XIVth International Workshop on Polarized Sources, Targets & Polarimetry
Leonid G. GerchikovLaboratory of Spin-Polarized Electron Spectroscopy
Department of Experimental PhysicsState Polytechnic University
St. Petersburg, Russia
Period Dependence of Time Response of Period Dependence of Time Response of Strained Semiconductor SuperlatticesStrained Semiconductor Superlattices
CollaboratorsCollaborators
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
• Introduction– 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
OutlineOutline
SPES PSTP2011
Best photocathodesBest 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)
92% 0.85% SPbSPU, 2007
SPES PSTP2011
SL SL InIn0.160.16AlAl0.20.2GaGa0.640.64As(5.1nm)/AlAs(5.1nm)/Al0.360.36GaGa0.640.64As(2.3nm)As(2.3nm)
2 4 6 8 10 12 14 16 18 20
0.1
1
50
60
70
80
90
100
QE
, %
SL thickness, pairs
o QE P
Po
lari
zatio
n,
%
SPES PSTP2011
Strained-wellStrained-well SL SL
Unstrained barrierab = a0
GaAs Substrate
Buffer Layera0 - latt. const
GaAs BBR
Strained QWaw > a0
Strained QWaw > a0
Unstrained barrierab = a0
SL
Large valence band splitting due to combination of deformation and quantum confinement effects in QW
SPES PSTP2011
MBE grown AlInGaAs/AlGaAs strained-well SLMBE grown AlInGaAs/AlGaAs strained-well SL
Eg = 1.536 eV, valence band splitting Ehh1 - Elh1 = 87 meV, Maximal polarization Pmax= 92% at QE = 0.85%
Composition Thickness Doping
As cap
GaAs QW 60 A 71018 cm-3 Be
Al0.4Ga0.6As SL
21 A31017 cm-3 Be
In 0.19Al 0.2Ga 0.65As 54 A
Al0.35Ga0.65As Buffer 0.3 m 61018 cm-3 Be
p-GaAs substrate
SPES PSTP2011
Experimental method
Photoexcitation
Pulse response experiment:Time resolved measurements of electron emission
excited by fs-laser pulse
Experimental method
Photoexcitation
Beam deflection
Pulse response experiment:Time resolved measurements of electron emission
excited by fs-laser pulse
Experimental method
Photoexcitation
Beam deflection
Pulse response experiment:Time resolved measurements of electron emission
excited by fs-laser pulse
Shift of transverse profile against slit
Experimental method
Pulse response experiment:Time resolved measurements of electron emission
excited by fs-laser pulse
Photoexcitation
Beam deflectionShift of transverse profile against slit
Polarization measurements
Pulse response of SL Pulse response of SL AlAl0.20.2InIn0.160.16GaGa0.640.64As(3.5nm)/ As(3.5nm)/
AlAl0.280.28GaGa0.720.72As(4.0nm) 15 periodsAs(4.0nm) 15 periods
Time dependence of electron emission
0 5 10 15 200.0
0.2
0.4
0.6
0.8
1.0
Em
issi
on,
arb.
un.
Time, ps
Experiment Calculations Non-exponential decay
1 < calc < 2
1 = 4 ps
2 = 12 ps
calc = 6 ps
Evidence of partial electron localization
SPES PSTP2011
Electronic transport in SLElectronic transport in SL
Recombination time r 100 ps
Time of resonant tunneling between neighbouring QWsQW = ħ/∆E exp(b), QW 20 fsTime of ballistic motion in SLSL = ħN/∆E
Time of electron tunneling from last QW to BBRf exp(2b), f 200 fs
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
Buffer BBRe1
hh1lh1
Localized states
h RecombinationPhotoexcitation
Recombination
Tunneling between QWs Tunneling to BBR
Electron scattering
Capture Detachment
Electronic transport in SLElectronic transport in SL
ˆˆˆ
ˆIH
i
t
Kinetic equation
– electronic density matrixH – 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 inElectronic diffusion in
SL SL bulk GaAsbulk GaAs
fp
t NV
NN
2
2
6
)1)(2/1(
S
L
D
Lt
3
2
D = 40 cm2/s – diffusion coefficient S = 107 cm/s – surface recombination velocity
fp dSdVD
periodSLdN
/,/2
,1222
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
N – number of SL periodsV = E/4 = ħ/4QW – matrix element of
interwell electron transition
Role of partial localization: pulse responseRole of partial localization: pulse response
No electron localizationSingle exponential decay
with decay time = t
Electron localization
Double exponential decayFast 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
SPES PSTP2011
-5 0 5 10
0.01
0.1
1
Em
issi
on,
arb.
un.
Perfect SL 6-905, no localization
Real SL 6-905, partial localization
Time, ps
Role of partial localization: QERole of partial localization: QE
02
2
gn
dx
ndD
r
m
Electron diffusion in SL Stationary pumping
n –total electron concentrationnm – concentration of miniband electronsnl – concentration of localized electronsnm < n = nm + nl
n
ng
n
dx
ndD m
rrr
mm
**2
2
,0
rd
rdc
rcrrD DL
** ,Decrease of diffusion length
Bulk GaAs LD 1mPerfect SL 6-905 LD = 0.4m Real SL 6-905 LD = 0.08m
Maximal QE, infinite working layer
D
D
L
LRBQE
1
1
SPES PSTP2011
Role of partial localization: QERole of partial localization: QE
QE as a function of working layer thickness
SPES PSTP2011
10 20 30 400.0
0.2
0.4
0.6
0.8
1.0
QE
, %
Number of SL periods
Perfect SL 6-905, no electron localization Real SL 6-905, partial electron localization
Pulse response of SL 5-998Pulse response of SL 5-998 AlAl0.20.2InIn0.160.16GaGa0.640.64As (3.5nm)/AlAs (3.5nm)/Al0.280.28GaGa0.720.72As(4.0nm) As(4.0nm)
15 periods15 periods
Time dependence of electron emission
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
timeLD = 0.27 m – diffusion lengthBSL = 0.88 - extraction probability
Parameters
0 5 10 15 20
0.1
1
Em
issi
on,
arb.
un.
Time, ps
Experiment Theory, no localization Theory, partial localization
SPES PSTP2011
Pulse response of SL 7-396Pulse response of SL 7-396 AlAl0.20.2InIn0.190.19GaGa0.610.61As (5.4nm)/AlAs (5.4nm)/Al0.40.4GaGa0.60.6As(2.1nm) As(2.1nm)
12 periods12 periods
Time dependence of electron emission Parameters
SPES PSTP2011
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
timeLD = 0.14 m – diffusion lengthBSL = 0.77 - extraction probability
-10 0 10 20 30 40
0.01
0.1
1 Experiment Theory, no localization Theory, partial localization
Em
issi
on,
arb.
un.
Time, ps
Pulse response of SL 6-905Pulse response of SL 6-905 AlAl0.20.2InIn0.160.16GaGa0.640.64As (5.1nm)/AlAs (5.1nm)/Al0.360.36GaGa0.640.64As(2.3nm) As(2.3nm)
10 periods10 periods
Time dependence of electron emission Parameters
SPES PSTP2011
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
timeLD = 0.077 m – diffusion lengthBSL = 0.59 - extraction probability
-5 0 5 10
0.01
0.1
1
Em
issi
on,
arb.
un.
Experiment Theory, no localization Theory, partial localization
Time, ps
Pulse response of SL 6-908Pulse response of SL 6-908 AlAl0.20.2InIn0.160.16GaGa0.640.64As (5.1nm)/AlAs (5.1nm)/Al0.360.36GaGa0.640.64As(2.3nm) As(2.3nm)
6 periods6 periods
Time dependence of electron emission Parameters
SPES PSTP2011
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
timeLD = 0.14 m – diffusion lengthBSL = 0.91 - extraction probability
-5 0 5 10
0.01
0.1
1
Experiment Theory, no localization Theory, partial localization
Em
issi
on,
arb.
un.
Time, ps
ResultsResultsSample Number of
periodsMiniband transport
time, t, psCapture
time, c, psDetachment 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 15 6.0 4.5 6.0 12 36 88
SL 7-395 12 4.5 3.7 200 45 11 55
SL 7-396 12 4.5 9.0 110 23 18 77
SL 6-905 10 2.5 2.1 130 40 10 59
SL 6-908 6 1.2 4.5 50 9.4 19 91
0 2 4 6 8 10 12 14 160
1
2
3
4
5
6
Tim
e, p
s
Number of periods
Fast decay time Miniband tranport time
SL 5 - 337 SL 5 - 998 SL 7 - 396 SL 7 - 395 SL 6 - 905 SL 6 - 908
SPES PSTP2011
10 20 30 400
10
20
miniband transport time, t
tunneling time, tunn
diffusion time, diff
Tim
e, p
s
Number of SL priods
10 20 30 400
10
20
miniband transport time, t
tunneling time, tunn
diffusion time, diff
response decay time, 1
Tim
e, p
s
Number of SL priods
Calculated response time dependence on Calculated response time dependence on
the length of SL 6 - 905-908 the length of SL 6 - 905-908
D
dNN
S
Nd
diff
tunn
difftunnt
3
)1)(2/1( 2
1111
ct
SPES PSTP2011
SummarySummary
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
OutlookOutlook
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!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
SPES PSTP2011
Tunneling resonancesEn = E0 − ∆E/2Cos(qnd) qn = πn/d(N+1)
∆E – width of e1 miniband
N – number of QW in SL
Time of resonant tunnelingSL = ħN/∆E N·exp(b)
Transport time = ħ/Γ N·exp(2b)
Γ << ∆E , >> SL
60 62 64 66 68 70 72 74 76 78 800.0
0.2
0.4
0.6
0.8
1.0
E, meV
p
s
T
0.1
1
10
100
Ballistic transportBallistic transport
60 62 64 66 68 70 72 74 76 78 800.0
0.2
0.4
0.6
0.8
1.0
0.1
1
10
100
p
s
E, meV
T
b bb
Optimal choice: bf = b/2p >> SL = ħN/∆E, p = 10-13 s, ∆E = 40 meV, ∆Ep /ħ = 6
Pulse response of SL Pulse response of SL AlAl0.20.2InIn0.190.19GaGa0.610.61As (5.4nm) / As (5.4nm) /
AlAl0.40.4GaGa0.60.6As(2.1nm) 12 periodsAs(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-10 -5 0 5 10 15 20 25 30 35 40
0
20
40
60
80
100-10 0 10 20 30 40
0.01
0.1
1
Em
issi
on, a
rb. u
n.
Pol
ariz
atio
n, %
Time, ps
Polarization exponential fit
Emission
Pulse response of SL 6-908 (Pulse response of SL 6-908 (6 periods)6 periods) at different wavelengthat different wavelength
Time dependence of electron emission
-4 -2 0 2 4 6 8 10
0.01
0.1
1
Em
issi
on
Time, ps
= 820nm = 800nm = 790nm
6pairs SL 6-908
700 750 800 850
10-2
10-1
100
20
40
60
80
100
QE
, %
Wavelength, nm
QE
Band edge
P
Po
lari
zatio
n,
%
Emission spectra P, QE
Transport below conduction band edgeTransport below conduction band edge
780 800 820 840 860 880
780 800 820 840 860 880
50
60
70
80
90
50
60
70
80
90
P, %
Polarization, exp. Polarization, theor.
Wavelenght, nm
kT
E
gtt
g
eE
0)()(
)()( 0
ts
sPP
1.44 1.46 1.48 1.50 1.52 1.54 1.560
5
10
15
20
25
30
35
40
, ps
E, eV
t, exp.
t=3e-(E-E
g)/kT
Calculations of SL’s energyCalculations of SL’s energy spectrum and spectrum and photoabsorption within 8-band Kane modelphotoabsorption within 8-band Kane model
Miniband spectrum:qq qEH ,, ),(ˆ
kk k
),(2
exp1
,,
, qAnzd
iued n
n
iqziq kk
k
Photoabsorption coefficient:
Polarization:
0P
h
GaAsSubstrate Buffer BBR SL
e
RGaAs
= 0.3h
GaAsSubstrate DBR Buffer BBR SL
e
RDBR
= 1
Goal: considerable increase of QE at the main polarization maximum and decrease of cathode heatingMethod: 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
Photocathode with DBRPhotocathode with DBR