Workshop on Sources of Polarized Electrons and High Brightness Electron Beams
Optimization of Semiconductor Superlattice for Spin-Polarized Electron Source
Leonid G. GerchikovLaboratory of Spin-Polarized Electron Spectroscopy
Department of Experimental PhysicsState Polytechnic University
St. Petersburg, Russia
CollaboratorsCollaborators
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
• 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&Outlook
OUTLINEOUTLINE
Goals of optimizationGoals of optimization
High maximal P at large QEHigh maximal P at large QE
High polarization of electron emission from High polarization of electron emission from
strained semiconductor SL at the expense of QEstrained semiconductor SL at the expense of QE
0.00 0.04
-0.04
-0.02
1.4
1.5
1.6
lh1
hh1
e1
k001
, A -1
Ene
rgy,
eV
k100
, A -1
valence band
bandbendingregion
electronemission
electrongeneration
heavy holem iniband
light holem iniband
InG aAs AlGaAs
E c
E v
550 600 650 700 750 800 850 900
10-5
10-4
10-3
10-2
10-1
100
101
0
20
40
60
80
100
QE
QE,
%
, nm
Polarization
Pola
rizat
ion,
%
SL Al0.2 In0.155 Ga0.65As(5.1nm)/Al0.36Ga0.64As(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
To get the bestTo get the best
PP QEQE•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
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)/
In0.19Al0.2Ga0.57As(5.4nm)
92% 0.85% SPbSPU, 2007
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
P&QE of electron emissionP&QE of electron emission
95.0,/
/
)()(
0
0
etsst
et
KK
P
KKPP
P0 - initial polarization,Kt , Ke – depolarization factors on stages of transport in SL and emission through BBR,s,t – transport and spin relaxation times in SL.
1.0,3.0
)()1()(
BR
BdRQE R – reflection from GaAs ,B – probability of electron emission through BBR.
Polarization spectrum
0,00 0,05 0,10
-0,15
-0,10
-0,05
1,5
1,6
1,7
hh4
lh2
hh3
hh2lh1
hh1
e2
e1
Kz, A-1
GaAs(9nm)/Ga0.6
Al0.4
As(9nm)
Ene
rgy,
eV
K||, A-1
Initial electron polarization Initial electron polarization PP00
Energy band spectrum
Main optical transitionshh1 – e1 lh1 - e1 hh2 - e2 lh2 - e2
Maximal P0 is determined by:• Valence band splitting Ehh-
lh= Ehh1 - Elh1
• Broadening of hole spectrum
Photoabsorption spectrum
1,40 1,45 1,50 1,55 1,60 1,65 1,70 1,750,0
0,5
1,0
1,5
2,0
2,5
3,0
3,5
4,0 Total Up Down Partial contributions
e2-lh2
e1-hh1
e1-lh1
e2-hh2
e2-lh1
e1-hh1
GaAs(9nm)/Ga0.6
Al0.4
As(9nm)
Ph
oto
ab
sorp
tion
Co
eff
icie
nt,
10
4 cm-1
Photon Energy, eV
Maximal P0 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
1.45 1.50 1.55 1.60 1.65 1.70 1.750
20
40
60
80
100
= 5meV =10meV =20meV
lh2-e2hh2-e2lh1-e1
hh1-e1
Po
lari
zatio
n,
%
Photon Energy, eV
Photoluminescence spectrum
Initial polarization losses amount up to 15% depending on structure quality and design- and Ehh-lh
Initial electron polarization Initial electron polarization PP00
Ehh-lh
Evl
Evh
lh1
hh1
AlInGaAs
AlGaAs
1.45 1.50 1.550
20
40
60
80
100
Po
lari
zatio
n,
%
Photon Energy, eV
Enlarge Ehh-lh to increase maximal P0
by increase of QW deformationE
hh-lh
Evl
Evh
lh1
hh1
AlInGaAs
AlGaAs
1.45 1.50 1.550
20
40
60
80
100
Po
lari
zatio
n,
%
Photon Energy, eV
Large strain deformation leads to structural defects and strain relaxation
1.45 1.50 1.550
20
40
60
80
100
Po
lari
zatio
n,
%
Photon Energy, eV
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
0 10 20 30 40 50 600
10
20
30
40
50
60
70
80
Val
ence
Ban
d S
plitt
ing,
meV
Deformation splitting, meV
Total Quantum effect
20
40
60 QW width
Electronic transport in SLElectronic transport in SL
I=I0T
RI0
I0
Ballistic electron tunneling though SL
Tres exp(-b) Tf exp(-2b) BBR
Tunneling probabilityT = I/I0
Tunneling time = ∫ |Ψ(x)|² dx/I
Tf << Tres
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 = ħ/∆E exp(b)
Transport time = ħ/Γ 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/2
Electronic diffusion in SLElectronic diffusion in SL
ˆˆˆˆ StH
ti
Kinetic equation - electronic density matrixH – effective Hamiltonian of SL in tight binding approximationSt{} – 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
fp
NV
NN
26)1)(2/1( N – number of QW in SL
V = E/4 – matrix element of interwell electron transition
Electronic diffusion in Electronic diffusion in SL bulk GaAsSL bulk GaAs
fp
NV
NN
26)1)(2/1(
SL
DL 3
2
D = 40 cm2/s – diffusion coefficient S = 107 cm/s – surface recombination velocity fp dSdVD
periodSLdN
/,2
,122
For SL Al0.2In0.2Ga0.6As(5.4nm)/ Al0.4Ga0.6As(2.1nm)D = 12 cm2/s , S = 3*106 cm/s
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
Inte
nsity
, a.
u.
Time, ps
Experiment* Calculations
D = 16 cm2/s , S = 3.4*106 cm/s
* K. Aulenbacher et al, Mainz, 2006
Strained-well SLStrained-well 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
MBE grown AlInGaAs/AlGaAs strained-well superlatticeMBE grown AlInGaAs/AlGaAs strained-well superlattice
SPTU & FTI, St.Petersburg
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
Choice of SL parametersChoice of SL parameters
• y - In concentration in QW• x - Al concentration in QW• z - Al concentration in barrier• a – QW width• b – barrier width
AlxInyGa1-x-yAs - QW AlxGa1-xAs - Barrier
y = 0.2, Ev = 76 meV x = 0.19, Eg = 1.536 eV a = 5.4 nm, Ehh-lh = 87 meV
z = 0.4, Uhh = 332 meV, Ulh = 258 meV, Ue = 234 meV, b = 2.1 nm, Ee = 31 meV
2 4 6-0.20
-0.15
-0.10
-0.05
0.00
Evl
Evh
Val
ence
Ban
d S
plitt
ing,
meV
Min
iban
d E
dges
, eV
QW (AlInGaAs) width, nm
hh1 lh1 hh2
30
40
50
60
70
80
90
Ehh-lh
SL AlSL Al0.0.1919 In In0.0.22 Ga Ga0.60.611As(5.As(5.44nm)/Alnm)/Al0.0.44GaGa0.60.6As(2.As(2.11nmnm))
Pmax= 92%, QE = 0.85%
650 700 750 800 850 90010-6
10-5
10-4
10-3
10-2
10-1
100
101
0
20
40
60
80
100Q
E,
%
, nm
QE, Experiment QE, Theory
P, Experiment P, Theory
Pol
ariz
atio
n,
%
650 700 750 800 850 9000
1
2
3
4
5
Dn
, Theory
Dn
, Experiment
Up
, Theory
Up
, Experiment
Pho
toab
sorb
tion
coef
ficie
nt,
m-1
, nm
650 700 750 800 850 90010-6
10-5
10-4
10-3
10-2
10-1
100
101
0
20
40
60
80
100
QE
, %
, nm
QE, Experiment QE, Theory
P, Experiment P, Theory
Pol
ariz
atio
n,
%
SL AlSL Al0.0.1919 In In0.0.22 Ga Ga0.60.611As(5.As(5.44nm)/Alnm)/Al0.0.44GaGa0.60.6As(2.As(2.11nmnm))
= 25 meV, P0max = 97%Polarization losses at• photoabsorption – 3%• transport and emission – 5%
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
Resonant enhancement of QE Resonant enhancement of QE
550 600 650 700 750 800 850 900 9500
2
4
6
8
10
0
20
40
60
80
QE
En
cha
nce
me
nt
W avelength, nm
QE enchancement
SPTU data
P-4, SL QT 1890 non DBR P-2, SL QT 1890 DBR
Pol
ariz
atio
n,
%
Accepted for publication at Semiconductors, 2008
Summary & OutlookSummary & Outlook
Photocathode based on optimized AlInGaAs/AlGaAs strained-well SL demonstrates Pmax= 92% at QE = 0.85%.
Maximal initial photoelectron polarization P0 = 97%. To increase P0 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.
Thanks for your attention!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
SL In0.155Al0.2Ga0.645As(5.1nm)/Al0.36Ga0.64As(2.3nm)
2 4 6 8 10 12 14 16 18 20
0,1
1
50
60
70
80
90
100
QE
, %
thickness, pairs
o QE P
Po
lari
zatio
n,
%
Reproducibility
550 600 650 700 750 800 850 900
10-4
10-3
10-2
10-1
100
101
0
20
40
60
80
100
QE
, %
, nm
QE-1, SL 7-389 T=300K Tht=540C 21,04,2007 Y7-307 Heating 540K
P-1, SL 7-389 T=300K Tht=540C 21,04,2007 P 7-307 Heating 540K 30.11.2006
Pol
ariz
atio
n,
%
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. dBRQY )()1()(
Initial electron polarization P0 for different values of hole spectrum broadening and smearing of absorption edge
Pol
ariz
atio
n, %
Photon energy, eV
two interval calc.*0.98 basis calc.*0.945 delta=10 meV basis calc.*0.945 delta=20 meV tail 30 meV, delta=25 meV tail 30 meV, delta=45 meV tail 11 meV, delta=25 meV tail 11 meV, delta=7 meV tail 11 meV, delta=7 meV,
gauss=40meV
1.4 1.5 1.6 1.7 1.8 1.9
20
40
60
80
100
SPEC T=540K SPEC T=570K
1.4 1.5 1.6 1.7 1.8 1.9
20
40
60
80
100
Pol
ariz
atio
n, %
Photon energy, eV
two interval calc.*0.98 basis calc.*0.945 delta=10 meV basis calc.*0.945 delta=20 meV tail 30 meV, delta=25 meV tail 30 meV, delta=45 meV tail 11 meV, delta=25 meV tail 11 meV, delta=7 meV tail 11 meV, delta=7 meV,
gauss=40meV SPEC T=540K SPEC T=570K
Polarization lossesPolarization losses
GaAs0.83P0.17/Al0.1In0.18Ga0.72As (5x4nm)x20
1.4 1.5 1.6 1.7 1.81E-5
1E-4
1E-3
0.01
0.1
1
QY
Photon energy, eV
=30 meV, =25 meV =30=30 meV, =45 meV =30=11 meV, =25 meV =30=11 meV, =7 meV SPEC T=540K SPEC T=570K
QE spectrum for different values valence band tails = 10-30meV extsssBPP /)()( 0
s – время спиновой релаксации , при T=300K, Na=4*1017cm-3
s = 7*10-11sext – время выхода электронов из СР в область BBR,ext = d/S + d2/12D, d – ширина СР, S – скорость поверхностной рекомбинации на границе BBR, D – коэффициент диффузии. При T = 300K S = 1/4<v> = 107cm/s.Для тонкого рабочего слоя d = 100nm ext = d/S,ext = 7*10-13sПоляризационные потери ext /s за время транспорта не более 1%
Потери поляризацииПотери поляризации при транспортепри транспорте
extsssBPP /)()( 0
High-Energy physics requirementsHigh-Energy physics requirements
• High electron polarization, P > 80%
Accelerator P, % 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
ReflectivityReflectivity
750 800 850 900 9500.0
0.2
0.4
0.6
0.8
1.0
Experiment, SL 7-396 DBR Theory, SL 7-396 DBRR
efle
ctiv
ity
W avelength, nm
Spectra of electron emission, P(Spectra of electron emission, P(), QE(), QE())
550 600 650 700 750 800 850 900
10-4
10-3
10-2
10-1
100
101
0
20
40
60
80
W avelength, nm
QE
, %
QE, SL 7-396 DBR QE, SL 7-395 no DBR
P, SL 7-396 DBR P, SL 7-395 no DBR
Pol
ariz
atio
n,
%
550 600 650 700 750 800 850 900
10-4
10-3
10-2
10-1
100
101
0
20
40
60
80
W avelength, nm
QE
, %
QE, Experiment SL 7-396 DBR QE, Theory SL 7-396 DBR
P, Experiment SL 7-396 DBR P, Theory SL 7-396 DBR
Pol
ariz
atio
n,
%
Spectra of electron emission, P(Spectra of electron emission, P(), QE(), QE())
Resonant enhancement of QE Resonant enhancement of QE
750 800 850 9000
10
20
30
W avelength, nm
QE
En
cha
nce
me
nt
Experiment SL 7-396 DBR Theory SL 7-396 DBR
Optimization of Photocathode structureOptimization of Photocathode structure
Buffer
GaAsSubstrate
DBR
SL
BBR
760 780 800 820 840 860 880 9000.0
0.2
0.4
0.6
0.8
1.0
Ref
lect
ivity
Wavelength, nm
• SL structure: layers composition and thickness are chosen to assure Eg= for P()=Pmax
Ehh-lh > 60meV for high polarization Ee1 > 40meV for effective electron transport
• DBR structure: 20x(AlAs(/4)/ (AlxGa1-xAs(/4)) Layer thickness l = /4n() for Bragg reflection x 0.8 for large reflection band width = 2n/n
• Fabry-Perot resonance cavity: BBR + SL + buffer layer Effective thickness = k /2 for QE() = QEmax
Effective thickness of BBR+SL /4
Simulation of resonant photoabsorptionSimulation 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
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
E, meV
ps
T
0.1
1
10
100
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