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Quantum size effect on excitons in microcrystals of cuprous halides embedded in alkali halide matrices
Journal of Luminescence 40&41 (1988) 737 738 North-Holland, Amsterdam
737
QUANTU’1 S IZE EFFECT ON ~)
Tadashi ITOH and Yasuo IWABUCHI Department of Physics. Tohoku University, Sendai 980, Japan Exciton luminescence spectra of CuCI, CuBr and Cui microcrystals embedded in alkali halide matrices are studied experimentally and are explained in terms of the size-quantized excitons with the idea of exciton confinement. From the analysis of the splittings of the exciton states into several components, exciton masses and k-linear terms are derived in these compounds.
especially in CuCl in NaC1. close correlation is
1. INTRODUCTION Broad exciton absorption and luminescence
found between the blue shift of the luminescence
bands characteristic of cuprous halides are
peak arid the average microcrystal size derived
observed in alkali halides heavily doped with
in the measurement of X-ray small angle scatter
ions and are thought to be ascribed to the
ing: the smaller the size in the order of nm, The amount of the blue
excitons of cuprous halide microcrystals embed-
the more the blue shift.
ded in transparent matrices of alkali halides.’
shift nearly coincides with that calculated from
In this paper, exciton luminescence spectra of
the size under the assumption of the exciton
Cud. CuBr and Cul niicrocrystals in NaCI, KBr
confinement model as has been proposed in the 2 study of CuCI micr-ocrystals in glass . where the
and KI matrices,
respectively,
are studied in
details at 77K under the selective excitation in the energy regions of the Z
3 and Z12 exciton
bands.
It is found that there appear several
following relation is used between the thickness (or radius) L of the microcrystal and the energy E~(L) of the size—quantized exciton:
exciton bands split off from the bulk exciton bands as the microcrystal size becomes small.
~2
~
E~(L)=Eb+~
2 (1)
.
ex
The splittings are well explained in terms of and N are the exciton energy and ex translational mass, respectively, for the bulk Here. the confinement of exciton translational motion. being different from the well-known electronhoim’ confinement in GaAs AlGaAs quantum wells.
crystal and Q the integer in the one-dimensional confinement. For the electron-hole confinement
2.
model the mass is replaced by the reduced mass.
D’PERIMENTAL
PROCEDURES
Single crystals
of alkali halides doped with
Cu halides nominally by 1 mol% were grown by a
Equation (1) holds for the Z3 exciton. four fold degeneracy of the
r8
However,
valence band and
transverse Bridgman method and a Kyropoulos method. The as grown crystals were opaque and
the k linear term therein make the Z12 exciton
were annealed to make them transparent.
states split into multicomponents for the finite 3 Ui) wavevector. For the confinement along
Lumi-
nescence spectra of these crystals immersed in direction, there exist three kinds of dipoleliquid nitrogen were measured under the selective excitation at inhomogenously broadened exciton bands with the use of monochromatized
allowed size-quantized Z12 exciton states whose lowest energies for 2—1 are given by .~2(.~.ex~2~ex) e 2
light of a Xe arc lamp. E2(L)_Ebf 3. RESULTS AND DISCUSSION In the samples with various heat treatments,
0022 2313/88/$03.50 © Elsevier Science Publishers By. (North-Holland Physics Publishing Division)
and
___________ 2
738
T. Itoh, Y. Iwabuchi
Cul in KI
‘—6 Ui
z
/
Quantum size effect on excitons in microciystals
77K
~3.3
Cul in KI
77K
-
~ k ___
~o0
~3(,
o0
LU
~2 U
~
~EFH Z’,~ :~ Ibulk
~
Ui
~3.02 Z
3
~ 0’ —~•‘‘1 3.0
~JiifflI.
I
3.1
L_
(15
3.5 EXCITATION ENERGY (eV)
4.0
E~(L) Eb+
2
ex 2
I
3.2
I
N
3.3 3.4 3.5 36 3.7 EXCITATION ENERGY (eV)
38
3.9
FIGURE 2 in energy between the peaks in the excitation spectra and the luminescence of Cul. Open circles and solid lines represent experi
Relations
FIGURE 1 Luminescence spectrum (dotted curve) and its excitation spectra at different luminescence energies (solid curves) in Cul microcrystals embedded in XI matrix.
~ (1~ 2~ ) 52
c~Is
~~KeX(~)
mental and theoretical values, respectively.
The following 9eV.cm parameters obtained; 0.08, and Mare ex (Z 3 )—5.9m 0. The peaks C and H are fitted by the 2S states of the 0.36xiO
...
ex
Z~ 2 and Z3 excitons.
where E2 and E’~are the energies of the light and heavy mass excitons,
ex and
the exciton
Luttinger parameters the exciton k linear arid term,BK7~the coefficient of The excitation spectra of the broad exciton
respectively.
The peak F
is ascribed to the 2 2 state of the heavy mass excitons.
The solid lines for C.H and F are 5 with obtained from the radius variational calculation the exciton Bohr of i.5nm and the exciton Rydberg constant of 62meV.
The peak D may be
luminescence bands in Cu-halide microcrystals
associated with the spherical microcrystals
are found to be composed of several peaks whose
where 2—1.43.
energies are strongly dependent on the energies
to the experimental data are fairly well.
of the observed luminescence. Figure 1 shows the lixninescence spectrum of Cul microcrystals
confinement along (lii) direction is certified in CuBr with the use of well known exciton
(in dotted curve) and its excitation spectra (in
parameters.3
solid curves) at various luminescence energies
obtained in CuCl ~
The overall theoretical fittings
The exciton parameters are also ~ç~X
0.89.
xQ, 8
indicated by arrows.
The peaks are classified
~K~X O.8zxlu
The
e’v.cm.
and
The exciton confinement
into two groups: one belongs to the Z12 exciton
model may be more adequate for CuCl and less for
and the other to the Z3 exciton.
GuI because the former has smaller Bohr radius
The relations
in energy between these peaks and the observed
than the latter.
luminescence are plotted in Fig.2 by open
still approximately valid in GuI even though the
circles. The luminescence band is associated with the radiative decay of the inhomogeneously
calculated size for giving the luminescence at 5.21eV is smaller than the Bohr radius.
broadened size quantized is Z12 free excitons
REFERENCES
having the energy of E~n• The resonant peak is
1. T. Itoh and T. Kirihara,
denoted by A. The peaks B and E can be ascribed to the iS Z12 exciton states having E~arid E .
31/32 (1984) 120. 2. A.I. Ekjmov and .A.A. Onushchenlco, Fiz. Tekh. Poluprovodn. 16 (1982) 1215. 3. Y. Nozue, 3. Phys. Soc. Jpn. 51 (1982) 1840. 4. B. Hoenerlage. C. Klingshirn and J.B. Grun,
2
The solid lines for B and E are calculated curves according to eqs.(2) and (3) by assuming ex 4 —0.37. The peak G is associated with the 15 Z3 exciton whose energy obeys eq. Cl) for 2 1
Nevertheless, the model is
J. Luminescence
phys. stat. sol. bIB (1976) 599. 5. N. Matsuura and Y. Shinozuka, 3. Phys. Soc. Jpn. 53 (1984) 5138.
737
QUANTU’1 S IZE EFFECT ON ~)
Tadashi ITOH and Yasuo IWABUCHI Department of Physics. Tohoku University, Sendai 980, Japan Exciton luminescence spectra of CuCI, CuBr and Cui microcrystals embedded in alkali halide matrices are studied experimentally and are explained in terms of the size-quantized excitons with the idea of exciton confinement. From the analysis of the splittings of the exciton states into several components, exciton masses and k-linear terms are derived in these compounds.
especially in CuCl in NaC1. close correlation is
1. INTRODUCTION Broad exciton absorption and luminescence
found between the blue shift of the luminescence
bands characteristic of cuprous halides are
peak arid the average microcrystal size derived
observed in alkali halides heavily doped with
in the measurement of X-ray small angle scatter
ions and are thought to be ascribed to the
ing: the smaller the size in the order of nm, The amount of the blue
excitons of cuprous halide microcrystals embed-
the more the blue shift.
ded in transparent matrices of alkali halides.’
shift nearly coincides with that calculated from
In this paper, exciton luminescence spectra of
the size under the assumption of the exciton
Cud. CuBr and Cul niicrocrystals in NaCI, KBr
confinement model as has been proposed in the 2 study of CuCI micr-ocrystals in glass . where the
and KI matrices,
respectively,
are studied in
details at 77K under the selective excitation in the energy regions of the Z
3 and Z12 exciton
bands.
It is found that there appear several
following relation is used between the thickness (or radius) L of the microcrystal and the energy E~(L) of the size—quantized exciton:
exciton bands split off from the bulk exciton bands as the microcrystal size becomes small.
~2
~
E~(L)=Eb+~
2 (1)
.
ex
The splittings are well explained in terms of and N are the exciton energy and ex translational mass, respectively, for the bulk Here. the confinement of exciton translational motion. being different from the well-known electronhoim’ confinement in GaAs AlGaAs quantum wells.
crystal and Q the integer in the one-dimensional confinement. For the electron-hole confinement
2.
model the mass is replaced by the reduced mass.
D’PERIMENTAL
PROCEDURES
Single crystals
of alkali halides doped with
Cu halides nominally by 1 mol% were grown by a
Equation (1) holds for the Z3 exciton. four fold degeneracy of the
r8
However,
valence band and
transverse Bridgman method and a Kyropoulos method. The as grown crystals were opaque and
the k linear term therein make the Z12 exciton
were annealed to make them transparent.
states split into multicomponents for the finite 3 Ui) wavevector. For the confinement along
Lumi-
nescence spectra of these crystals immersed in direction, there exist three kinds of dipoleliquid nitrogen were measured under the selective excitation at inhomogenously broadened exciton bands with the use of monochromatized
allowed size-quantized Z12 exciton states whose lowest energies for 2—1 are given by .~2(.~.ex~2~ex) e 2
light of a Xe arc lamp. E2(L)_Ebf 3. RESULTS AND DISCUSSION In the samples with various heat treatments,
0022 2313/88/$03.50 © Elsevier Science Publishers By. (North-Holland Physics Publishing Division)
and
___________ 2
738
T. Itoh, Y. Iwabuchi
Cul in KI
‘—6 Ui
z
/
Quantum size effect on excitons in microciystals
77K
~3.3
Cul in KI
77K
-
~ k ___
~o0
~3(,
o0
LU
~2 U
~
~EFH Z’,~ :~ Ibulk
~
Ui
~3.02 Z
3
~ 0’ —~•‘‘1 3.0
~JiifflI.
I
3.1
L_
(15
3.5 EXCITATION ENERGY (eV)
4.0
E~(L) Eb+
2
ex 2
I
3.2
I
N
3.3 3.4 3.5 36 3.7 EXCITATION ENERGY (eV)
38
3.9
FIGURE 2 in energy between the peaks in the excitation spectra and the luminescence of Cul. Open circles and solid lines represent experi
Relations
FIGURE 1 Luminescence spectrum (dotted curve) and its excitation spectra at different luminescence energies (solid curves) in Cul microcrystals embedded in XI matrix.
~ (1~ 2~ ) 52
c~Is
~~KeX(~)
mental and theoretical values, respectively.
The following 9eV.cm parameters obtained; 0.08, and Mare ex (Z 3 )—5.9m 0. The peaks C and H are fitted by the 2S states of the 0.36xiO
...
ex
Z~ 2 and Z3 excitons.
where E2 and E’~are the energies of the light and heavy mass excitons,
ex and
the exciton
Luttinger parameters the exciton k linear arid term,BK7~the coefficient of The excitation spectra of the broad exciton
respectively.
The peak F
is ascribed to the 2 2 state of the heavy mass excitons.
The solid lines for C.H and F are 5 with obtained from the radius variational calculation the exciton Bohr of i.5nm and the exciton Rydberg constant of 62meV.
The peak D may be
luminescence bands in Cu-halide microcrystals
associated with the spherical microcrystals
are found to be composed of several peaks whose
where 2—1.43.
energies are strongly dependent on the energies
to the experimental data are fairly well.
of the observed luminescence. Figure 1 shows the lixninescence spectrum of Cul microcrystals
confinement along (lii) direction is certified in CuBr with the use of well known exciton
(in dotted curve) and its excitation spectra (in
parameters.3
solid curves) at various luminescence energies
obtained in CuCl ~
The overall theoretical fittings
The exciton parameters are also ~ç~X
0.89.
xQ, 8
indicated by arrows.
The peaks are classified
~K~X O.8zxlu
The
e’v.cm.
and
The exciton confinement
into two groups: one belongs to the Z12 exciton
model may be more adequate for CuCl and less for
and the other to the Z3 exciton.
GuI because the former has smaller Bohr radius
The relations
in energy between these peaks and the observed
than the latter.
luminescence are plotted in Fig.2 by open
still approximately valid in GuI even though the
circles. The luminescence band is associated with the radiative decay of the inhomogeneously
calculated size for giving the luminescence at 5.21eV is smaller than the Bohr radius.
broadened size quantized is Z12 free excitons
REFERENCES
having the energy of E~n• The resonant peak is
1. T. Itoh and T. Kirihara,
denoted by A. The peaks B and E can be ascribed to the iS Z12 exciton states having E~arid E .
31/32 (1984) 120. 2. A.I. Ekjmov and .A.A. Onushchenlco, Fiz. Tekh. Poluprovodn. 16 (1982) 1215. 3. Y. Nozue, 3. Phys. Soc. Jpn. 51 (1982) 1840. 4. B. Hoenerlage. C. Klingshirn and J.B. Grun,
2
The solid lines for B and E are calculated curves according to eqs.(2) and (3) by assuming ex 4 —0.37. The peak G is associated with the 15 Z3 exciton whose energy obeys eq. Cl) for 2 1
Nevertheless, the model is
J. Luminescence
phys. stat. sol. bIB (1976) 599. 5. N. Matsuura and Y. Shinozuka, 3. Phys. Soc. Jpn. 53 (1984) 5138.