Defects in CdTe bridgman monocrystals caused by nonstoichiometric growth conditions

j...... o, C R Y S T A L GROW T H

Journal of Crystal Growth 128 (1993) 582-587 North-Holland

Defects in CdTe Bridgman monocrystals caused by nonstoichiometric growth conditions P. R u d o l p h , M. N e u b e r t a n d M. M i i h l b e r g Institut fiir Kristallographie und Materialforsehung, Fachbereich Physik, Humboldt-Universitiit zu Berlin, Invalidenstrasse 110, D-O-1040 Berlin, Germany

The stoichiometry of the Cd/Te melt composition for the Bridgman growth of CdTe in an evacuated and sealed ampoule is critically evaluated. It is determined by the accuracy of the initial weighing and a remarkable Cd loss in the vapour phase. Experimental results on Te inclusion and precipitation will be given. Size, density and axial distribution of inclusions and precipitates are correlated to the nonstoichiometryof the melt.

1. Introduction At present, the vertical Bridgman method is most convenient for growing single crystals of CdTe and related compounds [1-7]. In order to achieve high resistivity and infra-red (IR) transmission an exact stoichiometry control is advantageous. This will be complicated by the incongruent vaporization of CdTe melts. In sealed ampoules, the free space over the melt will be filled up with Cd gas. Simultaneously, the melt composition changes to a higher Te content. The present paper deals with a semi-quantitative estimation of melt composition variations and their consequences caused by a predominant Cd loss. Cd loss or Te enrichment causes two processes: (i) emergence of inclusion of Te-rich melt droplets (particles > 1 /zm in diameter) and (ii) precipitation of Te (particles 0.01 to 0.1 ~ m in diameter). The axial distribution profile of the total amount of included/precipitated Te excess was observed by I R transmission microscopy (i) and extinction spectroscopy (ii), respectively. It will be shown that growth from nonstoichio-

metric melts reflects the shape of solidus and liquidus lines near the congruent melting point.

2. Melt and vapour composition in closed ampoules Principally, the crystal growth of (semiconducting) compounds in sealed ampoules without any vapour pressure control is influenced by variations in the melt composition. Firstly, corresponding to the formula Cd0.5_,~yTe0.5+,Sy, a deviation 6 y may arise due to weighing errors preceding the CdTe synthesis. Thus, the resulting Te excess N w in atoms per cm 3 becomes N w = 2 6 y N o,

(1)

with N O= 1.47 x 10 22 c m -3, the number of Te atoms in stoichiometric CdTe. Secondly, the melt composition will be influenced by the formation of a gaseous phase over the melt. A nearly stoichiometric melt of CdTe evaporates incongruently at about ll00°C [8]. The different vapour pressures of Te 2 and Cd indicate that the vapour

0022-0248/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved

P. Rudolph et a L / Defects in CdTe Bridgman monocrystals caused by nonstoichiometric growth

phase established over the C d / T e melt consists to about 96% of Cd atoms. Using the Perfect-Gas Law, the concentration of excess Te atoms per cm 3 (Ne) in the melt caused by Cd evaporation becomes PcdNA hv Ne-= R T h e

583

Summarizing the above considerations, melts for conventional Bridgman growth exactly adjusted in stoichiometry can only be obtained taking into account the free volume in the ampoules.

(2)

with PCd the cadmium partial pressure, NA Avogadro's constant, R the universal gas constant, temperature T and h v / h L the ratio of the length of melt and free volume inside the ampoule (column 4 in table 1). For growth conditions (1100°C) the Cd partial pressure is roughly 105 Pa [9]. Thus, resulting Te excess caused by Cd loss is in the order of magnitude of N e ,-~ 5 X 1018 h v / h L c m - 3 . In practice, the values of the length ratios lie between 0.3 and 2, what results in Te excess concentrations of about 1018 to 1019 cm -3. This is a variation in melt composition not to be neglectable. Its order of magnitude is the same like that caused by weighing errors. Therefore, the total deviation from the exact stoichiometry of the melt Ntot becomes the sum of weighing errors N w and Are (Cd loss). Calculated values of Ntot are given in column 5 in table 1.

3. Segregation of the tellurium excess

Fig. 1 shows the T-y projection of the Cd-Te phase diagram in the vicinity of the congruent melting point. The figure has been drawn by means of data from our own and those of other authors, presented in ref. [8]. However, it must be noted that this figure must be considered to be largely tentative due to the uncertainty of thermodynamical data in such a narrow range (between 10 -4 and 10 -2 at%). The shapes of liquidus and solidus curves indicate that growth from Te rich melts always will be accompanied by Te segregation. A tentative equilibrium segregation coefficient k has been calculated from solidus and liquidus data (fig. 1). As can be seen k depends sensitively on growth temperature and Te excess concentration. Such variations of k may cause an increasing tendency for morphological instability at the phase boundary during growth.

Table 1 Compositional variations and free carrier concentrations in CdTe crystals grown from nearly stoichiometric and nonstoichiometric melts Sample number

Starting charge composition Cd0.5_~yTe0.5+~y

hv -hL

Total Te e x c e s s Ntot in melt resulting from 6y (eq. (1)) and Cd

Te excess in tip region of crystal estimated

Measured free carrier concentration (300 K) at different normalized

evaporation obtained from eq. (2) (cm 3)

from fig. 2 (cm -3)

axial positions g (cm 3) g = 0.2 g = 0.9

Deviation from stoichiometry 6y

Corresponding Te excess (eq. (1)) Nw(Te) (cm-3)

(1)

(2)

(3)

(4)

(5)

(6)

(7)

BG 10 BG 20 BR39 BR48 BG 14 BR27 BR29/2 BR 28/2 BR41

0 0 +607<10 +8×10 -2×10 -3×10 -23×10 -52x10 -lXl0

0 0 +1.8×1019 + 2 . 4 x 1018 - 5 . 9 × 10 w - 8 . 8 X 1017 _6.8×1018 - 1 . 5 x 1019 -2.9×1017

0.05 0.75 1.0 1.1 1.7 1.5 1.1 1.1 0.15

+2.6×1017 + 3 . 8 x 10 is + 2 . 3 × 1019 +8.0×1018 + 8 . 1 × 1 0 TM + 6 . 8 × 1 0 TM - 1 . 2 x 1 0 is - 1.0× 1019 +4.8X1017

+2x1017 + ( 2 - 5 ) × 1017 + ( 2 - 9 ) × 1017 + ( 2 - 8 ) × 1 0 I7 + ( 2 - 8 ) × 1017 + ( 2 - 7 ) × 1017 +0 -5×1016 +(2-3)>(1017

p = 7 × 1015 p=lxl014 p = 2× 1015 p = 1 × 1016 p = 6 × 1 0 1 5 p = 2 x 1016 p = 3 × 1 0 1 5 p = 9 × 1015 p = 1 x 1016 p=l×1015 p = 2 × 1016 p=2×1015 p = 3 x l 0 is n=5×1013 p = 3 × 1015 n=9×1014 p = 2 × 1 0 1 4 p ~ 8 × 1015

.5 .5 -5 -5 5 -s -5

(8)

P. Rudolph et aL / Defects in CdTe Bridgman monocrystals caused by nonstoichiometric growth

584

1100 ~ 1090

kcd i n CdTe

S - solldus L - liquldus -

1080

; 1o,o " lOZO

lOlO 1000

-

":

"t'#~ -- -- -- " ~ .~ /

W lO,O

stotch. ] I Ic m NBR41 / iI ~ ' tel: .J ' > ~ ' , ~ ' ~ - -

"

It

"

• lr/'2 /

I:/ I:/ t/ •

,,s21!

10_¢

I

kcd

I

10 -3

,

%T,~ ;s,

-.

_

kTe i n CdTQ

_,_

- -

I%

_*

,

I/ [

t ~' I

~ v II ~ " r II

~,

!

]

t

*~

f/ fll

:"

sit

",,,j.":o,

I I;~i~.<- -"~,.~..~ -

,

~I1~

BR39" "

I~1

1022

'

,

1

1020

Cd excess,

I

J tl

1018 cm -3

i

1016:1£)16 CdTe

~1I [ I I t .

I

I,:~:.t

i

1018

I~

1020

To excess,

I

1022 10

cm -3

I

I

I ~1

,f ,.~:A 10 -2 10 .4

kTe

Fig. 1. T - y projection of the Cd-Te phase diagram in the vicinity of the congruent melting point and estimation of corresponding equilibrium segregation coefficients. L]-L~ and S l - S 3 are liquidus and solidus curves, constructed after data of different authors: (A) Albers-De Haas; (zx) De Nobel; (©) Medvedjev; (D) Zlomanov; (~7) Grinberg; ( + ) Lorenz; ( × ) Khariv; (<>) own data (DTA); (Q) present paper; complete citations are given in ref. [8]. 4. E f f e c t s r e l a t e d to t e l l u r i u m e x c e s s

Solidification from slightly Te rich melts resuits in the generation of two different kinds of crystal imperfections: (i) Inclusions are assumed to originate due to morphological instabilities at the growth interface. Te-rich C d - T e melt will be captured from the diffusion layer in front of the interface. Therefore, the appearance of inclusions mainly depends on the relation between growth rates and temperature gradients at the interface (Tiller). Typical diameters of such inclusions are 1 to 2 / z m , but diameters up to 10 or 2 0 / z m have also been observed [%10-12] (see also fig. 2). In general, the presence of inclusions is an indication for nonstoichiometric growth conditions. (ii) Precipitates are released due to the retrograde slope of the solidus line towards lower temperatures. Precipitates are formed via condensation of Cd vacancies. If the precipitation process goes nearly to completion, it means that more than 90% of the Te excess will be precipitated; the precipitated amount of Te is equal to the maximum solubility of Te in solid CdTe near the melting point. Less than 100 s are estimated

to be the diffusion time needed for nearly complete precipitation at about 700°C (average precipitate distance 100 nm [1,14]). Thus, for current

10~6

-

precipitates

--~101'

. ~ ~ T l e o Te =?xcess Icm"3]

~1o", =

\

~10 ~

10e

1o

i )ji

10.3

" 77,(:,~;"

ld'

10-2 10"~ diameter of Te particles, ~Jm

10

Fig. 2. Comparison of size and densities of Te inclusions and precipitates in CdTe crystals grown from nonstoichiometric melts. Both kinds of imperfections are clearly separated.

P. Rudolph et al. / Defects in CdTe Bridgman monocrystals caused by nonstoichiometric growth growth conditions complete precipitation is guaranteed. The estimation is based on Cd tracer coefficients taken from [13]. It has to be noted again that inclusions and precipitates are considered as two completely different kinds of crystal imperfections in their generation mechanisms (see also section 6 and fig. 2). Assuming precipitates and inclusions to have spherical geometry, the total Te excess per cm 3 represented by them can be calculated as 4"n'PTeN A NT~ =

3ATe

Y'~ ri~Pi, i=1

585

6. Results and discussion

Various experimental and calculated data are compiled in table 1. Deviations from stoichiome-

(3)

with r~ the radius and Pi the density of the precipitates/inclusions, AT~ the relative atom mass of Te and PT~ the mass density of Te. The index i stands for each class of particle diameter.

a

5. Experimental procedure |

CdTe single crystals have been grown by the conventional vertical Bridgman method without an additional Cd source. The material has been synthesized using triply-distilled 6N Cd and zone-refined 6N Te, dropped under pure hydrogen atmosphere into carbon coated ampoules. Growth runs were carried out with material containing various amounts of Te or Cd excess as well as different h v / h L ratios (columns 2 and 4 in table 1). Crystals were grown with a growth rate of about 1 m m / h and a t e m p e r a t u r e gradient of about 8 K / c m . Finally, crystals were cooled to room t e m p e r a t u r e with a rate of about 20 K / h . For the following analysis, the crystals were cut into slices, lapped and chemomechanically polished. The distribution of Te inclusions was studied by I R transmission microscopy resolving particles with diameters down to 1 /xm. The free carrier concentration has been determined by means of Hall measurements as well as by I R extinction analysis [14]. Precipitates have been detected from the energy dependence of the scattering cross section [14].

e

®

|

b

11111 u ~h

l¢

C ~

.

%

_ ~Y~

"E

_

m u lU-lku'~kl Icbt

Fig. 3. IR transmission microscopy photographs of slices of crystal BR 41 taken from top, middle and end of the crystal (from top to bottom).

586

P. Rudolph et al. / Defects in CdTe Bridgman monocrystals caused by nonstoichiometric growth

try 6y and different ratios h v / h L are listed in columns 2, 3 and 4. Multiplying the total Te or Cd excess in the melt (column 5) with the corresponding values of the distribution coefficient k taken from fig. 1 yields the first-to-freeze Te excess concentration in the beginning of the crystals (column 6). It can be seen that variation of h v / h L is not a convenient method for influencing the deviation from stoichiometry. Rather, it must be done by scaling the starting material. Almost stoichiometric material, for instance in ampoules with h v / h L = 1, will only be obtained using starting material with a Cd excess of about 3y = (2-5) × 10 -4 (see BR 2 9 / 2 in table 1). Such crystals show excellent transmission behaviour and are almost inclusionfree. On the other hand, using Te-rich melt compositions, inclusions and precipitates are generally found (figs. 3 and 4). Distinction between precipitates and inclusions may be done by means of fig. 2. Size and density of precipitates differ from those of inclusions by orders of magnitude. Experimental data are clearly separated into two crowds of points which are related to the two different generation mechanisms as discussed

-

............... N~"

IR Sg Nto t

-

× -=

above. Accidentally, both mechanisms reflect the same order of magnitude of Te excess. Te excess arising from both precipitates and inclusions shows axial concentration gradients (for inclusions, cf. fig. 3). An analysis of the Te excess distribution is shown in fig. 4a (with respect to inclusions) and in fig. 4b (with respect to precipitates). The axial distribution of the Te inclusions may be explained rather with increasing morphological instability than with a segregation effect (cf. sections 3 and 4). The enrichment of the melt with Te during growth is reflected in a higher total Te amount captured at the growth interface. On the other hand, precipitation is found to be independent of initial Te excess greater than 10 m cm -3 (compare fig. 4b and columns 5 and 6 in table 1). For example, crystals BR 39 and BR 41 differ strongly in their starting melt composition, but show roughly the same amount of precipitated Te. This is not surprising because the amount of precipitated Te depends only on the shape of the solidus line (fig. 1), which represents the maximum solubility of Te in CdTe. In crystals grown from melts with small deviation from stoichiometry (BR 41), the axial distribution of the precipitated Te excess can be simply approxi-

•

X

X

0

bm 9

........... Pfanndistribution

X

function with k-0.015 (BR 39)

BR39 BG4

.....

"'

1

withk-O.52(BR41) / ,'"" / ,/ ./ . - ' " BR39/

| .............. ~ S ~~ ~*t ~ ~ NBR 445~ t

®

~"

~ Teprecipitates

ld' a

0

.

0.2

.

.

0.4

.

0.6

0.8

0

I

[

I

I

0.2

0.4

0.6

0.8

solidified fractiong Fig. 4. Axial distribution of the Te excess in CdTe crystals calculated after (3): (a) IR transmission microscopy analysis (inclusions) and (b) IR extinction analysis (precipitates).

P. Rudolph et al. / Defects in CdTe Bridgman monocrystals caused by nonstoichiometric growth

mated by Pfann's distribution function with a constant distribution coefficient k. For melts with high stoichiometry deviations (BR 39), such a fit is not successful, possibly because of variable values of k. Looking at fig. 1 (BR 41, BR 39) in contrary to other authors, the maximum solubility of Te in CdTe is obviously about 5 X 1017 cm -3. Electrical data of first and finally grown regions of the crystals are listed in columns 7 and 8. Free carrier concentrations were determined by Hall effect measurements and IR transmission analysis [14]. Obviously, concentrations at g = 0.9 are roughly the same while at g = 0.2 they differ by orders of magnitude. As shown in ref. [17], in the first grown parts of highly purified CdTe Bridgman crystals, extrinsic donors and acceptors mostly compensate each other. Thus, in this region the resulting carrier concentration is dominated by native point defects (Cd vacancies at the Te-rich side, or Te interstitials at the Cd-rich side, respectively). For present investigations, the concentrations of free holes and electrons do not exceed values of p = 6 × 1015 (BR 39) and n = 9 x 1014 (BR 28/2) which is related to the solution limits of native point defects and actual diffusion kinetics. The last-to-freeze region is dominated by residual acceptor impurities, the concentration of which exceeds that of donors and native point defects due to remarkable segregation [17,18].

Acknowledgement This work is supported by the VolkswagenStiftung under contract No. 1/65 988.

587

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