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Excited-state structure of the I7minus; center in AgCl
Solid State Communications, Vol. 6, pp. 741-744, 1968. Pergamon Press.
Printed In Great Britain
EXCITED-STATE STRUCTURE OF THE 1 CENTER IN AgC1 R. K. Ahrenkiel Research Laboratories, Eastman Kodak Company Rochester, N.Y. 14650 (Received 17 June 1968 by E. Burstein) Low temperature radiative lifetime measurements of f in AgC1 indicate the existence of two excited states separated by 0. 73 mV. An interpretation is given in terms of Jahn-Teller splitting of the excited P-state.
RECENT studies of iodine-doped AgC1 have shown discrete absorption and emission bands at 3. 13 eV and 2. 67 eV, respectively. 1 This situation is unlike the case of Br -doped AgC1 In which the host exciton states are shifted in energy by the Impurity and a virtual crystal model seems more appropriate.2 A model of the excitation1 was proposed to account for the weakness of the S to P transition (4 x 10~ oscil]ator strength and 5-i.isec radiative lifetime) and the relatively small Stokes shift. The ground state is described by a 1S 0 wavefunction localized on the I ion, whereas the ~P1 -type excited state is an effective mass
times much shorter than the radiative lifetime, one would observe a biphasic decay. As this is not observed here, one may write the total transition probability P
=~
g,P,~exp(-E~/KT)/L gjexp (-E~/KT),(l)
where E~is the energy of the jth state, with respect to the continuum, gj Is the degeneracy, and P~is the transition probability to the ground state. If there are two such excited states, then the total lifetime T = 1/P:
a. closely coupled to the Ag~(5s)conduction
[1
(g2/g1) exp(-~E/KT)
+ ________________
New studies of the radiative lifetime of the emission indicate a rather large increase in the lifetime of the excited state at pumped helium temperatures. Over the same temperature range, the quantum efficiency of the luminescence is constant. The data are shown in Fig. 1. The output of the photomultiplier tube was fed to a wide-band logarithmic amplifier developed by the author. This device converted exponential signals to linear signals for oscilloscope displays. The decay time could be determined from the slope, and the presence of nonexponential or biphasic signals (those of two additive exponential components) can be easily observed. The decay was found to be a single exponential over at least 4 decay times. This behavior may be described by thermal equilibrium of two or more excited states with different transition probabilities. If thermal equilibrium were not maintained for
I + (g2 /g1)(1/
T2)
(2)
exp (-~/KT)
A machine fit of (2) to the data is shown in Fig. 1. Choosing a range of ratios for g2/g1 from 1/5 to 5, the parameters ~ and ~E were chosen by the IBM 360 computer to minimize the least squares error. The data could be best fit by the following values. ~
10. 77 -‘sec
= — -
L,E
isec 0. 73 mV 2
..
= /
g2, g1
— -
Curves with g2/g1 = I and 3 are shown for comparison. The model described in reference I could 741
742
EXCITED-STATE STRUCTURE OF ~HE
I I
~
I0~-
-
Low-temperature radiative lifetime of the
-
2.67 eV I~emission in AgC1. The curve
~2
—
Vol. 6, No.10
FIG. I
-
81-
labeled g2 /g1
3
~ :~
=
2 is the least squares fit
to the data as indicated in the text.
2
01o
f CENTER IN AgCl
-
I 2
I 4
I 6
I 8
0
2
I 4
6
18
20
T (~K)
TABLE 1
-
Distortion symmetry
D4~
C2.
C2.
Representation (dimension)
Basis
F;
(1)
z
-
(2)
x,y
(1)
z
(1) (1)
x X~
21-; (1) ~ (1)
x,y z
+
~
+
F2
+
U3
+
1~~
be described as a Wannier exciton with the hole trapped at an impurity. Because of the very strong spin-orbit splitting, the hole may be excited into either of two spin states which differ in energy by about 0. 9 eV. This is the familiar Mott doublet observed in the exciton spectra of all the metal halides. ~ In reference 1, a tentative assignment of r~ was given to the hole state by comparison with the Cul and AgI exciton spectra. ~ The effective mass electron state transforms like the F~ conduction band. 4 using The excited-state the notationsymmetry of Bethe, ~canasbefollows: reduced,
1-B
(hole) x r~(envelope)X F~(electron) -
=
F3
-
-
(3)
+ 1-4 + 1-5
The only allowed dipole transition to the r~ ground state is from the state of symmetry F4: i. e., -
-
(T’~ r4(rad)l
-
1-3 +1-4
-
.
-~-T~)~ 0 for
-
1-4
(4)
of rareThe gases parentage and alkali of such halides terms hasinbeen the spectra discussed in the literature. ~8 The 1-4 term is
Vol. 6, No. 10
EXCITED-STATE STRUCTURE OF THE
—
+
r
symmetries, D~,, C~and C~produce two or more states which have dipole matrix elements to T~ These are listed In Table 1. Of these D~would seem to best satisfy the experimental results of two excited states with g2/g, = 2. Hence we tentatively Identify the higher, twofold degenerate state as having symmetry 1-2 and the lower, singlet as 1-5 as indicated in Fig. 2.
et”.s~=”~
I1~2(I)
t~E • 73mV~
r2 267ev
.
Z
______
30l~c -
743
distortions1’ from Oh symmetry which will split the F state. However, only three distortion 5
r;(2)
f CENTER IN AgC1
l0.77~ec
Using the model of Fig. 2, the ratio of matrix elements for the two transitions is found tobe: /=/(r,/r2) FIG. 2
1.89 This result is consistent with our diffuse wave-function model as the overlap integral would be relatively insensitive to changes in core symmetry. =
Proposed energy levels of the JahnTeller distorted I center. The polarization of the emitted radiation is enclosed in brackets. 3P related to the 3P 1 and 1- and are related to 3P 2. In the jj coupling limit, the 1 term is strongly mixed by spin-orbit interaction with a ~ term as a (3/2, 1/2) ii state, 3P., and 3P The 2 states are separated by the electrostatic interactions and this energy separation is 0. 12 eV in Xe, which is isoelectronic with I Hence the lower energy state of our proposed doublet is probably not the 3P 2 state as the energy 3P separation .~Eis much smaller. Also as 2 is a pure triplet, one would expect ~ >> r~ which is not observed here. .
We see from Table I that photons emitted from a F to F~transition are c-polarized with respect to the tetragonal axis, whereas the r to F~transition is rr_polarized. As the former are absent at I. 8°K,polarized excitation could produce polarized emission if the sense of the excitation can be “remembered” by the center. Such has been shown to be the case of Tl~in the alkali halides. ~ 13 The Jahn- Teller mechanism has been proposed to explain the polarized emission in that case. ~‘ Such experiments are in progress with the hope of finding the distortion symmetry of the excited I center.
Acknowledgements The author wishes to thank A. Gold and K. J. Teegarden, for helpful suggestions; W. Selke for building the cryogenic apparatus; and B. Service for help with the computer programming. —
According to the Jahn- Teller theorem, the orbitally degenerate state is unstable in a cubic environment and distortion occurs to reduce the degeneracy. There are nine possible
References I.
MOSER F.,
2.
JOESTEN B.L. and BROWN F.C.,
3.
CARDONA M.
4.
KNOX R. S., In Solid State Pl~ysics(Edited by SEITZ F. and TURNBTJLL D.) Suppl. 5. Academic Press, New York (1963). BETHE H.A., Ann. Phys. 3, 133 (1929).
5.
AHRENKIEL ILK. and LYU S., Phys. Rev. 161, 897 (1967).
,
Phys. Rev.
Phys. Rev. 148, 919 (1966).
129, 69 (1963).
-
744
EXCITED-STATE STRUCUTURE OF THE I
CENTER IN AgCl
Vol. 6, No.10
6.
OVERHAUSER A.W., Phys. Rev. 101, 1702 (1955).
7.
KNOX R.S,, J. Phys. Chem. SolIds 9, 265 (1958); Ibid. 9, 238 (1959); Phys. Rev. 110, 375 (1958).
8.
KNOX R.S. and INSHAUSPE N.,
9.
CONDON E. U. and SHORTLEY G. H., Press (1964).
10. JARN H.A. and TELLER E.,
Phys. Rev. 116, 1093 (1959). The Theory of Atomic Spectra
Cambridge University
Proc. H. Soc. A161, 220 (1937).
11. KOSTER G. F., PIMMOCK J. 0., WHEELER R. G. and STATZ H., two Point Groups M. I. T. Press, Cambridge, Mass. (1963).
Properties of the Thirty
12. KLICK C.C. and COMPTON W.D., J. Phys. Chem. Solids 7, 170 (1958). 13. EDGERTON R., 14. FUKUDA A.,
Phys. Rev. 138, A85 (1965).
MAKISHIMA S., MAHUCHI T. and ONAKA K.,
J. Phys. Chem. Solids 28,
1763 (1967).
—
Die Halbwertszeit der Luminszenz von I in AgC1 bei tiefen Temperaturen deutet aix! die Existenz von zwei angeregten Zuständen, die 0. 73 mV auseinander liegen, hin. Eine Interpretation, die auf ether Jahn- Teller Spaltung der angeregten P-Zust~ndeberuht, wird vorgelegt. -
Printed In Great Britain
EXCITED-STATE STRUCTURE OF THE 1 CENTER IN AgC1 R. K. Ahrenkiel Research Laboratories, Eastman Kodak Company Rochester, N.Y. 14650 (Received 17 June 1968 by E. Burstein) Low temperature radiative lifetime measurements of f in AgC1 indicate the existence of two excited states separated by 0. 73 mV. An interpretation is given in terms of Jahn-Teller splitting of the excited P-state.
RECENT studies of iodine-doped AgC1 have shown discrete absorption and emission bands at 3. 13 eV and 2. 67 eV, respectively. 1 This situation is unlike the case of Br -doped AgC1 In which the host exciton states are shifted in energy by the Impurity and a virtual crystal model seems more appropriate.2 A model of the excitation1 was proposed to account for the weakness of the S to P transition (4 x 10~ oscil]ator strength and 5-i.isec radiative lifetime) and the relatively small Stokes shift. The ground state is described by a 1S 0 wavefunction localized on the I ion, whereas the ~P1 -type excited state is an effective mass
times much shorter than the radiative lifetime, one would observe a biphasic decay. As this is not observed here, one may write the total transition probability P
=~
g,P,~exp(-E~/KT)/L gjexp (-E~/KT),(l)
where E~is the energy of the jth state, with respect to the continuum, gj Is the degeneracy, and P~is the transition probability to the ground state. If there are two such excited states, then the total lifetime T = 1/P:
a. closely coupled to the Ag~(5s)conduction
[1
(g2/g1) exp(-~E/KT)
+ ________________
New studies of the radiative lifetime of the emission indicate a rather large increase in the lifetime of the excited state at pumped helium temperatures. Over the same temperature range, the quantum efficiency of the luminescence is constant. The data are shown in Fig. 1. The output of the photomultiplier tube was fed to a wide-band logarithmic amplifier developed by the author. This device converted exponential signals to linear signals for oscilloscope displays. The decay time could be determined from the slope, and the presence of nonexponential or biphasic signals (those of two additive exponential components) can be easily observed. The decay was found to be a single exponential over at least 4 decay times. This behavior may be described by thermal equilibrium of two or more excited states with different transition probabilities. If thermal equilibrium were not maintained for
I + (g2 /g1)(1/
T2)
(2)
exp (-~/KT)
A machine fit of (2) to the data is shown in Fig. 1. Choosing a range of ratios for g2/g1 from 1/5 to 5, the parameters ~ and ~E were chosen by the IBM 360 computer to minimize the least squares error. The data could be best fit by the following values. ~
10. 77 -‘sec
= — -
L,E
isec 0. 73 mV 2
..
= /
g2, g1
— -
Curves with g2/g1 = I and 3 are shown for comparison. The model described in reference I could 741
742
EXCITED-STATE STRUCTURE OF ~HE
I I
~
I0~-
-
Low-temperature radiative lifetime of the
-
2.67 eV I~emission in AgC1. The curve
~2
—
Vol. 6, No.10
FIG. I
-
81-
labeled g2 /g1
3
~ :~
=
2 is the least squares fit
to the data as indicated in the text.
2
01o
f CENTER IN AgCl
-
I 2
I 4
I 6
I 8
0
2
I 4
6
18
20
T (~K)
TABLE 1
-
Distortion symmetry
D4~
C2.
C2.
Representation (dimension)
Basis
F;
(1)
z
-
(2)
x,y
(1)
z
(1) (1)
x X~
21-; (1) ~ (1)
x,y z
+
~
+
F2
+
U3
+
1~~
be described as a Wannier exciton with the hole trapped at an impurity. Because of the very strong spin-orbit splitting, the hole may be excited into either of two spin states which differ in energy by about 0. 9 eV. This is the familiar Mott doublet observed in the exciton spectra of all the metal halides. ~ In reference 1, a tentative assignment of r~ was given to the hole state by comparison with the Cul and AgI exciton spectra. ~ The effective mass electron state transforms like the F~ conduction band. 4 using The excited-state the notationsymmetry of Bethe, ~canasbefollows: reduced,
1-B
(hole) x r~(envelope)X F~(electron) -
=
F3
-
-
(3)
+ 1-4 + 1-5
The only allowed dipole transition to the r~ ground state is from the state of symmetry F4: i. e., -
-
(T’~ r4(rad)l
-
1-3 +1-4
-
.
-~-T~)~ 0 for
-
1-4
(4)
of rareThe gases parentage and alkali of such halides terms hasinbeen the spectra discussed in the literature. ~8 The 1-4 term is
Vol. 6, No. 10
EXCITED-STATE STRUCTURE OF THE
—
+
r
symmetries, D~,, C~and C~produce two or more states which have dipole matrix elements to T~ These are listed In Table 1. Of these D~would seem to best satisfy the experimental results of two excited states with g2/g, = 2. Hence we tentatively Identify the higher, twofold degenerate state as having symmetry 1-2 and the lower, singlet as 1-5 as indicated in Fig. 2.
et”.s~=”~
I1~2(I)
t~E • 73mV~
r2 267ev
.
Z
______
30l~c -
743
distortions1’ from Oh symmetry which will split the F state. However, only three distortion 5
r;(2)
f CENTER IN AgC1
l0.77~ec
Using the model of Fig. 2, the ratio of matrix elements for the two transitions is found tobe:
1.89 This result is consistent with our diffuse wave-function model as the overlap integral would be relatively insensitive to changes in core symmetry. =
Proposed energy levels of the JahnTeller distorted I center. The polarization of the emitted radiation is enclosed in brackets. 3P related to the 3P 1 and 1- and are related to 3P 2. In the jj coupling limit, the 1 term is strongly mixed by spin-orbit interaction with a ~ term as a (3/2, 1/2) ii state, 3P., and 3P The 2 states are separated by the electrostatic interactions and this energy separation is 0. 12 eV in Xe, which is isoelectronic with I Hence the lower energy state of our proposed doublet is probably not the 3P 2 state as the energy 3P separation .~Eis much smaller. Also as 2 is a pure triplet, one would expect ~ >> r~ which is not observed here. .
We see from Table I that photons emitted from a F to F~transition are c-polarized with respect to the tetragonal axis, whereas the r to F~transition is rr_polarized. As the former are absent at I. 8°K,polarized excitation could produce polarized emission if the sense of the excitation can be “remembered” by the center. Such has been shown to be the case of Tl~in the alkali halides. ~ 13 The Jahn- Teller mechanism has been proposed to explain the polarized emission in that case. ~‘ Such experiments are in progress with the hope of finding the distortion symmetry of the excited I center.
Acknowledgements The author wishes to thank A. Gold and K. J. Teegarden, for helpful suggestions; W. Selke for building the cryogenic apparatus; and B. Service for help with the computer programming. —
According to the Jahn- Teller theorem, the orbitally degenerate state is unstable in a cubic environment and distortion occurs to reduce the degeneracy. There are nine possible
References I.
MOSER F.,
2.
JOESTEN B.L. and BROWN F.C.,
3.
CARDONA M.
4.
KNOX R. S., In Solid State Pl~ysics(Edited by SEITZ F. and TURNBTJLL D.) Suppl. 5. Academic Press, New York (1963). BETHE H.A., Ann. Phys. 3, 133 (1929).
5.
AHRENKIEL ILK. and LYU S., Phys. Rev. 161, 897 (1967).
,
Phys. Rev.
Phys. Rev. 148, 919 (1966).
129, 69 (1963).
-
744
EXCITED-STATE STRUCUTURE OF THE I
CENTER IN AgCl
Vol. 6, No.10
6.
OVERHAUSER A.W., Phys. Rev. 101, 1702 (1955).
7.
KNOX R.S,, J. Phys. Chem. SolIds 9, 265 (1958); Ibid. 9, 238 (1959); Phys. Rev. 110, 375 (1958).
8.
KNOX R.S. and INSHAUSPE N.,
9.
CONDON E. U. and SHORTLEY G. H., Press (1964).
10. JARN H.A. and TELLER E.,
Phys. Rev. 116, 1093 (1959). The Theory of Atomic Spectra
Cambridge University
Proc. H. Soc. A161, 220 (1937).
11. KOSTER G. F., PIMMOCK J. 0., WHEELER R. G. and STATZ H., two Point Groups M. I. T. Press, Cambridge, Mass. (1963).
Properties of the Thirty
12. KLICK C.C. and COMPTON W.D., J. Phys. Chem. Solids 7, 170 (1958). 13. EDGERTON R., 14. FUKUDA A.,
Phys. Rev. 138, A85 (1965).
MAKISHIMA S., MAHUCHI T. and ONAKA K.,
J. Phys. Chem. Solids 28,
1763 (1967).
—
Die Halbwertszeit der Luminszenz von I in AgC1 bei tiefen Temperaturen deutet aix! die Existenz von zwei angeregten Zuständen, die 0. 73 mV auseinander liegen, hin. Eine Interpretation, die auf ether Jahn- Teller Spaltung der angeregten P-Zust~ndeberuht, wird vorgelegt. -