Limiting processes for the defect accumulation under electron irradiation in KBr at 4 K

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Limiting processes for the defect accumulation under electron irradiation in KBr at 4 K

A. Nouailhat

To cite this version:

A. Nouailhat. Limiting processes for the defect accumulation under electron irradiation in KBr at 4 K. Journal de Physique Colloques, 1980, 41 (C6), pp.C6-308-C6-311. �10.1051/jphyscol:1980678�.

�jpa-00220116�

JOURNAL DE PHYSIQUE Colloque C6, supplément au n° 7, Tome 41, Juillet 1980, page C6-308

Limiting processes for the defect accumulation under electron irradiation in KBr at 4 K

A. Nouailhat, G. Guillot and E. Mercier

Laboratoire de Physique de la Matière (*), Institut National des Sciences Appliquées de Lyon, 20, avenue Albert-Einstein, 69621 Villeurbanne Cedex, France

Résumé. — Les cinétiques de croissance de tous les défauts (F, F+, H, H2, 1 , Vk) créés dans KBr par irradiation électronique ont été étudiées dans un large domaine de concentration (1016-5 x 1019 cm"3), à 4 K, température à laquelle aucun des défauts n'est thermiquement mobile. Les lois de croissance sont interprétées en considérant la limitation du rendement de création des nouvelles paires de Frenkel par les interstitiels stabilisés. A très haute concentration, la possibilité de recombinaison des centres H, lors de leur déplacement sous forme de crowdion avec les centres F présents, entraîne une nouvelle diminution du rendement d'accumulation des centres F. Nos résultats suggèrent, en outre, une limitation indépendante de la croissance des centres F et F+, donc des pro- cessus de formation indépendants.

Abstract. — The growth kinetic in a wide range of concentrations (1016-5 x 1019 cm"3) of all defects (F, F + , H, H2,1, Vk) created in pure KBr by electron irradiation have been studied at 4 K, temperature at which no defect is thermally mobile. The kinetic shapes are explained by considering a local action of the stabilized interstitiel centers decreasing the creation yield of new Frenkel pairs. At concentration higher than 1019 cm"3, the decrease of the F center accumulation yield is due to the possibility of uncorrelated recombinations of the F centers and the H centers moving as dynamical crowdions. Our results suggest also an independent limitation of F and F⁺ center growth, thus independent formation processes.

1. Introduction. — In the alkali halides, the kinetics in the temperature range where no center is thermally mobile are of interest to study elementary phenomena of defect creation and accumulation without screening by thermal activated secondary reactions. In KBr, two kinds of Frenkel pairs, neutral F-H and charged ' F⁺- I , are created. The transformation F-H -»• F ⁺ -I which efficiency might depend on the defect concen- tration in the crystal [1] is not yet well understood.

This paper's purposes is to present an experimental study of the kinetics of all centers present under electron irradiation in KBr near 4 K and to analyse the kinetic shapes by simple models based on local action of centers inhibiting the creation of new Frenkel pairs. All results have been obtained using nominally pure KBr crystals purchased from the Harshaw Chemical Co. The apparatus has been described elsewhere [2]. The 20 to 60 keV electron beam having a density between 0.1 and 20 uA c m "² creates defects in a thin layer (5.7 u at 20 kV to 36.9 u at 60 kV) at the surface of the crystal. The energy deposition rate e lies between 10¹⁹ and 2 x 1021 eV c m- 3 s ~ \ Varying the electron beam energy allows concentration measurements between 10¹⁶ and 5 x 10¹⁹ c m^{- 3}, with optical densities (OD)

smaller than 3 at the peak of the absorption bands.

We have used results from ref. [3]

1) to determine the respective contribution of the Vk and H centers to the 380 nm absorption band.

2) to take into account the reaction F⁺ + e~ -> F under irradiation. The concentration of V^k centers has been experimentally determined to be 6.5 % of the sum of the F and F⁺ center concentrations. This amount corresponds to the number of F⁺ centers having trapped an electron, and transformed into F centers. So, to have the concentrations of centers at the equilibrium, we must substract it from the number of F centers and add it to the number of F+ centers.

All our results will be corrected in this way.

2. Experimental results. — Experimental accumu- lation kinetics have been measured as a function of the dose for all centers. They depend only on the dose received by the crystal. No dependence on the energy deposition rate £ has been evidenced in the range allowed by the apparatus.

The main results are following.

— The total concentration of defects grows mono- tonically as a function of the dose.

Figure 1 shows the F and F+ growth kinetics as a function of the dose. A typical logarithmic growth is pointed out in the dose range lower than a few

(*) Equipe de recherche associée au C.N.R.S.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980678

LIMITING PROCESSES FOR THE DEFECT ACCUMULATION UNDER ELECTRON IRRADIATION C6-309

8

c 2 0 -

Z O N E I ^w

8 0

0 O A A

I

ZONE

II 5- (a) , , ^{a t o}

0 .

10'" 10" 10" 10:'

DOSE

[eVcm

Fig. 1. - F(A) and F'(0) center accumulation kinetics and thelr sum (m) in KBr under electron irradiation at 4 K . (V = 20 kV, j = 0.2 pA cm-2 (a); j = 1 pA c m - 2 (b); j = 3 FA cm-2 (c).)

eV cm-3 (zone I). For higher doses (zone Il), the F center concentration grows linearly versus dose (Fig. 2), whereas the F C center concentration is

always logarithmic. At concentrations higher than 10'' F centers cm-3 (zone 111), a square root law is observed for the F centers as a function of the dose (Fig. 3). F C centers have not been measured in this concentration range. A simple phenomenological representation of F and F C center growth kinetics in zones I and I1 is given by the relation :

where x is the defect concentration, d the dose, A , B are phenomenological parameters.

- If the kinetics of the F' center and the comple- mentary I center are exactly proportional

this is not the case for the kinetics of the F center and the H center. H centers are known to undergo a strong attractive interaction to form H 2 and more complex aggregates [4]. So, the complementary beha- vior of the H, H, and F centers must be considered simultaneously. The H centers saturate at a value close to 1018 cm-3 and the H 2 center concentration versus F center concentration shows a quadratic growth in zone I. This curve is explained in the same way as the quadratic relation found by Itoh and Saidoh for the H and H 2 centers [5]. Taking into account the quadratic relation

1 /

=fiL lo ZONE

II I

n(H2) = k(n(F))2 , (2) and

n(H)

+

n(H)/n(F) = 1 - 2 kn(F) ₍₄₎

Fig. 2. - F(A) and F'(0) center accumulation kinetics in KBr under electron irradiation at 4 K. (V = 20 kV, J = 3

The curves are according to equations (5) and (6) with the following setofparameters : v = 7.2 x 10-19cm3,R+ = 1.3 x 10-2(eV)-1;

R = 2.05 x lO-"eV)-', R, = 1.4 x lo-' (eV)-'.

Flg. 3. - F center accumulation kinetics in KBr under electron irradiation at 4 K. (V = 20 kV, j = 10 pA cm-'.) The curve 1s according to equation (7) with 2 R, a, n(T)/rr,= 1.4 x 1014 cen- ter (eV)-I to fit the points in zone 111.

-

'

g 2 -

U n L L u

4 -

as shown in figure 4.

0 5 " 1

a

DOSE

[IO evcm31

-

4

Fig. 4. - n(H)/n(F) ratio in KBr under electron irradiation at 4 K (V = 55 kV, j = 2 pA ~ r n - ~ . ) A experimental points; l calcu- lated points according to n(H)/n(F) = 1 - 2 kn(F),

k = 1.39 x lo-'' c m 3 .

-

s1

E

.75 .5 -25

We can determine the factor k, in good agreement with [5]. At higher F center concentration, more complexe aggregates are formed.

A A

I = =

.,.

-

& A A x .

-

- .'.

4

a 1

ZONE1

10" 10'" lo2' 10" -

DOSE Lev c m i ZONE

III

. A .

* .

* l

, : A

C6-3 10 A. NOUAILHAT, G. GUILLOT AND E. MERClER

3. Model of limiting processes for the defect accu- So, using the arguments of [7], we can write : mulation. - A model for very low temperature growth 1

kinetics of defects must take into account two expe- n(Fi) =

-

+

and 1) no center is thermally mobile [6],

2) the Frenkel pairs are correlated.

The first point indicates that one must consider local properties to explain the decrease of the Frenkel pair creation efficiency. A mathematical representa- tion for it is the assumption of a forbidden volume, where the Frenkel pair cannot be formed, around some types of centers [7]. The second point can be deduced from first order recombination kinetics of neutral Frenkel pairs observed both after a pulsed irradiation in KBr at 8 K [8] and during thermal recombination stages [9]. Our experimental results in zones I and I1 are well fitted (Fig. 2) with the following hypo thesis.

a) The Icenter is the main responsible center for the forbidden volume. (i) The perturbation caused by an I center in its neighborhood is known to be more important than the one caused by the other centers [lo-131. (ii) The inhibition mechanism is due to the strain field around the I center causing the recombination of a newly formed Frenkel pair, on the basis of analogies with other cases of lowering of the pair creation efficiency by large dopants such as I - [14] or Rbi [15] in KBr.

6) The recombination occurs after the charge transfer from F to the H center resulting in F' and I centers [8, 161 : the F and F + center kinetics have to be described independently.

with ^G : forbidden volume associated to the I center, R f and R' : the initial formation rate of F+ and F centers respectively, and Ro : the residual formation rate for F centers in the forbidden volume.

The F center kinetics in zone I1 show that there is a residual formation rate in the forbidden volume.

The 112-power law observed in zone I11 is consistent with this assumption, if we expect in zone I11 an impor- tant role of the decorrelated recombinations of Frenkel pairs, as in the case of temperatures where only the interstitials are thermally mobile (e.g. LiF at room temperature, KBr at 77 K) [17-191, due to the range of the dynamic crowdion in the lattice when an interstitial is formed. So, following [17-191, we must have

where OF, a, are respectively the capture cross section of the interstitial by an F center and a interstitial aggregate (number n(T)). From data given in zone I1 and I11 and the assumption that the concentration n(T) is about lo1* ~ m - ~ , i.e. that all H centers at satura- tion are nucleation germs, we find a,/a,

-

is not very different from the ratio of the geometrical sections of H, and F centers.

DISCUSSION Question. ^- N. ITOH.

Have you tried to obtain the growth curve at 20 K , where the I center is substantially unstable. Such an experiment would prove the validity of your model of the inhibition of the F-H creation in the vicinity of the I center.

Reply. - A. NOUAILHAT.

Yes, but not exactly in this manner : we compare the vacancy creation rate at 4 K for the same amount of vacancy concentration in KBr irradiated in 4 K o r with a previous irradiation at 77 K. They are

different in the second case, the creation rate is about the same as for the original crystal. This confirms the role of I centers.

Question. - F. AGULLO-LOPEZ.

You are assuming that all defects are thermally stable. However, I am wondering whether defect mobility could occur under irradiation and lead to defect reactions and annihilation.

Reply. - A. NOUAILHAT.

N o ; I have no evidence of mobility of defects occurring under irradiation at 4 K.

References

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