Post on 09-Jan-2016
description
ВСЕ О ТРИОНАХ
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 • 9. Trion Zeeman splitting
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
Wavefunction for two electrons in the trion
)2,1()2,1()2,1( U
Singlet state +
Triplet state -
Sz = 0
Sz = 1,0
triplet
singletSz = 0
Sz = 0 Sz = -1
Sz = +1
Or if n 1 one electron is in 1S, and the second is in а 2S state bright triplet
Singlet and Triplet trion states
Unlm 0 , if l 0 one electron is in 1S and the second is in 2P state – dark triplet
)( 21 rre
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
Изменение концентрации при подсветке
0 50 100 150 2000
2
4
6
8
10ZnSe-based QWs
X+
PL ZnSe/ZnBeMgSeRefl. ZnSe/ZnBeMgSe ZnSe/ZnMgSSe ZnSe/ZnMgSSe
X- b
indi
ng e
nerg
y (m
eV)
QW width (Å)
Зависимость энергии связи триона от ширины ямы
Сила осциллятора экситона приходящаяся на элементарную ячейку равна силе осциллятора триона на один электрон, также Как для связанных экситонов
eX
T
Cn
0
0
Singlet and Triplet
Trion states in magnetic fields
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 method
Triplet trion in high 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
Dense 2DEG
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)
Surprising Trion stability against free electron screening
Экситон исчезает из спектра при относительно малых
концентрациях электронов, а трион остается
1.620 1.625 1.630
CdTe/CdMgTe 80A
T=1.6KB=0T
1.2x1011cm-2
8x1010cm-2
4x1010cm-2
<1010cm-2
0
X
X
X
X
X
X
0
0
0
Energy (eV)
Ref
lect
ivity
2.810 2.815 2.820 2.825
ZnSe/ZnMgSSe
ZnSe/ZnMgSSe 80A
X
T=1.6KB=0T
1.2x1011 cm-2
6x1010cm-2
3x1010 cm-2
4x109 cm-20
X
X
X
X
X
X
0
0
0
Energy (eV)
Ref
lect
ivity
Сила осциллятора экситона не зависит от плотности 2DEG
Затухание экситона растет с ростом плотности
Спектры поглощения (PLE) как функция концентрации
0
0.5
1.0
1.5
2.0
1605 1610 1615 1620
a
Energy (meV)
Ab
sorp
tio
n (
arb
it.u
n.)
0
0.5
1.0
1.5
1605 1610 1615 1620
b
Energy (meV)
Ab
sorp
tio
n (
arb
it.u
n.)
Trion Zeeman splitting as a function of the electron density
electron
photon
trion
exciton
Because the initial and the final state of the electron are the same (the same spin and the same Landau level) we should see only the exciton Zeeman splitting on exciton and on trion line
The value of the exciton and trion Zeeman splitting?
)( fininit eExTrphe
Photoluminescence
1,615 1,620 1,625 1,630
H=0T
Energy, eV
PL In
tens
ity, a
.u.
0 1 2 3 4 5 6 7 8
1,622
1,623
1,624
1,625
1,626
ne=4x1010 cm-2
Ene
rgy,
eV
Magnetic Field (T)
In PL the exciton and trion Zeeman splitting are equal
0 1 2 3 4 5 6 7 8
-0,8
-0,6
-0,4
-0,2
0,0
0,2
0,4
0,6
0,8
ne=8x1010 cm-2
Exc
T
Magnetic field (T)
Split
ting
(meV
)
0 1 2 3 4 5 6 7 81,621
1,622
1,623
1,624
1,625
1,626
1,627
1,628
1,629
1,630
T
Exc
Ene
rgy
(eV
)
Exciton and trion Zeeman splitting at high electron concentrations
This is possible only in the case if the initial and final spin state of the electron are not the same –
we need spin-flip
In the initial state the photon creates virtual state of the triplet trion. Because of very fast spin-flip of one of the electrons in the
final state we have the singlet trion (already real). This is the process reversal to the ExCR
For spin-flip we need spin-orbital interaction. This can be the triplet-singlet splitting of the trion
An incident photon creates a virtual trion in the triplet state. This trion produces a spin-flip with one of the electrons on the first Landau level. As a result, in the final state, we get a trion in the singlet state plus an electron on the second Landau level with opposite spin.
2121 eTreTrphee st
This reaction looks
Фотолюминесценция трионов
Спектры ФЛ в зависимости от концентрации электронов
Ebex >>EF
Ebtr ~EF
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
В магнитном поле линии триона и экситона «возрождаются»
1600 1610 1620 1630 1640
X
энергия, мэВ
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
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(
In Emission the initial state is: trion in a ground or excited states;
the final state is: an electron above Fermi level
The energy of the transition is
ephr
FTrTr EEEE
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
Conclusions
In 2D structures containing electron gas the scattering effects are enhanced.
In the presence of magnetic fields the electron
energy spectrum becomes discreet and the scattering processes revel as combined exciton- electron processes.
In such processes we can see directly only the
exciton transition but the state of the additional electron, which we can not see, reveals only in the final result.