BBR,  ext = d/S + d 2 /12D, d – ширина СР, S – скорость поверхностной рекомбинации на границе BBR, D – коэффициент диффузии. При T = 300K S = 1/4 = 10 7 cm/s. Для тонкого рабочего слоя d = 100nm  ext = d/S,  ext = 7*10 -13 s Поляризационные потери  ext /  s за время транспорта не более 1% Потери поляризации при транспорте

30. High-Energy physics requirements High electron polarization, P > 80% AcceleratorP, %Beam MAMI  85% QE > 1% eRHIC at BNL  70% 50-250 mA, QE > 0.5% ILC  80% QE > 0.5% 90% is better High QE for large beam currents Large electronic current requirement Light energy limitations: Surface charge saturation Heating High QE

31. Reflectivity

32. Spectra of electron emission, P( ), QE( )

34. Resonant enhancement of QE

35. Optimization of Photocathode structure SL structure: layers composition and thickness are chosen to assure  E g =   for P(   )=P max   E hh-lh > 60meV for high polarization   E e1 > 40meV for effective electron transport DBR structure: 20x(AlAs( /4)/ (Al x Ga 1-x As( /4))  Layer thickness l = /4n(  ) for Bragg reflection  x  0.8 for large reflection band width  = 2  n/n Fabry-Perot resonance cavity: BBR + SL + buffer layer  Effective thickness = k /2 for QE(   ) = QE max  Effective thickness of BBR+SL  /4

36. Simulation of resonant photoabsorption SL’s energy band structure, photoabsorption coefficient, polarization of photoelectrons. Method: kp – method within 8-band Kane model. A.V. Subashiev, L.G. Gerchikov, and A.I. Ipatov. J. Appl. Phys., 96, 1511 (2004). Distribution of electromagnetic field in resonance cavity, reflectivity, QE. Method: transfer matrixes. M.Born and E.Wolf. Princeples of Optics, Pergamon Press, New York, 1991

37. Ballistic transport