Phase diagrams and crystal growth of pseudobinary alloy semiconductors

, ~urnalofCrystal Growth 13/14 0972) 657-~662 © North.Holland PubUshtng Co.

657

PHASE DIAGRAMS AND CRYSTAL GROWTH OF PSEUDOBINARY ALLOY SEMICONDUCTORS* JACQUES STEININGER** and ALAN J, STRAUSS

Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts 02/73, U.S.A. The ternary Zn-42d-Te and pseudobinary CdTe-CdSe and PbTe-PbSe phase diagrams have been determined by thermal and X-ray analysis and analysed in terms of thermodynamic theories of liquid and solid solutions. The phase diagram data for two of the investigated systems has then been applied to the selection and application of two different techniques for growing pseudobinary alloy crystals: diffusional freezing and solution zoning,

1. Introduction The development of techniques for growing alloy crystals from liquid solutions m-*) has created a need for comprehensive and precise thermodynamic data, especially phase diagrams of liquid-solid equilibria in pseudobinary and ternary systems. The principal methods used for the determination of liquidus and solidus data (thermal analysis, metallographic or X-ray analysis of quenched samples, and determination of segregation coefficients) are non-equilibriumtechniques and may be subject to significant experimental errors. These errors are usually difficult to detect from thermod:/namic first principles because of our limited understa~ading of non-ideal solutions and because of the p .)city of basic thermodynamic data for many of these s, terns. this communication is concerned with the deterr, ~ation of the ternary Zn-Cd-Te and pseudobinary t Fe-CdSe and PbTe-PbSe composition-temperature 'se diagrams by thermal and X-ray analysis, The dting phase diagrams have been analyzed in terms < hermodynamic theories of liquid and solid solut )s. This led in particular to the development of a t method for the calculation of the liquidus-solidus , in homogeneous, monotonic alloy systems. The p tse did.gram data for two of the investigated systems, Z: -Cd-Te and CdTe-CdSe, have also been applied to * ['his work was sponsored by the Department of the Air Force. *~ Present address: Arthur D. Little, Inc., Cambridge, Massachusetts 02140, 12.S,A.

the selection and application of two different techniques for growing pseudobinary alloy crystals: diffusional freezing and solution zoning.

2. Phase diagrams 2.1. EXPERIMENTAL

The liquidus and solidus curves for the pseudobinary CdTe-ZnTe, CdTe-~CdSe and PbTe-PbSe systems (fig. 1) and the liquidus surface for the ternary Zn-CdTe system (fig. 2) have been determined by thermal analysis of high purity liquid and solid alloy samples in a specially constructed D.T.A. apparatus~-~). Particular attention was paid to thorough homogenization of both the liquid and solid samples by prolonged annealing at high temperature for periods of up to two weeks. The liquidus or solidus temperatures for noncongruently melting compositions were determined exclusively from the initial thermal arrests either on cooling or heating curves at slow rates of 2 °C/min. The accuracy of the thermal arrests was estimated to be better than + 1 °C for the liquidus curves and about _+2 or 3 °C for the solidus curves. The sub-solidus boundaries of the cubic and hexagonal phase fields in the CdTe-CdSe system have been investigated by X-ray analysis of annealed and quenched powder samples in the temperature range of 800 to 1050 '>C°). 2.2. RESULTS The CdTe-ZnTe and PbTe-PbSe systems show typ-

X I I I - 10

658

JACQUES STEImNG~R AND ALAN J, STRAUSS

k'l~ ........ I I

i ....i - i

~

I ..... I

I

';i uoo,o

w

i

"

ne 100¢ W

a. t~0

:S tlJ I--

SOLID - CUBIC_.I. .....

[ ....

CdTe

I ....... l ......

02.

I

I

G4 11~

I

~s

I

I

I

oJs I

............ j ...... i"

ZnT~.

1I ~

CdTe 01;~

I ...... i .... I "

I

I

0.4

I 0.6

I

I

1

O.S CdSl

l -

g w

E

_ , , , ~ ~

SOLI O

I .....1 _

l~

.,

I

o). 1 o!.

.sJ

MOLE FRACTION PbSe Fig. 1.

Phase diagrams o f the CdTe-ZnTe, C d T e - C d S e and PbTe-PbSe pseudobinary systems,

ical lens-shaped phase diagrams with sublinear variations in t~mperature with composition and relatively narrow liquidus-solidus gaps (fig. 1). The CdTe-CdSe ~ystem presents almost the same type of liquidus-soliJ

/E 3 (:)66 *C)

P~(324*C} /

(42z °c)

CdTe

ZnTe

009~_ °C)

(!290 °C }

E( (449"C)* ~

3. Thermodynamics

1.2(44"? oC)

3,1. PSEUDOBINARYSYSTEMS

Te (4495"c.,} Fig. 2.

dus pha~se diagram with a degenerate eutectic near 20 mole % CdSe. The narrow cubic-hexagonal 'wo. phase region inside the solidus field shows incre~ ~ing stability of the hexagonal phase with increasing emperature. The ternary liquidus isotherms in the Zn-Cd-T~ ~ystern (fig. 2) show a smooth variation in liquidus ~mperature between the binary Cd-Te and Zn-Te sys ms. The liquidus surface is strongly asymmetric with h her temperatures on the metal-rich side. The mark( it]crease in temperature along the pseudobinary ( re~ ZnTe composition line is attributed to ordering the liquid phase resulting from the strong interactio~ be. tween chalcogen and metal atoms.

Pbdse diagJ'am of the Zn-Cd.-Te ternary system.

The experimental ]iquidus and solidus data li ,' the

X I I I - 10

'~ :PHASE DIAGRAMS AND CRYSTAL G R O W T H OF PSEUDOBINARY ALLOY SEMICONDUCTORS TAnt~ 1 ifferenee between partial excess free energies of mixing in solid ,d liquid phases for binary and pseudobinary alloy systems System

Mean D (kcal/g-at)

Standard deviation (kcal/g-at)

--0~040

0.252 0.272 0.486

CdTe-ZnTe COTe-CdSe PbTe,-PbSe

+0.168 + 0.099

:tee pseudobinary systems have been used to calculate ,e values of the difference D between the partial excess t, ~e energies of mixing in the two phases o=

xT,

'

from the general a) liquidus-solidus equation:

659

tion of crystal growth techniques from non-stoichio. metric solutions, can be prohibitively time-consuming and prone to excessive experimental errors. Attempts have therefore been made to develop models of liquid solutions, that can provide a better understanding of these systems and can be used to calculate the ternary phase diagram data from the more easily determined and more reliable thermodynamic data of binary and pseudobinary systems. Preliminary results 9) however indicate that theoretical models based on physical or chemical concepts of the liquid phase (such as the regular, quasichemical, regular associated or non-random two-liquid solution models) fail to give a satisfactory representation of the strong physical interactions even in the binary systems. More consistent results however can be obtained with several empirical thermodynamic expressionsg).

4. Crystal growth

--

(l-

-Au, (,-

-o.

As shown in table 1, the values of D are remarkably small. This result has also been obtained for a large number of binary and pseudobinary systems which exhibit complete miscibility in the two phases and monotonic variations of the liquidus and solidus curvesa). It is attributed to the relatively limited (but not negligible) deviations from ideality in these systems. For this type o!"system, the ideal liquidus-solidus equation where D ib neglected can therefore give a good approximation c ~the relationship between equilibrium concentrations i, the two phases. This ideal equation is of particular i crest for the calculation of one of the boundaries of t : two-phase region (solidus or liquidus) when the ~er one (liquidus or solidus) and the enthalpies of ion of the terminal compounds are already known. 9ical applications a) include the prediction of one of two phase boundaries when experimental data are tvailable (such as for the ZnTe-ZnSe and HgTeTe systems) and the detection of thermodynamic int asistencies in published phase diagrams (Cu-Ni, I gs-lnP, HgTe-HgSe, PbTe-PbSe systems). 3 2. TERNARY SYSTEMS

the experimental determination of the ternary liquid,~s-solidus tie-lines, which are needed for the applica-

The major difficulty in the growth of homogeneous alloy crystals results from the differences in the equilibrium compositions of the liquid and solid phases, which lead to segregation during solidification and compositional variations in the grown crystals. 4.1. DIRECTIONAL FREEZING

Directional freezing of a liquid alloy solution under equilibrium conditions with complete mixing in the liquid phase results in the formation of solid alloy solutions of continuously varying composition along the growth axis. The theoretical profile shown in fig. 3 demonstrates the distribution for a constant segregation coefficient of 0.7. In reality, mixing is never complete and solidification proceeds under near-equilibrium conditions with a tendency to form a solute-rich boundary layer near the solidifying interface. As a result, the initial concentration gradient in the solid is even higher than that shown by the theoretical c~trve. If mixing is completely suppressed, the regime then becomes purely diffusional and the composition profile~°) takes the shape indicated by the curves 1, 2 or 3 corresponding to increasing values of the fi'eezing rate V. As indicated in fig. 3, it should be noted that the curves 1-3 for diffusional directional freezing are exactly similar to the more familiar profiles obtained for zone melting with progressively narrower liquid zones. These profiles are characterized by an initial transient

X l l l - !0

JACQUES

660

STEININGER

of steadily increasing solute concentration, a steady state region with a constant concentration equal to the initial melt composition and a final transient of rapidly increasing solute concentration. The region of constant composition is of particular interest for the preparation of homogeneous alloy crysTABLE 2

Constitutional supercooling in alloy systems

inca 1 - k

G V

Alloy system Ag-Au SnTe-PbTe CdTe-CdSe

CdTe-ZnTe HgTc-CdTc

InSb-AISb Co C, k m D ~' G

D

Cs

k

k

for Co = 0.50 0.49 0.40 0.40 0.35 0.19 0.05

m

G (>C/cm)

CC/mole fraction)

for V/D = I cm

90 110 186 210 600 270

0.9 13.7 23.2 45,0 490.0 1215.0

0.98 0.80 0.80 0.70 0.38 0.10

= initial melt composition, = solidus composition for Co = 0.50, = segregation coefficient, = liquidus slope, ~ diffusion constant in liquid, -: solidification rate ~= temperature gradient in liquid ahead of interfa:e.

I

Diffusional Freezing

Zone Melting 0

A N D A L A N I, S T R A U S S

tals. Its length can be increased at the expense at the two transient regions by increasing ,o) the rat~ of solidification V. In order to avoid constitutional su ,or. cooling however, it is necessary to maintain sufficie ~tly high values of the temperaturegradient G in the lh aid ahead of the interface. The minimum values reqt~ :ed for G in various alloy systems have been calcul ted from the phase diagram data using the familiar sin >li. fled relationship shown in table 2 for a conver..~nl numerical value of V/D = 1 cm, where D is the d l~u. sign constant in the liquid. For a typical valu< of D = 5 x 10- s cm2/sec, V is equal to about 4.3 cm, Jay which corresponds to commonly used rates of directional freezing. Table 2 shows that the minimum value of G is strongly dependent upon the values of the phase diagram parameters and can vary over more than three orders of magnitude for various systems. In contrast with most other crystal growth techniques, which strive to achieve near-equilibrium conditions, the use of directional freezing to obtain the diffusional profiles shown in fig. 3 requires the establishment of non-equilibrium conditions which may be difficult to maintain. In the present study, homogeneous cm-.~ize single crystals of CdTe-ZnTe alloys have been grown by directional freezing under conditions closely approx-

Q

®

V/D

t.O

5,0

J

4.0

0.2

@ t0,0

®

o.t

o ~o m

o

z o

z w z o

Directional Freezin9 with Complete Mixing

0.9

V: Rote of Freezing (cm/sec) 0,8

D: Diffusion

Constant (cm2/sec)

$,: Length of Molten Zone (cm) Co Initial Concentration

OTL o

Fig. 3.

L~K

i

!

2

I

l ..... 1 j . . . . . . . !. . . . . . . 4 5 6 ? DISTANCE ALONG GROWTH AXIS (cm)

3

i ...... 8

I, g

40

Theoretical composition profiles in directi,,>nal freezing of alloys; k = 0.7.

X i I I - 10

: P H A S E D I A G R A M S A N D CRYSTAL G R O W T H OF P S E U D O B I N A R Y ALLOY S E M I C O N D U C T O R S

0,70 INITIAL MELT °!°° /COMPOSITION

i[

I

0:50 i

o

i

a*o

.... !i:~:'~....

°1

F i NA L TRANSIENT

< .~ 0.30 cc z

- INITIAL ~ S T E A D ~ I TRANSIENT STATE

0.20 I 0.1¢J

o

Fig, 4. alloy.

t.O Z.O ~.0 DISTANCE ALONG GROWTH AXIS (cm)

4.0

Composition profile of directionally frozen CdTe-ZnTe

imating a purely diffusional regime. To minimize mixing in the melt, we used resistance heating, temperature gradients limited to about 30 °C/era and small vertical ampoules about I cm in diameter. Fig. 4 shows the result of an electron microprobe analysis of one such ingot, grown at a rate of 4 era/day, which exhibits a typical diffusion-controlled profile, with a steady state region of constant concentration equal to the initial melt composition of 50 mole°~ ZnTe. The middle regions of the crystals were examined by electron microprobe and metallographic analysis and found to be homogeneous with no evidence of dendritic or cellular grc~wth. The segregation coefficient for the first-tofi,:ze tip of this ingot (corresponding to the initial e, dlibrium freezing) had a value of 0.7, in excellent ~v -~ementwith the phase diagram obtained by thermal a lysis6). The amount of solute accumulated in the ~" ndary layer was determined by integration along t initial transient and used to calculate the diffusion ficient in the steady state region, giving a value of < 10-ScmZ/sec. The minimum temperature gra~' ~t required to avoid constitutional supercooling was t Lcalculated to be about 30 °C/cm in good agree~ ~t with the experimental evidence obtained by varyir the freezing rate between 1 and 10 cm/day. 4

. SOLUTION ZONING

i'he data of table 2 show that for certain alloy syste~ ~s the thermal gradients required to avoid constitu-

661

tional supercooling at reasonable rates of growth can become quite significant. Relatively high and stable temperature gradients can be obtained by using various technical devices, such as the heat pipe st 1) which are to be discussed in another session of this Conference12). For certain systems however, it obviously becomes imperative to use a more suitable crystal growth technique. In the present study, the possibility of applying the temperature gradient solution zoning technique, previously used for the growth of lI-VI compound crystals4), has been investigated for stoichiometric solutions in the CdTe-CdSe system and for non-stoichiometric solutions in the Zn-Cd-Te system. The experimental procedure used was the same as for compound crystals except that two separate charges of homogenized alloys were prepared: a zone charge about I cm long with a composition corresponding to the liquidus and a feed charge about 5 cm long with a composition corresponding to the solidus. A sealed quartz ampoule containing the two charges was placed in a vertical furnace with a small temperature gradient of about 10 °C/cm at the temperature corresponding to the selected equilibrium liquidus and solidus compositions. In the case of the CdTe-CdSe alloys, the two charge compositions were selected to correspond to compositions on the pseudobinary phase diagram, which wa~ accurately known. After a period of approximately 10 days, the zone charge was found to have migrated upward through the feed charge leaving behind crystals having the composition of the feed. This method is particularly attractive for pseudobinary systems with wide liquidus-solidus gaps. Its success depends on precise knowledge of the equilibrium liquidus and solidus compositions and on good control of the temperature and temperature gradient in the system. The pseudobinary liquidus temperatures in the CdTe-ZnTe system are higher than in the CdTe-CdSe system, and attempts were made to grow pseudobinary crystals at lower temperatures by passage of a nonstoichiometric zone containing excess Te. The equilibrium liquidus temperatures were determined from the ternary liquidus surface. The ternary liquidus-solidus tie-lines are not known however. In order to determine the equilibrium composition for the feed charge it was rather arbitrarily assumed that there was no metal/metal segregation on solidification, i,e. that the lie-lines

X I I I - 10

662

JACQUES SrE N NOER AND ALAN J. S T R A U S S

corresponded to lines o f constant C d / Z n ratio, This assumption is p r o b a b l y n o t w a r r a n t e d since the crystals grown by this t e c h n i q u e were small a n d inhomogeneous, indicating the possibility o f t e r n a r y constitutional supercooling. This result confirms t h e need f o r further studies o f t h e phase diagram o f this ternary s~tem.

References 1~ W, G. Pfann, Zone Melting (Wiley, New York, 1958). 2~ W. M, Yim and J, P, Dismukcs, in: Crystal Growth, Ed. H. S, Peiser (Pergamon, Oxford, 1967) p, 187.

XIII-

i

3) G, A. Wolff, H. E,:LaBelle, Jr, and: B. N, Das, Trans, I~~et, So¢. AIME 242 (1968) 436, 4) J. Steininger and R, E, England, Trans, Met. Soc, AIME ~42 (1968) 444. 5) J. Steininger, A. J. Strauss and R. F. Brebrick, J. Elct r0. ehem~ So¢,117 (1970) 1306. • 6) A. J. strauss and 3. Steininger, J. Eleetrochem. Soc. 17 (1970) 1420. 7) J. Steininger, Met. Trans. 1 (1970) 2939. 8) J. Steininger, J, AppL Phys. 41 (1970) 2713. 9) J. Steininger and RI F. Brebrick, Electroehem. Soe. Sp ng Conf. Washington, D. C. (1971), 10) V. G. Smith, W. A. Tiller and J. W. Rutter, Can. J. F ys, 33 (1955) 723. I1) G. Y. Eastman, Sci. Am. 218 (1968) 38. 12) J. Steininger and T. B. Reed, J. Crystal Growth 13/14 (I ~.72) 106.

!0