Charged exciton complexes (trions) in low dimensional structures

Charged exciton complexes (trions) in low dimensional structures

by Dmitri Andronikov

at JASS 2005

Introduction

Experiment

Results and discussion

Conclusions

Outline

Introduction

Experiment

Results and discussion

Conclusions

Outline

X

X +

electrons hole

+ +-

electron holes

X- Trion X+ Trion

Similar to hydrogen ion H- if me<<mh Similar to ionized hydrogen molecule H2+

if me<<mh

What are Trions?

Short history of trions

1958 Theoretical prediction of trion existence by Lampert

1977-78 Discovery of charged excitons in bulk Ge, Si and CuCl

1993 First report on X- trion in a CdTe/CdZnTe semiconductor QW structure

1995 First report on X+ trion in a GaAs QW

1212110

2

1rurururuU nlmnlmnlm

Spatial part of the wavefunction

+ singlet state

- triplet state Unlm 0 , only if L 0 (1S state and 2P state)

Spin part of the wavefunction

Wavefunction of an ion with two electrons

)2,1()2,1()2,1( U

singlet state triplet stateSz = 0 Sz = 1,0

])2/1,2/1[]2/1,2/1([2

1sin

0 gl

2/1,2/11 trip

2/1,2/12/1,2/12/10 trip

2/1,2/11 trip

e

triplet

singletSz = 0

Sz = 0 Sz = -1

Sz = +1

or if one electron is in 1S state, and the other is in 2S state

Singlet and triplet trion states

Singlet and triplet trion states in the magnetic field

transitions

transitions

-3/2

+3/2

Triplet

Singlet

ge=-1.56

electron -1/2

+1/2

Sz

e=0

+1/2

-5/2

+3/2

-3/2

+5/2

-1/2Sz

e=+1

Sz

e=0

Sz

e=-1

In the magnetic field each trion level splits into two due to Zeeman effect thus giving 6 triplet and 2 singlet levels

The allowed optical transitions must satisfy the optical selection rule Sfinal+Sinit = ±1. This gives 6 possible transitions to/from trion singlet and triplet states

GaAs CdTe ZnSe

4.2 meV 10 meV 20 meV

9 meV 20 meV 30 meV

1 meV 2.5 meV 5 meV

EXbulk

EXQW

ETQW

3D

2D100A QW

Exciton and trion binding energies in 3D and 2D structures

13.6 eV 20

4

2me

EH

HD

X Em

E2

03 /

D

X

DXD

X EE

E 32

32 4

2/11

3.0eV2.8eV

ZnMgSSeZnSeZnMgSSe

lh1

hh1

e1

CdMgTe

QW

CdMgTe

100A 100A

1.8eV1.6eV

I

CdTe

2DEG concentration varies from ne=5*109 cm-2 to 9*1011 cm-2

2DEG

Structures with modulation doping

Trion PL and reflectivity spectra

2,81 2,820

Excited by UV-linesP

exc=60 mW

undoped

Ref.

PL

XX

Energy (eV)

Sig

nal i

nten

sity

(a.

u.)

2,81 2,820

4.8 meV

B=0, T=1.6K

doped, ne=5 1010cm-2

PL

Ref.

X

X

Energy (eV)

The formation time of a trion in ZnSe based structures is of the order of 2 –4 ps compared to radiative lifetime of the exciton 40-50ps

electron

photon

trion

exciton

Singlet trion in the magnetic field

2,81 2,82 2,83 2,840

ZnSe

4.4 meV

5.5 meV doped, ne=5 1010cm-2

B=7.5T, T=1.6K

Xlh

Xlh

Xhh

Xhh

Energy (eV)R

efle

ctiv

ity (

a. u

.)

0 1 2 3 4 5 6 70.0

0.5

1.0

=3

=1=2

Magnetic field (T)

ne=1.5x1011 cm-2

Deg

ree

of p

olar

izat

ion

ne=9x1010 cm-2

0.0

0.5

1.0

=1

ge=+1.15

ne=6x1010 cm-2

0.0

0.5

1.0

0 1 2 3 4 5 6 7

=1

Landau levels

LL4

LL3

LL2

LL1

>1<1

LL4

LL3

LL2

LL1

LL4

LL3

LL2

LL1

EF=const(B)

ne=const

T=1.6K T=0 K

LL2

LL1=4

=3

=2

=1

Магнитное поле

энер

гия

Фер

ми

For the filling factors less than 1 only the lowest electron Landau level will be populated leading to full spin polarization of the 2D electron gas

The polarization of the trion reflectivity line can be used to determine the electron concentration by a pure optical method

e (-1/2) X(+1/2, -3/2)

T(-1/2, +1/2, -3/2)

eB

hcne

Introduction

Experiment

Results and discussion

Conclusions

Outline

hh1

e1

CdMgTe

QW

CdMgTe

100A 100A

1.8eV1.6eV

I

CdTe

Two samples with different 2DEG concentration were analyzed ne=3*1010 cm-2

and 3.7*1011 cm-2

2DEG

Experimental structures

light filter

z

lum

ines

cenc

e

exci

tati

on s

igna

l

H || z

L1 SM

optical fiber

laser with = 532 nm

pulse electromagnet

He cryostat

probe with a sample

the

insi

de

of

the

pro

be

PC CCD camera

monochromator

circ

ular

pol

ariz

er

sample

linea

r po

lari

zer

0 100 200 300 400 5000

10

20

30

40

50

Mag

net

ic f

ield

, T

time, ms

Magnetic field pulse

Experimental setup

Pulse magnet power source

Supplying power to the world's strongest long-pulse magnet at Los Alamos' National High Magnetic Field Laboratory is a 1.4 billion-watt generator, itself the largest among magnetic power sources. It can produce enough energy to power the entire state of New Mexico.

Introduction

Experiment

Results and discussion

Conclusions

Outline

triplet trion line has been found

1600 1620 1640

Tt

d

Ts

X-1 25T

energy, meV

Tt

d

Ts

X-1

30T

T

t

d

Ts

X-1

27.5T

1610 1620 1630 1640

Ts

Tt

d X

0T

45T

-

Polarized magnetoluminescence of the sample with ne=3*1010 cm-2

PL maxima

3 meV

0 10 20 30 401610

1615

1620

1625

1630

1635

TT

b

X

TT

d

Ts

- +

ne=3*1010 cm-2

T=1.6K

ener

gy,

meV

Magnetic field, T

The dark triplet trion line appears at 20T magnetic field and splits from the exciton line with the maximum splitting of 3meV at 45T

Luminescence spectra analysis I

PL intensity

0 5 10 15 20 25 30 35 40 450

500

1000

1500

2000

2500

3000

3500

4000

4500

X

Tt

d

X

TS

T=1.6K ne=3*1010 cm-2

PL

inte

nsi

ty, a

rb. u

nit

s

Magnetic field, T

Luminescence spectra analysis II

The Gauss fit of the exciton-dark triplet trion band allowed us to distinguish the triplet trion line from the exciton line down to magnetic field lower than 15T

Field dependence of the PL lines for the sample with ne= 3.7*1011 cm-2

0 10 20 30 40

1610

1615

1620

1625

1630

1635

=3=4

=2

SU

Ts

Tt

d

Ts

ExCR

ne=3.7x1011 cm-2

T=1,6K

en

erg

y, m

eV

magnetic field, T

For the sample with higher electron concentration the triplet line can be followed down to the fields as low as about 13T

Luminescence spectra analysis III

Mag

neti

c fi

eld0

1000

2000

3000

0

1000

2000

3000

1610 1620 1630 16400

1000

2000

3000

X

Ts

X

0,3

0

27T

Ts

Tt

b

45T X

PL

, a

.u.

Re

fle

cti

vit

y

0,3

0

T=1.6K

6T

ne=3x1010 cm-2

X

Ts

XTs

XTs

Ts

XTt

d

Ts

Ts

X

0.3

0T

t

d

energy, meV

Reflectivity

At 6T magnetic field the reflectivity line of the singlet trion is fully polarized

In reflectivity no line is found that would energetically coincide with the position of the dark triplet trion line found in the PL

(+1/2,+1/2,-3/2)

triplet trion

(-1/2,-3/2)

(-1/2,+3/2)

(-1/2,+1/2,-3/2)

(-1/2,+1/2,+3/2)

(+1/2,-3/2)

(+1/2,+3/2)

(+1/2)

(-1/2)2DEG

singlet trion

Exciton

Singlet and triplet trion states formation mechanism

The triplet trion level is formed from the lowest Zeeman sublevels of both electrons and excitons and thus will be the most populated

form = 10 ps, X = X- = 30 ps, K = 12 ps, rec

X = 40 ps, recTs = 60 ps rec

Tt = 50recTs.

Tt

d

rec

b

rec

d-1/2

h

e

m

-1/2 -

+3/2 -3/2 -+

rec

rec

rec

rec

X

e

e

e

e

X

h

X

K

-2

-2

form

form

X

h

X -

-

+

+

+2

+2

Tt

b

Ts

Cold X

Hot X

Calculation of the exciton-electron energetic system

0 10 20 30 40

Ts

+

Ts

-

X-

X+

Tt

d

T=1.6K

ne=3*1010 cm-2

Magnetic field, T

The intensity of the triplet PL is already noticeable at sufficiently low magnetic field

experiment calculation

0 10 20 30 400

500

1000

1500

2000

2500

3000

3500

4000

4500

X

Tt

d

X

TS

T=1.6K ne=3*1010 cm-2

PL in

tens

ity, a

rb. u

nits

Magnetic field, T

The results of the PL calculation

Introduction

Experiment

Results and discussion

Conclusions

Outline

Optically active and forbidden singlet and triplet trion states have been observed in reflectivity and PL spectra.

A model explaining the appearance of the dark triplet trion state in the PL spectra from the studied structures state has been suggested. It is based on the fact that the singlet trion state formation mechanism is suppressed by the magnetic field, meanwhile the formation of the optically inactive triplet trion state, observed in the experiment, is stimulated in the magnetic field at low temperatures.

A model calculation based on the system of kinetic equations of the PL of the trion exciton energetic system has been carried out. The model took into account the singlet and triplet trion formation mechanisms in the magnetic field. The results of the calculation are in good agreement with the experiment.

Conclusions

THANK YOU!!!!