charged exciton complexes (trions) in low dimensional structures
Post on 06-Jan-2016
48 Views
Preview:
DESCRIPTION
TRANSCRIPT
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!!!!
top related