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
–
•
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
–
–
•
SPES
Comparison of theory and experiment. Determination
of localization times
Dependence of the response time on number of SL
periods
Conclusions
PSTP2011
Best photocathodes
Sample
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
Composition
PSTP2011
SL In0.16Al0.2Ga0.64As(5.1nm)/Al0.36Ga0.64As(2.3nm)
P
o QE
100
1
QE, %
80
70
60
0.1
50
2
4
6
8
10
12
14
16
SL thickness, pairs
SPES
PSTP2011
18
20
Polarization, %
90
Strained-well SL
GaAs BBR
Unstrained barrier
a b = a0
Strained QW
aw > a0
SL
Strained QW
aw > a0
Unstrained barrier
a b = a0
Buffer Layer
a0 - latt. const
GaAs Substrate
SPES
PSTP2011
Large valence band splitting
due
to
combination
of
deformation and quantum
confinement effects in QW
MBE grown AlInGaAs/AlGaAs strained-well SL
Composition
Thickness
Doping
As cap
GaAs QW
Al0.4Ga0.6As
In 0.19Al 0.2Ga 0.65As
Al0.35Ga0.65As
60 A
SL
Buffer
21 A
54 A
0.3 mm
71018 cm-3 Be
31017 cm-3 Be
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
Experimental method
Pulse response experiment:
Time resolved measurements of electron emission
excited by fs-laser pulse
Photoexcitation
Experimental method
Pulse response experiment:
Time resolved measurements of electron emission
excited by fs-laser pulse
Photoexcitation
Beam deflection
Experimental method
Pulse response experiment:
Time resolved measurements of electron emission
excited by fs-laser pulse
Photoexcitation
Beam deflection
Shift of transverse
profile against slit
Experimental method
Pulse response experiment:
Time resolved measurements of electron emission
excited by fs-laser pulse
Polarization measurements
Photoexcitation
Beam deflection
Shift of transverse
profile against slit
Pulse response of SL Al0.2In0.16Ga0.64As(3.5nm)/
Al0.28Ga0.72As(4.0nm) 15 periods
Evidence of partial electron
localization
Emission, arb.un.
Time dependence of electron emission
1.0
Experiment
Calculations
Non-exponential decay
1 < 
0.8
0.6
0.4
0.2
0.0
0
5
10
Time, ps
SPES
PSTP2011
15
20
calc

< 2
1 = 4 ps
2 = 12 ps
calc = 6 ps
Electronic transport in SL
Electron scattering
Buffer
BBR
e1
Localized states
Photoexcitation
h
Capture Detachment
Tunneling between QWs
Recombination
Tunneling to BBR
Recombination
hh1
lh1
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
SPES
PSTP2011
Time of electron tunneling from
last QW to BBR
f  exp(2b), 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
Electronic transport in SL
Kinetic equation
ˆ i ˆ
 ˆH   I ˆ 
t 
 – 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
bulk GaAs
SL
 ( N  1 / 2)( N  1)
t 
 N f
2
6V  p
2
N – number of SL periods
V = E/4 = ħ/4QW – matrix element of
interwell electron transition
N  1, d  SL period
D  2V d  p /  , S  d /  f
2
2
2
L2 L
t 

3D S
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
Emission, arb. un.
1
Perfect SL 6-905,
no localization
Real SL 6-905,
partial localization
0.1
Electron localization
Double exponential decay
Fast decay rate
1-1 = t-1 + c-1
Slow decay rate
2-1 = d-1( c/(t+ c))
0.01
-5
0
5
10
1 < t < 2
Time, ps
No electron localization
Single exponential decay
with decay time  = t
SPES
PSTP2011
t - miniband transport time
c - capture time
d - detachment time
Role of partial localization: QE
Electron diffusion in SL
Stationary pumping
d 2 nm n
D
 g 0
2
r
dx
Decrease of diffusion length
Bulk GaAs LD  1mm
Perfect SL 6-905 LD = 0.4mm
Real SL 6-905 LD = 0.08mm
Maximal QE, infinite
working layer
SPES
PSTP2011
n –total electron concentration
nm – concentration of miniband electrons
nl – concentration of localized electrons
nm < n = nm + nl
d 2 nm nm
nm
*
D
 *  g  0,  r   r
2
n
dx
r
 c r
LD  D ,  
 d r
c 
 d  r
*
r
*
r
B1  R LD
QE  
1  LD
Role of partial localization: QE
QE as a function of working layer thickness
Perfect SL 6-905, no electron localization
Real SL 6-905, partial electron localization
1.0
QE, %
0.8
0.6
0.4
0.2
0.0
10
20
30
Number of SL periods
SPES
PSTP2011
40
Pulse response of SL 5-998
Al0.2In0.16Ga0.64As (3.5nm)/Al0.28Ga0.72As(4.0nm)
15 periods
Time dependence of electron emission
Emission, arb.un.
1
Parameters
t = 5.8 ps – miniband transport
Experiment
Theory, no localization
Theory, partial localization
time, calculated parameter
c = 4.5 ps – capture time, fitting
parameter
d = 6.0 ps – detachment time, fitting
parameter
0.1
 = 12 ps – total extraction time
r*= 44 ps – effective recombination
0
5
10
Time, ps
SPES
PSTP2011
15
20
time
LD = 0.27 mm – diffusion length
BSL = 0.88 - extraction probability
Pulse response of SL 7-396
Al0.2In0.19Ga0.61As (5.4nm)/Al0.4Ga0.6As(2.1nm)
12 periods
Time dependence of electron emission
Emission, arb.un.
1
Parameters
t = 4.5 ps – miniband transport
Experiment
Theory, no localization
Theory, partial localization
time, calculated parameter
c = 9.0 ps – capture time, fitting
parameter
0.1
d = 110 ps – detachment time,
fitting parameter
0.01
-10
0
10
20
Time, ps
SPES
PSTP2011
30
40
 = 23 ps – total extraction time
r*= 15 ps – effective recombination
time
LD = 0.14 mm – diffusion length
BSL = 0.77 - extraction probability
Pulse response of SL 6-905
Al0.2In0.16Ga0.64As (5.1nm)/Al0.36Ga0.64As(2.3nm)
10 periods
Time dependence of electron emission
Emission, arb. un.
1
Experiment
Theory, no localization
Theory, partial localization
Parameters
t = 2.5 ps – miniband transport
time, calculated parameter
c = 2.1 ps – capture time, fitting
parameter
0.1
d = 130 ps – detachment time,
fitting parameter
 = 40 ps – total extraction time
r*= 3.6 ps – effective recombination
0.01
-5
0
5
Time, ps
SPES
PSTP2011
10
time
LD = 0.077 mm – diffusion length
BSL = 0.59 - extraction probability
Pulse response of SL 6-908
Al0.2In0.16Ga0.64As (5.1nm)/Al0.36Ga0.64As(2.3nm)
6 periods
Time dependence of electron emission
Experiment
Theory, no localization
Theory, partial localization
Emission, arb. un.
1
Parameters
t = 1.2 ps – miniband transport
time, calculated parameter
c = 4.5 ps – capture time, fitting
parameter
d = 50 ps – detachment time, fitting
0.1
parameter
 = 9.4 ps – total extraction time
r*= 12 ps – effective recombination
0.01
-5
0
5
Time, ps
SPES
PSTP2011
10
time
LD = 0.14 mm – diffusion length
BSL = 0.91 - extraction probability
Results
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
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
Sample
6
Time, ps
5
Fast decay time
Miniband tranport time
4
3
SL 5 - 337
SL 5 - 998
SL 7 - 396
SL 7 - 395
SL 6 - 905
SL 6 - 908
2
1
0
0
2
4
6
8
10
12
Number of periods
SPES
PSTP2011
14
16
Calculated response time dependence on
the length of SL 6 - 905-908
 t   tunn   diff
miniband transport time, t
tunneling time, tunn
diffusion time, diff
Nd
 tunn 
S
2
( N  1 / 2)( N  1)d
 diff 
3D
response decay time, 1
Time, ps
20
10
 11   t1   c1
0
10
20
30
Number of SL priods
SPES
PSTP2011
40
Summary
Partial
electron localization leads to nonexponential 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
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
Ballistic transport
100
1.0
0.8
T
0.4
1
0.2
0.0
60
62
64
66
68
70
72
74
76
78
0.1
80
E, meV
b
b
b
T
 ps
10
0.6
100
Tunneling resonances
0.8
En = E0 − ∆E/2Cos(qnd)
q0.6n = πn/d(N+1)
∆E
– width of e1 miniband
0.4
N
– number of QW in SL
0.2
0.0
Time of resonant tunneling
E, meV
SL = ħN/∆E  N·exp(b)
Transport time
 = ħ/Γ  N·exp(2b)
Γ << ∆E ,  >>  SL
60
62
64
66
68
70
72
74
76
78
10
 ps
1.0
1
0.1
80
choice:
p >> SL = ħN/∆E, p = 10-13 s, Optimal
∆E = 40 meV,
∆Ebf p=/ħb/2
=6
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
0
10
20
1
60
0.1
40
20
0.01
0
-10
-5
0
5
10
15
20
Time, ps
25
30
Gradual depolarization
40
Emission
Polarization
exponential fit
80
Polarization, %
30
35
40
with
Emission, arb. un.
-10
100
s = 81ps
Long tail of
emission current - emission from
localized states
Pulse response of SL 6-908 (6 periods)
at different wavelength
Time dependence of electron
emission
Emission spectra
P, QE
6pairs SL 6-908
P
QE
100
1
0
10
0.1
-1
10
60
40
-2
10
0.01
-4
-2
0
2
4
Time, ps
6
8
10
700
750
800 Band edge
Wavelength, nm
20
850
Polarization, %
80
QE, %
Emission
 = 820nm
 = 800nm
 = 790nm
Transport below conduction band edge
780
90
800
820
840
860
880
90
Polarization, exp.
Polarization, theor.
80
70
70
60
60
50
50
P, %
80
780
800
820
840
860
880
Wavelenght, nm
40
35
t, exp.
30
t=3e
-(E-Eg)/kT
, ps
25
20
15
10
5
0
1.44
1.46
1.48
1.50
E, eV
1.52
1.54
1.56
 t ( )   t ( Eg )0 e

  Eg
kT
s
P( )  P0
 s   t ( )
Calculations of SL’s energy spectrum and
photoabsorption within 8-band Kane model
Miniband spectrum: ˆ
Hk ,q  E(k, q)k ,q
k ,q 
1 ik iqz
 2 
e
u
exp
nz  An, (k , q)
i


d
 d

 ,n
Photoabsorption coefficient:
Polarization:
 
P0 
  
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
h
Photoabsorption in
the working layer:
L << 1,
 - photoabsorbtion
coefficient,
e
GaAs
Substrate
Buffer
BBR
SL
L - thickness of SL
Resonant
enhancement by
factor
2/(1-(RDBRRGaAs) 1/2)2
Heating is reduced
by factor L
RDBR= 1
GaAs
Substrate
RGaAs= 0.3
e
DBR
Buffer
SL
BBR
h