Direct Observation of Tetragonal Distortion in Epitaxial Structures

DOI: 10.1021/cg100146x

Published as part of a virtual special issue of selected papers presented in celebration of the 40th Anniversary Conference of the British Association for Crystal Growth (BACG), which was held at Wills Hall, Bristol, UK, September 6-8, 2009.

2010, Vol. 10 3436–3441

Direct Observation of Tetragonal Distortion in Epitaxial Structures through Secondary Peak Split in a Synchrotron Radiation Renninger Scan )

Alan S. de Menezes,† Adenilson O. dos Santos,†,‡ Juliana M. A. Almeida,†,§ Jos
e R. R. onica A. Cotta,† Sergio L. Morelh~ ao,^ and Lisandro P. Cardoso*,† Bortoleto, M^ IFGW, Universidade Estadual de Campinas, CP 6165, 13083-970 Campinas, SP, Brazil, ‡CCSST, ucleo Universidade Federal do Maranh~ ao, 65900-410 Imperatriz, MA, Brazil, §Campus de Itabaiana-N
de Fı´sica, Universidade Federal de Sergipe, Itabaiana, SE, 49500-000, Brazil, Engenharia de Controle e ^ ao Paulo, Automac-a~o, Unesp, 18087-180 Sorocaba, SP, Brazil, and Instituto de Fı´sica, Universidade de S~ CP 66318, 05315-970 S~ ao Paulo, SP, Brazil )

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Received January 30, 2010; Revised Manuscript Received June 14, 2010

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ABSTRACT: This paper reports a direct observation of an interesting split of the (022)(022) four-beam secondary peak into two (022) and (022) three-beam peaks, in a synchrotron radiation Renninger scan (φ-scan), as an evidence of the layer tetragonal distortion in two InGaP/GaAs (001) epitaxial structures with different thicknesses. The thickness, composition, (a^) perpendicular lattice parameter, and (a ) in-plane lattice parameter of the two epitaxial ternary layers were obtained from rocking curves (ω-scan) as well as from the simulation of the (022)(022) split, and then, it allowed for the determination of the perpendicular and parallel (in-plane) strains. Furthermore, (022)(022) ω:φ mappings were measured in order to exhibit the multiple diffraction condition of this four-beam case with their split measurement.

1. Introduction The strain in pseudomorphic systems causes important changes in their band gap structure, including the shift of energy states and the breaking of energy band degeneracy. Such effects provide flexibility in varying the energy levels in quantum heterostructures and in controlling the effective masses of charge carriers. The ability of engineering these parameters offers the possibility of customizing the optical and electric properties of the devices based on semiconductor heterostructures. However, these properties are strongly dependent on the morphology of the interfaces between the different materials. Ternary alloys of Inl-xGaxP are of growing interest for both electronic and optical devices. Much work has focused on the alloy In0.49Ga0.51P because it can be grown lattice-matched to GaAs substrates. The use of mismatched epitaxial layers, however, allows much greater freedom to design heterostructure devices with desired optical and electronic properties. If the mismatch between the epilayer and the substrate is small and the layer is thin, the mismatch will be entirely accommodated by strain in the layer. In this case, the symmetry of the epilayer lattice distorts from cubic to tetragonal (Poisson effect). Tetragonal distortion of epitaxial films of cubic structure grown on substrates of similar structure but of slightly different lattice parameter is still an important scientific and technical problem. Experimentally it is characterized by a variety of techniques, including X-ray diffraction,1-4 transmission electron microscopy,5 backscattering spectrometry with ion channeling,6 and *Corresponding author. E-mail address: [email protected]. pubs.acs.org/crystal

Published on Web 07/14/2010

other spectrometric techniques.7 The most accurate results are given by the X-ray techniques, mainly double- and triple-crystal diffractometry. A very useful technique which presents high resolution and sufficiently sensitive for the analysis of single crystal materials is X-ray multiple diffraction (XRMD). This technique provides peaks that are very sensitive to subtle variations in the crystal lattice, for instance, due to an external electric field applied, and therefore, it has been successfully applied in the study of piezoelectricity.8-10 For the semiconductors, it had been successfully applied to the study of epitaxial layered heterostructures, in which the lattice of the layer and substrate can be studied in a separate way, just by the angular selection of one adequate layer or substrate peak. Furthermore, some special and very useful reflections simultaneously diffracted by the substrate or layer lattice can be detected, under adequate experimental conditions, and then, they can provide simultaneous information for both lattices (substrate and layer) and are called hybrid reflections (HR)11 of the XRMD. This technique has also been successfully used in the study of ion implanted semiconductors to allow for the characterization of parallel and perpendicular strain in the semiconductor surface,12 and it has also been used in association with the HR to probe the interface between amorphous-crystalline Si, that is the interstitial rich region in the shallow junction of B in Si.13 More recently,14 XRMD has also been applied as a high resolution fine probe for studying Feþ ion implantation in Si to observe the formation of two implanted regions after the ion beam induced epitaxial crystallization (IBIEC) process as well as to confirm the β-FeSi2 formation in the annealed sample already obtained by r 2010 American Chemical Society

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transmission electron microscopy, Raman spectroscopy, and grazing incidence X-ray diffraction results. The versatility and advantage of XRMD is that, just by choosing the adequate primary reflection, it can be turned into a high resolution probe with enough sensitivity to detect changes in the symmetry of the crystalline lattice. It has already been shown (Chang)15 that, in the InGaAsP/InP(001) system, the (000)(006)(224)(222)(224)(222) six-beam case, involving the (000) incident beam, the (006) primary diffracted beam, and the four other secondary diffracted beams, which appears as a unique secondary peak for the InP cubic lattice (substrate), splits into two four-beam case peaks for the InGaAsP tetragonally distorted lattice (layer). In this work, the occurrence of tetragonal distortion in InGaP ternary layers epitaxially grown on GaAs(001) causes symmetry changes in the profile of some secondary peaks of the (004) Renninger scan. Then, it gives rise to a huge split in some of these secondary peaks which can be used to provide the quantitative analysis of these tetragonal distortions.

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Figure 1. Scheme to explain the split in the (022)(022) secondary reflection due to the tetragonal distortion effect, with the top view on the right side. The subscript i (o) means in (out) in the scheme.

where Ho is the primary reciprocal lattice vector, H is the secondary reciprocal lattice vector, Hp = (H 3 H0)(H0/H02), and λ is the wavelength of the incident beam. When the crystal rotates around the normal to the surface to produce the RS, symmetry mirrors are then established according to the symmetry of the normal primary vector (4-fold axis in the GaAs (001) case). Besides these mirrors, one additional mirror is also established by rotation when the secondary reciprocal lattice node enters and leaves the Ewald sphere. Therefore, in the RS obtained for the GaAs primary (004) reflection, there will be two distinct mirror types which are repeated each 90 of the measured RS, that is four mirrors due to the 4-fold symmetry

Then, one can see that, for bulk conditions (a^ = a , β = 90), the (022)(022) four-beam peak will always appear in the same angular position and it does not depend on the λ value. Another point associated with this four-beam peak, appearing exactly at the φ = 45 symmetry mirror, is its sensitivity to b and c lattice parameters. However, the observation of the φ = 135 symmetry mirror shows that the (202)(202) four-beam peak also appears and, in this case, the sensitivity is to a and c lattice parameters. It should be pointed out that with the detected split in this couple of secondary peaks it is possible to characterize the tetragonal (or even orthorhombic or monoclinic) distortions.

2. Theory

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2.1. X-ray Multiple Diffraction (XRMD). The multiple diffraction phenomenon arises when an incident beam simultaneously satisfies the Bragg law for more than one set of lattice planes within the crystal. For this, the plane called primary (ho, ko, lo) is adjusted to diffract the incident beam. With the rotation (φ angle) of the sample around the primary reciprocal lattice vector, several other planes called secondary (hs, ks, ls) and coupling (ho-hs, ko-ks, lo-ls) will also enter in diffraction conditions simultaneously with the primary. These coupling planes establish the interaction between the primary and the secondary reflections. In the pattern Iprimary versus φ, called the Renninger scan (RS),16 positive (umweganregung) and negative (aufhellung) secondary peaks can appear distributed according to the symmetry of the primary vector and also considering the symmetry plane established by the φ rotation. In the former, intensity is transferred from the secondary beam to the primary and generally happens when the primary reflection is forbidden by the crystal space group or even weak, and in the last, the contrary happens. The secondary peak position in the RS is given by φ = φo - β, and the - signal defines the entrance and the exit of the secondary reciprocal lattice point in the Ewald sphere by rotation. φo is the angle between H^ (the component of H on a plane perpendicular to Ho) and R, the reference vector. The secondary peak position equation is given as a function of the unit cell parameters17 ðH 2 - H H0 Þ 1 ð1Þ cosð βhkl Þ ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 2 1 H02 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi H 2 - Hp2 4 λ2

(360/4 = 90) plus four mirrors due to the rotation around the primary planes normal (90/2 = 45). 2.2. On the (022)(022) Four-Beam Secondary Peak Split. As stated before, XRMD arises when the incident beam simultaneously satisfies the Bragg law for more than one set of lattice planes within the crystal, and therefore, this technique is also called n-beam diffraction. A very interesting case, discussed in this paper, is the (022)(022) four-beam case, which appears as a secondary negative (aufhellung) peak for the GaAs cubic lattice, that is one incident beam (000), one primary diffracted beam (004), and two secondary diffracted beams (022) and (022). The representation of this case in the Ewald sphere is shown in Figure 1. It represents a four-beam case in the RS of a cubic lattice (a = b = c) because the reciprocal lattice points corresponding to the (022) and (022) planes (points 1 and 2 in the figure) touch simultaneously the Ewald sphere, leaving (in-out) it or either entering (out-in) it, by φ rotation. This explains the subscripts io or oi in Figure 1. As one can see in the figure, this happens because the angle between H^ of the (022) and (022) planes is 180 (β = 90). When there is a tetragonal distortion in the crystal lattice (a = b 6¼ c), the β angle decreases and, then, the (022) and (022) reciprocal lattice points (10 and 20 in the figure) touch the Ewald sphere one each time, under φ rotation. Then, it provides two distinct three-beam peaks in the distorted crystal RS. The dashed vectors in the side view of Figure 1 stand for the H^ of the (022) and (022) planes for the distorted tetragonal lattice. Considering the (004) primary reflection and (022) or (022) as the secondary reflection, eq 1 becomes ða2^ - a2jj Þλ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð2Þ cosð βÞ ¼ ajj a^ a2^ - 4λ2

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Table 1. Lattice Parameters, Thickness, Strains, and Relaxation Degree Obtained from the Rocking Curve and (022)(022) Four-Beam BSD Peak Split #A #B

Tnominal (nm)

Tcalcd (nm)

X (Ga)

a||

a^

ε||  10-3

ε^  10-3

R (%)

400 800

370 800

0.434 0.417

5.6535 5.6536

5.6863 5.6943

-2.88 -3.57

2.9 3.61

0.9 1.0

Figure 2. Simulation of the split of the (022)(022) secondary peak appearing in the InGaP RS due to the layer tetragonal distortion.

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For a thin film deposited onto a thick substrate, when the bending effect is negligible and elastic stresses are not relieved by dislocations, the unit cell of the epitaxial layer presents tetragonal distortion. From elasticity theory,18 a simple connection between ε^ and ε follows 2ν εjj ð3Þ ε^ ¼ 1-ν

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where ν is Poisson’s ratio of the layer, ε^ is the strain perpendicular to the interface, given by (a^ - a0)/a0, and ε is the strain parallel to the interface, given by (a - a0)/a0. a^, a , and a0 are the perpendicular, parallel, and relaxed lattice constants of the layer, respectively. The relaxed lattice constant can be obtained from the equation below 4ν a^ þ ajj 1 -ν ð4Þ a0 ¼ 4ν 1þ 1-ν Figure 2 shows the split simulation of the (022)(022) peak as a function of the perpendicular/parallel lattice parameters (strain) ratio using the UMWEG19 program. This program uses the kinematical theory in the analysis of multiple diffraction phenomenon, and it allows simulation of RS for single crystals or even epitaxial layers. By observing this figure, one can see that it is possible to detect strain ratios as low as 10-5 directly from the split in this four-beam secondary peak of the RS. 3. Experimental Section

The samples used in this work to study the tetragonal distortion of epilayers by XRMD are identified and shown in Table 1. In1-xGaxP epilayers were grown by chemical-beam epitaxy (CBE) on top of semiinsulating GaAs(001) substrates. Trimethylindium and triethylgallium, with H2 as a carrier gas, were used as group-III sources. Thermally cracked AsH3 and PH3 were used as group-V sources. A 300-nm GaAs buffer, with growth rate of 0.72 μm/h, precedes the In1-xGaxP epilayers, which were grown at a rate of 0.95 μm/h in both samples.

Figure 3. Experimental and calculated rocking curves of the samples. The growth temperature was 550 C for buffers and epilayers. Two samples with different layer thicknesses (#A, 400 nm; #B, 800 nm) were used in the measurements of the tetragonal distortion study. High-resolution rocking curves were obtained on a Philips X’Pert MRD diffractometer with Cu Ka radiation using a geometry with a Ge(220) asymmetric four-crystal monochromator and a Ge(220) channel-cut analyzer at LPCM, IFGW, UNICAMP as well as at the XRD1 beamline of the Brazilian National Synchrotron Laboratory (LNLS), Campinas, SP, Brazil (Figure 3). XRMD measurements were carried out at XRD1 beamline;LNLS. The wavelength used in our experiments was 1.5493(1) A˚. A beam size of the order of 1.0 mm  1.0 mm was used in the measurements. The Huber threeaxis diffractometer used in the experiments is mounted at station XRD1 of the LNLS and provides high resolution measurements with step sizes of 0.001 in both the ω and φ axes.

4. Results and Discussions In this work, the structural characterization of the samples was carried out using rocking curves and RS as well as the mapping of the BSD reflections of the X-ray multiple diffraction. The preliminary characterization of sample #A was obtained by means of symmetric rocking curves (RC) that have provided information on the thickness, composition, and perpendicular lattice parameter (a^). Regarding samples #B, no interference fringes were measured, which indicates the occurrence of one or even both of the following two effects: the ternary layer is thicker (800 nm), and the interface layer/ substrate is not good enough. As is well-known, the period of the interference fringes is related to the layer thickness and, then, the layer thickness could not be figured out. On the other hand, the composition and perpendicular lattice parameter are shown in Table I. Figure 4 shows the measured and calculated RC20-22 for each analyzed sample.

Figure 5 shows a portion of the #A sample RS around the φ = 45 symmetry mirror for the substrate and layer lattices. The (004) reflection is used as primary in both cases. The calculation of the RS and the indexing of the secondary peaks was obtained using the UMWEG19 program, and one can see the occurrence of four- and five-beam case peaks for the substrate lattice that appear as negative peaks (aufhellung). This occurs because the intensity of the substrate primary reflection is reasonably strong and, thus, all secondary beams interact with the primary by receiving intensity from it. In turn, as the intensity of the layer primary reflection is smaller than the substrate one, positive (umweganregung) and negative asymmetrical peaks are measured in the layer RS range. One can notice that the (022)(022) four-beam BSD peak (substrate) has been split into (022) and (022), two three-beam BSD peaks, when the crystal is aligned in the layer lattice. Regarding the (442)(111)(115) five-beam peak (substrate), it was split, producing one (442) three-beam peak and one (111)(115) four-beam peak. The (442) secondary does not appear in the layer RS because its intensity is very weak. Regarding the other three four-beam peaks, they do not appear because their intensity is reduced due to the layer

Figure 6. Calculated azimuthal positions φ for the (022) and (022) secondary reflections as a function of a^/a . The dashed lines stand for the measured splits for the #A and #B samples, corresponding to Δφ = 0.217 (#A) and 0.267 (#B).

thickness. The peaks identified as (111)HR and (111)HR are the above-mentioned hybrid reflection peaks; that is, the (004) primary beam diffracted by the (004) substrate planes toward the detector is interacting with the [111] secondary beam, coming from the consecutive diffractions by the (111) secondary and (115) coupling layer planes, also diffracted toward the detector. In this case, there is a destructive interaction between the substrate primary and layer secondary beams, since a hybrid aufhellung peak was measured in the substrate RS. The indexing of the hybrid peaks was obtained by using the hybrid path equations23,24 and was confirmed through the calculation of the layer lattice parameters from the (022)(022) split. It should be pointed out that the primary plane is in the substrate lattice whereas the secondary and coupling planes are in the layer lattice, which shows these HRs are very useful for characterization of the layer and substrate lattices simultaneously, because they carry simultaneous information on both lattices. Figure 6 shows the measured and calculated (022)(022) fourbeam BSD peak for the substrate and layer (#A sample) RS region around φ = 45. The split and the inversion of intensity can be clearly observed when the crystal is aligned for the layer lattice. In the fitting process, the perpendicular lattice parameter (a^) obtained from the (004) rocking curve was kept constant (Table I), while the parallel lattice parameter (b) was varied until providing the best fit between the experimental and the calculated data. The (202)(202) four-beam BSD peak (appearing at φ = 135 mirror) was also measured in order to provide the other lattice parameter (a). Since the a and b in-plane lattice parameters obtained from the RS fit show the same value, which is different from c (= a^), the layer presents a tetragonal distortion. It is important to mention here that, with the measurement of the (022)(022) and (202)(202) couple of peaks, one is able, in principle, to detect orthorhombic or even monoclinic distortion in the layer. Using the a^ and a obtained with the RC and XRMD methods, respectively, one can calculate the perpendicular and in-plane strains using the equations given in section 2. Poisson’s ratio was obtained through the Vegard’s law. Table I shows inplane and perpendicular lattice parameters and strains and the relaxation degree of the layer. Using eq 2, one can plot φ vs a^/a (Figure 6) to show the split and the variation of the φ position in

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Figure 5. Measured and calculated RS region showing the secondary peak inversion and split (Δφ = 0.217) of the (022)(022) four-beam BSD peak.

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Figure 4. Experimental and calculated RS for the substrate and layer lattices, where it is possible to see the split of the (022)(022) peak in the layer lattice. The (111)HR and (111)HR pointed in the substrate RS but not calculated are hybrid reflection peaks from the layer lattice.

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simulation of the (022)(022) split, since the perpendicular lattice parameter obtained by RC is fixed, it is possible to obtain the in-plane layer lattice parameter and, then, to obtain a complete characterization of the tetragonal distortion present in the layer. From ω:φ mapping, it is possible to know whether the in-plane layer lattice parameters are matched or not to the substrate parameters, just by direct observation of the layer and substrate streaks coincidence. By using the obtained layer lattice parameters (RC and tetragonal split), it was possible to figure out the in-plane and perpendicular strains of the layers in the two samples. It was also indicated in this work the possibility to detect orthorhombic or even monoclinic distortion in semiconductor epitaxial layers simply by measuring the (022)(022) and (202)(202) couple of peaks and by simulating their split. Acknowledgment. We gratefully acknowledge the LNLS staff for valuable help during the experiments of multiple diffraction at the XRD1 beamline and the financial support from the CNPq, CAPES, and FAPESP (Proc. 07/08609-3) Brazilian agencies. List of Symbols and Abbreviations Glossary

Figure 7. “X” streaks on ω:φ mappings of the (022)(022) BSD peak for the #A and #B samples.

the RS of both (022) and (022) peaks. Since φ = φo - β and φo is a constant, then Δφ = Δβ. Since (022) and (022) are both BSD reflections, it is worthwhile to investigate the distribution of the in-plane strain through the ω:φ mappings, that is a coupled scan in the incidence (ω) and azimuth (φ) angles. These mappings were carried out for the (022)(022) four-beam diffraction condition and are shown in Figure 7. The substrate (S) and layer (L) peaks are identified in the figure. Under φ rotation, the path of each (022) and (022) secondary reflection when crossing the Ewald sphere provides the two streaks forming an “X”, also seen in the figure. The intersection point over the (004) GaAs reflection is the exact condition of the four-beam diffraction where all substratesecondary reflections are excited. Its azimuth position corresponds to φo = 45 if the reference vector is taken along the [110] direction, and it does not depend on the used wavelength. We can see that the secondary reflections’ streaks due to the substrate lattice coincide with the streak of the secondary reflections due to the layer lattice; this always occurs for BDS peaks when the layer in-plane lattice parameter matches with the substrate in-plane lattice parameter. 5. Conclusions In this work, we have demonstrated one more application of the XRMD technique in the structural study of semiconductor heterostructures. The tetragonal distortion that occurs when a layer is grown on a substrate with different lattice parameters was clearly detected by means of this technique through the (022)(022) four-beam BSD peak split using the (004) primary reflection. The samples were submitted to a preliminary RC analysis in order to obtain information about the thickness composition, and perpendicular lattice parameter of the layer. With the

φ ω RC RS XRMD HR LPCM

rotation angle rotation angle rocking curve Renninger scan X-ray multiple diffraction hybrid reflections of XRMD Laboratory of Preparation and Characterization of Materials IFGW Institute of Physics Gleb Wataghin XRD1 X-ray diffraction beamline of LNLS LNLS Brazilian National Synchrotron Laboratory BSD Bragg surface diffraction

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