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On the radioluminescence of Ba, Sr and Ca fluorides

P. BROVETTO, V. MAXIAand M. SALIS

Istituto di Fisica Superiore dell’Università - Cagliari, Italy

Istituto Nazionale di Fisica della Materia e Gruppo Nazionale di Struttura della Materia Cagliari, Italy

(ricevuto il 20 Maggio 1997; approvato il 7 Luglio 1997)

Summary. — The radioluminescent spectra of BaF2, SrF2and CaF2samples excited

by X-rays at room temperature have been recorded in the 375 to 730 nm range. The BaF2 and SrF2 spectra consist of a continuous emission the intensity of which

decreases from 375 to 500 nm, followed by broad bands in the 650 nm region also present in the thermoluminescence spectra. With the CaF2 samples, only the

continuous radioluminescent emission was observed. Taking into account the Prener and Williams recombination scheme, the continuous radioluminescent emission is explained by the recombination of excitons bound to Frenkel defects due to the displacement of fluorine ions in interstitial positions.

PACS 78.60 – Other luminescence and radiative recombination. PACS 71.35 – Excitons and related phenomena.

1. – Introduction

In the last few years considerable attention has been devoted to the luminescent properties of alkali earth fluorides [1]. A topic of special interest is represented by the radiative recombinations of excitons trapped by Frenkel defects [2, 3]. In alkali earth fluorides, a certain density of Frenkel defects is present, due to the displacement of some F2 _{ions in interstitial positions, which leaves F}2 _{vacancies. When crystals are}

excited by ionizing radiations, electrons and holes are captured by F2 _{vacancies and}

F2 _{interstitials, respectively, thus originating F and H centres. Recombination of the}

nearest F-H pairs, that is, exciton recombination, gives rise to a radioluminescent (RL) emission. Since in fluoride crystals there are many defects of different kinds, this process, in general, is accompanied by recombination of carriers trapped in these defects, so that rather complex RL spectra are often observed.

Keeping this state of affairs in mind, and for the purpose of better understanding the real mechanism of the RL emission, we performed investigations on the RL of alkali earth fluorides excited at room temperature with soft X-rays. The thermoluminescence (TL) of these fluorides was also investigated to ascertain the

P.BROVETTO,V.MAXIAandM.SALIS 1584

presence of deep trapping levels which may play a role in the RL emission. Frenkel defects, on the contrary, allow only for fleeting traps, so that no contribution to TL emission is expected.

2. – Experiments

High-purity polycrystalline samples of Ca, Sr and Ba fluorides were excited at room temperature (295 K) with soft X-rays (Cu Ka) while their RL spectra were recorded in the 375 to 730 nm range utilizing a device based on a continuous interferential filter. Figures 1, 2 and 3 show the spectra obtained with Ca, Sr and Ba samples, respectively. In all spectra, a continuous emission whose intensity decreased from 375 to more than 500 nm was present. RL spectra of Sr and Ba fluorides showed, moreover, a broad band at 644 and 659 nm, respectively. Figures 4 and 5 show the contours of TL emissions of Sr and Ba fluorides, respectively, as recorded in the above-mentioned spectral range for temperatures rising with a speed of about one KOs from 300 to 680 K. The Sr fluoride emission was characterized by two glow peaks with wavelengths of about 650 nm and temperatures of 380 and 520 K, respectively. The Ba fluoride showed a single glow peak at 665 nm and 430 K. No TL emission was detected with the Ca fluoride sample. Taking into account a small displacement due to the different experimental conditions, it is clear that the 644 and 659 nm bands observed in the RL spectra of Sr and Ba fluorides samples are the same that appear in their TL spectra at 650 and 665 nm, respectively. This conclusion is substantiated by the fact that no emission band was present either in RL or TL spectra of Ca fluoride.

Fig. 2. – Radioluminescent spectrum of Sr fluoride.

Fig. 3. – Radioluminescent spectrum of Ba fluoride.

3. – The radioluminescence kinetic model

The recombination of excitons bound to Frenkel defects originated by F2 _ion

P.BROVETTO,V.MAXIAandM.SALIS 1586

Fig. 4. – Contour plot of the thermoluminescent emission of Sr fluoride.

by means of the Prener and Williams scheme [4, 5]. This maintains that the recombina-tion rate W(r) is related to the distance r between F and H centres by a law of the form

W(r) 4Wmaxexp [2rORc] ,

(1)

with Wmaxa constant and Rc a critical length equal to half the donor Bohr radius, that

is, the F centre radius. It follows from eq. (1) that Rccan be identified, in practice, with

the minimum distance between the recombining F and H centres, which is, in turn, the minimum size of the Frenkel defects (separation between F2 _{ion vacancies and}

interstitials). Considering that there is a distribution of distances between F and H centres, the kinetic set for the RL emission is (see fig. 6)

(2) dnc dt 4 f 2 Aenc(Ne2 ne) 1seexp

k

l

!

m

k

l

n

k

l

!

k

l

Fig. 5. – Contour plot of the thermoluminescent emission of Ba fluoride. with Ne4

!

!

The meaning of symbols is as follows: f the rate of electron and hole injection in conduction and valence bands; nc and nvdensities of electrons in the conduction band

and of holes in the valence band, respectively; neand nh(ri) densities of electrons in F

centres and of holes in H centres lying at a distance ri, respectively; Neand Nh(ri) the

corresponding densities of F2 _{ion vacancies and interstitials, respectively; A}

e and Ah

probabilities of electron trapping by F2_{ion vacancies and interstitials, respectively; s} e

and sh frequency factors for the thermal releasing of trapped electrons and holes,

respectively; Eeand Ehdepths of electron levels below the conduction band and height

of hole levels above the valence band, respectively. Equations (2) to (5) are rate equations for the exchange of carriers between the different levels, eq. (6) accounts for the electric neutrality of the activated crystals.

It follows from eq. (5) that the intensity of the RL emission, originated by recombination of electrons in F centres with holes in H centres lying at a distance ri, is

given by

I(ri) 4neW(ri) nh(ri) .

(7)

On the other hand, according to the Prener and Williams model, the energy of photons released in this process is related to the distance riby [4, 5]

hni4 EG2 (EF1 EH) 1

e2

eri

, (8)

P.BROVETTO,V.MAXIAandM.SALIS 1588

Fig. 6. – Electron-hole recombination scheme for the radioluminescent emission of alkali earth fluorides according to the Prener and Williams mechanism.

EG standing for the forbidden energy gap and e for the static dielectric constant. In

principle, by eliminating ribetween eqs. (7) and (8), the intensity of the RL emission is

obtained as a function of wavelength. This, of course, requires the knowledge of the actual values of the electron density ne and hole density nh(ri), which in turn entails

integration of the kinetic equations (2) to (6). Owing to the non-linearity of these equations, this constitutes a rather complex task. Such an integration, however, can be avoided by taking into account that after a very short time all carrier densities attain steady values. This is allowed if the rate of carrier production fulfills the condition

f GNe

!

i 41 a

W(ri) Nh(ri) 4Imax,

(9)

Imax standing for the maximum RL emission intensity achieved when all carrier traps

are saturated. For weak X-ray excitations, condition (9) is at once verified, which allows us to put dOdt40 in eqs. (2) to (5). In this way, we obtain from eq. (5)

n–h(ri) 4

Nh(ri)

1 1

(

)

–

vAh

, (10)

n–e, n–h, n–vstanding for the steady values of densities. According to eq. (10), the density

of trapped holes is smaller for the H centres nearest to F centres. In fact, taking into account that at room temperature we have shexp [2EHOkT ] ` 0 , it follows from

eqs. (10) and (1) that n–h(ri) KNh(ri) when riK Q . Utilizing eq. (10), eq. (7) can be

rewritten in the form

I(ri) 4 n–eNh(ri) 1 1n–eW(ri) On – vAh W(ri) , (11)

which, together with eqs. (1) and (8), enables us to obtain the spectral composition of the RL emission.

some rearrangements of the previous equations are needed. By introducing into eq. (8) the critical length Rc defined in eq. (1), a corresponding critical photon energy hnccan

be accounted for: hnc4 EG2 (EF1 EH) 1 e2 eRc . (12)

By considering the critical wavelength lc4 cOnc and eliminating the quantity

EG2 (EF1 EH) from eqs. (8) and (12), we obtain, with simple transformations,

ri Rc 4

g

h

a standing for the fine structure constant. In eq. (13) no approximation has been

utilized. It follows, from eq. (13), that lc is the minimum allowable wavelength

corresponding to ri4 Rc. For wavelengths not overly greater than lc, such that

li2 lcblc, eq. (13) can be written in the simplified form

r Rc

`_{1 1} l 2lc L , (14)

in which the subscript i has been dropped and a length L , given by

L 4 a 2 pe l2 c Rc , (15)

has been introduced. In this way, taking into account the amplitude factor

A(l) 4 n

–

eNh(r) e21

1 1n–eWmaxexp [2rORc] On–vAh

, (16)

in which r is related to l by means of eq. (14), eq. (11) takes the form

I(l) 4 A(l) exp

k

l

which shows that the initial behaviour of the RL emission, when l 2lc is smaller than

lc, is essentially exponential. In eq. (17), the distribution of distances between F and H

centres is regarded as continuous while, on the contrary, only distances compatible with the lattice geometry should be accounted for in principle. This simplification, however, is made necessary because recorded spectra show a continuous trend in which no sign of a discrete structure is detectable.

To compare eq. (17) with recorded RL spectra, it is convenient to rewrite it in the form 2log

y

z

y

z

where l04 375 nm is the initial wavelength of the spectra shown in figs. 1, 2 and 3.

P.BROVETTO,V.MAXIAandM.SALIS 1590

obtained the plots shown in figs. 7, 8 and 9, respectively. Ca fluoride is characterized by a remarkably rectilinear plot, while with Sr and Ba fluoride only the first 50 nm reveal a rectilinear behaviour.

4. – Discussion and conclusion

In principle, the lack of linearity of the logarithmic plots shown in figs. 7, 8 and 9 is to be ascribed both to the variation of the amplitude factor A(l) and, for Sr and Ba fluorides, to the presence of TL bands in the region near 650 nm. Since Ca fluoride, which does not show a TL emission, yields a nearly rectilinear plot for wavelengths up to 500 nm, the conclusion can be drawn that the most important reason for deviation from linearity is the emission originated by the deep traps active in the TL process. As to the nature of these traps, we must consider that all alkali earth fluorides are characterized by the fluorite lattice. In the fluorite cells, eight equivalent positions exist in which alkali ions can be held. Since the cells contains only four ions, room is available for interstitials. Thus, the traps responsible for TL can be ascribed to the displacement of alkali ions in interstitial positions lying in cells placed at a distance from the initial ion position. This introduces separated couples of vacancies and interstitials bearing opposite-sign charges into the lattice. These are active in TL as electron and hole traps. It is to be kept in mind, however, that the actual density of these defects is dependent on the thermal treatments, as well as on the sample origin. A protracted annealing of samples allows, in general, a reduction in defect density. In this way, Ca fluoride samples with a defect density small enough to extinguish the TL emission were obtained. With Sr and Ba fluoride samples, a residual TL emission was still present.

In table I, values of the length L obtained from the logarithmic plots of figs. 7, 8 and 9 are shown. Utilizing eq. (15), these values enable us to derive the critical length Rcfor

Fig. 8. – Logarithmic plot of the radioluminescent emission of Sr fluoride.

the three fluorides if values of the critical wavelength lc are known. Since lc is the

minimum wavelength of the RL emission corresponding to the closest pairs of F-H centres, the actual value of lc is less than, but not significantly different from, l0, the

initial wavelength of the recorded TL spectra. This is to say that l0can be regarded as

an upper limit of lc. In this way, taking into account data on the dielectric constant [6],

P.BROVETTO,V.MAXIAandM.SALIS 1592

TABLE I. – Parameters for the interpretation of the radioluminescent spectra of Ca, Sr and Ba fluorides by the Prener and Williams recombination model.

CaF2 SrF2 BaF2 L(nm) e Rc(Å) a (Å) 67.7 6.81 3.5 5.45 39.5 6.33 6.5 5.75 45.1 7.33 5.0 6.25

the values of Rcshown in table I were obtained. These values represent upper limits of

the critical length, that is, of the minimum distance between F2 _{ion vacancies and}

interstitials. In table I, the cell parameters a of the three fluorides are reported as well. It appears that Rcis in all cases not very different from a. This leads to the conclusion

that the Frenkel pairs which allow for the minimum wavelength in RL spectra are kept within a single crystal cell.

As to the distribution of Frenkel pair separations, that is, of the density Nh(r) of

interstitial F2 _{ions lying at a distance r from F}2_{ion vacancies, no definite conclusion}

can be drawn. Indeed, as appears from eq. (16), the density Nh(r) is related to the

amplitude factor A(l) which, as said before, cannot be obtained from the logarithmic plots of the recorded RL spectra owing to the presence of 650 nm emission bands. In any case, apart from this drawback, it appears correct to conclude that the observed features of the fluoride RL emission can be properly explained by the Prener and Williams recombination mechanism.

R E F E R E N C E S

[1] CATLOWC. R. A., J. Phys. C, 12 (1979) 969. [2] GLYNNT. J., J. Lumin., 48-49 (1991) 783.

[3] CHAO-SHUSHI, KLOIBERT. and ZIMMERERG., J. Lumin., 48-49 (1991) 597. [4] PRENERJ. S. and WILLIAMSF. E., J. Electrochem. Soc., 103 (1956) 342.

[5] THOMASD. G., HOPFIELDJ. J. and AUGUSTYNIAKW. M., Phys. Rev., 140 (1965) 202. [6] MUSICANTS., Optical Materials (Marcel Dekker, New York) 1985.