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Stabilities of the self-trapped holes and excitons in alkali halides
Journal of Luminescence 40&41 (1988) 451—452 North-Holland, Amsterdam
451
STABILITIES OF THE SELF-TRAPPED HOLES AND EXCITONS IN ALKALI HALIDES Y. NAKAOKA
and T. HIGASHIMURA
Department of Physics, Osaka City University, Sumiyoshi-ku, Osaka, Japan We study theoretically the stability of halides, AH, A=Li, Na, K, Rb, and H=Cl, obtained experimentally and the present Ex emission is three-center like state,
self-trapped hole and self-trapped exciton in alkali Br, I. From a good correspondence between the emissions numerical results, it is found that a probable origin of while that of ii and a emissions is two-center state.
1. INTRODUCTION The self-trapped hole(STH) and the
which includes both site diagonal and off— diagonal terms. The electron-phonon
self-trapped exciton(STE) in alkali halides have been supposed a priori to be two-center
interaction(HeL) is derived from the continum approximation; the deformation potential and the
type, Vk and Vk+e, respectively. However, it is not sufficient to suppose the two-center type origin to explain three types of emissions(n,o
Fr~hlichinteractions. The trial function of STE is taken as follows: for a hole
and Ex emissions) which are observed
I~~>=N(A_
experimentally. It is very important to investigate the possibility of the existence of
1a11+A0a~÷A1a~)lg> and for an electron I~e(r)N(X_lf_l(r)+AOfO(r)+Alfl(r))
another origin of intrinsic emissions. In the present work, we calculate energies of four
Here, a~is a creation operator for a hole at n site, Ig> represents the ground state, the
types of localized states for STE and STH and study the stability of their states in alkali halides,
electron trial2(r_n)2) functionwhere is defined a is a as variational fn(r)=exp(_~o parameter and A 0(+1) are parameters to determine STE state. Both N and N are normalization
2. MODEL The present model is starting from the facts
factors. We can treat four states for the sets of
that the effective mass of hole is heavy and that the mass of electron is very light. We
parameters, (A1,A~,A1). (i) (0,l,0)=1STE, the localized state at a single H site. (ii)
construct the hole Hamiltonian with site representation on the basis Hamiltonian of the smallis polaron 1 while the electron theory obtained from the effective mass approximation2,
(x,1,x)=3’STE, the three—center like self— trapped exciton where A is determined by the variational method (Sometimes this state is
The total Hamiltonian of exciton-phonon
(1) (2)
called the extended one-center state). (iii) (0,1,1)=2STE, the localized exciton state at
system is given as
H=H~+H~+HC+HL+HeL+HhL;H~and are kinetic energies of electron and hole, respectively, Hc is the Coulomb interaction, HL is the lattice energy. The notable points are
two adjacent H sites, Vk+e. (iv) (1,1,1)= 3STE, the three-center self-trapped exciton. We have calculated hole energies for states extended more than three sites, using exp(-~n)
follows. The crystal discreteness is reflected in the hole—phonon interaction(HhL)1,
type
as
0022—2313/88/$03.50 © Elsevier Science Publishers B.Y.
(North-Holland Physics Publishing Division)
trial functions. The total energies of corresponding states coincide within a few
452
Y. Nakaoka, T. Higashimura
1
32
31
3231
/
TABLE1
3231323
:ue5n0~nSe8resrim~t~
~
~
E~
E~(ac)
Eh(op) d~TH R
FIGURE 1 Cluster dependence of kinetic and relaxation energies for four types of STH.20.(a) v4.O (b) vl.O (c) vO.50 (d) vO.
percent.
Self-trapped holes and excitons
From this, we have concluded that it
Li Na
3’(?) 2(71,0)
31(Ex)* 3’(Ex)
3’(Ex) 3’(Ex)
K
2(71)
2(71,0)
2’~3’(m,o,Ex)
Rb 2(m) * Ref. 4.
2(n,o)
2(m,o,Ex)
2STH is stable. Numerical results on STE and STH in alkali
is sufficient to consider the above four states to examine the stability of STE.
halides are given in Table 1. The stability of holes and excitons depends on crystals. In NaC1, KC1, KBr and rubidium halides 2STE and
3. NUMERICAL RESULTS AND DISCUSSION
2STH are most stable. 3’STE and 3’STH are most stable in lithium and sodium halides
The total energies of STE and STH are calculated for the four types of localized
except NaC1.
states in twelve alkali halides. The energy of STE is ~ where E~and E~
theoretically that 2STE coexists with 3’STE. There is a good correspondence between the
are relaxation energies and E~ is the
interference energy. Since the electron in the present model is spatially extended enough, the
classification of emissions observed experimentally and the theoretical results, as shown in Table 1. Therefore, we are convinced
stability of STE is essentially determined by
that the origin of
the hole state. Thus, we discuss the stability of STH in detail3,
and that of Ex emission is 3’STE. To ascertain this identification, more precise
The energy of STH is given as ESTH=E~+E~(ac)+ E~(op),where ac and op stand for the acoustic and optical modes. We find that the site off—
experiments are necessary; for example ODEPR in lithium halides at low temperatures.
diagonal term in E~(ac) plays an important role
REFERENCES
to stabilize 2STH selectively. The relaxation h . . . energy, E 0(ac) shows a typical minimum at 2STH,
1. T. Iida and R. Monnier, phys. stat. sol. (b) 74 (1976) 91.
as shown in Figure 1.
Furthermore, it becomes
clear that the difference in the stability
depending on crystals essentially comes from the difference in cation-to-anion mass ratio
(v”M~/M)which is contained in E~(op).
For
example, the ratio v is 0.055 for Lii, 1.1 for KC1 and 2.4 for RbCl. When the ratio v is small 3’STH is stable while when v is large
Especially in KI, it is certain
It
and a emissions is 2STE
2. T. Higashimura, Y. Nakaoka and T. lida, J. Phys. C, 17 (1984) 4127. 3. Y. Nakaoka, phys. stat. sol. (b) 127 (1985) 327. 4. H. Nishimura, private comunication.
451
STABILITIES OF THE SELF-TRAPPED HOLES AND EXCITONS IN ALKALI HALIDES Y. NAKAOKA
and T. HIGASHIMURA
Department of Physics, Osaka City University, Sumiyoshi-ku, Osaka, Japan We study theoretically the stability of halides, AH, A=Li, Na, K, Rb, and H=Cl, obtained experimentally and the present Ex emission is three-center like state,
self-trapped hole and self-trapped exciton in alkali Br, I. From a good correspondence between the emissions numerical results, it is found that a probable origin of while that of ii and a emissions is two-center state.
1. INTRODUCTION The self-trapped hole(STH) and the
which includes both site diagonal and off— diagonal terms. The electron-phonon
self-trapped exciton(STE) in alkali halides have been supposed a priori to be two-center
interaction(HeL) is derived from the continum approximation; the deformation potential and the
type, Vk and Vk+e, respectively. However, it is not sufficient to suppose the two-center type origin to explain three types of emissions(n,o
Fr~hlichinteractions. The trial function of STE is taken as follows: for a hole
and Ex emissions) which are observed
I~~>=N(A_
experimentally. It is very important to investigate the possibility of the existence of
1a11+A0a~÷A1a~)lg> and for an electron I~e(r)N(X_lf_l(r)+AOfO(r)+Alfl(r))
another origin of intrinsic emissions. In the present work, we calculate energies of four
Here, a~is a creation operator for a hole at n site, Ig> represents the ground state, the
types of localized states for STE and STH and study the stability of their states in alkali halides,
electron trial2(r_n)2) functionwhere is defined a is a as variational fn(r)=exp(_~o parameter and A 0(+1) are parameters to determine STE state. Both N and N are normalization
2. MODEL The present model is starting from the facts
factors. We can treat four states for the sets of
that the effective mass of hole is heavy and that the mass of electron is very light. We
parameters, (A1,A~,A1). (i) (0,l,0)=1STE, the localized state at a single H site. (ii)
construct the hole Hamiltonian with site representation on the basis Hamiltonian of the smallis polaron 1 while the electron theory obtained from the effective mass approximation2,
(x,1,x)=3’STE, the three—center like self— trapped exciton where A is determined by the variational method (Sometimes this state is
The total Hamiltonian of exciton-phonon
(1) (2)
called the extended one-center state). (iii) (0,1,1)=2STE, the localized exciton state at
system is given as
H=H~+H~+HC+HL+HeL+HhL;H~and are kinetic energies of electron and hole, respectively, Hc is the Coulomb interaction, HL is the lattice energy. The notable points are
two adjacent H sites, Vk+e. (iv) (1,1,1)= 3STE, the three-center self-trapped exciton. We have calculated hole energies for states extended more than three sites, using exp(-~n)
follows. The crystal discreteness is reflected in the hole—phonon interaction(HhL)1,
type
as
0022—2313/88/$03.50 © Elsevier Science Publishers B.Y.
(North-Holland Physics Publishing Division)
trial functions. The total energies of corresponding states coincide within a few
452
Y. Nakaoka, T. Higashimura
1
32
31
3231
/
TABLE1
3231323
:ue5n0~nSe8resrim~t~
~
~
E~
E~(ac)
Eh(op) d~TH R
FIGURE 1 Cluster dependence of kinetic and relaxation energies for four types of STH.20.(a) v4.O (b) vl.O (c) vO.50 (d) vO.
percent.
Self-trapped holes and excitons
From this, we have concluded that it
Li Na
3’(?) 2(71,0)
31(Ex)* 3’(Ex)
3’(Ex) 3’(Ex)
K
2(71)
2(71,0)
2’~3’(m,o,Ex)
Rb 2(m) * Ref. 4.
2(n,o)
2(m,o,Ex)
2STH is stable. Numerical results on STE and STH in alkali
is sufficient to consider the above four states to examine the stability of STE.
halides are given in Table 1. The stability of holes and excitons depends on crystals. In NaC1, KC1, KBr and rubidium halides 2STE and
3. NUMERICAL RESULTS AND DISCUSSION
2STH are most stable. 3’STE and 3’STH are most stable in lithium and sodium halides
The total energies of STE and STH are calculated for the four types of localized
except NaC1.
states in twelve alkali halides. The energy of STE is ~ where E~and E~
theoretically that 2STE coexists with 3’STE. There is a good correspondence between the
are relaxation energies and E~ is the
interference energy. Since the electron in the present model is spatially extended enough, the
classification of emissions observed experimentally and the theoretical results, as shown in Table 1. Therefore, we are convinced
stability of STE is essentially determined by
that the origin of
the hole state. Thus, we discuss the stability of STH in detail3,
and that of Ex emission is 3’STE. To ascertain this identification, more precise
The energy of STH is given as ESTH=E~+E~(ac)+ E~(op),where ac and op stand for the acoustic and optical modes. We find that the site off—
experiments are necessary; for example ODEPR in lithium halides at low temperatures.
diagonal term in E~(ac) plays an important role
REFERENCES
to stabilize 2STH selectively. The relaxation h . . . energy, E 0(ac) shows a typical minimum at 2STH,
1. T. Iida and R. Monnier, phys. stat. sol. (b) 74 (1976) 91.
as shown in Figure 1.
Furthermore, it becomes
clear that the difference in the stability
depending on crystals essentially comes from the difference in cation-to-anion mass ratio
(v”M~/M)which is contained in E~(op).
For
example, the ratio v is 0.055 for Lii, 1.1 for KC1 and 2.4 for RbCl. When the ratio v is small 3’STH is stable while when v is large
Especially in KI, it is certain
It
and a emissions is 2STE
2. T. Higashimura, Y. Nakaoka and T. lida, J. Phys. C, 17 (1984) 4127. 3. Y. Nakaoka, phys. stat. sol. (b) 127 (1985) 327. 4. H. Nishimura, private comunication.