EXCESS ELECTRON COLOR CENTERS IN THE ALKALI HALIDES

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Submitted on 1 Jan 1967

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EXCESS ELECTRON COLOR CENTERS IN THE

ALKALI HALIDES

W. Compton

To cite this version:

JOURNAL DE PHYSIQUE Colloque C 4, supplkment au no 8-9, Tome 28, Aofit-Septembre 1967, page C 4-10

EXCESS ELECTRON COLOR CENTERS IN THE ALKALI HALIDES

(*)

by W. D. COMPTON

Coordinated Science Laboratory University of Illinois, Urbana, Illinois

Abstract. - The F center is the prototype of the excess electron color centers. Although many of the properties of this center are well understood, some interesting questions still remain concerning the nature of its relaxed excited state. The influence of uniaxial stress upon the lumi- nescences has yielded new evidence for the diffuse nature of this state. A contrast will be made of the influence of uniaxial stress upon the absorption and the luminescence.

The association of F centers forms higher order complex centers. Studies of the polarization of the optical absorption and the luminescence bands, the stress induced splittings of the zero phonon lines, the magneto-optic effect associated with absorption, and the electron spin resonance have been particularly valuable in establishing the symmetry and microscopic configuration of a number of these centers. A brief review will be given of the properties of the neutral complex, the singly ionized complex, and the complex centers that have trapped an extra electron. Some recent results will be presented of the excitation spectra of the luminescence of a number of theabsorption bands associated with the M center and of the magneto-optic effect of the R center.

R6sum6. - Le centre F est le prototype des centres a exces d'electron. Bien que beaucoup des propriktbs de ce centre soient bien comprises, quelques questions intbessantes restent poskes au sujet de l'ttat excite relax&. L'influence de contraintes uniaxiales sur la luminescence a apporte de nouvelles evidences sur la nature diffuse de cet etat. I1 est utile de comparer l'influence de contraintes uniaxiales sur l'absorption et sur la luminescence.

L'association de centres Fforme des centres plus complexes. Les etudes de la polarisation optique et de la luminescence, le dedoublement des raies a zero phonon sous l'influence des contraintes uniaxiales, l'effet magneto-optique associe a l'absorption et la resonance paramagnetique Blectro- nique ont permis d'etablir la symetrie et la configuration microscopique de beaucoup de ces centres complexes. Une breve revue des proprietes des centres neutres est donnee ainsi que celles des etats une fois ionises et celles des centres complexes qui ont pikg6 un Uectron supplkmentaire. Quelques resultats recents seront prCsentCs concernant le spectre d'excitation de la luminescence de nombre de bandes d'absorption associCes au centre M, ainsi que l'effet magnkto-optique du centre R.

The F center is the prototype of the excess electron color centers. Although many of the properties of this center are well understood, some interesting questions still remain concerning the nature of its related excited state. The influence of uniaxial stress upon the lumi- nescence has yielded new evidence for the diffuse nature of this state. A contrast will be made of the influence of uniaxial stress upon the absorption and the luminescence.

The association of F centers forms higher order complex centers. Studies of the polarization of the optical absorption and the luminescence bands, the stress induced splittings of the zero phonon lines, the magneto-optic effect associated with absorption, and the electron spin resonance have been particularly valuable in establishing the symmetry and micros-

(*) A portion of this work was supported by a grant from the

National Science Foundation.

copic configuration of a number of these centers. A brief review will be given of the properties of the neutral complex, the singly ionized complex, and the complex centers that have trapped an extra electron. Some recent results will be presented of the excitation spectra of the luminescence of a number of the absorp- tion bands associated with the M center and of the magneto-optic effet of the R center.

The F Center.- The excess electron color centers in the alkali halides constitue a family of defects that have received a substantial amount of attention [l]. Starting with the simplest of these centers, the Fcenter, and progressing to larger and larger complexes contai- ning two, three, four and perhaps more, one moves from the M to the R and perhaps to the N centers. In nearly all cases, the understanding of the properties of the higher complex centers has been determined by the detailed understanding of the F center itself.

EXCESS ELECTRON COLOR CENT 'ERS IN THE ALKALIHALIDES C 4 - 11

Since the model of the F center is so simple, it has been

traditional to describe the system by a single dimension configuration coordinate model, such as that shown in figure 1. Here is represented the total energy of the system for the ground state and the excited state of the system with optical absorption represented by the arrow A-B and emission represented by the arrow C-D. According to the Franck-Condon principle, these arrows are drawn vertically to indicate that the transition takes place in a time short compared to any lattice motion. The minimum of the ground state A is displaced from the corresponding minimum in the excited state C , since the electronic configuration of the system in the ground and excited states is different. The Stokes shift is substantial in these centers with the luminescence occurring at approximately one-half of the photon energy of the absorption. The different couplings of the electronic system to the lattice in the two states result in the change of curvature of the total energy curves with configuration coordinate.

l I I

X A XC XI Conf ~ g u r a t ion coordinate

FIG. l. - Configuration coordinate diagram for a well- localized defect center. Absorption is indicated by A + B and emission by C + D .

Although this simple picture is able to explain many of the characteristics of the optical properties of the

r

center, it is clearly a gross over-simplification of the actual circumstances. For example, there must be more than a single configuration coordinate which is impor- tant in determining the total energy of the center. Second, this model ignores completely the dynamic nature of the lattice surrounding the defect. Third, since the luminescence process is described as the inverse of the absorption process, this model fails to explain the long lifetime of the excited state for radia- tive recombination [2].

Since the half-width of the absorption and lumines- cence bands at low temperatures is determined, in large part, by the interaction of the center with the lattice phonons, it seemed appropriate to look in more detail at the nature of this interaction. In particular, a great deal has been learned about the details of this interac- tion by noting the changes that occur in the shape and position of the absorption and luminescence bands in the presence of externally applied uniaxial stresses. We will briefly review the influences that uniaxial stresses have upon the absorption band and then turn to a discussion of the influence of this perturbation upon the luminescence.

In considering the effects of an externally applied stress or the effects due to the dynamic motion of the ions surrounding the F center, it is convenient to consi- der the symmetry of the lattice surrounding the defect. As viewed from the center of the vacancy, the lattice has cubic symmetry. The normal modes of the lattice may be classified by their symmetry by specifying the irreducible representation of the octahedral group for which they form a basis function. Henry, Schnatterly and Slichter [3] have demonstrated, in first order, that the ground state of the F center is not perturbed by lattice distortions and that the only normal coordinates which perturb the excited state are those of Tl, T,, or T, symmetry. The electronic ground state of the center is

rl

symmetry with the excited state being of

r,

symmetry. The group representation, the basis func- tion for that group, and the nature of the displacements of the ions in the first shell surrounding the defect are shown in figure 2. The question now is, how can the

Group Basis Type of First Shell

Representation Function Distortion I o n D~splacements

l-l x 2 + y 2 + ~ 2 Breathing

+

6

( x 2 - y 2 ) Tetragonal

7F

Trigonal

X.

Trigonol

7%-

FIG. 2. -Notation for the normal modes that transform according to the irreducible representations P I , r 3 and Ts of

C 4 - 12 W. D. COMPTON coupling to one of these particular modes of lattice

vibrations be measured ?

The application of a hydrostatic pressure induces lattice distortion having T 1 symmetry and, therefore, a

measurement of the change in the first moment of the absorption band of the F center can be used to mea- sure this coupling. Henry, Schnatterly and Slichter [3] have shown that application of uniaxial stresses in the

<

100

>

and

<

110

>

directions can be used to mea- sure the coupling to lattice modes of

r3

and T5 sym- metry. The measurement consists of observing the difference in the first moment of the absorption band for light polarized paralled to and perpendicular to as stress applied along the

<

100

>

or

<

110 >

lattice directions. The first moment change arising from a S 100

>

stress measures the coupling to the

r,

mode, whereas the change in the first moment arising from stress in the

<

110

>

direction measures the

r,

mode.

Jacobs [4], Gebhardt and Maier, [5] and Schnatterly

[6] have made measurements of the influence of

externally applied stresses upon the F centers in a variety of alkali halide crystals. Figure 4 is an example of the type of data that Schnatterly [7] obtained for changes in the P center absorption in RbCl with a

<

100

>

stress. Af is defined as the difference in the shape function of the absorption band for light polari- zed parallel and perpendicular to the stress direction and is essentially proportional to the difference in the absorption coefficient for these two polarizations. The magnitude of the maximum in the value of Af was proportional to the magnitude of the applied stress. The changes in the first moment, in terms of the energy change per unit strain, can be expressed accor- ding to the following three equations

where P is the hydrostatic pressure that is applied,

<

AE,,

> -

< AE,

>

is the difference in the first moment change as measured with light polarized pa- rallel and perpendicular to the stress, F[,oo, and are the magnitude of the applied stresses, and Cij s are the elastic stiffness constants.

The results given in table 1 have been determined by Schnatterly [6]. It is to be noted that the energy

shift per unit strain induced by the

r,

and

r,

symme- try distortions is somewhat smaller than that induced by a

r,

symmetry distortion.

TABLE 1

Values of B,, B,, and B,, obtained using eq. 1 to 3. Measured at 80 OK. Taken from Schnatterly [6]

Sample

The broadening of the F-absorption band results from the dynamic distortions of the lattice by phonons having the same symmetry as those which can be induced by external means. Henry, Schnatterly, and Slichter [3] have shown that, to first order, changes in the third moment of the absorption band with exter- nally applied stresses can be used to determine the contribution of each of the three symmetry modes to the total broadening of the band. Figure 3 indicates how this is possible. On the left are indicated the unperturbed excited states of the F center having three-fold degeneracy. In the center, the excited states are indicated as being split by lattice distortions of

KC1 KBr K1 NaCl RbCl

Unperturbed Splitting of Effect of on Excited State Excited State Additional Small

by Tl

,r3

and Distortion of

r5

Symmetry

r3

Symmetry Lotiice Distortion

r Z

B, (eV)

-X,Y,Z ---@-Y Y Mixing

8.0 f 0.2 7.2 f 0.2 6.9

+

0.2 12.1

+

0.2 6.9

+

0.2

FIG. 3. - Schematic illustration of the effect of perturba- tions of lattice vibrational modes of various symmetries upon the F center excited state and the effect of adding an additional external stress of r3symmetry to the lattice modes.

EXCESS ELECTRON COLOR CENTERS IN THE ALKALIHALIDES C 4 - 1 3

symmetry T , , r 3 , and

r,,

respectively. On the right hand side is indicated what the effect is of an additional externally applied uniaxial stress of T 3 symmetry. If the center has been perturbed by a T 1 or T 3 lattice phonon, then the additional pertubation by a T 3 dis- tortion from an applied stress simply contributes to a further splitting of the energy levels in the same amount as if the lattice phonons were not present. If, however, a T , lattice phonon has removed the degeneracy of the excited state, then the application of a distortion with

r3

symmetry will result in a mixing of the wave func- tions between the upper and lower split-off states. The net result of these considerations is that there will be an energy shift in the absorption band if the externally applied T 3 symmetry stress is added to a splittingdue to phonons of

r,

and I', type distortion. If the externally applied

r,

type distortion is added to a

I',

lattice phonon distortion, then a change in the shape of the absorption band will also occur. It is the change in the shape of the absorption band that allows one to deter- mine the contribution of the T 3 and

r,

type phonons to the breadth of the absorption band. Schnatterly [6] has found the results given in table 2 for the contribu- tions to the second moment of the P band due to the lattice distortions of

r,, r3

and

r,

symmetries and due to the spin-orbit interactions. These data indicate that the breathing mode is typically responsible for about seventy percent of the second moment of the F center absorption band for measurements at 80 OK. Tetragonal interactions and trigonal interactions each contribute about fifteen percent to the second moment in a typical case. It should be particularly noted that B,, and B,, have the same sign, contrary to the predictions of the point ion lattice model. This suggests that the interaction is dominated by repulsion with the closed ion shells of the first and second shells rather than by the Coulomb interaction with the nearest

neighbors. It is quite clear, therefore, that the simple configuration coordinant curve indicating a single coor- dinate is at best an average over these three modes with a weighting which must be considered roughly proportional to these interaction intensities.

Let us now turn to an examination of the effects of externally applied uniaxial stress upon the lumines- cence of the F center. It is important to first recall that there is no polarization in the luminescence of the F center when it is excited with polarized light even

I I I I I I \dl i i

I

FIG. 4. - Change in the absorption shape function f where

Af = Afil(E)

-

Afi(E) for RbCl using a ( 100 ) applied stress. The dashed line indicates the extrapolated K-band dichroism.

Contribution to the second moment of the P band due to dynamic lattice distortions of Tl, T2, T5 symmetries and the spin-orbit interaction. Measured at 80 OK. Taken from Schnatterly [6].

C 4 - 14 W. D. COMPTON

FIG. 5. - Percentage induced polarization of F center lumi- nescence vs applied stress along the [001] direction in kg/mm2 for NaCl, KCl, RbCl and NaF. Samples were held at 80 OK and measurenlents were taken at a wavelength near the peak of the luminescence bands.

down to temperatures near 2.5 OK. It is only upon induces a change in the intensity of the light being application of an external stress that a polarization is emitted with polarization parallel compared to that observed. Application of a uniaxial stress along the with polarization perpendicular to the applied stress. It

<

100

>

crystallographic directionleads to aninduced does not represent a splitting of the excited state as polarization in the luminescence that is proportional to occurs in the absorption. The temperature dependence the applied stress. This is indicated in figure 5 for a of the induced polarization for KC1 is indicated in figure 6 for temperatures between 20 OK and 140 OK.

number of alkali halides. The measurement was made in such a way that only the difference in the lumines- cence intensity for light polarized parallel and perpen- dicular to the applied stress was detected. This was normalized to the total intensity of the luminescence, thereby giving a percentage-induced polarization. In contrast to the results shown in figure 4 for the absorp- tion band, the percentage-induced polarization was found to be independent of wavelength of the lumines- cence for all of the alkali halide crystals studied. That is, the polarization signal was always proportional to the height of the luminescent band. Thus, the stress

1.1 .9 z '2' a a .7 -I

X

a .6 W 0 3 a 3 .5 W

2

"

.4 0 a

g

-3 .2 .I O .2 4 .6 .E 1.0 1.2 1.4

FIG. 6.

-

Percentage induced polarization of KC1 F center luminescence vs temperature for a [001] stress of 0.40 kg/mrnZ.

l r l l l l l l l l l l l l '

-

Material: KC1

-

I. -3

Concentration: 2 X 10 cm

Wavelength of the Luminescencrc R . 9 8 ~

-

-

-

-

-

-

-

-

-

-

-

3

!

*

1

1

i f

i i

[ l

f

-

-

Applied Stress: 0 . 4 0 Kg/mm2

-

-

-

-

0 - l l l l l l l l l l l l l l l 2 0 4 0 60 80 KX) 120 140 160

The absence of a temperature dependence or wave- length variation of the induced polarization allows one to put an upper limit on the splitting of the relaxed- excited state for a given stress. In KCl, for instance, at a stress of 0.40 kg/mm2 along the c 001

>

direction, the splitting of the excited state must be less than 1.3 X 1 0 - ~ eV. Similar values are also found for F centers in the other alkali halides that have been mea- sured. This splitting is about two orders of magnitude smaller than is found in the unrelaxed-excited state of the F center from the measurements on the absorption band. It is also of interest to note that the application of a stress along the

<

100 > direction results in the luminescence having a maximum intensity at right angles to the stress with a lower intensity parallel t o

TEMPERATURE IN K'

EXCESS ELECTRON COLOR CENTERS IN THE ALKALIHALIDES C 4 - 15 the:applied stress. Application ofa stress along < 110

>

1.0

direction induced no detectable polarization into the

luminescence signal.

=-.

0

S Since there appears to be no splitting of the relaxed- _.- a,

g

0.5 excited state of the F center with an applied external

-

a,

stress, one has to look elsewhere for an explanation of

the induced polarization. Fowler [8] has suggested

.--

_C

_g

that the relaxed-excited state of the F center is quite o S

0-

diffuse as compared to the tightly-bound ground Q)

state or the unrelaxed-excited state. If this is the case .- + > 0.2 0

then it is not surprising that the wave function in the _$ relaxed-excited state will be insensitive to the lattice

motion in the immediate neighborhood of the vacancy. _0.1

Thus, the application of external stresses will not split o 20 40 60 80 100 X 1016

Concentration of F-centers (cm-3)

the excited state and, therefore, will not materially

affect the transition energy. The changes in the transi- FIG. 7.

-

Relative quantum efficiency of F center iumines- tion probability for directions parallel and perpendi- cence vs concentration of F centers in KC1 at 77 OK. Samples cular to the applied stress are believed to result then X-irradiated at 77 O K .

from a mixing of higher states of T , type symmetry

into the ground state. The amount of mixing necessary to account for the amount of polarization is only a few tenths of a percent for a stress of 0.50 kg/mm2 along the

<

001

>

direction. The absence of an induced polarization with application of a stress along

<

110

>

indicates that there is no mixing of a T , type state into

the ground state by this symmetry stress, again because the interaction is apparently determined by repulsive forces rather than by a Coulomb interaction.

The above discussion of the influence of stress upon the absorption and luminescence bands of the F center indicates clearly that this is an important tool for the study of electron lattice interactions of centers with degenerate excited states. This is a technique that can likely be applied to a number of centers in other materials. As an example, Gebhardt has recently discussed the application of these techniques to a study of the spectra of transition metal ion centers [9]. Before turning away from the Fcenters to the higher complex centers, it seems appropriate to briefly discuss the results of an experiment that is largely unexplai- ned at this time. Miehlich [l01 and Compton and Kabler [l l ] have studied the concentration quenching of the luminescence of the F center in potassium chlo- ride. Miehlich's work was carried out on additively colored crystals while that of Compton and Kabler was done on material X-irratiated at low temperatures. The results of the latter workers are shown in figure 7. The relative quantum efficiency normalized to unity at low concentrations is plotted on a semi-logrithmic scale as a function of F- center concentration and satisfies quite accurately the equation given on the figure. The parameter R, found from the slope of this

line is 77

A.

Miehlich found a value of 82.3 f 4.5

A

for this parameter. This simple expression can be interpreted to mean that two F centers that are separa- ted by a distance greater than 77

a

will luminesce with an efficiency of unity, whereas two P centers closer than 77

A

will be quenched and will relax without emission of a photon. Measurements by Swank and Brown [2] of the radiative lifetime of the excited F centers indicated that there was no dependence of this lifetime upon the F center concentration. It seems, therefore, that an interaction between F centers exists over a distance of the order of 77 and that the quenching mechanism does not provide an alternative mode of decay for the centers that luminesce. A pro- per explanation of the interaction mechanism that gives rise to this quenching is still not known.

The M Center.

-

The model of the M center as two F centers located on nearest neighbor sites in a

C 4 - 1 6 W, D. COMPTON Thus, both the ground and the first excited states are

non-degenerate in the case of the M center.

Studies using polarized light have indicated that there are a number of transitions that can be associated with the M center with several of these absorptions corresponding approximately to that of the F band. In KBr, Susman has shown that there are six transitions having symmetry < 110

>

and five having symmetry

< 100

>.

The origin of some of these is unknown in terms of the detailed configuration of the excited states to which the transition is made.

Luminescence characteristic of the M absorption band can be excited by optical excitation into the principal M absorption band or by excitation into any of a variety of the absorptions at higher energy that are associated with the M center. There has been some speculation in the past that energy transfer processes are important in the generation of luminescence charac- teristic of the M center following absorption by pho- tons of energies corresponding to that of the absorp- tions in the F band region [14]. That is, a photon is absorbed by an

F

center with the energy being sub- sequently transferred to an M center which then luminesces. Recent results by Boettler [l81 indicate that this is indeed not the case and that the lumines- cence results from the direct absorption of light in the absorption bands which overlap the F absorption band [19]. These results were obtained by a careful comparison of the excitation spectrum for the lumi- nescence with the absorption spec trum. Figure 8 illustrates a general comparison between the absor-

WAVELENGTH IN M +

FIG. 8. -Absorption and corrected excitation spectra at

77 OK for a KC1 crystal with F, M, R and N centers present.

o

. . .

corrected excitation spectrum

A

.

.

.

absorption spectrum.

ption and excitation spectra for a KC1 crystal containing F, M, R and N centers. It should be noted that the excitation is a more sensitive technique in some cases than is the absorption in determi- ning the presence of small concentrations of these higher complex centers.

A detailed comparison of the absorption and exci- tation spectra of M centers is given in figure 9. The agreement between the halfwidth and peak positions of the Gaussian plots of the absorption and excitation

WAVELENGTH IN MP

ENERGY I N cV

FIG. 9.

-

Gaussian plots of the absorption and corrected excitation spectra of M centers in KC1 at 77 OK (Sample 79 D). The ordinate variable, A, i n this figure and in subsequent figures

is the ratio of the height of the spectrum at any energy E divided

by the peak height of the spectrum. o .

. .

absorption spectrum.

A .

. .

corrected excitation spectrum,

spectra indicates that the quantum efficiency for luminescence of the M center with direct excitation into the M-absorption band is constant across the absorption band. The quantum efficiency for lumin- escence of the M center with excitation directly into the M band was determined by comparison with the efficiency of luminescence of F centers in a crystal in which there were no other centers present. This comparative measurement indicates that the quantum efficiency for luminescence of the M center is 1.0

+

0.15.

EXCESS ELECTRON COLOR CENTERS IN THE ALKALIHALIDES

WAVELENGTH IN MP

FIG. 10. - Gaussian plots of the absorption and corrected excitation spectra of F centers at low concentrations in KC1 at 77 OK (Sample 78 D).

o. .

.

absorption spectrum, A

.

.

.

corrected excitation spectrum.

between the absorption and excitation spectra for excitation in the F-band region. Figure 11 indicates this discrepancy. Careful measurements with crystals in which the M centers have been aligned such that their optic axes are all parallel to a single direction and with a measuring technique that eliminates any unpo- larized component of the luminescence, indicate that the excitation spectra agree quite well with the absorp- tion from the ground Z state to one the higher IT-like

excited states. This is the so-called M , transition. This

transition underlies the F band but is not coincident with it in either peak position or in half-width. It is possible to conclude from this measurement that the excitation to this higher excited state is a result of direct absorption by the center and that the relaxation process from that IT-like state to the first excited C- like state occurs in such a way that the quantum efici- ency for luminescence with excitation into this absorp-

WAVELENGTH IN M p

FIG. 11.

-

Absorption and corrected excitation spectra of the F-band region for Sample 79 D, with M centers present. Measured at 77 OK.

C 4 - 1 8 W. D. COMFTON tion band is near unity. A similar result has been found

by Podini [20] for NaF crystals.

Seidel [l71 has measured the electron spin resonance of the excited triplet state of the M center. This state has a long halflife of about 50 S in KC1 and is optically

generated by excitation with light in a variety of spectral regions between 580 mp and 365 mp. Although some of the absorption bands that have been observed in the case of the M centers may arise from direct absorption between the singlet ground state and this triplet excited state, there seems to be no clear indica- tion that there are absorptions associated with each of the regions in which one sees strong photogeneration of the triplet state. Schneider [21] has recently suggested that the photo-excitation of the triplet M center results from the absorption of photons by F centers with the

transfer of energy from the F centers to M centers, leaving the M center in the triplet state. This result is quite interesting in that it suggests again the possibility of energy transfer between an excited F center and another defect in its neighborhood. Further studies in this direction would certainly be of interest.

Some recent theoretical calculations of the energy levels of the M center have led S. F. Wang [22] and

R. Knox [23] to suggest that one of the small absorp- tion bands seen by Okamoto and Susman [l91 in the absorption of the M center is probably not associated

with the transition from the singlet ground state to the singlet excited state. Instead, they suggest that the transition may be between the singlet ground state and a triplet excited state and that the small absorption is a result of the forbiddenness of this transition. Wood and Meyer [24] have recently calculated the electronic structure of the triplet states of the M center in LiF

and LiC1. They find that the energy levels of the triplet and singlet ground states lie quite close together. This leads them to suggest that the triplet ground state of the M center may decay by temporary dissociation

into two F centers or that the mode of decay may involve a thermally excited transition between the triplet ground state and a nearly degenerate singlet ground state. Although the latter transition would be highly forbidden, it is suggested that lattice vibrations greatly reduce this restriction in the crystal.

Kabler et al. 1251 report that a preliminary search did not reveal any luminescence that could be uni- quely associated with the triplet ground state. The mechanism of generation of the M center in its triplet ground state does not appear to involve radiative transition from a higher state.

Extensive studies have been underway for a number of years on the properties of an Fcenter perturbed by a

nearest neighbor alkali ion that is an impurity in the host lattice. These are the so-called FA centers. In

analogy with the situation for F centers, Schneider [26]

has examined the properties of the so-called M A

centers in KCI. Crystals of KC1 containing various concentrations of NaCl and LiCl were additively colored in potassium vapor and M centers were intro- duced at room temperature by optical irradiation into the F band. An absorption band on the long wave-

length side of the M band was found in both cases with the intensity of this band varying in proportion to the amount of the cation impurity in the material. In the case of the lithium-doped material, the MA band

was well separated from the M band, the two bands

being located, respectively, at about 870 and 800 mp at low temperatures. Similarly, the peak of the lurnin- escence band for these centers was shifted to longer wavelengths, with the peak appearing at about 1.22 p and 1.08 ,U for the M A and M centers, respectively. From measurements of the symmetry properties of this center using polarized light, Schneider suggests that the alkali impurity ion lies in the (100) plane containing the M center and that the substitutional site

along the

<

110

>

direction that bisects the center gives a configuration that is most reasonable. There is also evidence that the higher energy absorption bands associated with the M center, i. e., in the vicinity of the F band, are likewise affected by the presence of the

alkali ion impurity. S. F. Wang [27] has calculated the transition energies associated with absorptions of the perturbed M center. He finds reasonable agreement

with the absorption bands reported by Schneider. The primary effect of the impurity is to shift the ground state down in energy by about 0.13 eV, with very little effect being introduced into the higher energy states. The R Center.

-

A large number of experiments have now led to the acceptance of the model of the R center as being due to three nearest neighbor F centers located on the corners of an equilateral triangle lying in the (111) plane. This model assignment has been made as a result of measurements on the polarization of the luminescence bands [13, 141, the equilibrium between F, M and R centers in crystals irradiated at

room temperature [28], the results of the optical studies of the zero phonon line associated with the R, band with applied uniaxial stress [29], and particularly the electron spin resonance measurements on the R center [30, 311. Thelatter two experiments have been particu- larly useful in elucidating the electronic configurations of the ground and excited states of this defect.

EXCESS ELECTRON COLOR CENTERS I N THE ALKALIHALIDES C 4 - 1 9 accompany the absorption. In principle, a photon can

be absorbed with no transfer of energy to the lattice, thereby giving an absorption line whose breadth is determined only by the lifetime of the excited electronic state at absolute zero. Fitchen, et a1 [29] were the first to offer a systematic explanation of the sharp line structure that is associated with the broad band absorption in several of the absorption bands of the complex color centers. The integrated absorption under the sharp line associated with a given broad absorption band depends upon the most probable number S of phonons that are involved in the transition. This can be estimated either from the zero-point width of the broad absorption band, H, or from the Stokes shift, A, bet- ween the absorption and the luminescence. If o, is the frequency of the dominant lattice modes that produce the broadening of the transition, the inte- grated absorption of the sharp line relative to the broad band at absolute zero is given by eqn. 4.

Since the zero phonon line is quite sharp, it is easy to detect a small displacement in energy resulting from an externally applied stress. This provides a technique for directly determining the symmetry of the defect that is responsible for the absorption. Application of stresses in a variety of crystallographic directions will result in a splitting into a number of components with the relative intensities of each of the components depending upon the non-equivalent orientations relative to the axis of the stress [32, 331. Attempts have also been made to use the separation between the zero and higher num- ber phonon absorptions, associated with the broad band, to determine the particular lattice phonon that is active in the broadening of the broad adsorption line [34].

The careful study of the effects of stress on the optical absorption, both the sharp line and the broad band, for the

R

center in KC1 has been reported by Silsbee [35].

These results, together with the theoretical analysis that was made of them, has established a number of important properties concerning the R center. The stress splitting of the zero phonon line implies that this absorption results from a transition from a doubly degenerate ground state to a singlet excited state. This sharp line is associated with the R, broad band. The symmetry of the various states are as follows : the ground state is of E symmetry ; the excited state, to which the

R,

transition is made, has A, symmetry ; and the transition that gives the

R,

absorption band is made

to a state of E symmetry. This model predicts and there have been found transitions lying in the region of the M band and the N band which also arise from the

R

center.

The ground state of the R center is a quartet of states of ' E symmetry, having a two-fold orbital or vibronic degeneracy and a two-fold spin degeneracy. Krupka and Silsbee [36] have made a careful study of the electron spin resonance of this center. The effective Hamiltonian that describes this system in the presence of magnetic and strain fields contains terms in the electronic interaction with the strain field, the orbital Zeeman interaction, the spin-Zeeman inter- action, and the spin-orbit interaction. Silsbee [35] determined the contribution of the electronic inter- action with the strain field, whereas the contributions of the three magnetic interaction terms in the effective Hamiltonian were determined by Krupka and Silsbee [36]. In calculating these contributions, it was assumed that both the operators and the electronic states are independent of the vibrational coordinants of the center. Thus, the elements of the effective Hamiltonian among the vibronic states occur as products of the pure electronic matrix element and a vibrational overlap integral. The magnitude of the vibrational overlap depends quite sensitively upon the vibrational coupling. A moderate to strong Jahn-Teller effect results in a reduction in the orbital moment and the spin-orbit energy. The observed spin-orbit parameter, go,, and the spin-orbit energy, A,, are related to the orbital g-value and the spin-orbit parameter by a factor that is approximately e-k2, where k is propor- tional to the ratio of the Jahn-Teller energy to the characteristic vibronic energy [37].

Krupka and Silsbee determine the following values for the constants.

From these values and the calculation of the relative sizes of g,, and A,, they were able to determine that

g o , = l . l and A E = - - 4 . 8 c m - ' . The reduced values were

C 4 - 2 0 W. D. COMPTON dichroism technique in which the change in the

transmission of the sample was determined for right and left circularly polarized light travelling parallel to the magnetic field. It is possible under the proper assumptions to determine from the data on the circular dichroism the same parameters that have been deter- mined above for the ground state system by the electron spin resonance. Duval, et a1 report that for a magnetic field between 1 000 and 9 350 oersteds and for temper- atures between 3.4 and 8 OK the change in the area of zero phonon line for right and left circular polarized light is proportional to HIT2. Fr~mthesemeasurements, they are able to determine the reduced spin-orbit interaction factor to be 2, =

-

1.3 cm-' f 0.3. The dynamic Jahn-Teller reduction factor, k2, was found to be approximately equal to 3. Thus, the unreduced spin-orbit interaction constant determined by Duval, et a1 would be about

-

26 cm-', a factor of 5 larger than that deduced by Krupka and Silsbee.

Similar measurements have been carried out by Burke and analyzed using the method of moments as developed by Henry, et a1 [3]. This analysis for the zero phonon line of the R, band yields the following

where g,, and

A,

are the reduced orbital g-factor and the spin-orbit factor as defined above and where g, is the magnetic spin g-factor as determined by Krupka and Silsbee to be 2.03. Figure 12 gives a plot of the

FIG. 12. -Difference in the first moment of the R2 zero phonon line as measured with right and left circular polarized light as a function of temperature. H = 46.6 X 103 gauss.

W - 2 5 -

4

X 2 0 -

signal observed in the circular dichroism experiment by Burke plotted as a function of 1/T for the R, zero

I I I I -

*,i4-

$--+-y

-_

phonon line in KC1. Except for the highest temperature point at 20 OK, the data fit well the expression in eqn 5. From these data, the values for the reduced factors can be determined and are found to be

2

p-$-

15 - -

A

I KC1 R2 zero phonon line

?j 10- First moment change -

v Hool = 46.6 kg

I

and g,, = 5.5 f 1.5 X 10-', where a small correc- tion of about 15

%

has been made to account for the ellipticity of polarization of the light in the (111) plane of the centers. These results are in excellent agreement with those published by Krupka and Silsbee and, therefore, give strong independent support for the analysis and description of the center that has been proposed by these workers. A plot of similar data is given in figure 13 for the R, broad band in KCl.

KC1 RI bond

.

First moment chanae

Fro. 13. -Difference in the first moment of the R1 broad band as measured with right and left circular polarized light as a function of temperature. H = 46.6 X 103 gauss.

Combining these measurements on the R, band with those for the zero phonon line, the latter being a measure of the magnetic effects in the ground state only, it is possible to determine some properties about the excited E symmetry state to which the R, band transition corresponds. Again it is noticed that the circular dichroism signal is proportional to 1/T. From these data, one finds that the spin-prbit interaction and the orbital g-value for the excited state of the R, band can be expressed as follows.

EXCESS ELECTRON COLOR CENTERS IN THE ALKALIHALIDES C 4 - 2 1 and significant properties of this center are now well

established.

The N Center.

-

The situation with regard to the N centers is very complicated and uncertain at this point. Pick [40] suggested that the absorption bands labelled N I and N2 resulted from transitions in two distinct centers arising from two distinct configurations of four P centers. Schnatterly and Compton [28] presented evidence from the equilibrium concentration between the complex centers during x-ray irradiation that suggested that the N2 band could be associated with a defect involving four F centers, but that the NI band was more simply related to the concentration of M centers than with a higher order complex. Subsequent studies by Schneider [41] indicate that two distinct centers contribute to the absorption band in the spectral region that has been assigned to the N I centers. Further evidence for the complicated nature of the absorption in this region of the spectrum is given by Schneider and Kabler 1421. The studies of their lumi- nescence spectra suggest that a considerable portion of the absorption in the N , band region may, in fact, result from transitions that are associated with the R center. A number of observations of the symmetry of the defects giving rise to absorptions in this spectral region have been made from the stress splitting of zero phonon lines associated with these absorptions. The defects giving rise to these absorptions have not been well established [33, 34, 35, 431. It seems impossible at this point to be certain whether the models for the N

centers have, in fact, been verified or whether the absorption in this spectral region is due to a variety of other centers. It is also possible that the concentra- tion of the various centers that contribute to absorption in this wavelength region depends strongly upon the technique of generating the centers.

The Ionized Aggregate Centers. - In analogy to the F center, which can trap a second electron to become the so-called P' center, so also absorption bands have been observed that are associated with the M and R centers that have trapped an extra electron to form, respectively, the M' and R' centers. The broad band absorption associated with these centers was reported some years ago by Hirai, et al. [44]. Recently, zero phonon lines associated with these broad bands have been observed and identified with the M' and R' centers [45]. The identification of these lines as belonging to transitions in the M' and R' centers depends on thefollowing :

2. The symmetries of the centers, as determined from measurements with uniaxial stress, are consis- tent ;

3. The photochemistry required to generate these centers is consistent with these models, and

4. The peak of these zero phonon lines fits a Mollwo- Ivey plot.

Of particular importance is the observation that the emission spectrum for the M' center exhibits a resonance line and mirror emission band, as is predicted by the model for a center in which the emission occurs between the same pair of states as the absorption.

A number of studies have been reported of the zero phonon line and broad band absorptions associated with the ionized aggregate centers, specifically the ionized M and R centers. These are often referred to as the F: and F$ centers, respectively [46]. These studies

have again given evidence of the nature of the elec- tronic states involved and of the coupling of these states to the lattice. Again, the stress dependence of the zero phonon line and the existence of mirror absorp- tion and luminescence is an extremely important tool in understanding the nature of these centers.

C 4 - 22 W. D. COMPTON

Rkfkrences

[l] See for example, books by MOTT (N. F.) and GURNEY (R. W.), Electronic Processes in Ionic Crystals D,

Oxford Univ. Press, London and New York,

1948 ; PRZIBRAM (K.), c( Irradiation Colours and Luminescence u, Pergamon Press, New York,

1956 ; SCHULMAN (J. H.) and COMPTON (W. D.),

c( Color Centers in Solids I), Pergamon Press, New York, 1962 ; and MARKHAM (J. J.), (( F Cen-

ters in Alkali Halides D, Academic Press, New

York, 1966 ; and review articles by COMPTON (W. D.) and RABIN (H.), 16, 121, Advances in Solid

State Physics, Academic Press, New York (1964) ;

and PICK (H.), 38, Springer Tracts in Modern

Physics, Springer, Berlin, 1965.

[2] SWANK (R. K.) and BROWN (F. C.), Phys. Rev., 1963, 130, 34.

[3] HENRY (C. H.), SCHNATTERLY (S. E.) and SLICHTER (C. P.), Phys. Rev., 1965, 137, A 583.

[4] JACOBS (I. S.), Phys. Rev., 1954, 93, 993.

[S] GEBHARDT (W.) and MAIER (K.), Phys. Status Solidi,

1965, 8, 303.

[6] SCHNATTERLY (S. E.), Phys. Rev., 1965, 140, A 1364. [7] Taken from the Ph. D. thesis of SCHNATTERLY (S. E.), Univ. of Illinois, Urbana, Illinois (1965) unpu- blished.

[S] FOWLER (W. B.), Phys. Rev., 1964, 135, A 1725. [g] GEBHARDT (W.), private communication.

[l01 MIEHLICH (A.), 2. Physik, 1963, 176, 168.

[l11 COMPTON (W. D.) and KABLER (M.), International Symposium on Color Centers in Alkali Halides, University of Illinois, Urbana, Illinois, October

1965.

[l21 UETA (M.), J. Phys. Soc. Japan, 1952,7, 107. [l31 VAN DOORN (C. Z.) and HAVEN (Y.), Philips Res.

Repts, 1956, 11, 479.

[l41 LAMBE (J.) and COMPTON (W. D.), Phys. Rev., 1957, 106, 684.

[l51 VAN DOORN (C. Z.), Phys. Rev. Letters, 1960, 4, 236. [l61 FARADAY (B. J.), RABIN (H.) and COMPTON (W. D.),

Phys. Rev. Letters, 1961, 7, 57 and 433. 1171 SEIDEL (H.), Physics Letters, 1963, 7 , 27.

[l81 BOETTLER (J.), Ph. D. thesis, University of Illinois, Urbana, Illinois (1966) unpublished.

[l91 OKAMOTO (F.), Phys. Rev., 1961, 124, 1090 ; and SUSMAN (S.), Ph. D. thesis, Illinois Institute of Technology (1963) unpublished.

1201 PODINI (P.), private communication, to be published.

[21] SCHNEIDER (I.), Phys. Rev. Letters, 1966, 17, 1009. [22] WANG (S. F.), Progr. of Theoretical Phys., 1965, 34,

193.

[23] KNOX (R.), as quoted on page 7.21 of Susman [19]. [24] WOOD (R. F.) and MEYER (A.), Solid State Commu-

nications, 1964, 2, 225.

[25] KABLER (M.), RABIN (H.), KLICK (C.) and SCHNEIDER (I)., private communication.

1261 SCHNEIDER (I.), Phys. Rev. Letters, 1966, 16, 743. [27] WANG (S. F.), private communication.

[28] SCHNATTERLY (S.) and COMPTON (W. D.), Phys. Rev.,

1964, 135, A 227.

[29] FITCHEN (D. B.), SILSBEE (R. H.), FULTON (T. A.) and WOLF (E. L.), Phys. Rev. Letters, 1963, 11, 275 ;

and SILSBEE (R. H.), Bull. Am. Phys. Soc., 1964, 9, 88.

[30] KRUPKA (D. C.) and SILSBEE (R. H.), Phys. Rev. Letters, 1964, 12, 193.

[31] SEIDEL (H.), SCHWOERER (M.) and SCHMID (D.),

2. Phvsik. 1965. 182. 398.

[32]

KAPLIANSKII

(A. A.), optics and Spectroscopy, 1964, 16. 329.

[33]

JOHANNSON

(G.), LANZL (F.), V. D. OSTEN (W.) and

WAIDELICH (W.), Physics Letters, 1965, 15, 110. [34] PIERCE (C. B.), Phys. Rev., 1964, 135, A 83.

[35] SILSBEE (R.), Phys. Rev., 1965, 138, A 180.

[36] KRUPKA (D. C.) and SILSBEE (R. H.), Phys. Rev.,

1966, 152, 816.

[37] HAM (F. S.), Phys. Rev., 1965, 138, A 1727.

1381 DUVAL (P.), GAREYTE (J.) and MERLE D'AUBIGNE(Y.),

Phvsics Letters. 1966. 22, 67. [39] B U R K ~ (W.), to be'

[40] PICK (H.), 2. Physik, 1960, 159, 69.

[41] SCHNEIDER (I.), Solid State Communications, 1966, 4, 91.

[42] SCHNEIDER (I.) and KABLER (M.), J. Phys. Chem. Solids, 1966, 27, 805.

[43] PIERCE (C. B.), Phys. Rev., 1966, 148, 797.

[44] HIRAI (M.), IKEZAWA (M.) and UETA (M.), J. Phys. Soc. Japan, 1962, 17, 1483.

[45] FITCHEN (D. B.), FETTERMAN (H. R.) and PIERCE (C B.), Solid State Communications, 1966, 4, 205. [46] SCHNEIDER (I.) and KABLER (M. N.), Physics Letters,

1965,17,213 ; ibid Phys. Rev., 1965,140, A 1983 ;

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