XIVth International Workshop on Polarized Sources, Targets & Polarimetry

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



Experimental method

Photoexcitation

Beam deflection



Shift of transverse profile against slit

Experimental method



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


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



Time dependence of electron emission Parameters

SPES PSTP2011




parameter

d = 110 ps – detachment time,

fitting parameter




-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




SPES PSTP2011




parameter

d = 130 ps – detachment time,

fitting parameter


r*= 3.6 ps – effective recombination


-5 0 5 10

0.01

0.1

1

Em

issi

on,

arb.

un.


Time, ps


6 periods6 periods


SPES PSTP2011




parameter

d = 50 ps – detachment time, fitting

parameter

= 9.4 ps – total extraction time



-5 0 5 10

0.01

0.1

1


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


-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

XIVth International Workshop on Polarized Sources, Targets & Polarimetry

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