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CLIFFORD C. KLICK
Vol. 57
EMISSION AND ABSORPTION IN LUMINESCENT CENTERS A T LOW TEMPERATURES BY CLIFFORD C. KLICK Chemistry Branch, Metallurgy Division, Naval Research Laboratory, Vashington 25, D. C. Received March I d , 1965
Measurements on emission and absorption of luminescent centers at low temperatures show these results: the emission and absorption bands remain broad a t the lowest temperatures; emission and absorption band-widths vary as the square root of the temperature at high temperatures, but vary a t a lesser rate and approach a constant value a t low temperatures: and some systems show an emission composed of equally spaced “lines.” These data are compared with a model which treats the luminescent center as a one dimensional harmonic oscillator.
Experimental Results.-Measurements of luminescence emission or optical absorption spectra have been made on a variety of materials at temperatures down to 4°K. These include impurityactivated materials which are not photoconducting, such as KC1:Tll and K1:Tl; impurity-activated materials which are photoconducting, such as ZnS :Ag and ZnS :Cu; and materials t o which no chemical impurity has been added, such as ZnW04 and CdS.2 The first and most striking result of all these measurements is that neither the emission nor absorption bands narrow t o line structure as the temperature is reduced but have a width at half maximum of several hundred angstroms. In Fig. 1 there is given a curve of radiometer response to the emission of a commercial P-2 phosphor (ZnS :Cu Ag). The dotted curve is the result of the measurement a t room temperature and the solid curve a t liquid helium temperature. It is apparent that neither the silvp band at 4500 b. nor the copper band at 5200 A. shows appreciable narrowing as the temperature is reduced.
the emission of ZnzSiOe:Mn which have extended into the low temperature range. A number of empirical equations have been proposed t o fit the experimental data for this and other phosphors. 2 .o
0
50 I
100
T E M P ER ATUR E (O KJ. 200 300 400 500 600 700 800 9001000 I I I I l l 1
+
100 a5
3
80
E 60
E
2
Y
2
40 20
0 4000
4500 5000 5500 6000 Wave length in Ingstroms. Fig. 1.-Radiometer response to emission of P-2 phosphor (ZnS: Cu Ag). Dotted curve is emission at 300’ K., solid curve at 4’ K.
+
A second important result comes from the determination of the width of the emission or absorption bands over a wide temperature range for a few substances. Among these are measurements on emission of tungstate phosphors3g4and ZnzSiO4 :Mq4t6 and absorption measurements on KC1:Tll and Fcenters6in the alkali halides. In Fig. 2, the experimental points show the results of investigations on (1) P. D. Johnson and F. J. Studer, Phva. Rev., 82, 976 (1951). (2) C. C. Klick, J . Opt. SOC.Am., 41,816 (1951). (3) H.Brinkrnan and C. C. Vlarn, Phvsica, 14,650 (1949). (4) C. C. Vlam, ibid., ll, 609 (1949). (6) C. C. Klick and J. H. Schulman, J . Opt. SOC.Am., 40, 609 (1950). (6) E. Burstein and J. J, Qberly, Phye. RIV., 78, 349 (1960).
SQUARE ROOT OF TEMPERATURE ( O K . ) . Fig. 2.-Curves showing relative width of absorption 01 emission bands versus square root of the absolute temperature for various values of vibrational frequency using equation (1). The width of the band a t 300 K. is assigned a value of unity. The experimental points are measurements on ZnS2SiOd:Mn. O
Mott and Gurney’ have proposed a dependence of the width of the emission or absorption band on the square root of temperature, from simple considerations concerning the configurational coordinate curves. The straight line through the origin in Fig. 2, drawn according t o this relationship, shows that it is a good approximation a t high temperatures but fails t o predict the broad band structure observed a t low temperatures. A third result of low temperature emission spectra is the appearance in some phosphors of a detailed fine structure consisting of a series of “lines” (7) N. F. Mott and R. W. Gurney, “Electronic Processes in Ionie Crystals,” Oxford Prsam, New York, N. Y.. 1840, pa 117.
EMISSION AND ABSORPTION IN LUMINESCENT CENTERS
Nov., 1953
equally spaced in energy. These have been observed in the “edge emission” of ZnSs and CdS,8,9 in a variety of uranium compounds,*0and in the mineral scapolite and related compounds.ll The edge emission of CdS is illustrated in Fig. 3 for temperatures of 77 and 4OK. Spectrographic measurements of the width of the lines a$4”K. indicate that they are approximately 10 A. wide in single crystal material prepared without flux2 Wave length in hgstroms. 4900 5000 5100 5200 5300 5400 5500 5600
2.4 2.3 2.2 Energy in electron volts. Fig. 3.-Relative number of emitted quanta for “edge emission” of CdS as a function of wave length. The solid curve represents measurements at 4’ K.; the dashed curve a t 77°K. Excitation ia by 3650 A. radiation. The curve of the 5461 A. line indicates the resolution of the measuring instrument. 0
2.5
The Impurity Interaction Model.-One explanation for the broad low temperature emission and absorption spectra is that the random distribution of chemical impurities and lattice defects causes a distribution in the energies of individual centers for optical processes. While this mechanism must always be effective in producing some broadening of the spectra, there are several experimental results which indicate that this is probably not the main effect. 1. Measurements on the edge emission lines of CdS were made on single crystal material and on powdered material prepared in the usual way by firing in the presence of a fluxing agent.2 The line width at halfomaximum of the single crystal materigl was 10 A. and of the powdered samples about 50 A. Thus, there is in this case a distinct effect due to impurities and defects, but it is an order of magnitude less than the band widths usually observed ’at low temperatures. 2. Measurements on the low temperature emission of K I :T1 both as a single crystal and a powder ground from the crystal failed to show a broadening due to the grinding.2 3. The green emission band in ZnS :Cu showed no noticeable change in width when the concentration was changed from lou6 t o 10-3.2 Similar results are found for ZnzSi04:Mn with manganese concentrations in the range of 0.004612to 0.26.13 (8) F. A. Kroger, Phusica, ‘I, 1 (1940). (9) C. C. Klick, Phys. Reu., 89, 274 (1953). (10) G. H. Dieke and A. B. F. Duncan, “Spectroscopic Properties of Uranium Compounds,” McGraw-Hill Book Co., New York, N. Y., 1949. (11) Unpublished results of R. D. Kirk, Naval Research Laboratory. (12) E. Nagy, J . Opt. Sac. Am., 39, 42 (1949). (13) J. H. Schulman, R. J. Ginther and E. W. Claffy, J . Elactrochem, sac., 98, 57 (1949).
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4, The absorption band width of F-centers in alkali halides does not appear to be dependent on concentration in the range up to l 4 nor on thermal quenching or cold work.6 The One-dimensional Harmonic Oscillator Model.-Schon16 apparently first suggested that the broad band emission spectra which were observed might be due to a zero point vibrational energy associated with the luminescent center. In this section a one-dimensional harmonic oscillator model will be described and the predictions of this model compared with experiment. Figure 4 illustrates schematically the situation for low temperature luminescence. A similar description may be given for absorption. In this model the curves giving the variation of energy of the center with displacement from the equilibrium are parabolas. Quantum mechanics shows that this continuous energy distribution is replaced by a series of equally spaced energy levels with spacing hv where v is the frequency of the vibrating system. This frequency will generally be different for the ground and excited states of the system. The lowest vibrational level is hv/2 above the minimum of the classical curve.
La
c3 = w
a W
GROUND STATE
I COORDINATE DISTANCE.
Fig. 4.-Schematic description of the configuration coordinate curves for the ground and excited states of a luminescent center.
As the temperature is reduced, then, a situation is reached in which essentially all the excited state centers exist only in the lowest vibrational level. The probability distribution as a function of displacement is Gaussian as is illustrated in Fig. 4. I n general the equilibrium configuration of the luminescent center will be different in the ground and excited state of the center and the optical transition from the excited state will not be to the lowest vibrational levels of the ground state. The resulting emission will be a series of equally spaced lines with energy difference hv, where v, is the frequency of vibration of the ground state of the luminescent center. As mentioned in the first section this type of emission has been observed; Kirk” has noted as many as eleven lines in some of his compounds. In the large majority of materials line structure has not been observed and it may be that the broadening due t o impurities and lattice defects generally obscures this fine structure. For systems in which line emission is not observed and in which transitions are to levels many vibra(14) R. Kaiser, 2. Physa’k, 188, 482 (1962).
(15) M. 8ah6n, Ann. Phyeik, Series 6, 3, 343 (1948).
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CLIFFORD C.KLICK
tional quanta above the lowest level, the correspondence principle allows the ground state to be represented by the classical curve. The justification for this approximation has been considered in more detail by Williams and HebblBand by Lax.” To the extent that the classical curve between A and B of Fig. 4 is a straight line, the Gaussian distribution of centers in the excited state will result in a Gaussian emission spectrum. Experimentally, emission and absorption bands are generally “bell shaped.” I n the case of tungstate phosphors, such as MgW04, a serious attempt has been made to show that the emission is accurately Gaussian.l* As the temperature of a luminescent material is raised, the centers which are in the excited state will exist not only in the ground vibrational state but also in higher vibrational levels. The vibrational amplitude will extend over a larger coordinate distance for the higher levels and result in transitions to a wider range of the ground state configuration curve such as from C to D in Fig. 4. The resulting width of the emission (or absorption) band as a function of temperature has been given by Williams and Hebbl6 as AE = C[(hv/2k) coth (hv/2kT)I1/;
(1)
where AE is the band width in energy, C is a constant, Y is the vibrational frequency of the center in the excited state for emission spectra and of the ground state for absorption spectra, k is Boltzmann’s constant, and T is temperature on the absolute scale. This equation reduces to Mott and Gurney’s expression at high temperatures and becomes a constant at low temperatures. In Fig. 2 there is plotted a family of curves of relative band width as a function of temperature for a number of vibrational frequencies. By plotting experimental data on curves like those of Fig. 2 or by inserting them into equation (1) directly, it is possible to ascertain vibrational frequencies. In Table I there are collected some results on the vibrational frequencies obtained either from measurements on bandwidth or vibrational fine structure. The frequencies so obtained fall in a reasonable range. TABLE I Material KC1:TlI F-Centers in KClR ZnWOaP ZnzSiO4:Mn~~~ Ens, edge emissions CdS, edge emission899 KzUOz(SOr)z1~ KZUOI(SO~P~~ Scapolite11 Scapolite11
Method pf investigation Band width Band width Band width Band width Fine struoture Fine structure Fine structure Fine structure Fine structure Band width
Vibrational frequency (sec.-9 and state of center 4 x 1012, ground state 3 X 1012, ground state 8 X 1012, excited state 6 X 1012, excited state 1.1 x 1018, ground state 9 . 4 X 1011,ground state 2 . 0 X 1018, excited state 2 . 5 x 1018, ground state 1 . 6 X 1018, ground state 2 x 1018, excited state
An attempt has been made to identify the vibrational frequency found by the band width method with frequencies found by other methods.20 In (16) F. E. Williams and M. H. Hebb, Phys. Rev., 84, 1181 (1951). (17) M. Lax, ibid., 86, 640 (1962); 86, 660 (1952). (18) See reference (4) for recent results and references to previous investigations. (19) E. L. Nichols and H. L. Howes, Phy8. Rev., 14, 293 (1919). (20) The importance of such an identification has been emphasised in a private eommunlartion from F,Beiti.
Vol. 57
the case of CsBr :T1 the thallium is surrounded by the same number of bromine ions as inTlBr and a comparison may be made between the vibrational frequencies of the thallium in the two cases. Exact agreement should not be expected because of differences in interatomic distances and the change from cesium to thallium as the metalion of the host lattice. From Restrahl measurements on TIBrzl the vibrational frequency is estimated to be 2.2 X 1Ol2 sec.-l; measurements on the absorption band of CsBr :T1 as a function of temperature indicate a frequency of 1.3 X 10l2sec.-l. It is planned to repeat this experiment with CsCl :T1 and T U . The lower polarizability of the chlorine ion may improve the numerical agreement. On the basis of the simple model discussed in this section, it has previously been shownz2that measurements on the absorption and emission spectra of an impurity center allow the determination of the configuration coordinate curves for the ground and excited states. Such complete data are not yet available for a simple system. The method has been applied to data on KC1:Tl by assuming the effective mass of the system to be that used by Will i a m ~in~ his ~ *theoretical ~ ~ treatment of this material and there is good agreement with Williams’ results. The method also has been used in an investigation of the luminescence of divalent mang a n e ~ e . This ~ ~ method may prove to be a simple way of obtaining information about the interaction of ions using experimental data. The use of the one-dimensional harmonic oscillator model raises a number of questions. Why should a center in a three dimensional material be able to be represented by such a model and to what does the model correspond physically. It has generally been a s s ~ m e d ~ ~ ~that 2 4 ~ the ~ 6 physical situation represented by the model is one in which the ions immediately surrounding the center all oscillate synchronously in a radial direction from the center. The coordinate distance then is the distance from the center to any one of the nearest neighbor ions and the effective mass of the center is that of the ions surrounding the center. Corrections to the mass may be made t o include the effect of motions of ions which are not nearest neighbors. It is probable that while other modes of vibration than the synchronous radial one exist, this mode of vibration causes a much larger change in energy of the impurity than any other and is predominant in determining the emission and absorption band widths. It may also be mentioned here that neither the spacing of the lines in materials showing fine stmcture nor the relative widths of various lines gives any indication that more than one frequency is involved in emission. While this model offers a simple explanation of a number of phenomena in emission and absorption spectra, the extent to which it can be applied in a (21) “International Critical Tables,” Vol. 5, McGrsw-Hill Book Co.. Inc., 1929, p. 261. (22) C. C. Klick, Phys. Rev., 86, 154 (1952). (23) F. E. Williams, J . Chem. Phys., 19, 457 (1951). (24) F. E. Williams, Phys. Rev., 8Z, 281 (1951). (25) C. C. Klick and J. H. Schulman, J . O p t . SOC.Am., 48, 910 (1952). (26) T. Invi and Y.Uemura, Prog, Thro, Phyr., I , 395 (lQ50).
W
t
8
Nov., 1053
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quantitative way is still uncertain and is a problem to which further work may be applied. Lax1’ has recently discussed in detail the approximations involved in this model.
sec. -1-so that it would appear that even where line emission is not observed the optical modes of vibration are predominant in influencing the emission.
DISCUSSION
frequencies which were obtained from fine structure observations are of the order of 1013 vibrations per second whereas those which were obtained primarily from band widths are generally smaller, not much, just a factor of 2 or 3. Perhaps it’s a fine distinction, but one might say that if the coordinate which is important in the problem is an optical coordinate then you observe a frequency which is closely related to that optical vibrational frequency. On the other hand, if the coordinate that you are observing is a linear combination of coordinates which involves both acoustical and optical coordinates with some weighting, then you will get an average frequency which will be somewhat lower than the optical vibration frequencies and therefore, there is some correlation shown in the experimental data, namely, those for which fine structure does not appear had generally smaller vibrational frequencies than those in which fine structure was observed.
R. H. BUBE.-h applying your model to a photoconducting phosphor, do you consider your excited state level with the zero-point energy to be a level below the conduction band in which a free electron is trapped before making a transition to the ground state? C. C. KLrcK.-This is the simplest picture. Should it be shown however that there was a photoconducting phosphor in which transitions were from the conduction band directly to the ground state, the low temperature broad band emission might be understood in terms of the distortion of the conduction band near the luminescent center. M. LAx.-Dr. Klick has raised the question of the legitimacy of using a single coordinate description. For a crystal, the configuration energy in a given electronic state is a function of the positions of all the nuclei. And in principle, a many body description is necessary. However, an investigation of the Franck-Condon principle, in its semiclassical form [J.Chem. Phys. 20,1752 (1952)l reveals that a description in terms of a small number of coordinates is possible providing the configurational energy di$erence between the two electronic states involved is a function only of the small number of coordinates. (The term coordinate is understood, here, to mean any of the nuclear positions, or any linear function of the nuclear positions.) The above mentioned condition will usually be met only if the trapped electron is highly localized, or highly diffuse. Dr. Klick has obtained some beautiful experimental results in which a series of sharp lines are resolved in the emission or absorption spectra. It may be worthwhile to emphasize that these unusual results are found only a t low temperatures in certain crystal-activator systems. A series of completely sharp lines will, strictly speaking, be observed only if the normal modes that participate in the configurational energy difference all have the same frequency. A series of discrete but (dispersively) broadened lines will occur if the above-mentioned modes vary slightly in frequency as, for example, the modes of a single optical branch. An additional (thermal) broadening will be produced if the energy difference involves the low energy acoustical phenons. The extent of this additional broadening depends on how strongly the low energy modes influence the configurational energy difference, and on the temperature. Unless the separation between the optical phenon lines is large compared to the broadening due to dispersive and thermal effects,the line attern will not be resolved. If the trapped electron is highry localized, it will not be influenced much by acoustic modes and the chances are good that the lines will be resolved, KLIcK.-The frequencies obtained from the band width method are still quite high-of the order of 10’2 to 10’3
LAx.-May I have the last slide (Table I) of the speaker? I would like to point out on that slide that those vibrational
KLIcK.-There is another purely experimental explanation of the apparent trend toward lower frequency obtained by band width measurements as compared with fine structure measurements. Since fine structure will only be observed if the peaks are well separated compared to their width, the conditions are modt favorable for observation when the frequency of vibration is high. By contrast an inspection of Fig. 2 shows that the variation of band width with temperature is most pronounced a t low frequencies. Thus the two effects are most easily observed in different regions of the frequency spectrum.
F.E. WILLIAMs.-The problem of fine structure versus no fine structure in emission spectra can be clarified by considering several specific simple luminescent materials. I n the case of phosphors activated with tetravalent manganese, for example, the tetravalent manganese-activated magnesium oxide phosphor, a fine structure in the emission spectrum is observed. Because of the large coulon~beffect of the tetravalency, the charge density of the manganese is highly localized, and only the interactions of the activator ion with the nearest neighbors are dependent on the electronic state of the manganese. Therefore, the one dimensional configuration coordinate model is particularly applicable and applied quantum mechanically predicts the fine structure of emission. In other cases, such as magnesium oxide activated with divalent manganese or potassium chloride activated with thallium, no fine structure in the emission spectrum is observed. I n these cases, the charge density of the activator ion is still quite localized, although not as localized as in the case of the tetravalent activator ion, so that even though the principal interaction that is dependent on the state of the activator isstill the interaction with the nearest neighbors, additional optical or acoustical vibrations characteristic of other interactions slightly dependent on the electronic state of the activator ion fill in the spectrum to yield a bellshaped continuum.
