Observation of Brillouin scattering in mixed InxGa1−xP crystals

0038-1098/81/370049-04502.00[0

Solid State Communications, Vol. 40, pp. 4 9 - 5 2 . Pergamon Press Ltd. 1981. Printed in Great Britain.

OBSERVATION OF BRILLOUIN SCATTERING IN MIXED In~Gal_~P CRYSTALS E. I(difa'j~im~iki,R. Laiho and T. Levola Wihuri Physical Laboratory, University of Turku, 20500 Turku 50, Finland and B. Bayramov A.F. Ioffe Physico-Technical Institute of the Academy of Science of the USSR, Leningrad, USSR

(Received 18 March 1981 by 114.Cardona) Brillouin scattering is observed in the InxGa~_~P solid solution with 0.38 t> x >/0. The composition dependences of the longitudinal and transverse acoustic phonons propagating along the [ 111 ] direction are investigated and compared with the expressions derived by Lakshmi et al. from the random element isodisplacement theory. Pronounced broadening of the Brillouin peaks is observed with the increasing amount of In in GaP.

MIXED TERNARY A~BI_xC ALLOYS have been a subject of considerable research activity because of their interesting intrinsic properties and practical applications. The basic properties of these compounds, including lattice dynamics, are influenced by the disorder of their structure. Extensive investigations into the vibrational spectra of the AxB~-xC-type crystals have been made by using Raman scattering as well as i.r. reflection and absorption measurements [ 1-5 ]. These methods provide information about the frequencies of the long wavelength optical phonons in the centre, and short wavelength optical and acoustic phonons at the boundary, of the Brillouin zone. It is established that there are three types of composition dependent behaviour of long wavelength longitudinal and transverse optical phonons in mixed crystals, e.g. one-mode, two-mode and intermediate type behaviour. This classification is made according to the number of phonon frequencies observed for each of the allowed optical mode of the pure crystals. Most of the I I I - V alloys show two-mode behaviour and only InxGal_~P is known to exhibit onemode behaviour [6-8]. Among the models proposed for the vibrational properties of disordered systems, the random element isodisplacement model (REI), originally proposed by Chen et al. [5], and its various modifications, have been successfully applied to a number of mixed crystals. InxGa~_xP is an important material for fabrication of light emitting and laser diodes. One of the main difficulties in its crystal growth is the large difference (8%) between the lattice constants of pure InP and GaP. There is also a marked difference in their interatomic force constants. These difficulties can be overcome by adding a small amount of As into InxGal_xP.

It is believed that the force constant disorder plays an important role here. Recently disorder induced Raman scattering from the BriUouin zone edge acoustic phonons was observed in InxGa~_xP [9]. To our knowledge, Brillouin scattering, which arises from the zone centre acoustic phonons, has not been reported for this crystal. In this communication we present results of Brillouin scattering in InxGal_xP for the composition range 0.38 >i x >i 0. The main emphasis was to determine the influence of the composition on the frequencies and the widths of the Brillouin peaks. The REI model was utilized to derive information of the interatomic force constants. The sample crystals were grown from nonstoichiometric melts with the modified Bridgman technique [10]. From the polycrystalline boules single crystal parts were selected, oriented and prepared to the final size of about 1 x 2 x 3 mm 3. The composition of the crystals was determined by the electron microprobe analysis with the accuracy of about -+ 2%. The samples were carefully chosen to be as homogeneous as possible. They exhibited n-type conductivity. From the Raman measurement of the LOft') phonon-plasmon mode the free carrier concentration was estimated to be about 1017 crn -3. The Brillouin measurements were made at room temperature by using a three- or five-pass Fabry-Perot interferometer as the spectral instrument. For the beginning the frequencies and the full widths at half height (FWHH) of the Brillouin peaks were measured in several samples of pure GaP with the free carrier concentration about 101~cm-3. The measurements were made by observing back scattering along the [111 ] crystal direction. In this geometry the frequencies AVLAtTA)of the Brillouin 49

BRILLOUIN SCATTERING IN MIXED InxGal_xP CRYSTALS

50

Vol. 40, No. 1

shifted components of the scattered light, for the LA(I') and TA(I') phonons, are connected with the combinations of the elastic coefficients

Table 1. The BriUouin shifts, measured at k = 568.2 nm, and the values Of TLA for the LA(P) phonons propagating along the direction [111] in InxGal_xP

7LA = (Cn + 2Ct2 + 4C~)/3

X

AV (GHz)

"fLA (101°Nm -2)

FWHH (MHz)

0 0.09 0.16 0.28 0.32

79.9 75.7 75.1 73.0 71.3

18.5 16.8 16.6 16.0 15.6

< 100

and

7TA = (Cll -- C12 + C44)/3

by the equation TLA(TA) :

~k2p(X)~LAOPA ~(X) 4n (X)2

(1)

Here the wavelength of the exciting laser is represented by k, and the mass density of InxGa~_xP is given by p(x). Due to the linear variation of the lattice parameter with x [1 I] it is assumed that also p(x) varies linearly between the densities of Gap and InP. The value ofn(x) and its dependence on composition was investigated by measuring the refraction of a prism of InxGal_xP at the Kr-laser wavelengths 568.2 and 647.1 nm, which were the lines used in the Brillouin measurements. In agreement with the previous results [12], n(x) was found to deviate from the linear interpolation between the values quoted for GaP and InP [13, 14]. However, this deviation is rather small and it was found sufficient, compared with the other experimental uncertainties, to use a linear function n(x) in the equation (1). The Brillouin data for the 7LA mode are given in Table 1. As further shown by Table 1, in InxGal_xP the Brfllouin peaks corresponding to 7LA shift to lower frequencies with the decreasing mole fraction of Ga, whereas those corresponding to 7TA indicate little dependence on x in the range of compositions investigated. In the measurement made at k = 568.2 nm the value of AVTA= 41.5 GHz was obtained leading to 7TA = 5.0 X 10~°Nm -2. For pure GaP the values of 7LA(TA) were found to agree very well with those calculated from the existing Brillouin scattering and ultrasonic data collected in [15 ]. The dependence of 7LA and 7TA on compositions was analyzed by using the expressions of l.zkshmi et al. [16] for the elastic coefficients of solid solutions. This derivation is based on the REI model [5], which presupposes that the ions are randomly distributed and that no effects of order are present. As evidenced by our measurements of the Brillouin linewidths at different compositions, these assumptions may not be strictly valid in InxGa~_xP. On the other hand, the behaviour of long-wavelength optical phonons has been successfully discussed in this alloy system by using a version of the REI model [17]. From the formulation of Lakshmi et al. we can calculate 7LA in the form xm' (1 -- 0x)(1 -- e ) x GaP (1 -- Ox) ~'LA "~- ")tLA "l- TL A ~ ' " 2 ~ (1 --X) (1 l eX~ (1 t:xj

154 282

(1 -- Ox) + ATLA (1 ex----~ -x(1 --x),

(2)

where 3'~A mP and 7LA o ~ refer to the values 0fTLA for the pure crystals, and

A'YLA

1

ao [(16A"-- 8A'-- 8A)0 + + (12B"-- 14B'-- 14B)o].

(3)

It is assumed that the first-neighbour interactions can be given by two force constants, namely (a,/3), between Ga and P, and (a', 13')between In and P. The secondneighbour force constants are given by (.4, B) for Ga---Ga, (A', B') for I n - I n and (A",B") for Ga-In. The lattice parameter of pure GaP is denoted by 2ao as well as all the force constants denoted by subscript 0 correspond to their values at the lattice constant of pure GaP. As in the original REI model [5], each of the force constants are assumed to depend linearly on the composition: a ~o

a' ~o

/3 /30

= 1 -- Ox.

/3' /30

A' + B' (A' + B')o

A" + B" (A" + B")o (4)

The parameter e is defined as e = (aine --aGae)[a6~. The input data used to fit the experimental values of 7LA with equation (2) are given by Table 2. The force constants ao and a~ are determined from the frequencies of the transverse optical phonons of GaP and In_P, respectively, and (.4, B)o and (A', B ')o are calculated from the elastic coefficients of pure GaP and InP. A" and B" are left as adjustable parameters for the secondneighbour interactions in InxGal_xP. The best fit curves of 7LA and TTA are shown by the solid lines in Fig. 1. They were obtained under the conditions A3'LA(TA) :/: 0, A" = 10 N m -1 and B" = 20 N m -1. It can be concluded that the second-neighbour interaction between Ga and In has an important contribution to the elastic properties of the InxGat-xP mixed crystal. It must be noted, however, that within the REI model the

Vol. 40, No. 1

BRILLOUIN SCATTERING IN M I X E D InxGal_xP CRYSTALS

51

Table 2. Values o f the parameters used to fit the experimental and calculated composition dependences Of "YLA and ?TA as shown in Fig. 1. Cij are given in 10~°Nm -2 and ~TO in cm -~. The force constants are given in units o f N m -l

c,, GaP InP In=Gal_xP

14.2 10.2

6.25 5.75

7.05 4.60

364.5 304.5

42.0 33.5

t3o, ,

ao,a ,

Bo,S ,

30.5 24.6

8.40 7.41

0.44 -- 0.79

a"

10.0

B"

20.0

Cto = / a A B ~ O , see [1]. 0 = 0.3223, see [1]. 20

SOO M H z

J

rLA

E z

~olO

J o 0.0 GaP

I

I

1

I

0.2

0.l,

0.6

O8

x

1.0 InP

Fig. 1. Comparison between the experimental and calculated (solid lines) dependences of ?LA and "YTAon composition. second-neighbour force constant cannot be simply related to pure elastic forces between atoms but they contain information on the density of states and gaps of the members of the mixed crystal [18]. Because of the relatively weak scattering intensity from the ?TA mode, the FWHH values of the Brillouin peaks were measured only for the ?LA mode. For the correction of the linewidths it was assumed that the recorded spectrum is a convolution of the original Lorentzian line shape with the instrumental profile of a multi-pass Fabry-Perot interferometer [19]. In this way the linewidth of pure GaP was estimated to be less than 100 MHz. As shown by Fig. 2 the linewidths observed in InxGal_xP depend strongly on composition. Compared with pure GaP the FWHH of Ino.3sGao~s2Pis increased by a factor of 3. We attribute this effect to the compositional disorder caused by formation of either In- or Ga-rich parts of the crystal which are called here simply clusters. Non-random atomic distribution can be anticipated from the different thermodynamic properties of InP and GaP, which influences the distribution of cations when the alloy is solidified from the

Fig. 2. Dependence of the recorded Brillouin linewidth of the 3'LA mode on composition in In=Gal_=P. The Rayleigh lines are shown only for GaP. The instrumental linewidth is 110 MHz. melt. Because the ionicities of InP and GaP differ considerably [8] the formation of dusters will cause local fluctuations of polarizability. These are reflected in the distribution of the frequency of the Brillouin scattered light through the variations of the refractive index. In a mixed crystal also fluctuations in the number of the nearest and the next nearest neighbours are inevitably present. In contrast to the phonons, which in the present experiments had the wavelength of about 80 nm, the influence of these fluctuations is confined within a few lattice spacings. As a result they can be expected to have less influence to the line width than the defects which have the diameter of the order of the phonon wavelength or more. The available Brillouin data for mixed crystals is very limited. In the course of the present work brief comparative measurements were made in the system KxRbl_xBr, where no clustering should be present. It was found that the Brillouin lines shifted with the change of the composition of the samples but their widths remained nearly constant. The formation of dusters has earlier been confirmed in Ino.sGao.sP by the diffuse X-ray scattering measurements [20]. The present results suggest that segregations are present already at concentrations

52

BRILLOUIN SCATTERING IN MIXED InxGal_xP CRYSTALS

Ino.lGao.9P. It would be interesting to repeat these measurements in epitaxially grown samples. Because in this case the growing temperature is about 300°C lower than used in the Bridgman method, it can be expected from the thermodynamic point of view that higher tendency towards cluster formation would be characteristic to epitaxial InxGal_xP.

8. 9. 10. • 11.

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