APPLIED PHYSICS LETTERS
VOLUME 78, NUMBER 19
7 MAY 2001
Lattice parameter in GaNAs epilayers on GaAs: Deviation from Vegard’s law Wei Lia) and Markus Pessa Optoelectronics Research Centre, Tampere University of Technology, P.O. Box 692, FIN-33101 Tampere, Finland
Jari Likonen Chemical Technology, Technical Research Center of Finland, P.O. Box 1404, FIN-02044 VTT, Finland
共Received 23 January 2001; accepted for publication 9 March 2001兲 The N content and lattice parameter of GaNx As1⫺x epilayers on GaAs (0⬍x⬍0.03) were determined by secondary ion mass spectroscopy and x-ray diffraction measurements, respectively. A significant deviation of the lattice parameter variation in GaNx As1⫺x from Vegard’s law between GaAs and cubic GaN was observed, which leads to overestimation of the nitrogen content by up to 30% for x⭐2.5%. The physical origin of this negative deviation is discussed. © 2001 American Institute of Physics. 关DOI: 10.1063/1.1370549兴 The Ga共In兲AsN alloy has attracted considerable attention in recent years both because of practical and fundamental points of view.1–4 More recently, promising results have been obtained in light emitting devices with wavelengths in the 1.3–1.55 m range.5–7 It is well known that the incorporation of nitrogen into GaAs causes the bulk band gap to decrease dramatically. On the other hand, due to the large lattice mismatch between GaAs and zinc-blende-type GaN, small amounts of substitutionally incorporated N will give rise to a substantial tensile strain in pseudomorphic GaNAs layers on GaAs.8 The most promising range of N composition in the Ga共In兲NAs alloy seems to be less than 2%, where the band-gap reduction is sharp and the material quality quite good. Higher-N compositions may lead to nonrandom alloys,9 and photoluminescence efficiency has been observed to be severely degraded.4,5 For the determination of the nitrogen content of Ga共In兲NAs epilayers on GaAs, the x-ray diffraction 共XRD兲 technique is often used. However, by XRD the lattice spacings are determined, and not directly the N content of the Ga共In兲Nx As1⫺x alloys. Thus, the calculation of these values requires assumptions on the variation of the lattice parameters and of the elastic constants with x. A linear interpolation 共Vegard’s law兲 between the values of GaAs and cubictype GaN has been commonly assumed to be justified. In this letter, we have measured the N content in a series of GaNx As1⫺x (0⬍x⬍3%) samples by secondary ion mass spectroscopy 共SIMS兲 and the lattice constant in the epilayers by XRD rocking scans. A considerable negative deviation from Vegard’s law in the variation of the lattice constant with N content is observed as N composition over 1.5%, leading to an overestimation of the nitrogen content by up to 30%. The growth of GaNx As1⫺x 共1000-Å-thick兲 samples with a 100-Å-thick cap layer and different N concentrations 共0⬍x ⬍3%兲 was performed in a gas-source molecular-beam epitaxy 共MBE兲 system. Group-III fluxes are produced by thermal effusion cells, group-V flux is provided by a thermally a兲
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cracking AsH3 , and reactive nitrogen is provided by a radiofrequency 共rf兲 plasma cell. The GaNAs films were grown at 440 °C to incorporate N into the GaNAs layers. The detailed growth conditions were reported in Ref. 5. N-implanted samples were used for the calibration of SIMS measurements of nitrogen concentration in GaNAs. Nitrogen ions 共14N⫹ , 50 keV兲 were implanted into semiinsulating GaAs wafers at room temperature. A total N dose of 1⫻1016 ions/cm2 was implanted. SIMS measurements were provided by a VG Ionex IX70S instrument. Cs⫹ ions were used as primary ions and the primary ion energy used was 12 keV. The nitrogen concentration was deduced from the SIMS profile based on the signal ratio of 83GaN/69Ga. For all samples, XRD rocking scans around the 共004兲 Bragg reflections were recorded to measure the lattice constants. From reciprocal space mappings around the 共115兲 reciprocal lattice point it was verified that all of the samples were grown fully pseudomorphic. Figure 1 shows a 共004兲 rocking curve of a typical sample 共solid line兲, together with a simulation in which the RADS commercial software is used based on dynamical theory 共dashed line兲. A GaNAs peak and some thickness fringe peaks are clearly observed. This suggests that the film has a high epitaxial quality. We have measured the sample at different regions 共the sample size is 1 in. in diameter兲 and the results are quite reproducible, indi-
FIG. 1. XRD 共004兲 rocking curve of a GaNAs sample 共solid line兲. The dashed line is the corresponding simulation based on the dynamical theory.
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Appl. Phys. Lett., Vol. 78, No. 19, 7 May 2001
FIG. 2. Dependence of the lattice constant in growth direction (a⬜ ) of pseudomorphically strained GaNx As1⫺x epilayers with N content. Dashed line: calculated lattice parameters according to the Vegard’s law between GaAs and cubic phase GaN; solid line: polynomial fit of our experimental results; and black squares represent our experimental results.
cating the N composition is homogeneous across the epilayer. The strain in the epilayers, and hence, the lattice constant in the growth direction, a⬜ , can be calculated from the N content x via a⬜ ⫽a 储 ⫹ 共 a 0 ⫺a 储 兲
冉
冊
C 11⫹2C 12 , C 11
where the in-plane lattice constant a 储 is that of the substrate 共a GaAs ⫽ 5.6535 Å兲, a 0 is the relaxed lattice parameter of the GaNx As1⫺x alloy and C 11 and C 12 are the elastic constants for GaNAs. Since the elastic constants for GaNAs are not available, a linear interpolation between the values of GaAs and cubic-phase GaN was used to calculate C 11 and C 12 . As for the possible bowing of the GaNAs elastic constants, the maximum error for the 5% N composition was estimated by assuming the extreme cases of GaAs and GaN elastic constants, which were 5.06% and 4.52%, respectively.8 Figure 2 shows the lattice constant in the growth direction (a⬜ ) of the GaNx As1⫺x epilayers as a function of the N content. The dashed line is calculated considering a linear interpolation between the GaAs and cubic-GaN lattice parameters: a 0 ⫽(1⫺x)a GaAs⫹xa GaN , with a GaN ⫽ 4.52 Å. The black squares represent the measurements of a⬜ as obtained from the XRD rocking curves plotted against the nitrogen content determined by SIMS. The intrinsic uncertainties of the SIMS method are indicated by the error bars 共10%兲. The solid line represents the fit of our experimental result: a 0 ⫽a GaAs⫺1.0605x⫺20.95x 2 . It is obvious from Fig. 2 that as the nitrogen concentration increases above about 1.5% there exists a large discrep-
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FIG. 4. Lattice mismatches of GaNAs/GaAs caused by substitutional NAs , split interstitial As–N complex, and split interstitial N–N complex with N content in logarithms.
ancy if Vegard’s law is used to determine the lattice parameter, which leads to overestimation of the nitrogen content up to 30%. The physical origin of the negative deviations of the lattice parameters from Vegard’s law could be mainly due to the large size mismatch between the solute and the solvent atoms. It can also be due to the nonrandom alloys 共N clustering兲 at these higher-nitrogen concentrations, since Vegard’s law is strictly valid only if N atoms are statistically randomly distributed in the alloy formation process. On the other hand, although most N atoms are believed to occupy predominantly the As sublattice, the N atoms might energetically prefer moving out from their substitutional to the neighboring interstitial sites as the N incorporation exceeds a certain level 共this prediction has been confirmed by recent channeling experiments10,11兲. Our calculations show that the formation of isolated interstitial nitrogen in GaNAs is unlikely because of their high formation energy in the lattice.11 Instead, N complexes such as As–N and N–N split interstitials are energetically favored to form, occupying a single lattice site 共shown in Fig. 3兲. The formation of split interstitial N–As complexes induces a compressive strain in the epilayer while N–N complexes cause less tensile strain as compared to the substitutional NAs atom, as shown in Fig. 4. 共The detailed results will be published in a separate paper.兲 Therefore, the incorporation of these nonsubstitutional N atoms will also contribute to the measured deviation from Vegard’s law. In addition, these defects would play an important role in carrier capture and the recombination process 关e.g., act as non-radiative centers in asgrown Ga共In兲NAs material on GaAs兴. In summary, GaNx As1⫺x epilayers on GaAs were grown by gas-source MBE using a rf plasma nitrogen source. We have performed a systematic investigation of the dependence of the lattice parameter on the N content in a series of GaNx As1⫺x samples 共x⬍0.03兲 grown pseudomorphically on GaAs共001兲 substrates. A significant deviation of the lattice parameter variation in GaNx As1⫺x from Vegard’s law between GaAs and GaN was observed, which leads to overestimation of the nitrogen content by up to 30 % for x⭐ 2.5%. The physical origin of this negative deviation could be mainly due to the formation of N-related defects in GaNx As1⫺x . This, in turn, has significant consequences on the correct description of the band-gap variation with nitrogen content and other physical properties.
FIG. 3. Atomic structures for 共a兲 the split interstitial As–N complex and 共b兲 This work was supported by the Academy of Finland. split interstitial N–N complex are drawn. Ga is the light circle. Downloaded 04 Oct 2001 to 130.188.1.19. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/aplo/aplcr.jsp
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M. Weyers, M. Sato, and H. Ando, Jpn. J. Appl. Phys., Part 2 32, L853 共1992兲. 2 J. N. Baillargeon, K. Y. Cheng, G. F. Hofler, P. J. Pearah, and K. C. Hsieh, Appl. Phys. Lett. 60, 2540 共1992兲. 3 S. Miyoshi, H. Yaguchi, K. Onabe, R. Ito, and Y. Shiraki, Appl. Phys. Lett. 63, 3506 共1993兲. 4 M. Kondow, K. Uomi, K. Hosomi, and T. Mozume, Jpn. J. Appl. Phys., Part 2 33, L1056 共1994兲. 5 W. Li, J. Turpeinen, P. Melanen, P. Savolainen, P. Uusimaa, and M. Pessa, Appl. Phys. Lett. 78, 91 共2001兲.
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A. Egorov, D. Bernklau, D. Livshits, V. Ustinov, Z. Alferov, and H. Riechert, Electron. Lett. 35, 1251 共1999兲. 7 M. Fischer, M. Reinhartd, and A. Forchel, Electron. Lett. 36, 1208 共2000兲. 8 K. Uesugi, N. Morooka, and I. Suemune, Appl. Phys. Lett. 74, 1254 共1999兲. 9 L. Bellaiche and A. Zunger, Phys. Rev. B 57, 4425 共1998兲. 10 S. G. Spruytte, M. C. Larson, W. Wampler, C. W. Coldren, P. Krispin, H. E. Petersen, S. Picraux, K. Ploog, J. S. Harris, Proceedings of the 11th International Conference on Molecular Beam Epitaxy, Bejing, China, 2000 共unpublished兲. 11 W. Li and T. Rantala 共unpublished兲.
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