1. 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

2. 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

3. 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

4. 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

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

6. 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

7. 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 = eV, valence band splitting Ehh1 - Elh1 = 87 meV,
Maximal polarization Pmax= 92% at QE = 0.85%
SPES PSTP2011

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

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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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 LD = 0.4m
Real SL LD = 0.08m
Maximal QE, infinite working layer
SPES PSTP2011

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

19. Time dependence of electron emission
Pulse response of SL 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 = extraction probability
SPES PSTP2011

20. Time dependence of electron emission
Pulse response of SL 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 = extraction probability
SPES PSTP2011

21. Time dependence of electron emission
Pulse response of SL 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 = m – diffusion length
BSL = extraction probability
SPES PSTP2011

22. Time dependence of electron emission
Pulse response of SL 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 = extraction probability
SPES PSTP2011

23. 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

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

25. 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

26. 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

27. 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

28. 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 = s, ∆E = 40 meV, ∆Ep /ħ = 6
Optimal choice: bf = b/2

29. 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

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

31. Transport below conduction band edge

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

33. 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