JOURNAL DE PHYSIQUE Colloque C8, supplement ...

JOURNAL DE PHYSIQUE Colloque C8, supplement au n o 12, Tome 47, decembre 1986

LOCAL STRUCTURE AND THERMODYNAMICS OF 11-VI AND 111-V SEMICONDUCTORS BY EXAFS

N. MOTTA('),

A. BALZAROTTI* and P. LETARDI"

C.E.N.G., D.R.F., Service de Physique, Groupe Structure, 85X, F-38041 Grenoble Cedex, France '~ipartimentodi Fisica, I1 ~ n i v e r s i t idi Roma, Via 0. Raimondo, I-00173 Roma, Italy " ~ a b o r a t o i r e MAI, Area della Ricerca di Roma del C.N.R., V. Salaria Km 29.300, C.P 10, I-00016 Monterotondo Scalo, Roma, Italy

- L'ordre a courte distance des solutions solides 11-VI a 316 etud16 par EXAFS. Les 'energies de dlstors~ondes cinq tbtraedres formant le rhseau de ces solutlons ont'ete $valuees par un slmple mod&k.de VFF (Valence Force Field). Nous avons calcul6, dans ce rnodele. les .energies libres de mhlange, les distributions de probabllite et les diagrammes de phases pour differents alliages 11-VI et Ill-V, ?I partir de I'approxirnation quasi chimlque du 111 ordre. &!.&K&& - The short-range order of 11-Vl substitut~onal solld solutions is Investigated experimentally uslng the EXAFS technique. The d ~ s t o r t ~ oenergies n of the flve tetrahedra which form the basic lattice framework of these solutlons are evaluated by a simple Valence-Force-Field (VFF) model. Wlthin the modifled ( I l l order) Quas~Chemical Approximation, we compute the free energy of rnixlng, the probability distribution and the coherent phase diagrams of several 11-VI and Ill-V pseudoblnary a1~oys.

Ill-V and Il-VI pseudoblnary solld solutlons of the AI-,BXC (catlon ailoy) and DBxA,-, (anlon alloy) type can generate. In prlnclple, a great number of sem~conductorsw ~ t ah varlety of band gap wldths Several of these alloys have Important present or potentlal appl~catlons In heterojunction and optoelectron~cdev~ces.A large number of X-ray diffraction measurements on pseudoblnary alloys are available [I]. They show that these materials have a z~nc-blendestructure, w l t h one of the t w o fcc sublatt~cesoccup~edby the C anlon (D catlon) and the other occup~edby both 8 and A cat~ons (anions). Wlth few exceptions, the lattlce parameter a(x) f u l l f ~ l sthe Vegard's law [2]. 1.e ~t varles almost llnearly between the values of pure compounds So far, the most common model for solld solutlons was the Vtrtua/ Crystal Appruxtmatim (VCA). As In zlncblende structures the bondlength IS r = a m , In the frame of VCA both the AC and BC d~stancesobey the rule Y ( x ) = a ( x ) m = Z ( x ) 1.e. they are equal and vary as the lattlce parameter does. I n turn, the Paullng's tetrahedral bond conservation rule gives Z(x)=rBC and Y(x)=rAC 1.e. equal t o that of the pure compounds. A dlrect measurement of these dlstances has been recently obtalned by means of the EXAFS technique 131. The EXAFS measurements lndlcate a blmodal d~strlbutlonof bondlengths, closer t o the Paullng l l m ~ than t t o the VCA.

("on

leave from Dipartimento di Fisica. 11 Universiti di Roma. Via O. Raimondo. 1-00173 Roma

(Italy)

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986880

JOURNAL DE PHYSIQUE

C8-404

The EXAFS measurements were performed at the PULS facility at the Frascat~Laboratory (Italy) with the light emitted by the ADONE storage ring. The alloys considered are Cdl-,ZnXTe, HgSexTel-, (x=0,0.25,0.5.0.75.1) and Cdl-,Hg,Te (x=0,0.1,0.3,0.5,0.7.1). Both In the CdTe-ZnTe and HgTe-HgSe alloys the m~xedcompounds have rather different lattice parameters, and the alloys follow the the lattice parameters of the blnarles (x=0.1) are very Similar. A l l Vegard's taw. For Cdl-,Hg,Te these systems form solid solutions i n the whole range x=Oi 1 and were measured in t r a ~ m i S ~ l 0atn room temperature. S~nglecrystals of pure compounds and of their alloys were grown wrth a modified Bridgman method. Their homogeneity and composition was checked with X-ray diffraction. The extraction of the EXAFS modulat~onfuwtion X(k) from the experimental spectra was made with the standard procedure of data reduct~on[31.The structural analysis was performed i n k-space by Using pure AB and AC compounds as standards to determlne the phase and amplitude backscattering The fit in k space has been carr~edout both with the MINUIT routlne [4Jand with a very recent global minimization routlne called SIGMA [S], whlch seems to be more efficient when the range of variability for the parameters i s larger.

-

The F(r)'s are shown in Fig. l a (or Cdl-$nxTe around the Lll edge of Te (4341 eV) and in Fig. l b lor HgSexTel -x around the LI(I edge of Hg (12284 eV). In both the alloys the dillerewe In the borldlengths &tween the binary compounds are large allowing us to distinguish unambiguou~ly between the VCA-like and the Pauling-like behaviours. Thanks t o the good signal-to-noise ratio and sufficient separation from the outer

distance r [A]

Fig.1 The radlal dlstributlon functlon F(r) extracted from the measured EXAFS around a) the LIll edge of Te i n Cdl Z,.nT,e and b) the Lll edge of Hg in HgCdxTel-,.

distances. The experimental results on different alloys L3,6.71allow us to state the following general conclusions on the structure of pseudobinary solid solutions: 2.8100

-

2.8076

Cd-To

$2.8000

Fig.:, NN d~stancesin Hgl-,CdxTe from EXAFS (+) and from X-ray diffraction (solld line).

2.7876 + EXAFS

2.7960

0

0.2

0.4

0.8

0.8

mole fraction x

1

F1g.3 The five possiole tetrahedra in a pseudoblnary alloy. i) they have crystalline order . i i ] In the alloy the band-lengths have almost the same value as in pure compounds. Thus NN distances display a bimodal distrib~tionffi~ 44) iii) On the chemically disordered sublattice the distances approach the VCA limit whereas in the ordered one the distances are bimodal. Thls implies that the latter sublattice i s much more distorted than the former. iv) The same behaviour characterizes both cation and anion alloys.

H C4-84TO

Cd-To

0

0.2

0.4

0.6

0.8

We have recently developed a model for the microscopic structure of zinc-blende pseudobinarg alloys that incorporate all these points [31. WG focus our attention on the tetrahedral coordination of the zincblende, i.e. we consider the tetrahedra with the four vertices on the disordered sublattice and a cation D (DB@l-x anion alloys) or an anion C (AI-xBxC cation alloy3 inside as the basic units t o build the crystal. These tetrahedra can be fwnd in five different configurations according to the number n=0,1,2,3,4 of B-type atoms at their vertices (Fig.3). We suppose that all the physical properties of the alloy will. be obtained by a suitable average of the corresponding properties of these tetrahedra. The EXAFS results show a tendency to mantain bonds similar to those of pure compounds, so we have derived the tetrahedral properties, such as Zn(x) and Yn(x) through the minimizatim of the tetrahedron distortion energy qn within the Valfma Field (VFF) scheme of Keatlng [81. In order to get the mean distances measured by EXAFS, i.e. Z(x) and Y(x), we have choosen a suitable probability distribution Tor. the five possible tetrahedra. A random distribution 131 and a T dependent distribution:

1

mole fraction x

Fig.4 Experimental and calculated NN distances for different pseudobinwy alloys. fcEXAFS: dashed line: calculated with a random probability; solid line: ca\culatcd:QCA The exper. points of Inl-xGaxAs were taken from ref. [?I.

derived within the Ill order Quasi Chemical Approximation [9] were used. Here A=~-"~~=A(x,T)is the only real and positive solution of the fourth-order polinomial equation!

JOURNAL DE PHYSIQUE

The distribution probability P ( ~ depends ) not only on x, as the Bernoulli distribution does, but also on T. It i s peculiarto each alloy, as it depends on w (chemical interaction energy for a pair of neighbours) and on the elastic properties of the two compounds mixed via the y,,'s. The distances calculated w i t h the latter probability distribution are i n better agreement w i t h the experiments (Fig.4). showing sensitive deviations from the and randomness, expecially for Inl-,GaXAs

CdZnTe

0.15

-1

5

--7i

T-LOO K 0.10

T-180 K 0.05

2

nm

T=260 K

0.00

4.05 -O.O~

-0.10 -0.10

T=350 K

Starting from the probability distribution (4) we can calculate the Gibbs free energy of mixing and hence the phase diagrams of the alloys I9.101. We can observe that the alloys whose enthalpy i s not fully dominated by the elastic energy (i.e. the lattice-matched Hgl-,Cd,Te alloy) behave qualitatively as Bragg-Williams solutions (Fig.5a) mole traction x A different behaviour characterizes the alloys Fig.5 Calculated free energy of m!xing (A) and phase dominated by the elastic deformation energy dlagrams (0) for Hgl -,CdxTe and Cdl -,ZnXTe. (Fig.5b). Apart from the usual change from a c o n V e f i o ~ c o n c a v efunction when the temperature is lowered, the g1"(x]'s of these materials show regions of convexity around the mole fraction x=0.25,0.50,0.75. Due t o the shape of gm, in this case the phase diagrams are rather cbmplex, and three narrow metastable regions develop around the stoichimetric concentrations. Our results suggest that this could be a general feature for pseudobinary ailoys whose thermodynamic properties are governed by the elastlc energy.

Starting from the EXAFS results we have developed a thermodynamic model of zincblende pseudobinaru alloys which incorporates on equal grounds both the elastic deformation and the charge rearrangement. The model does not require adjustable parameters and proves particularly valuable in describing the local structure, the clustering properties and the equil~briumphase diagrams of lattice-matched and mismatched alloys.

It i s a pleasure t o acknowledge the valuable collaboration of M.T.hyzyk, A.Kisiel, M.Podgorny and M.Starnawska during joint work on the subject. We are grateful t o the PULS staff of Frascati where the EXAFS measurements described here have been performed.

REFERENCES [ I ] See, for instance, a) N. K. Abrikosov, V. F. Bankina, L. V. Poretskaya. L. E. Shelimova, E.V. 11-VI. 1.V-VI and V-VL comoounds.Plenum Press, New York (1969) b) J. Skudnova, C. Woolley, and 8. Ray. J. Phys. Chem. Solids 13. 151 (1960) [2] L. Vegard, 2. Phys. 5, 17 (1921) 131 A. Balzarotti. M. T. Czyzyk. A. Kisiel. N. Motta, M. Podgorny, N. Zimnal-Starnawska, Phys. Rev. B 30, 2295 (1984): Phys.Rev.3 1,7526 ( 1 985) Cern Comp. Center Prog. Lib. 0506-D571 (1976) 141 F. James, and M. Roos, [51 F.Aiuffi-Pentini, V.Parisi, A Z i r i l l i , Tech. Summ. Rep. of Wisconsin - Madison Mathematics Research Center *2791 *2806 (1985) [61 N. Motta. A. Bztlzarotti. P. Letardi, M. Podgorny. M.T. Czyzyk. A.Kisiel, R. Zimnal-Starnawska. Solid State Comm. 53. 509 (1985) [?I J. C. Rikkelsen, Jr and J. B. Boyce, Phys. Rev. B 28, 7130 (1983) [B] P. N. Keating, Phys. Rev. 145. 637 (1966) 191 M.T. Czyzyk, M. Podgorny. A. Balzarotti. P. Letardi. N. flotta, A. Kisiel, M. Zimnal-Starnawska, Z. Phys. B-Condensed Matter 62, 153 (1986). [I01 P.Letardi, N.Motta, A.Balzarotti. lnt.Rep. ROM2F/B6/008 I1Univerity of Rome - Italy (1986).