Investigations on inhomogeneous impurity distribution caused by growth centers

Journal of Crystal Growth 15

(I 972) 243-248

C, North-Holland Publishing Co.

INVESTIGATIONS CAUSED

ON INHOMOGENEOUS

BY GROWTH

IMPURITY

DISTRIBUTION

CENTERS

L. MALlCSK6 and L. JESZENSZKY Instilute

forExperimental Physics, Technical Unioersity, XI. Budafoki at 8, Budapest (I 121, Hungary

Received 24 March 1972; revised manuscript

received 28 May 1972

Small and flat hills consisting grown from solutions. Our tribution of the impurities metric method,suitable for ured on KC1: Ph 2c doped

of atomic or polyatomic layers can often be observed on the crystal faces earlier work has predicted that in the surroundings of such growth hills, the disincorporated into the crystals would be inhomogeneous. Using a spectrophotomicroanalysis, the expected inhomogeneous impurity distribution could be meassingle crystals grown from solutions.

In the present paper some investigations are reported, the results of which prove experimentally the existence of inhomogeneous dopant distribution around growth centers of solution grown KCl:Pb”’ doped single crystals.

1. Introduction In our earlier paper’) it was shown that under certain conditions the growth-rate dependence of the concentration of tin or lead dopants incorporated into KC1 crystals grown from aqueous solutions could be well approached using Chernov’s equations’) obtained by theoretical considerations. These equations contain the thickness of the growth layers as a constant parameter. From the literature it is known that on the faces of crystals grown from different mother phases and under very different circumstances, flat hills consisting of atomic or polyatomic layers can be observed. The centers of these hills seem to be sources of growth layers (“growth centers”)3-9). These growth centers are believed to be caused mainly by defects present on the crystal faces ‘O-l 3). Indeed, in the middle parts of

2. Experiments 2.1.

these hills, in some cases terraces of spiral contour could be recognized suggesting a dislocational origin3p6.8,9). The photomicrographs found in the literature have shown that the thickness of the layers belonging to a given growth center, varies generally from the middle point out. Thus, at a stationary growth of a crystal face, an inhomogeneity in the distribution of impurities incorporated into the crystal has to appear around the growth centers due to the dependence of the impurity concentration on the layer thickness. Such inhomogeneous impurity distributions may also play an important role in the formation of dislocations during crystal growth. 243

GROWTH OF KCI: Pb’+ DOPED SINGLE CRYSTALS

The crystals for investigations were grown in desiccators by evaporation at constant room temperature of aqueous solutions of KC1 doped with 0.05 or 0.10 mole% PbCl,. Pieces, about 10 x 1.5x 3 mm3, cleaved from a high purity, melt-grown KC1 crystal, and bordered by (100) cleavage faces were used as growth-seeds. The supersaturation of the solution, and thus the growth rate of crystals, were controlled by the size of the evaporation openings cut out on the covers of the closed crystallizing vessels. The solutions were not stirred during growth. In this way KC1 single crystals were grown with different growth rates in order of magnitude from 10m4 to 10m3 pm/set (see fig. la). 2.2.

OPTICAL INVESTIGATION OF THE GROWING FACES

The crystal faces were optically observed both during and after the growth. A few days after starting the growth process, one could observe growth hills consisting of fine concentric circular layers. The hills could be observed on the faces through a reading microscope or a magnifier, or even with unaided eye at a suitable illumination. After several more days the

244

I..

MALICSK6

AI\;D

L.

JESZENSZKY

Fig. 2. Sketch to the preparation of specimens from a crystal part including a growth hill. P, ~ seed crystal part, Pz part grown from solution. C ~~ growth center, r -~ radial distance.

tensively studied with a reflection optical microscope. Fig. I b shows a typical layer structure of a growth hill. The dark stripes, seen along the contours of the growth layers, appear due to relief effect. In the central area of the hill, below a radial distance of about IOe2 cm, no lamination can be observed. But, farther apart the layers are well recognizable, and the dark stripes become more and more wide. This suggests that the thickness of layers usually increases with the distance from the growth center. 2.3.

INVESTIGATION DOPANT

OF

THE

CONCENTRATION

RADIAL AROUND

DISTRIBUTION GROWTH

OF CEN-

7ERS

2

lb) big.

I.

(a) A photograph

of a KCI:Pb’

grown from aqueous solution, (100)

llat faces. (b) Layer structure

face of a KCI:Pb’ solution. Magn. 26

doped

doped

single crystal

by

(I I I) and mainly

of a grouth

hill on an (100)

and bordered single crystal

grown

from

aqueous

of the hills on the faces became already permanent. the arrangement of the layers became more remarkable, and a stationary growth of the hills respective the faces took place. After the completion of the growth process, the layer structure of the hills on the (100) “flat” faces was inspreading

3 I Pwparution

of’specitmws

Crystals which have at least one growth hill of about IO mm minimum diameter on one of the faces have been chosen for the investigation of the radial change of dopant concentration around growth centers. From these crystals small columns, about IO x 3 x I mm3, were cleaved out through the hill centers as shown in fig. 2. Then the columns were split along the length axis into about 0.5 mm thin small plates. The radial distances of the middle points of these volume-elements from the hill centers were determined under an optical microscope. The dopant concentrations in these small specimens were measured using a polarographic’ ) and a spectrophotometric method. 2, 3 2. Sprc~tsopitotott~etric~ c~oncmtratiotts

For the determination cimens, the sodium-salt

tktertnitxitiott

of’ tltc rlopwtt

in the spwitttcns

of the lead content of the speof 4-(2-pyridil-azo)-rezorcynol

INVESTIGATIONS

ON 1NHOMOGENEOUS

IMPURITY

DlSTRlBUTlON

CAUSED

BY GROWTH

CENTERS

245

(shortly: PAR) was used as a reagent14.15). A 0.05:4 PAR-salt solution made with CO,-free, twice distilled water was used as reagent solution. In alkaline buffers of 10.0 pH the sodium-salt of PAR forms water soluble, orange-red complexes with lead. The buffer system of boric acid-sodium hydroxide was made as usual’4,’ 6). The pH-values were measured with an electronic titri-pH-meter of type OP 401/l Radelkis, Hungary, using a combined glass electrode. Calibrationof thespectrophotometer. From Pb(NO,), of analytical grade a stock solution of 2.000 mg Pb/ml was prepared. Adding 2-3 ml buffer solution and then 0.800 ml reagent solution to the original or already diluted stock solution of some tenth ml in a 10.0 ml flask, this mixture was diluted with further buffer solution to the end volume. Thus, twelve orange-red calibration solutions of exact lead contents between 0.2 and 7 pg Pb/ml were made. The extinctions of these calibration solutions were measured in comparison with the extinction of a rejkrence solution, a lead-free, lemon-yellow buffer solution containing the same reagent concentration as the calibration ones. For the measurements a spectrophotometer of type Spectromom 202 (MOM, Hungary) was employed. The extinctions were measured in the range between 480 and 560 nm at room temperature with an error of max. ,504. The peak, characteristic for lead, appeared at about 519 nm. According to the Lambert-Beer law, the maximum extinctions E were proportional to the lead concentrations C: E = &C,

(1)

where E is a constant. For E it was obtained: E = (0.173 kO.008) ext. unit ml/pg Pb. From this value the molar extinction coefficient could be calculated : (3.58 f 0.17) x lo4 ext. unit liter/g-ion Pb. The solutions prepared from the crystal specimens evidently contain also potassium chloride, besides the lead. Therefore, it was checked whether the big surplus of KCl, as compared to the amount of lead, influences the extinction values. For this aim calibration solutions, containing also KC1 in different amounts, were prepared, and their extinctions were determined using the above reference solution. At the same lead concentrations, the extinction values of the solutions containing KC1 agreed with those of KCl-free solutions within

6

2

i- L-mn~4 Fig. 3. The radial concentration distribution of dopants around growth centers in crystals grown from solutions doped with 0.10 moleoh Pb, and grown with different normal rate measured in units of 1O-4 pm/set: (i-) 2.9; (.?) 3,9; (II) 5.2; (x) and (I-) 5.7; (0) 40 (dopant concentration in solution: 0.05 molea< Pb).

k3 x 10m3 extinction unit, about the allowed limit of error for our spectrophotometer. In practice, the different KCl-concentrations of solutions for measurement did not seem to disturb the exact determination of the lead content of the crystal specimens. Determination qf’ the lead content in crystal specimens. The crystal specimens in 10.0 ml volumetric flasks of known mass were weighed with an accuracy of f I x lo-’ g. The specimens were then dissolved in 2-3 ml buffer solution at room temperature. After adding 0.800 ml aliquots of PAR reagent solution they were diluted with buffer solution to the end-volume of 10.0 ml. Using the known equation (I), from the extinction values of these solutions the concentrations of lead dopants incorporated into the crystals could be determined. 3. Results The spectrophotometric studies showed that around growth centers, the concentration of lead dopant in KC1 crystals is not uniform in the radial direction. The results obtained on crystals grown with different growth rates are presented in fig. 3. The curves have a typical course. Going out from r = 0, the concentration of lead dopant increases. After arriving at a maximum at about r = l-2 mm, the dopant concentration falls down to a constant value. The rising parts of the curves

246

I..

MALICSKh

Y

2 Fig. 4.

of (I/b’)

The data of the In [CC,-B’,)/S’,]

7 lmml

measurements

AND

1.. JESLENSZKY

-6

4

of tig. 3 plotted in terms

versus r. The

marks

correspond

to

those in fig. 3.

Fig. 5.

The Pb-concentration

of the normal

growth

uithin

(b) Mith the data from our earlier

only by one or two points of measurement in each case. The explanation is that specimens of thickness smaller than about some tenth of a mm could not be prepared. It can also be seen that the constant levels, corresponding to the average dopant concentration in crystals, become higher and higher with the increase of the growth rate. Lt turned out that the decreasing parts of the curves in the range of distances r greater than l-2 mm, can be approached by an equation of the form: are marked

C,(r) = B; + B; exp ( - D’r),

(2)

where B;, B; and h’ are constants. To prove this the results of measurement of fig. 3 were now plotted in terms of (l/l,‘) in [(C,-s;,/u;] versus r in fig. 4. According to eq. (2), all the points belonging to measurements on different crystals fit to a straight line of 45”. 4. Discussion In order to analyse the relation between the average thickness of growth layers and the dopant concentration within the crystal, it is reasonable to start from the results of an earlier work of ours’): It was shown in this paper that under certain restrictions the growth rate dependence of the average concentration of lead, respectively tin dopants incorporated into KCI crystals

KCI crystals as a function

rate. (a) with the data of the prcscnt paper: work’).

during their growth from solutions can be well approximated by the equation derived theoretically by Chernov2). For two limiting cases, the mentioned theory gives relationships between the dopant concentration and the growth rate of crystals in the following forms used earlier by us: if I‘ < D//I, then C’,(c) = C,-t(C‘,

il -C’,)

41)

2

( i

+tc,-C,)

h+

I’

/I 4D’

(3)

and if 179 Dih, then c‘,(P)

=

C’, +

i’

c, ,7 -(C,,-cc,

pD.

(4)

I’

Here: within the C,(G) = the average dopant concentration crystal grown with normal growth rate L’. in a growth layer c, = the dopant concentration freshly deposited, in a surc, = the equilibrium dopant concentration face film of thickness /. dopant concentration inside c, = the equilibrium the crystal, D = the diffusion coefficient of dopants inside the crystal, p = a velocity coefficient for the exchange of dopant particles between the crystal surface and its surroundings, /I = the thickness of a growth layer.

INVESTIGATIONS

Using

ON INHOMOGENEOUS

the results of the present

IMPURITY

investigations,

DISTRIBUTION

seen

in fig. 3, it was found that in the range of growth rate u = (l-7) x 10e4 um/sec, the average concentration of lead dopants within the KC1 crystals C, is approximately proportional to the growth rate according to eq. (3). But, in the range v = 4 x 10e3-2 x 10m2 um/sec, as it was shown in our earlier work’), eq. (4) is satisfied (see curves a and b in fig. 5). In the case of a selected growth center on a given crystal face grown stationarily, the normal growth rate can be considered as a constant for the whole growth hill. But, as the optical observations in section 2.2 suggested, the layer thickness varies radially on the growth hill. Consequently, the layer thickness can be considered as the parameter which may determine a radial distribution of the dopant concentration around a growth center. Introducing the following terms: D

E A* .= const.,

V

c, + (C, -

C,)

lo 40

+

&

(Cl -C,)

C, -(C,

const., (5)

I.

;D =

(Cl -C,)

s A, =

A, = const.,

- C,) @! = B, = const., V

C,i

3

B2

=

con&,

eqs. (3) and (4) and their corresponding conditions can then be transcribed into the simple forms showing explicitly the dependence of the dopant concentration on the layer thickness : if I2 < h”, then C,(h) = A 1+ A,It ;

(6)

if h S h*, then C,(h) = B, + q.

(7)

Going out from the center of a hill the layer thickness 17 increases steadily with the radial distance r. At the same time, according to eq. (6) the dopant concentration C, also increases. But, in a certain vicinity of h* the eq. (6) is no more valid. Above this critical value the eq. (7) will be satisfied, and the dopant concentration shows a decreasing course. This was demonstrated on the curves of fig. 3 where the critical thicknesses may lie at the radial distance r* of about l-2 mm corresponding to the places of the peaks. As compared to the relation (2), found experimen-

CAUSED

tally for the decreasing

BY

GROWTH

CENTERS

247

leg of the C,(r) curves shown in

fig. 3, with eq. (7), a relation of the form 17 = h, exp (b’r) can be derived for the radial change of the layer thicknesses. Here B,/B; is marked by h,. This relation makes it possible to draw some conclusions with regard to the origin of the growth hills. According to the measurements, the constants b’ in eq. (2) have values of about 0.8 mm- ‘. Far from the hill centers, about r = 5 mm, the layer thicknesses, which could already be measured directly through a microscope, amount to some urn. From these data the thicknesses /I,, of the layers close to the hill centers can be estimated at about 10e6 cm. This value is greater than the value of the Burgers vector of the screw dislocations usual in alkali halide crystals. It is reasonable to think that the growth hills observed on the crystal faces are caused by special groups of dislocations located close to the hill centers. Central areas without visible lamination, about 10m4 cm2, could microscopically be observed at the growth hills. The dislocation density in the crystals, determined by etching, was about lo6 cmp2. Thus, the number of dislocations in these central areas may in average have been about 102. Provided that each dislocation contributes an atomic layer of lo- * cm thickness to the growth layers formed collectively by the group of the “central” dislocations, then a thickness of about low6 cm can be calculated for h,. The value of h, obtained above and that estimated on the basis of the dislocation density, are in acceptable agreement. Consequently, some previous opinions on a defect origin, especially a dislocational origin, of growth hills seem to be supported also by the results of the present paper. It has been proved that, according to our theoretical expectations, around growth centers an inhomogeneous distribution of dopants is formed within the crystal, as a consequence of the radial change of the thickness of growth layers. The authors hope that on the basis of the present results some information can be obtained in connection with the formation of new dislocations during the growth process of crystals. Investigations in this direction are in progress. Acknowledgment

The authors would like to thank Dr. Kund Raksanyi for his valuable advice in connection with the spectrophotometric analysis. The manual help of Miss I. Bathes and Mr. A. Janosi is gratefully acknowledged.

248

L.

MALICSKi)

ANI)

L.

JESZENSZKY

8) L. Malicsk6,

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