TRIONS in QWs Trions at low electron density limit 1. Charged exciton-electron complexes (trions) 2....
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Transcript of TRIONS in QWs Trions at low electron density limit 1. Charged exciton-electron complexes (trions) 2....
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
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
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
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
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.