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Trapped exciton states in the alkali halides
J. Phys. Cheer. Solids
Pergamon
Press 1966. Vol. 27, pp. 943-946.
TRAPPED EXCITON
Printed in Great Britain.
STATES IN THE ALKALI HALIDES*
G. BALDINI and K. TEEGARDEN Institute of Optics, University (Received
of Rochester,
Rochester,
N.Y.
18 November 1965)
Abstract-The absorption spectra of thin films of RbCl containing 1 mol. % of RbI and KC1 containing 1 mol. yO of KI measured at low temperature are presented. These spectra show structure which is analogous to the structure seen in the exciton spectra of pure KI and RbI. Both the well known spin orbit doublet and lines corresponding to effective mass states of the bound hole-electron pair appear. An attempt is made to calculate the effective mass of an electron in the host crystal from the absorption spectra. A value of 0.66 is obtained for the case of RbCl : RbI.
INTRODUCI’ION
THE exciton structure of large band gap insulators such as the alkali halides has usually been thought of in terms of the Frenkel or tight binding approximation.(l) This approximation is also generally applied to the electronic structure of impurities in these materials. The possible existence of WANNIER,(~) or loosely bound exciton states in the case of the alkali halides was discussed by MOTT and GURNEY@)some time ago. The existence of such states in the pure alkali halides has been demonstrated by FISCHER and HILSCH,(~) while HOPFIELD and WORLOCH@)have used the Wannier model in an evaluation of their experiments on two-quantum absorption in pure KI and CsI. Wannier-Mott exciton states have been also observed in films of the pure solid rare gases by BAL.DINI,(~)who has also observed(s) hydrogen-like states of substitutional impurities in alloys of the solid rare gases which can be described in terms of the effective mass approximation. The present work is concerned with similar states in alloys of the alkali halides, principally RbCl containing a small amount of RbI. In this system absorption lines appear which can be associated with the energy levels of an electron and a hole localized in the
substitutional iodide impurity. These lines resemble the absorption structure of pure RbI, modified by the different dielectric constant and Madelung energy of the host. It is suggested that they can be explained as the well-known spin orbit doublet characteristic of the exciton spectrum of the alkali halides and higher lying states which can be discussed in terms of the effective mass approximation.
EXPERIMENTAL Films of KC1 and RbCl containing about 1 mol. y0 of KI and RbI respectively were produced by vacuum evaporation of powdered mixtures onto a fused silica substrate. The substrate was held at about 300°K during evaporation, and subsequently warmed in vacuum to about 420°K and held at this temperature for about 15 min to anneal the samples. All these operations were performed in the cryostat used for the optical absorption measurements at low temperature. Absorption measurements were made with apparatus described elsewhere.t5) The use of heavily doped samples in this experiment made it possible to discriminate between the fundamental absorption of the host and the higher * Research sponsored in part by the Air Force Office lying absorption bands of the iodide impurity. In of Scientific Research, Office of Aerospace Research, lightly doped single crystals these bands tend to United States Air Force, under AFOSR Grant Number overlap the absorption edge of the host and are AF-AFOSR-236-65, and in part by the U.S. Army therefore hard to observe. Research Office, Durham. 943
G.
944 DISCUSSION
BALDINI
and
OF RESULTS
The absorption spectrum at 10°K of a thin film of RbCl containing approximately 1 mol. y0 of RbI is shown in Fig. 1. Four absorption lines are resolved. These lie at 6*42,6*87,7*13 and 7.33 eV. The resemblance between this spectrum and the absorption spectrum of pure RbI is to be noted. The two lines at 6.42 and 7.33 eV presumably correspond to the spin orbit doublet found in the pure salt. That is, they correspond to transitions
K.
TEEGARDEN
spin orbit doublet is taken to be the n = 1 state, No such series associated with the high energy component of the doublet appears because of overlap with the fundamental edge of the host. Similar lines have been observed in the case of KC1 : KI, at 80°K. These are shown in Fig. 2. The interpretation of the spectrum of this system is completely analogous to one given above for RbCl : RbI. In the effective mass approximation, the energy levels of an electron in the field of a trapped hole are given by the hydrogenic formula: hv, = Eo-G/n2,
RbCI:
RbI
(I%)
n = 1,2,3, . . .
where G is the binding energy of the trapped exciton and Eo is the ionization energy of the iodide impurity. The binding energy is given by: G=-
Rm* 82
OG1
PHOTON
ENERGY
IN eV
FIG. 1. The absorption spectrum at 10°K of a film of RbCl containing approximately 1 mol y0 of RbI.
between the ps ground state of the halide ion and a pss excited configuration. The separation of these lines is 0.91 eV, which agrees quite well with the splitting expected in the I- ion.(s) The two lines which lie between the doublet at 6.87 and 7.13 eV, may be analogous to the structure found by FISCHER and HILSCH@) between the lines of the spin orbit doublet in pure RbI films. We interpret them as being excited Wannier states of an exciton trapped at the iodide impurity in the chloride host. The line at 6.87 eV is taken to be a hydrogen-like state with principal quantum number n = 2, with the line at 7.13 eV corresponding to n = 3. The lowest energy component of the
Here R is the ordinary Rydberg, 13.6 eV; E is an appropriate dielectric constant and m* is the effective mass of an electron. Obviously the n = 1 state of the trapped exciton cannot be expected to fit this series because the relatively small dielectric constant of the alkali halides makes the effective mass approximation incorrect for this state. We can try to use the n = 2 and n = 3 states to calculate both Eo and G from the observed values of hv2 and hvs. This calculation yields G = 1.86 eV and Eo = 7.23 eV for RbCl : RbI. From the observed binding energy, the ratio m*/@ can be calculated. This ratio is found to be O-137. If we take E to be the optical dielectric constant of RbCl, or 2.19, we are led to a value of m* = 0.66 electron mass units for the effective mass of an electron in RbCl. Using this dielectric constant, the radii of the electron orbits for the n = 2 and n = 3 states are found to be 7.05 A and 15.9 A respectively. The corresponding frequencies of the electronic motion are w = 1.41 x 1015 rad./sec and 6.36 x 1014 rad./sec, respectively. These values are consistent with the use of the optical dielectric constant in the calculations. A similar analysis of the data for KC1 : KI is not too meaningful since the n = 3 state is poorly resolved at 80°K in this system. An attempt was made to observe similar structure in the alloy KF : KI, however no meaningful results were
TRAPPED
EXCITON
-
STATES
I
I
KCI:KI
(I%)
I.5 -
IN
THE
ALKALI
’ 7.69aV ’
HALIDES
945
I
80°K
: j I.0 1
:
/J 750
‘J-
6.65 eV
OL 6-O
I 6.5
ev
7.18 ev
I 7.0 PHOTON
I 7.5 ENERGY
I 80
I 85
IN aV
FIG. 2. The absorption spectrum at 80’K of a film of KC1 containing approximately 1 mol. y! of KI.
obtained, perhaps because of the large size of the I- ion relative to r. CONCLXJSLONS The above results indicate the presence of effective mass states associated with substitutional I- ions in RbCl and KCI. This interpretation of the absorption spectra is analogous to a similar treatment of rare gas alloys.(s) The remarkable similarity between the electronic structure of the solid rare gases and the alkali halides is emphasized by these results. The work of FISCHER and HILSCH(~) on Wannier exciton states in the alkali iodides is substantiated by the present experiments on alkali halide alloys, since they show that effective mass states are not as unique a phenomenon in the alkali halides as previously supposed.
It is known that the pure KI and RbI luminescence at low temperature when exposed to ultraviolet light absorbed in the fundamental band region of the crystals.(7ls) FABLER,@) and MURRAY and KELLER(~@ have shown that this luminescence is due to the recombination of an electron with a self-trapped hole, or Vk-center. The luminescence of the system KC1 : KI has been studied by MAHR.@~) Two emission bands appear when light is absorbed in any of the iodide impurity bands. We suggest that the luminescent center in this case is a halide molecule ion composed of an iodide ion and an adjacent chloride ion. Experiments with polarized light similar to those used to study the intrinsic luminescence of the alkali iodides could be used to determine the validity of this suggestion.
946
G. BALDINI
and
REFERENCES 1. For a review of the Frenkel and Wannier exciton models and their application to various solids see: KNOX R., Theory of Excitons, Supplement 5 of Solid St. Phys., Academic Press, New York and London (1963). 2. MOTT N. F. and GURNEY R. W., Electronic Processes in Ionic Crystals, second edition, pp. 95-100. Oxford University Press, Oxford (1948). 3. FISCHER F. and HILXH R., Nachr. Akad. Wiss. Giittingen, II: Math-Physik IQ. No. 8, 241 (1959).
K.
TEEGARDEN 4. HOPFIELDJ. S. and WORLOCK J. M., Phys. Reu. 137,
Al455 (1965). 5. BALDINI G., Phys. Rew. 128,1562 (1962).
6. BALDINI G., Phys. Rev. 137, A508 (1965). 7. TEEGARDEN K., Phys. Rev. 105,1222 (1957).
8. TEEGARDEN K. J. and WEEKSR., J. Phys. Chem. Solids 10, 211 (1959). 9. KABLER M. N., Phys. Rev. 136, Al296 (1964). 10. MURRAY R. B. and KELLER F. J., Phys. Rev. 137, A942 (1965). 11. MAHR H., Phys. Reo. 130, 2257 (1963) ; Phys. Rev. 132, 1880 (1963).
Pergamon
Press 1966. Vol. 27, pp. 943-946.
TRAPPED EXCITON
Printed in Great Britain.
STATES IN THE ALKALI HALIDES*
G. BALDINI and K. TEEGARDEN Institute of Optics, University (Received
of Rochester,
Rochester,
N.Y.
18 November 1965)
Abstract-The absorption spectra of thin films of RbCl containing 1 mol. % of RbI and KC1 containing 1 mol. yO of KI measured at low temperature are presented. These spectra show structure which is analogous to the structure seen in the exciton spectra of pure KI and RbI. Both the well known spin orbit doublet and lines corresponding to effective mass states of the bound hole-electron pair appear. An attempt is made to calculate the effective mass of an electron in the host crystal from the absorption spectra. A value of 0.66 is obtained for the case of RbCl : RbI.
INTRODUCI’ION
THE exciton structure of large band gap insulators such as the alkali halides has usually been thought of in terms of the Frenkel or tight binding approximation.(l) This approximation is also generally applied to the electronic structure of impurities in these materials. The possible existence of WANNIER,(~) or loosely bound exciton states in the case of the alkali halides was discussed by MOTT and GURNEY@)some time ago. The existence of such states in the pure alkali halides has been demonstrated by FISCHER and HILSCH,(~) while HOPFIELD and WORLOCH@)have used the Wannier model in an evaluation of their experiments on two-quantum absorption in pure KI and CsI. Wannier-Mott exciton states have been also observed in films of the pure solid rare gases by BAL.DINI,(~)who has also observed(s) hydrogen-like states of substitutional impurities in alloys of the solid rare gases which can be described in terms of the effective mass approximation. The present work is concerned with similar states in alloys of the alkali halides, principally RbCl containing a small amount of RbI. In this system absorption lines appear which can be associated with the energy levels of an electron and a hole localized in the
substitutional iodide impurity. These lines resemble the absorption structure of pure RbI, modified by the different dielectric constant and Madelung energy of the host. It is suggested that they can be explained as the well-known spin orbit doublet characteristic of the exciton spectrum of the alkali halides and higher lying states which can be discussed in terms of the effective mass approximation.
EXPERIMENTAL Films of KC1 and RbCl containing about 1 mol. y0 of KI and RbI respectively were produced by vacuum evaporation of powdered mixtures onto a fused silica substrate. The substrate was held at about 300°K during evaporation, and subsequently warmed in vacuum to about 420°K and held at this temperature for about 15 min to anneal the samples. All these operations were performed in the cryostat used for the optical absorption measurements at low temperature. Absorption measurements were made with apparatus described elsewhere.t5) The use of heavily doped samples in this experiment made it possible to discriminate between the fundamental absorption of the host and the higher * Research sponsored in part by the Air Force Office lying absorption bands of the iodide impurity. In of Scientific Research, Office of Aerospace Research, lightly doped single crystals these bands tend to United States Air Force, under AFOSR Grant Number overlap the absorption edge of the host and are AF-AFOSR-236-65, and in part by the U.S. Army therefore hard to observe. Research Office, Durham. 943
G.
944 DISCUSSION
BALDINI
and
OF RESULTS
The absorption spectrum at 10°K of a thin film of RbCl containing approximately 1 mol. y0 of RbI is shown in Fig. 1. Four absorption lines are resolved. These lie at 6*42,6*87,7*13 and 7.33 eV. The resemblance between this spectrum and the absorption spectrum of pure RbI is to be noted. The two lines at 6.42 and 7.33 eV presumably correspond to the spin orbit doublet found in the pure salt. That is, they correspond to transitions
K.
TEEGARDEN
spin orbit doublet is taken to be the n = 1 state, No such series associated with the high energy component of the doublet appears because of overlap with the fundamental edge of the host. Similar lines have been observed in the case of KC1 : KI, at 80°K. These are shown in Fig. 2. The interpretation of the spectrum of this system is completely analogous to one given above for RbCl : RbI. In the effective mass approximation, the energy levels of an electron in the field of a trapped hole are given by the hydrogenic formula: hv, = Eo-G/n2,
RbCI:
RbI
(I%)
n = 1,2,3, . . .
where G is the binding energy of the trapped exciton and Eo is the ionization energy of the iodide impurity. The binding energy is given by: G=-
Rm* 82
OG1
PHOTON
ENERGY
IN eV
FIG. 1. The absorption spectrum at 10°K of a film of RbCl containing approximately 1 mol y0 of RbI.
between the ps ground state of the halide ion and a pss excited configuration. The separation of these lines is 0.91 eV, which agrees quite well with the splitting expected in the I- ion.(s) The two lines which lie between the doublet at 6.87 and 7.13 eV, may be analogous to the structure found by FISCHER and HILSCH@) between the lines of the spin orbit doublet in pure RbI films. We interpret them as being excited Wannier states of an exciton trapped at the iodide impurity in the chloride host. The line at 6.87 eV is taken to be a hydrogen-like state with principal quantum number n = 2, with the line at 7.13 eV corresponding to n = 3. The lowest energy component of the
Here R is the ordinary Rydberg, 13.6 eV; E is an appropriate dielectric constant and m* is the effective mass of an electron. Obviously the n = 1 state of the trapped exciton cannot be expected to fit this series because the relatively small dielectric constant of the alkali halides makes the effective mass approximation incorrect for this state. We can try to use the n = 2 and n = 3 states to calculate both Eo and G from the observed values of hv2 and hvs. This calculation yields G = 1.86 eV and Eo = 7.23 eV for RbCl : RbI. From the observed binding energy, the ratio m*/@ can be calculated. This ratio is found to be O-137. If we take E to be the optical dielectric constant of RbCl, or 2.19, we are led to a value of m* = 0.66 electron mass units for the effective mass of an electron in RbCl. Using this dielectric constant, the radii of the electron orbits for the n = 2 and n = 3 states are found to be 7.05 A and 15.9 A respectively. The corresponding frequencies of the electronic motion are w = 1.41 x 1015 rad./sec and 6.36 x 1014 rad./sec, respectively. These values are consistent with the use of the optical dielectric constant in the calculations. A similar analysis of the data for KC1 : KI is not too meaningful since the n = 3 state is poorly resolved at 80°K in this system. An attempt was made to observe similar structure in the alloy KF : KI, however no meaningful results were
TRAPPED
EXCITON
-
STATES
I
I
KCI:KI
(I%)
I.5 -
IN
THE
ALKALI
’ 7.69aV ’
HALIDES
945
I
80°K
: j I.0 1
:
/J 750
‘J-
6.65 eV
OL 6-O
I 6.5
ev
7.18 ev
I 7.0 PHOTON
I 7.5 ENERGY
I 80
I 85
IN aV
FIG. 2. The absorption spectrum at 80’K of a film of KC1 containing approximately 1 mol. y! of KI.
obtained, perhaps because of the large size of the I- ion relative to r. CONCLXJSLONS The above results indicate the presence of effective mass states associated with substitutional I- ions in RbCl and KCI. This interpretation of the absorption spectra is analogous to a similar treatment of rare gas alloys.(s) The remarkable similarity between the electronic structure of the solid rare gases and the alkali halides is emphasized by these results. The work of FISCHER and HILSCH(~) on Wannier exciton states in the alkali iodides is substantiated by the present experiments on alkali halide alloys, since they show that effective mass states are not as unique a phenomenon in the alkali halides as previously supposed.
It is known that the pure KI and RbI luminescence at low temperature when exposed to ultraviolet light absorbed in the fundamental band region of the crystals.(7ls) FABLER,@) and MURRAY and KELLER(~@ have shown that this luminescence is due to the recombination of an electron with a self-trapped hole, or Vk-center. The luminescence of the system KC1 : KI has been studied by MAHR.@~) Two emission bands appear when light is absorbed in any of the iodide impurity bands. We suggest that the luminescent center in this case is a halide molecule ion composed of an iodide ion and an adjacent chloride ion. Experiments with polarized light similar to those used to study the intrinsic luminescence of the alkali iodides could be used to determine the validity of this suggestion.
946
G. BALDINI
and
REFERENCES 1. For a review of the Frenkel and Wannier exciton models and their application to various solids see: KNOX R., Theory of Excitons, Supplement 5 of Solid St. Phys., Academic Press, New York and London (1963). 2. MOTT N. F. and GURNEY R. W., Electronic Processes in Ionic Crystals, second edition, pp. 95-100. Oxford University Press, Oxford (1948). 3. FISCHER F. and HILXH R., Nachr. Akad. Wiss. Giittingen, II: Math-Physik IQ. No. 8, 241 (1959).
K.
TEEGARDEN 4. HOPFIELDJ. S. and WORLOCK J. M., Phys. Reu. 137,
Al455 (1965). 5. BALDINI G., Phys. Rew. 128,1562 (1962).
6. BALDINI G., Phys. Rev. 137, A508 (1965). 7. TEEGARDEN K., Phys. Rev. 105,1222 (1957).
8. TEEGARDEN K. J. and WEEKSR., J. Phys. Chem. Solids 10, 211 (1959). 9. KABLER M. N., Phys. Rev. 136, Al296 (1964). 10. MURRAY R. B. and KELLER F. J., Phys. Rev. 137, A942 (1965). 11. MAHR H., Phys. Reo. 130, 2257 (1963) ; Phys. Rev. 132, 1880 (1963).