TRIONS in QWs

Trions at low electron density limit • 1. Charged exciton-electron complexes (trions) • 2. Singlet and triplet trion states • 3. Modulation doped QWs • 4. Trions in optical spectra • 5. Action of magnetic fields on the trions

Trions at high electron density limit • 6. Combined exciton cyclotron resonance • 7. Combined trion cyclotron resonance • 8. Combined exciton electron processes in PL spectra

KOCHERESHKO V.P. A.F.Ioffe Physico-Technical Institute

In cooperation with R.Suris, D.Yakovlev, S.Crooker, D.Andronikov, G.Karczewski et al.

LOW 2DEG DENSITY

Two electrons+one hole states

•Trions at weak magnetic fields •Trions at high magnetic fields •Excited states of trion

X

X +

electrons

hole

+ +-

electronholes

Negatively charged Trion X-

similar to ion H- Positively charged Trion X+ Similar to ionized molecule H+

Charged exciton – electron complex (trion)

1212110

2

1rurururuU nlmnlmnlm

Spatial part of the wavefunction

+ singlet state

- Triplet state

Spin part of the wavefunction

Wavefunction for two electrons in the trion

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

Singlet state Triplet state Sz = 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

triplet

singletSz = 0

Sz = 0 Sz = -1

Sz = +1

Or if one electron is in 1S, and the second is in а 2S state

Singlet and Triplet trion states

Unlm 0 , only if L 0

Experimental studies of trions

3.0eV

2.8eV

ZnMgSSe ZnMgSSeZnSe

lh1

hh1

e1

CdMgTe

QW

CdMgTe

100Å 100Å

1.8eV

1.6eV

I

CdTe

2DEG density varied from ne=5*109 см-2 to 9*1011 см-2

2DEG

Modulation doped structures

Optical processes with the trion participation

2,81 2,820

Excited by UV-linesP

exc=60 mW

undoped

Ref.

PL

XX

Energy (eV)

Sign

al in

tens

ity (

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)

Trion formation time in ZnSe structures is of the order of 2 –4 psec

electron

photon

trion

exciton

Singlet trion in magnetic fields

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

ZnSe

4.4 meV

5.5 meV

Xhh

and Xlh resonances appear

in opposite circular polarizations

doped, ne=5 1010cm-2

B=7.5T, T=1.6K

Xlh

Xlh

Xhh

Xhh

Energy (eV)

Ref

lect

ivity

(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

The circular polarization of the trion absorption (reflectivity line ) in magnetic fields can be used to determine electron concentration by pure optical methods

Triplet trion in magnetic fields

1610 1620 1630 1640

Energy

Phot

olum

ines

cenc

e

Ts

Tt

d X

0T

45T

-

1600 1620 1640

Tt

d

Ts

X-125T

energy, meV

Tt

d

Ts

X-130T

T

t

d

Ts

X-1

29.5T

0 10 20 30 401610

1615

1620

1625

1630

1635

TT

b -X

+1X

-1

Ts

+

TT

d -

Ts

-

- +

ne=3*1010 cm-2

T=1.6K

En

erg

y, m

eV

Magnetic field, Т

Etripbind = 3 meV

Singlet and Triplet in high fields

EXCITON-ELECTRON SCATTERING

(excited states of a trion in magnetic fields)

Exciton – electron scattering

1,63 1,64 1,65 1,66 1,67

PLE

ne=8x1010cm-2

0T 5T

ExCR2

ExCR1

T=1.6K

Lg I

ExCR2

ExCR1

X (1s,hh)

X (1s,lh)

Energy (eV)

PL in

tens

ity

1,64 1,66

detected at -

B=5T

The scattering leads to high energy tail of the exciton absorption line. In magnetic fields it splits into separate lines because the electron spectrum becomes discrete = excited states of trions in magnetic fields.

electron

photon exciton

Exciton – electron scattering

In magnetic fields in QWs the exciton electron scattering leads to the electron transitions between Landau levels - ExCR

We can neglect the trion binding energy because

*eExphe

c

eexc

c

e E 2

3

2

1

The intensity of the ExCR absorption line is comparable with the intensity of the exciton line

bTrc

bex EE

Combined exciton –cyclotron resonance ExCR

The ExCR line shifts LINEARLY from the exciton resonance to high energies with increase of magnetic fields

)1(M

mN ec

eExCR

Combined processes in PL

0 10 20 30 40 50

1610

1620

1630

1640

1650

X

Ts

ССR

ne=3.7x1011 cm-2

T=1.6K

ener

gy, m

eV

Magnetic field, T

Comparison of PL and reflectivity PL and SU

0 10 20 30 40

1610

1615

1620

1625

1630

1635

FL

2c

c

(1/2)c

=3

=4

=2

SU

Tt

Ts

CCR

ne=3.7x1011 cm-2

T=1,6K

ener

gy, m

eV

magnetic field, T

In Absorption the initial state is an electron below Fermi level , the final states is a trion in ground or excited states

The energy of this transition is In Emission the initial state is a trion in ground or excited states, the final state is an electron above Fermi level

The energy of the transition is

Trphe

eTr EE

ephr

EETr

Taking into account trion binding energy

Recombination

In the recombination: there is a trion in the initial state; in

the final state there is photon and one electron on one of Landau levels

SU CCR

2

1

0

Trion LL

electron LL

PLAbs

3

2

1

0

In our magnetic fields we have hierarchy of energies:

where are binding energies of exciton and trion respectively. Hence we can assume that these magnetic fields are small for exciton and strong for trion, and the trion has energies:

The residual electron after the trion annihilation can have energy:

, and Е* corresponds to the empty Landau levels above the Fermi level of 2DEG.

bTrc

bex EE

bTrcexTr ENEE

2

1

cME

2

1

MULTY ELECTRON PROCESSES IN PL

What is the “MOSS-BURSTEIN” SHIFT?

In heavily doped QW in zero magnetic fields the PL line is shifted to the low energies from its position in low doped structure. The value of this shift is of the order of Fermi energy

0 10 20 30 401605

1610

1615

1620

1625

1630

1635

SU

Tt

PL

Ts

Ts

Tt

X

ener

gy,

meV

Magnetic field, T

3.7x1011cm-2 3x1010cm-2

Shake-up

1,596 1,598 1,600 1,602 1,604 1,606 1,608 1,610

5/2hc

3/2hc

1/2hcn

e=2x1011cm-2

T=1.6 K

EF

ETr

B=7.5T

B=0

PL

Int

ensi

ty, a

rb. u

.

Energy, eV

Shake up процессы SU

*ephTr

c

etr NE )2

1(

c

etr NE )2

1(

Linear shift of the trion line in magnetic fields

In the final state after the trion recombination a free electron remains. It can appears in the unoccupied states above Fermi level

In magnetic fields the Fermi energy decreases as

FtrFtr EEEE

c

e2

1

ne=const

T=1.6K T=0 K

LL2 LL1

=4=3

=2

=1

Magnetic field

Ferm

i ene

rgy

1605

1615

1625

10 30

Theory

)(2/)(exp

)(2

)4/()( 22

2BnE

B

eBE nph

n

n

Figure gives the energy positions of maxima of emitted bands which are described by equation

GFtrcph EBBBEBEn 2)()()(

The shape of the states in presented by the Gaussian form

DENSE 2D ELECTRON GAS

Three electrons+one hole states

In the dense 2DEG two-electron processes emerge in the spectra TrCR

*eTrphee

c

etr

c

e

c

e E 2

3

2

1

2

1

c

etrE 2

1

There are two electrons in the initial state; an incident photon creates an exciton which binds with one of the electrons forming a trion; and the second electron excites on the second Landau level

Trion Cyclotron Resonance

0 1 2 3 4 5 6 7 8

1,606

1,608

1,610

1,612

1,614

1,616

1,618

2

ne=8x1010 cm-2

open symbol -

solid symbol -

31

ExCR11.00 meV/T

TrCR10.64 meV/T

ExCR2

X

X

Lin

e po

siti

on (

eV)

Magnetic field (T)

Line of the TrCR is observable at filling factors > 1. The intensity of the TrCR line is proportional to the second

power of the 2DEG density

0 2 4 6 8 100

T=1.6K

Electron concenctration, ne (1010cm-2)

Inte

nsity

of T

rCR

-lin

e

0 20 40 60 80 100 120

ne

2 (1020cm-4)

0 1 2 3 4 5

=1 =1=1

(b)

6×1010

cm-2

8×1010

cm-2

1×1011

cm-2

Ref

lect

ivity

Magnetic field (T)

Inte

nsity

of T

rCR

-line

1,605 1,610

(a)

6×1010

cm-2

8×1010

cm-2

1×1011

cm-2

XX

ExCR

TrCR

T=1.6KB=2.5T

0

0

Energy (eV)

Conclusions

In 2D structures contained electron gas the screening effects are suppressed, and the scattering effects are in contrary enhanced.

Electron energy spectrum in a 2D structure becomes discreet and the scattering processes emerge as narrow lines of combined resonances.

In PL the Moss-Burstein shift displays in combined exciton electron processes.