Optical determination of growth variants in ordered GaInP

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Solid State Communications, Vol. 101, No. 10, pp. 757-760, 1997 (g) 1997 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0038-1098/97 $12.00 + .00

Pergamon

Pll: S 0 0 3 8 - 1 0 9 8 ( 9 6 ) 0 0 6 5 2 - 7

OPTICAL DETERMINATION OF GROWTH VARIANTS IN O R D E R E D GaInP F. Alsina, a'~ M. Garriga, b M. I. Alonso, b S. Tortosa, b J. Pascual, a'b C. Geng, e F. Scholz c and R. W. Glew d a Departament de Fisica, Universitat Autbnoma de Barcelona, 08193 Bellaterra, Spain b Institut de Ci6ncia de Materials de Barcelona, CSIC, Campus de la UAB, 08193 Bellaterra, Spain c 4. Physikalisches Institut, Universit~it Sttutgart, Pfaffenwaldring 57, D-70550 Stuttgart, Germany d BNR-Europe Ltd. London Road, Hariow, Essex CM 17 9NA, United Kingdom

(Received 19 September 1996; accepted 30 October 1996 by F. Yndurdtin)

Measurements on the dependence of the ellipsometric parameters as a function of azimuthal angle allow the determination of the dielectric tensor including its orientation with respect to the sample surface. This is done in ordered GalnP at the fixed energy of 3.3 eV where the anisotropy manifests at largest. In such material this method allows to discriminate between the presence of singly or doubly ordered variants and, in the former case, allows to establish which one of the two subvariants ([111 ] or [ 1i 1]) is grown. © 1997 Elsevier Science Ltd. All rights reserved Keywords: A. semiconductors, D. optical properties, D. order-disorder effects.

Epitaxial growth of Gao.5Ino.sP by Metal Organic Vapour Phase Epitaxy (MOVPE) is widely known to produce spontaneous ordering in the cationic sublattice of the alloy along [111] or [171] direction (or both) depending on the substrate misorientation [1]. The resulting ordered structure can be viewed as a monolayer (GaP)l/(InP)l superlattice heterostructure along the ordering direction. However, complete ordering is not achieved and, in fact, one obtains partially ordered GalnP epilayers where the successive cation planes along the ordering direction are not pure Ga and pure In. The presence of alternating Ga-rich and In-rich planes can be written as Gao.5+~/2Ino.5-0/2P/Gao.5-~/2 lno.s+~/2P, where r/ (1 >_ r/ >__0) is the so-called ordering parameter. The ordered structure is a uniaxial crystal, hence with two different components of the dielectric tensor perpendicular (e±) and parallel (elL) to the ordering axis, in contrast to the isotropic dielectric tensor of the random alloy. Optical anisotropy has been reported on the E0 interband transition were symmetry reduction effects induce polarization dependence in the optical I Present address: National Renewable Energy Laboratory, 1617 Cole Boulevard, Golden , CO 80401, USA.

spectra [2, 3]. More recently, anisotropic behaviour of the dielectric function in the vicinity of the El interband transition has been shown by us [4] and explained in terms of ordering-induced symmetrybreaking effects [5]. Besides the energy splitting of the transition, we evidenced a noticeable difference in the absolute values of the E± and Ell components around the El energy. The present work is focused on the anisotropic behaviour of the dielectric function. Measurements consist in evaluating the variation of the ellipsometric parameters tan • and cos A as a function of sample azimuthal angle at a given energy [6]. This method allows us to obtain the components of the dielectric tensor and its orientation at the given energy. The orientation of the dielectric tensor relative to the sample surface is given by the two Euler angles ot and/3, where ct is the angle between the optical axis and the surface normal, and/3 is the angle between the projection of the optical axis onto the sample surface and the normal to the plane of incidence. Moreover, concerning the occurrence of spontaneous ordering, we can determine if a single or two ordering axes are present and, for the former case, which one of the two possible variants ([111 ] or [ I i 1]) is grown. The reflection of a

757

758 OPTICAL DETERMINATION OF GROWTH VARIANTS IN O R D E R E D GaInP Vol. 101, No. 10 plane wave at the interface between two media can be described by [7]:

Ers

=

Rsp Rs,

Eis

'

A =30o 0.45

(I)

(Eip, Ei,) and reflected (E, m Er,) light beams is described by the generally nondiagonal reflection matrix. The relationship for the ratio between reflected X, and incident Xi light polarization states is given by:

0.44

0D n

I

I

I

=

% =

(Rsp/Rs,) + Xi +

(2)

From reflection ellipsometry measurements one obtains XdXr. This ratio is often expressed in terms of the ellipsometric parameters as follows: Xi _ tan • e iA. Xr

-0.876

-0.882

(3)

In a general crystal orientation, the off-diagonal terms of the reflection matrix in Eq. (1) vanish only for isotropic materials. Then the ratio given by Eq. (3) is constant for any angle/~, at a given angle q9 of incidence. Otherwise, the ratio Xi/X, depends on the relative position of the dielectric tensor with respect to the incidence plane and changes as a function of the azimuth angle ft. We have analyzed two GalnP epilayers grown by conventional MOVPE on (001)-GaAs substrates, as described in more detail elsewhere [8,9]. We used GaAs substrates misoriented 5 ° and 6 ° from the [001] direction towards the (111)A and (111)B planes in order to obtain, respectively, double and single variant ordered samples. In the former case, transmission electron microscopy (TEM) and transmission electron diffraction (TED) studies show that the ordered domains are plate-like with typical dimensions of 150×20 nm, and the two ordered variants grow in the same extent. On the contrary, when the misorientation is towards (111)B, growth of a single variant is enhanced and the ordered domains become larger, extending vertically along the whole epilayer thickness. The ordering parameter r/is about 0.4 and 0.5 for the selected double and single variant samples, respectively, as has been inferred from studies on E0 interband transitions. Ellipsometric measurements on the growth surface were done at room temperature using a spectral ellipsometer with rotating polarizer. Data were taken at the fixed energy 3.3 eV, around which the largest anisotropy was previously observed [4], as a function offl in steps of 5 °. The angle of incidence was q9 = 65 ° and the analyzer angle A = 30 °. Figure 1 displays the variation as function of/~ (flscan) of tan ~ and cos A for the single-variant ordered

-180

J

i

i

0

180

360

540

fl (deg) Fig. 1. Experimental ellipsometric parameters tan XI' and cos A as a function of azimuthal angle/~ (squares) at 3.3 eV on a single variant ordered GalnP with r / = 0. 5. The solid line represents the best fit to the data with a uniaxial model. sample. Solid lines give the best fit to the exact equations for reflection in a uniaxial material [7, 10], where the fit parameters e±, erl and ot were found to be: e. = (10.9, 14.7), Ell = (11.4, 15.8) and ot = 44 °. The obtained errors were _0.1 for the e components and _+7° for or. The value of or, corrected in order to take into account the surface misorientation of 6 ° respect the exact [001] direction, coincides within error with the value 54.7 °, indicating that the ordered subvariant present in the sample is the [ 1i I ]. Regarding the shape of the/%scan patterns, their periodicity is of 360 ° because the optic axis is off-plane. In contrast, the patterns of/~-scans for the double variant sample presented in Fig. 2 exhibit a period of 180 °, characteristic for a case where the optical axis lies on the sample surface, or a biaxial case with the c-axis normal to the surface. The first possibility must be clearly excluded and we are left with the second. The appearance of the biaxiai behaviour can be explained by the balanced addition of every uniaxial site provided the small dimensions of the ordered domains and in the growth of the two ordered variants in the same extent. The solid lines in Fig. 2 are the best fit to the data considering an effective biaxial material with the principal axes pointing along [110], [1i0] and [001]. The components of the dielectric tensor are taken as: e. = e±, eh = (1/3)e± + ( 2 / 3 ) E I I , and

Voi. 101, No. 10 OPTICAL D E T E R M I N A T I O N OF GROWTH VARIANTS IN O R D E R E D GalnP 759

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p (Oeg) Fig. 2. Experimental ellipsometric parameters tan and cos A as a function of azimuthal angle/3 (squares) at 3.3 eV on a double variant ordered GalnP with r/= 0.4. The solid line represents the best fit to the data with the biaxial model described in the text. ec = (2/3)ei + (1/3)ell. From the fit we obtain for the components of the uniaxial dielectric tensor: e± = (10.6, 15.2) and ell (11.3, 16.0), which are slightly different from those obtained in the preceeding case. Furthermore, if we compare the difference of the two components, ell - e±, the agreement is reasonably good in view of the, to some extent, dissimilar degree of order in the two analyzed samples and the approximation made in the double variant case. The polarization of the reflected light arises from oscillating dipoles induced in the material by the electric field of the incident light. The oscillation direction of these dipoles in anisotropic materials is in general not parallel to the incident electric field. Excluding certain high symmetry orientations with a linear relationship between incident and reflected states, the anisotropic media couple p and s components as described by the bilinear equation, Eq. (2). Therefore, the response of the material and the incoming polarized field are interdependent. Given that in a rotating polarizer ellipsometer the analyzer selects different polarization components of the reflected light, one should find some dependence with its position (A) in our/% scans. Equivalently, in a system with rotating analyzer the position of the polarizer selects the components of the initial state. To illustrate this, we present in Figs. ---

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(Oeg) Fig. 3. Ellipsometric parameters for a biaxial crystal calculated for o( = 0 ° (that is, a sample with two variants) as a function of azimuthal angle/3 and for three different positions of the analyzer. The angle of incidence was 65 ° . 3 and 4 simulated/~-scans for three different analyzer settings for biaxial and uniaxial materials respectively, using typical values of E± and Ell measured in our samples. The Euler angle ~ was chosen to be 0 ° for the biaxial and 54.7 ° for the uniaxial material. In the first case (Fig. 3) one observes a dependence of tan ~ and cos A upon A except for/3 = 0 °, 90 °, 180 °, and 270 °. The curves for different analyzer angles cross in the four positions for which two of the axes of the dielectric tensor lie in the incidence plane and R,p, Rp, vanish. In the second case (Fig. 4), the three curves cross together only at/3 = 90 ° and 270 ° when the optical axis lies on the incidence plane. Notice that in both examples the analyzer angle A = 5° allows that the

760 OPTICAL DETERMINATION OF GROWTH VARIANTS IN O R D E R E D GaInP Vol. 101, No. 10

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ing the sample to obtain the value of the dielectric tensor and establish the orientation of the preferential axis in partially ordered alloys. First, we have proven that the single variant ordered GalnP displays, at energies near the E] interband transition, a uniaxial behaviour with the optical axis pointing along the ordering direction. Second, double variant samples can be treated, under some specific condition regarding dimensions of ordered domains and extent of the two ordered variants, as an effective biaxial material with c-axis pointing along the growth direction. Acknowledgements--This work has been partially supported by the projects DGICYT No. PB94--0719 and CICYT MAT94-1336. One of the authors (S. T.) wishes to thank the D G R (Generalitat de Catalunya) for a fellowship.

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# (deg) Fig. 4. Ellipsometric parameters for a uniaxiai crystal calculated for ot = 54. 7 ° (that is, a single variant sample) as a function of azimuthal angle # and for three different positions of the analyzer. The angle of incidence was 65 ° . anisotropy manifests with a larger variation ofellipsometric parameters and, for the uniaxial case, together with a more evident breaking of the 180 ° periodicity and of the symmetry around 0 °, 90 °, 180°, etc .... Then, even in a situation of weak anisotropy one could find an analyzer angle where the anisotropic nature of the material would be evidenced and the components of the dielectric tensor determined. In practice we found that singular behaviour of tan • and cos A is obtained for small values of A for which the increment in the variation of tan't1 is overthrown by a lowering of the signal to noise ratio. We have used the characteristic patterns shown by the ellipsometric parameters and generated by rotat-

REFERENCES

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