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GaN distributed Bragg reflectors using in situ curvature measurements and ex situ X-ray diffraction
Materials Science and Engineering A 528 (2010) 58–64
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Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Strain profiling of AlInN/GaN distributed Bragg reflectors using in situ curvature measurements and ex situ X-ray diffraction C. Berger, P. Moser, A. Dadgar, J. Bläsing, R. Clos, A. Krost ∗ Institute of Experimental Physics, Otto-von-Guericke-University, Universitaetsplatz 2, 39016 Magdeburg, Germany
a r t i c l e
i n f o
Article history: Received 18 February 2010 Received in revised form 14 April 2010 Accepted 15 April 2010
Keywords: In situ curvature measurements Group-III nitrides X-ray diffraction
a b s t r a c t In this work, we show the use of in situ curvature and X-ray measurements to evaluate the metal organic vapor phase growth process of distributed Bragg reflectors consisting of an AlInN/GaN system. At first, it is investigated how the initial wafer bow and the heating of the bare substrates influences the curvature measurements. The strain induced by thermal mismatch and lattice mismatch is discussed at the example of multilayer AlInN/GaN Bragg mirror structures on sapphire substrate. We will demonstrate that thereby an estimation of the composition in the AlInN layers is possible. Additionally the samples were examined with multiple X-ray diffraction techniques, as symmetrical and asymmetrical reciprocal space maps, grazing-incidence in-plane diffraction and X-ray reflectivity. These results are compared with the in situ measurements. © 2010 Elsevier B.V. All rights reserved.
1. Introduction In the last few years, it has turned out that in situ curvature measurements are a very appropriate tool to assess the strain appearing in thin film structures already during the epitaxial growth process. Through the observation of the curvature behavior of the wafer, it was possible to trace the different sources for strain in GaN heteroepitaxy [1]. Being used in a qualitative manner, the method was very successful to investigate the impact of low temperature AlN interlayers to reduce the stress in thick AlGaN layers on sapphire, which allowed strain-free films without the formation of cracks [2]. Furthermore curvature measurements were used to obtain a flat wafer with a homogeneous temperature distribution during the deposition of InGaN multiple-quantum-wells (MQWs). Because of the strong temperature dependence of the indium incorporation, this leads to much better wavelength uniformity across the wafer [3]. Nowadays, the availability of high-resolution curvature sensors even allows the determination of the lattice constants of ternary nitrides or of the strain state of MQWs [4,5]. Here, we apply the method to investigate the growth of distributed Bragg reflectors (DBRs) based on AlInN/GaN. Such mirrors give the possibility to increase the light extraction efficiency and to get a narrower and more directional emission, when inserted below the active region of a light-emitting device [6]. Furthermore, through the very high reflectivity, which can be realized with DBRs, it is possible to fabricate microcavities for vertical cav-
∗ Corresponding author. Fax: +49 391 6711130. E-mail address: [email protected] (A. Krost). 0921-5093/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2010.04.053
ity surface emitting lasers (VCSELs) [7] or even to achieve strong coupling between excitons and photons [8]. Consisting of many periods of two alternating materials with different refractive index, DBR structures become very thick and therefore are very vulnerable to the appearing of cracks or lattice relaxation of the films. To prevent these material degrading issues, the combination of AlInN and GaN as quarter-wave layers is very promising, because AlInN can be grown lattice matched to GaN with an indium content of about 18% and strain-free deposition of the films is enabled [9–11]. Using an in situ curvature sensor, we show how the strain state of the layers can be estimated during the growth process of 10-fold AlInN/GaN Bragg reflectors. In order to interpret the curvature measurements correctly, it first has to be ensured that the influence of different effects on the signal is clearly known. Additionally to the strain-induced change in wafer bow, which can be attributed on the one hand to lattice mismatch between the different layers and to intrinsic stresses through the coalescence of three-dimensional islands or doping effects, and on the other hand to the thermal mismatch between the films and the substrate, there are two other contributions having a significant effect on the wafer curvature. The first fact to be considered is that the wafers have an initial bow, which originates from the fabrication process and the polishing of the substrates. An inevitable anisotropy of these processed surfaces leads to a variation of the curvature value while the wafer is rotating. The other effect is a concave bowing of the bare substrate arising during heating. This behavior can be explained by a vertical temperature gradient within the substrate, due to the thermal irradiation of the upper surface and the cooling effect of the gases flowing above the wafer. All these effects were examined
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and their individual influence on the curvature measurement will be discussed. 2. Experimental setup The in situ curvature measurements were carried out with an optical reflection method. It uses two parallel laser beams with a well-defined distance, which are reflected on the wafer surface and then are detected by a CCD camera, where their distance is analyzed. Depending on the shape of the surface, this distance becomes larger or smaller. Having a concave wafer, the spot distance is decreased and one gets a positive curvature signal. For convex samples it is vice versa. During the experiments, two different apparatus were mounted on the Aixtron AIX200/4 RF-S horizontal MOVPE-reactor. The first was a self-built sensor, equipped with a He–Ne laser and a Fabry–Perot etalon, to get two laser-spots being reflected of the wafer surface. More details on this buildup can be found in Ref. [12]. This system provides the curvature and the reflectance of the sample at a wavelength of 633 nm. The other setup was a commercially available EpiCurveTT® system by LayTec, which delivers in addition emissivity-corrected pyrometry and reflectance at 950 nm. The total resolution that was achieved with the curvature sensor is about ±5 km−1 , whereby relative changes of the curvature with a magnitude of ±1 km−1 could be measured. The substrates being used were single side polished 2 inch c-plane sapphire wafers with a thickness of 430 m. The bare substrate bending at higher temperatures was also examined for 500 m thick silicon (1 1 1) wafers. Symmetrical X-ray diffraction and X-ray reflectivity (XRR) measurements were accomplished on a newly developed concurrent X-ray diffractometer equipped with a rotating anode CuK␣ -source, a curved Johannson-type Ge(1 1 1) monochromator for convergent beam optics, a Bruker D8 high-resolution goniometer, and a two-dimensional area detector (Vantec 2000) as described in Ref. [13]. Reciprocal space mapping was carried out on a URD6 (Seifert/FPM) system equipped with a position sensitive detector, and depth-dependent in-plane lattice parameters as well as X-ray transmission and X-ray standing wave measurements were performed with a grazing-incidence diffractometer [13]. Furthermore, high-resolution X-ray diffraction (HRXRD) was accomplished on a GE/Seifert XRD 3003 HR system and ex situ 3D-bow measurements were done on an OEG Flatscan optical 3D surface profilometer.
Fig. 1. Transients of reflectance and curvature during the rotation of a sapphire substrate. The curvature (lower curve) and the dots are raw data and the black upper curve shows the smoothened reflectance.
Periodic oscillations appear in the curvature, with an amplitude of about 40 km−1 , and in the reflected intensity as well. Apparently, the period of the reflectance oscillations corresponds to the length of one wafer rotation, but the curvature oscillation turns out to be exactly twice as fast. This is not quite surprising, because after a rotation of 180◦ , the two parallel laser beams are already deflected in nearly the same manner, whereas the reflectance reaches its starting value only just after a full rotation. To understand and to clarify these curvature oscillations, a 3D-bow measurement of this wafer was made, which can be seen in Fig. 2. This reveals that the wafer has a saddle shaped surface profile with a convex curvature in one direction and a concave curvature perpendicular to it. Assuming a spherical surface shape in each direction, the curvature of the two main directions can be calculated straightforward to C≈
2h x2
where h is the height difference to the center and x is the corresponding lateral distance from the center. Doing so, one gets two values which differ from each other by an absolute value of nearly 50 km−1 . This agrees very well with the height of the in situ curvature oscillations, so it can be concluded that the anisotropy of the wafer surface is the main cause for the noise and variation of
3. Experimental results 3.1. Initial wafer bow When performing in situ curvature measurements, the raw data taken by the sensor are usually smoothed by taking a moving average over several seconds to obtain a straight transient. However, during wafer rotation it was observed that the raw values of the curvature strongly vary in a range of about ±15 to ±35 km−1 , which is different with each wafer placed into the reactor. This variation is therefore often a lot greater than the growth related changes of curvature to be analyzed, which can be in the magnitude of 1 km−1 . Often this resolution limiting effect is assigned to wafer wobble under gas-foil rotation, but, assuming a spherical surface of the sample, wobbling itself cannot explain this heavy variation, since the direction of beam reflection is not significantly influenced by the tilting of a spherical surface for a few degrees. Rather this behavior seems to originate from the wafer itself. Thus a bare sapphire substrate was placed in the reactor and the rotation was set very slowly with an estimated cycle duration of 5 s. The sensor took 10 measurement values in 1 s, so one gets about 50 values for a single rotation. Fig. 1 shows the resulting transients.
Fig. 2. 3D surface profile of the sapphire substrate from Fig. 1. The curvature C is calculated along the x- and y-axis, assuming a spherical profile.
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Fig. 3. Position-dependent ω-scans of the (0 0 0 6) sapphire reflex (from the substrate in Fig. 2), for the two directions parallel to the flat (left) and antiparallel to the flat (right).
the curvature during rotation. Noteworthy, the shape of the surface differed significantly for each one of several measured substrates. To figure out if the measured curvature belongs to a true bending of the substrate, i.e., the lattice planes show the same curvature, or if it is just caused through a thickness variation of the wafer due to the polishing during the fabrication process, position-dependent ω-scans of the (0 0 0 6) plane of sapphire were made to obtain the orientation of the lattice planes across the wafer. This can be done through the observation of the shift of the peak position in dependency of the position where the X-rays strike the sample (Fig. 3). In contrast to the 3D-bow measurement, where the wafer simply was lying on a table, here the sample was mounted vertically on a flat plate with a little piece of sticky tape, to ensure that the wafer still can bend freely. The curvature then follows to C=
2 sin(ω/2) x
with x as the shift of the point focus on the sample and ω as the related change of the peak position. These measurements revealed that the lattice planes show the same curvature behavior in both directions with a very small concave bending, whereby it has to be mentioned that the determined value is at the limit of what can be measured with this method, since it cannot be excepted that the shifting of the x-position does not introduce a slight peak position shift of 0.01◦ . Nevertheless, the surface profile showed a completely different curvature behavior. This means that the main part of the surface profile comes from a fluctuating thickness of the wafer and not from a bending of the substrate. This was also confirmed by
measurements with an outside micrometer on different positions on the wafer (Fig. 3). 3.2. Curvature caused by heating It was observed that already the heating of the bare silicon or sapphire leads to a concave bending of the substrates. This effect is also described in Ref. [5] and can be explained with a vertical temperature gradient within the wafer. It arises from the heating of the backside and thermal irradiation of the frontside of the substrate. The dependency between the temperature difference of the two sides and the curvature C can be expressed by C(T ) = ˛
T
back
− Tfront hs
where hs is the substrate thickness and ˛ is the thermal expansion coefficient. In the experiment, the reactor temperature was ramped up and down with various durations in a range of 400–1100 ◦ C. The wafers were under a H2 atmosphere with a flow rate of 8 sccm and the pressure was 100 mbar. No significant influence of the heating rate on the substrate bow could be seen. Fig. 4 shows that on the one hand the increase of the curvature was not linear, in contrast to the findings in Ref. [5]. On the other hand, the sapphire substrates exhibit a stronger bowing than the silicon substrates. But due to the smaller thermal expansion of silicon, the calculated temperature difference is even slightly higher than in the sapphire substrate. Thereby it has to be noted that the temperature differences are rather small with a value of
Fig. 4. Change of curvature during heating of bare sapphire (430 m) and silicon (500 m) substrates.
C. Berger et al. / Materials Science and Engineering A 528 (2010) 58–64
Fig. 5. In situ curvature measurement of a 10-fold distributed Bragg reflector, based on AlInN/GaN, grown on sapphire. The red line shows the true temperature measurement of the susceptor and the black line shows the corrected curvature, without initial wafer bow and temperature-induced substrate bow. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
about 4 K at 1100 ◦ C for both substrates, but already these values lead to a considerable bending. However, the greater temperature gradient in the silicon was at first unexpected, because of its much better thermal conductivity. Assuming that the thermal losses through the frontside only are caused by heat radiation, the temperature difference in the thermal equilibrium is roughly given by the Stefan–Boltzmann law T =
4 hs εTfront
with ε the emissivity, the Stefan–Boltzmann constant and the thermal conductivity. The answer to the larger temperature difference in silicon seems to be its enhanced emissivity as compared to sapphire. Being dependent on, e.g. surface morphology and doping concentration, the emissivity of silicon in the examined temperature range should be much higher than of sapphire [14–16]. 3.3. Strain-induced wafer bow Fig. 5 shows the in situ measurement of the growth of a 10-fold AlInN/GaN Bragg reflector. The buffer consists of two thick GaN layers separated by a low temperature AlN interlayer to induce compressive stress in the second one and avoid cracking. In addition two in situ SiN masks are inserted to stop the vertical propagation of threading dislocations and to reduce their density. As known, AlInN and GaN prefer very different growth temperatures around 700 ◦ C and 1000 ◦ C, so the temperature has to be repeatedly changed by more than 300 ◦ C in the growth process, which leads to the corresponding curvature changes. With the knowledge of the temperature depending substrate bow the measurement can be corrected by this effect by simply substracting it from the original measurement; so one gets the pure strain-induced bow caused by lattice mismatch and the different thermal expansion coefficients. As a result, the curvature changes at the beginning of the process are removed, which reveals that the first part of the buffer grows nearly strain-free. Moreover, upon temperature change the impact on the bending becomes smaller representing the bare thermal mismatch now. This removal of the temperature depending substrate bow becomes especially important when the temperature changes during the deposition of a single material, since only in this manner, the correct slope of the curvature can be determined. The goal when growing such structures is to achieve a lattice matched growth of the AlInN layers on the GaN. This can be real-
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Fig. 6. In situ curvature measurements of three DBR structures with different AlInN compositions, as determined by X-ray diffraction ([In]a = 11.4%, [In]b = 18%, [In]c = 21%). Please notice that the transients were shifted vertically for better visibility and the growth times were also changed.
ized at an In-concentration of about 18%. In Fig. 6 the curvature measurements of the growth of three DBR structures are illustrated, whereby the indium content in the AlInN was varied. First of all, it can be seen that the LT–AlN interlayer induces compressive strain to the following GaN. Afterwards, all samples show a different behavior during the deposition of the AlInN layers. Sample (a) shows an increasing concave curvature during AlInN deposition, which is associated with a tensile strain within the layers. While in sample (b) the curvature proceeds slightly in the concave direction too, sample (c) shows a compressively strained AlInN layer. The oscillation of the curvature signal for that sample during the GaN buffer growth is assigned to a thickness gradient in the film [17]. In order to determine the indium concentration in the layers, the increase of curvature during the growth of the individual AlInN layers was averaged and evaluated. Correctly, one has to use a approach for multilayer systems [18], which considers the influence of the strain in all underlying layers. However, due to their short growth time, the GaN strain in the DBR is not exactly known. Moreover exact material parameters are missing. Therefore, as a first approximation of the lattice mismatch εm , a simplified expression was applied here, which is equilvalent to the classical Stoney formula [19]: C=
6εm Mf hf Ms h2s
Ms,f is the biaxial moduli, and hs,f is the thickness of the sapphire substrate and the film, respectively. Because of the lack of values for the elastic constants for AlInN, the biaxial modulus has been interpolated to Mf = 450 GPa using the values from AlN and InN [20]. As values for GaN and sapphire, MGaN = 478 GPa [20] and Ms = 607 GPa [21] have been taken. The thicknesses of the GaN and AlInN layers in the DBR have been determined by the fitting of symmetrical /2-HRXRD measurements (distance of the interference fringes), because they are too thin to do a reliable fit with Fabry–Perot oscillations. They were determined to 43 nm for GaN and 48 nm for AlInN, respectively. These values were confirmed by FE–SEM images. The lattice mismatch is given by εm =
af (T ) − as (T ) as (T )
with af being the in-plane lattice constant of AlInN, interpolated by Vegard’s law as well, and as being the in-plane lattice constant of GaN. Assuming that AlInN and GaN have nearly the same thermal
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Table 1 Strain values obtained from in situ curvature measurements and thereof calculated material composition [In]curve in comparison with the concentration obtained by X-ray diffraction. Sample
af /aGaN
[In]curvature (%)
[In]XRD (%)
a b c
−6.5 × 10−3 −9 × 10−4 4.6 × 10−3
13.2 17.5 21.6
11.6 18.0 21.0
expansion coefficient [22–24], the temperature dependence can be neglected. Having a closer look on Fig. 6, strain relaxation seems to appear in sample (a), indicated by the drop of the linear slope during the growth of the first AlInN layer. Usually, this prevents the analysis of the layer composition, but nevertheless, strain is accumulated again in the following layers, so Stoney’s equation was applied for this sample as well. To control these results and to get a deeper understanding of the vertical strain state in the structures, reciprocal space mapping was performed around the (0 0 0 2) and (1,1,−2,4) reflection. From the asymmetric RSMs, the a- and c-lattice constants were determined so that the indium concentration could be compared to the in situ findings, as shown in Table 1. Astonishingly, the values show quite a good agreement, in spite of the simplifications. Considering the asymmetric RSMs in Fig. 7, for sample (b) and (c), the AlInN peak is aligned vertically above that of the GaN buffer implying a pseudomorphic growth of the DBR. However, in sample (a) the AlInN has a different in-plane lattice constant from the buffer. That means that lattice relaxation actually occurred, which is, however, not complete. The degree of lattice relaxation with
Fig. 8. In-plane lattice constants in dependence of the incoming angle ˛.
respect to the underlying GaN is: aAlInN − aGaN arelaxed − aGaN AlInN
=
3.172 − 3.183 = 48% 3.160 − 3.183
From grazing-incidence in-plane diffraction (GIID) the a-value of the structures was determined depth dependently. Through a stepwise increase of the incoming angle ˛, the penetration depth of the X-rays is changed, so that one first just gets a signal from the upper few nanometers and then one goes to depths of up to about 500 nm. Fig. 8 shows the a-values obtained from these depth-dependent measurements. The nearly lattice matched sample (b) shows one
Fig. 7. Reciprocal space maps around the symmetrical (0 0 0 2) and the asymmetrical (1,1,−2,4) reflection for the three samples, the red line in the asymmetrical RSM shows the positions on which reflections of fully relaxed AlInN are expected.
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Fig. 9. Grazing-incidence in-plane diffraction in comparison to X-ray transmission scattering. Fig. 10. X-ray reflectivity and X-ray standing wave measurements.
in-plane lattice parameter that stays constant within the DBR. Sample (c), with higher indium content, shows initially the same value, but then it becomes slightly larger, to decrease afterwards again. When the increase is registered for ˛ ≈ 0.4◦ , the X-rays are able to penetrate the first AlInN layer, which means that therein the aconstant becomes a little larger. With higher incoming angles, more information from the following GaN layer is gathered, and the lattice parameter in average becomes smaller again. In sample (a), the fitting of the diffractograms reveals two contributions which apparently belong to GaN and AlInN, respectively. Obviously the AlInN, which is tensely strained, also induces compressive strain to the GaN layers in the reflector and reduces its in-plane lattice constant. Hence, there is an interaction between the AlInN and GaN, which influence themselves mutually. That the AlInN already is seen at low incoming angles ˛, is explained by the rough surface of the sample, which allows the X-rays to advance deeper into the films. The effect of the AlInN on the GaN becomes also obvious in the comparison of the GIID with X-ray transmission scattering (XTS) measurements. In the latter method, the (1,0,−1,0) reflection was examined as well, with the difference that the beams now goes through the whole structure, including the substrate in Laue geometry. This is why the main part of the diffracted intensity comes from the thick GaN buffer. In Fig. 9, the comparison for the three samples is plotted, whereas for the GIID, a low ˛ has been chosen to see just the uppermost GaN layer. While sample (a) shows a clear difference between these two types of measurement, the GIID and XTS measurements for sample (b) and (c) are nearly the same, which is a strong indication that the AlInN is grown pseudomorphically. On the contrary, in sample (a), the GaN in the DBR has a lower a-lattice constant than in the GaN buffer, caused by induced compressive strain through the AlInN layers with insufficient indium. The distortion of GaN can be recognized in the asymmetric RSM too, where the GaN reflection is streched asymmetrically in the lower left direction, i.e., compressively strained GaN. Moreover, the superlattice fringes are arranged vertically in the RSM, which denotes that the DBR acts detached from the buffer. The smoothness of the interfaces and the homogeneity of the layer thicknesses was reviewed by X-ray reflection and X-ray standing wave (XSW) measurements. XSW is a technique, which is similar to XRR, but here X-ray source and detector are not arranged in a line, but rather the detector is positioned at the diffraction angle of the (1,0,−1,0) reflex. Hence, the method is a superposition of GIID and XRR. Only when the sample has smooth interfaces
and homogeneous layer thicknesses as well as a good crystalline quality without relaxation, the XSW scan should basically show the same Kiessig oscillations as the XRR scan. However, the presented samples show no well pronounced oscillations, as shown in Fig. 10. This behavior is indicative for a great roughness of the interfaces or for thickness fluctuations in the stack. This issue is mostly pronounced for the relaxed sample (a), marked through the steep decrease of the intensity. To corroborate these results, the samples were further investigated by AFM measurements. While sample (b) and (c) have comparable smooth surfaces with a RMS value of 6 nm (20 m× 20 m), sample (a) shows three-dimensional brainlike structures on the surface. Hence, this sample suffers from a strong inhomogeneity of the layer thicknesses, as observed in FE–SEM images. These pictures confirm the rough interfaces for all three samples as well, especially on the top of the AlInN layers, where dips with a seize of about 10 nm appear. Sample (d), a 10-fold DBR, which was grown earlier with thinner AlInN layers, has smoother interfaces and therefore exhibits stronger oscillations in the XRRand XSW-scan. This implies a deterioration of the interfaces with increasing AlInN thickness.
4. Summary The influence of the wafer anisotopy on the noise level in in situ curvature measurements was demonstrated. It was shown that, besides sapphire substrates, silicon substrates show a concave curvature when heated up as well, which leads to a larger vertical temperature gradient than in sapphire, explained through the higher emissivity of silicon. Furthermore it was shown with the example of the growth of AlInN/GaN DBRs that the bowing measurements can be corrected from the temperature-induced substrate bow to get only the curvature caused by strain. It was demonstrated that in situ measurements are very suitable to estimate the concentration in AlInN layers with an accuracy of approximately ±1%, if the layers are strained and do not exhibit cracks and if they are smooth enough to reflect the laser spots specularly. Consequently the method is a great addition or even an alternative to other ex situ experiments in order to control the strain and composition of thin films. For validation of the results and for a deeper insight into the structural properties of the structures, they were furthermore analyzed by various X-ray diffraction techniques.
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Acknowledgement Financial support from the German Science Foundation (DFG) in the framework of SFB 787 is greatly acknowledged. References [1] A. Krost, A. Dadgar, G.R. Strassburger, R. Clos, Phys. Stat. Sol. A 200 (2003) 26. [2] H. Amano, M. Iwaya, T. Kashima, M. Katsuragawa, I. Akasaki, J. Han, S. Hearne, J.A. Floro, E. Chason, J. Figiel, J. Appl. Phys. 82 (2003) 28. [3] F. Brunner, V. Hoffmann, A. Knauer, E. Steinmetz, T. Schenk, J.-T. Zettler, M. Weyers, J. Crystal Growth 298 (2007) 202. [4] A. Knauer, T. Kolbe, S. Einfeldt, M. Weyers, M. Kneissl, T. Zetter, Phys. Stat. Sol. A 206 (2009) 211. [5] F. Brunner, A. Knauer, T. Schenk, M. Weyers, J.-T. Zettler, J. Crystal Growth 310 (2008) 2432. [6] H. Ishikawa, T. Jimbo, T. Egawa, Phys. Stat. Sol. C 5 (2008) 2086. [7] T.-C. Lu, C.-C. Kao, H.-C. Kuo, G.-S. Huang, S.-C. Wang, Appl. Phys. Lett. 92 (2008) 141102. [8] G. Christmann, R. Butté, E. Feltin, J.-F. Carlin, N. Grandjean, Phys. Rev. B (2006) 153305. [9] J. Dorsaz, J.-F. Carlin, S. Gradecak, M. Ilegems, J. Appl. Phys. 97 (2005) 084505.
[10] A. Gadanecz, J. Bläsing, A. Dadgar, C. Hums, A. Krost, Appl. Phys. Lett. 90 (2007) 221906. [11] J.-F. Carlin, C. Zellweger, J. Dorsaz, S. Nicolay, G. Christmann, E. Feltin, R. Butté, N. Grandjean, Phys. Stat. Sol. B 242 (2005) 2326. [12] A. Krost, A. Dadgar, F. Schulze, J. Bläsing, G. Strassburger, R. Clos, A. Diez, P. Veit, T. Hempel, J. Christen, J. Crystal Growth 275 (2005) 209. [13] A. Krost, J. Bläsing, Mater. Sci. Eng. A 524 (2009) 82. [14] T. Sato, Jpn. J. Appl. Phys. 6 (1967) 339. [15] S.C. Jain, S.K. Agarwal, W.N. Borle, S. Tata, J. Phys. D: Appl. Phys. 4 (1971) 1207. [16] E.R. Dobrovinskaya, L.A. Lytvynov, V. Pishchik, Sapphire: Materials, Manufacturing, Applications, Springer, 2009. [17] W.G. Breiland, S.R. Lee, D.D. Koleske, J. Appl. Phys. 95 (2004) 3453. [18] R. Clos, A. Krost, in: T. Li, M. Mastro, A. Dadgar (Eds.), III–V Compound Semiconductors: Integration with Silicon-Based Microelectronics, CRS Press, 2010. [19] G. Stoney, Proc. R. Soc. Lond. A 82 (1909) 172. [20] S.L. Rumyantsev, M.S. Shur, M.E. Levinshtein, Int. J. High Speed Electron. Syst. 14 (2004) 1. [21] Online information: http://www.marketechsapphire.com/pages/sapphprops.html (accessed 22.01.10). [22] S. Figge, H. Kröncke, D. Hommel, B. Epelbaum, Appl. Phys. Lett. 94 (2009) 101915. [23] C. Roder, S. Einfeldt, S. Figge, D. Hommel, Phys. Rev. B 72 (2005) 085218. [24] K. Wang, R.R. Reeber, Appl. Phys. Lett. 79 (2001) 1602.
Contents lists available at ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Strain profiling of AlInN/GaN distributed Bragg reflectors using in situ curvature measurements and ex situ X-ray diffraction C. Berger, P. Moser, A. Dadgar, J. Bläsing, R. Clos, A. Krost ∗ Institute of Experimental Physics, Otto-von-Guericke-University, Universitaetsplatz 2, 39016 Magdeburg, Germany
a r t i c l e
i n f o
Article history: Received 18 February 2010 Received in revised form 14 April 2010 Accepted 15 April 2010
Keywords: In situ curvature measurements Group-III nitrides X-ray diffraction
a b s t r a c t In this work, we show the use of in situ curvature and X-ray measurements to evaluate the metal organic vapor phase growth process of distributed Bragg reflectors consisting of an AlInN/GaN system. At first, it is investigated how the initial wafer bow and the heating of the bare substrates influences the curvature measurements. The strain induced by thermal mismatch and lattice mismatch is discussed at the example of multilayer AlInN/GaN Bragg mirror structures on sapphire substrate. We will demonstrate that thereby an estimation of the composition in the AlInN layers is possible. Additionally the samples were examined with multiple X-ray diffraction techniques, as symmetrical and asymmetrical reciprocal space maps, grazing-incidence in-plane diffraction and X-ray reflectivity. These results are compared with the in situ measurements. © 2010 Elsevier B.V. All rights reserved.
1. Introduction In the last few years, it has turned out that in situ curvature measurements are a very appropriate tool to assess the strain appearing in thin film structures already during the epitaxial growth process. Through the observation of the curvature behavior of the wafer, it was possible to trace the different sources for strain in GaN heteroepitaxy [1]. Being used in a qualitative manner, the method was very successful to investigate the impact of low temperature AlN interlayers to reduce the stress in thick AlGaN layers on sapphire, which allowed strain-free films without the formation of cracks [2]. Furthermore curvature measurements were used to obtain a flat wafer with a homogeneous temperature distribution during the deposition of InGaN multiple-quantum-wells (MQWs). Because of the strong temperature dependence of the indium incorporation, this leads to much better wavelength uniformity across the wafer [3]. Nowadays, the availability of high-resolution curvature sensors even allows the determination of the lattice constants of ternary nitrides or of the strain state of MQWs [4,5]. Here, we apply the method to investigate the growth of distributed Bragg reflectors (DBRs) based on AlInN/GaN. Such mirrors give the possibility to increase the light extraction efficiency and to get a narrower and more directional emission, when inserted below the active region of a light-emitting device [6]. Furthermore, through the very high reflectivity, which can be realized with DBRs, it is possible to fabricate microcavities for vertical cav-
∗ Corresponding author. Fax: +49 391 6711130. E-mail address: [email protected] (A. Krost). 0921-5093/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2010.04.053
ity surface emitting lasers (VCSELs) [7] or even to achieve strong coupling between excitons and photons [8]. Consisting of many periods of two alternating materials with different refractive index, DBR structures become very thick and therefore are very vulnerable to the appearing of cracks or lattice relaxation of the films. To prevent these material degrading issues, the combination of AlInN and GaN as quarter-wave layers is very promising, because AlInN can be grown lattice matched to GaN with an indium content of about 18% and strain-free deposition of the films is enabled [9–11]. Using an in situ curvature sensor, we show how the strain state of the layers can be estimated during the growth process of 10-fold AlInN/GaN Bragg reflectors. In order to interpret the curvature measurements correctly, it first has to be ensured that the influence of different effects on the signal is clearly known. Additionally to the strain-induced change in wafer bow, which can be attributed on the one hand to lattice mismatch between the different layers and to intrinsic stresses through the coalescence of three-dimensional islands or doping effects, and on the other hand to the thermal mismatch between the films and the substrate, there are two other contributions having a significant effect on the wafer curvature. The first fact to be considered is that the wafers have an initial bow, which originates from the fabrication process and the polishing of the substrates. An inevitable anisotropy of these processed surfaces leads to a variation of the curvature value while the wafer is rotating. The other effect is a concave bowing of the bare substrate arising during heating. This behavior can be explained by a vertical temperature gradient within the substrate, due to the thermal irradiation of the upper surface and the cooling effect of the gases flowing above the wafer. All these effects were examined
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and their individual influence on the curvature measurement will be discussed. 2. Experimental setup The in situ curvature measurements were carried out with an optical reflection method. It uses two parallel laser beams with a well-defined distance, which are reflected on the wafer surface and then are detected by a CCD camera, where their distance is analyzed. Depending on the shape of the surface, this distance becomes larger or smaller. Having a concave wafer, the spot distance is decreased and one gets a positive curvature signal. For convex samples it is vice versa. During the experiments, two different apparatus were mounted on the Aixtron AIX200/4 RF-S horizontal MOVPE-reactor. The first was a self-built sensor, equipped with a He–Ne laser and a Fabry–Perot etalon, to get two laser-spots being reflected of the wafer surface. More details on this buildup can be found in Ref. [12]. This system provides the curvature and the reflectance of the sample at a wavelength of 633 nm. The other setup was a commercially available EpiCurveTT® system by LayTec, which delivers in addition emissivity-corrected pyrometry and reflectance at 950 nm. The total resolution that was achieved with the curvature sensor is about ±5 km−1 , whereby relative changes of the curvature with a magnitude of ±1 km−1 could be measured. The substrates being used were single side polished 2 inch c-plane sapphire wafers with a thickness of 430 m. The bare substrate bending at higher temperatures was also examined for 500 m thick silicon (1 1 1) wafers. Symmetrical X-ray diffraction and X-ray reflectivity (XRR) measurements were accomplished on a newly developed concurrent X-ray diffractometer equipped with a rotating anode CuK␣ -source, a curved Johannson-type Ge(1 1 1) monochromator for convergent beam optics, a Bruker D8 high-resolution goniometer, and a two-dimensional area detector (Vantec 2000) as described in Ref. [13]. Reciprocal space mapping was carried out on a URD6 (Seifert/FPM) system equipped with a position sensitive detector, and depth-dependent in-plane lattice parameters as well as X-ray transmission and X-ray standing wave measurements were performed with a grazing-incidence diffractometer [13]. Furthermore, high-resolution X-ray diffraction (HRXRD) was accomplished on a GE/Seifert XRD 3003 HR system and ex situ 3D-bow measurements were done on an OEG Flatscan optical 3D surface profilometer.
Fig. 1. Transients of reflectance and curvature during the rotation of a sapphire substrate. The curvature (lower curve) and the dots are raw data and the black upper curve shows the smoothened reflectance.
Periodic oscillations appear in the curvature, with an amplitude of about 40 km−1 , and in the reflected intensity as well. Apparently, the period of the reflectance oscillations corresponds to the length of one wafer rotation, but the curvature oscillation turns out to be exactly twice as fast. This is not quite surprising, because after a rotation of 180◦ , the two parallel laser beams are already deflected in nearly the same manner, whereas the reflectance reaches its starting value only just after a full rotation. To understand and to clarify these curvature oscillations, a 3D-bow measurement of this wafer was made, which can be seen in Fig. 2. This reveals that the wafer has a saddle shaped surface profile with a convex curvature in one direction and a concave curvature perpendicular to it. Assuming a spherical surface shape in each direction, the curvature of the two main directions can be calculated straightforward to C≈
2h x2
where h is the height difference to the center and x is the corresponding lateral distance from the center. Doing so, one gets two values which differ from each other by an absolute value of nearly 50 km−1 . This agrees very well with the height of the in situ curvature oscillations, so it can be concluded that the anisotropy of the wafer surface is the main cause for the noise and variation of
3. Experimental results 3.1. Initial wafer bow When performing in situ curvature measurements, the raw data taken by the sensor are usually smoothed by taking a moving average over several seconds to obtain a straight transient. However, during wafer rotation it was observed that the raw values of the curvature strongly vary in a range of about ±15 to ±35 km−1 , which is different with each wafer placed into the reactor. This variation is therefore often a lot greater than the growth related changes of curvature to be analyzed, which can be in the magnitude of 1 km−1 . Often this resolution limiting effect is assigned to wafer wobble under gas-foil rotation, but, assuming a spherical surface of the sample, wobbling itself cannot explain this heavy variation, since the direction of beam reflection is not significantly influenced by the tilting of a spherical surface for a few degrees. Rather this behavior seems to originate from the wafer itself. Thus a bare sapphire substrate was placed in the reactor and the rotation was set very slowly with an estimated cycle duration of 5 s. The sensor took 10 measurement values in 1 s, so one gets about 50 values for a single rotation. Fig. 1 shows the resulting transients.
Fig. 2. 3D surface profile of the sapphire substrate from Fig. 1. The curvature C is calculated along the x- and y-axis, assuming a spherical profile.
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Fig. 3. Position-dependent ω-scans of the (0 0 0 6) sapphire reflex (from the substrate in Fig. 2), for the two directions parallel to the flat (left) and antiparallel to the flat (right).
the curvature during rotation. Noteworthy, the shape of the surface differed significantly for each one of several measured substrates. To figure out if the measured curvature belongs to a true bending of the substrate, i.e., the lattice planes show the same curvature, or if it is just caused through a thickness variation of the wafer due to the polishing during the fabrication process, position-dependent ω-scans of the (0 0 0 6) plane of sapphire were made to obtain the orientation of the lattice planes across the wafer. This can be done through the observation of the shift of the peak position in dependency of the position where the X-rays strike the sample (Fig. 3). In contrast to the 3D-bow measurement, where the wafer simply was lying on a table, here the sample was mounted vertically on a flat plate with a little piece of sticky tape, to ensure that the wafer still can bend freely. The curvature then follows to C=
2 sin(ω/2) x
with x as the shift of the point focus on the sample and ω as the related change of the peak position. These measurements revealed that the lattice planes show the same curvature behavior in both directions with a very small concave bending, whereby it has to be mentioned that the determined value is at the limit of what can be measured with this method, since it cannot be excepted that the shifting of the x-position does not introduce a slight peak position shift of 0.01◦ . Nevertheless, the surface profile showed a completely different curvature behavior. This means that the main part of the surface profile comes from a fluctuating thickness of the wafer and not from a bending of the substrate. This was also confirmed by
measurements with an outside micrometer on different positions on the wafer (Fig. 3). 3.2. Curvature caused by heating It was observed that already the heating of the bare silicon or sapphire leads to a concave bending of the substrates. This effect is also described in Ref. [5] and can be explained with a vertical temperature gradient within the wafer. It arises from the heating of the backside and thermal irradiation of the frontside of the substrate. The dependency between the temperature difference of the two sides and the curvature C can be expressed by C(T ) = ˛
T
back
− Tfront hs
where hs is the substrate thickness and ˛ is the thermal expansion coefficient. In the experiment, the reactor temperature was ramped up and down with various durations in a range of 400–1100 ◦ C. The wafers were under a H2 atmosphere with a flow rate of 8 sccm and the pressure was 100 mbar. No significant influence of the heating rate on the substrate bow could be seen. Fig. 4 shows that on the one hand the increase of the curvature was not linear, in contrast to the findings in Ref. [5]. On the other hand, the sapphire substrates exhibit a stronger bowing than the silicon substrates. But due to the smaller thermal expansion of silicon, the calculated temperature difference is even slightly higher than in the sapphire substrate. Thereby it has to be noted that the temperature differences are rather small with a value of
Fig. 4. Change of curvature during heating of bare sapphire (430 m) and silicon (500 m) substrates.
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Fig. 5. In situ curvature measurement of a 10-fold distributed Bragg reflector, based on AlInN/GaN, grown on sapphire. The red line shows the true temperature measurement of the susceptor and the black line shows the corrected curvature, without initial wafer bow and temperature-induced substrate bow. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
about 4 K at 1100 ◦ C for both substrates, but already these values lead to a considerable bending. However, the greater temperature gradient in the silicon was at first unexpected, because of its much better thermal conductivity. Assuming that the thermal losses through the frontside only are caused by heat radiation, the temperature difference in the thermal equilibrium is roughly given by the Stefan–Boltzmann law T =
4 hs εTfront
with ε the emissivity, the Stefan–Boltzmann constant and the thermal conductivity. The answer to the larger temperature difference in silicon seems to be its enhanced emissivity as compared to sapphire. Being dependent on, e.g. surface morphology and doping concentration, the emissivity of silicon in the examined temperature range should be much higher than of sapphire [14–16]. 3.3. Strain-induced wafer bow Fig. 5 shows the in situ measurement of the growth of a 10-fold AlInN/GaN Bragg reflector. The buffer consists of two thick GaN layers separated by a low temperature AlN interlayer to induce compressive stress in the second one and avoid cracking. In addition two in situ SiN masks are inserted to stop the vertical propagation of threading dislocations and to reduce their density. As known, AlInN and GaN prefer very different growth temperatures around 700 ◦ C and 1000 ◦ C, so the temperature has to be repeatedly changed by more than 300 ◦ C in the growth process, which leads to the corresponding curvature changes. With the knowledge of the temperature depending substrate bow the measurement can be corrected by this effect by simply substracting it from the original measurement; so one gets the pure strain-induced bow caused by lattice mismatch and the different thermal expansion coefficients. As a result, the curvature changes at the beginning of the process are removed, which reveals that the first part of the buffer grows nearly strain-free. Moreover, upon temperature change the impact on the bending becomes smaller representing the bare thermal mismatch now. This removal of the temperature depending substrate bow becomes especially important when the temperature changes during the deposition of a single material, since only in this manner, the correct slope of the curvature can be determined. The goal when growing such structures is to achieve a lattice matched growth of the AlInN layers on the GaN. This can be real-
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Fig. 6. In situ curvature measurements of three DBR structures with different AlInN compositions, as determined by X-ray diffraction ([In]a = 11.4%, [In]b = 18%, [In]c = 21%). Please notice that the transients were shifted vertically for better visibility and the growth times were also changed.
ized at an In-concentration of about 18%. In Fig. 6 the curvature measurements of the growth of three DBR structures are illustrated, whereby the indium content in the AlInN was varied. First of all, it can be seen that the LT–AlN interlayer induces compressive strain to the following GaN. Afterwards, all samples show a different behavior during the deposition of the AlInN layers. Sample (a) shows an increasing concave curvature during AlInN deposition, which is associated with a tensile strain within the layers. While in sample (b) the curvature proceeds slightly in the concave direction too, sample (c) shows a compressively strained AlInN layer. The oscillation of the curvature signal for that sample during the GaN buffer growth is assigned to a thickness gradient in the film [17]. In order to determine the indium concentration in the layers, the increase of curvature during the growth of the individual AlInN layers was averaged and evaluated. Correctly, one has to use a approach for multilayer systems [18], which considers the influence of the strain in all underlying layers. However, due to their short growth time, the GaN strain in the DBR is not exactly known. Moreover exact material parameters are missing. Therefore, as a first approximation of the lattice mismatch εm , a simplified expression was applied here, which is equilvalent to the classical Stoney formula [19]: C=
6εm Mf hf Ms h2s
Ms,f is the biaxial moduli, and hs,f is the thickness of the sapphire substrate and the film, respectively. Because of the lack of values for the elastic constants for AlInN, the biaxial modulus has been interpolated to Mf = 450 GPa using the values from AlN and InN [20]. As values for GaN and sapphire, MGaN = 478 GPa [20] and Ms = 607 GPa [21] have been taken. The thicknesses of the GaN and AlInN layers in the DBR have been determined by the fitting of symmetrical /2-HRXRD measurements (distance of the interference fringes), because they are too thin to do a reliable fit with Fabry–Perot oscillations. They were determined to 43 nm for GaN and 48 nm for AlInN, respectively. These values were confirmed by FE–SEM images. The lattice mismatch is given by εm =
af (T ) − as (T ) as (T )
with af being the in-plane lattice constant of AlInN, interpolated by Vegard’s law as well, and as being the in-plane lattice constant of GaN. Assuming that AlInN and GaN have nearly the same thermal
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Table 1 Strain values obtained from in situ curvature measurements and thereof calculated material composition [In]curve in comparison with the concentration obtained by X-ray diffraction. Sample
af /aGaN
[In]curvature (%)
[In]XRD (%)
a b c
−6.5 × 10−3 −9 × 10−4 4.6 × 10−3
13.2 17.5 21.6
11.6 18.0 21.0
expansion coefficient [22–24], the temperature dependence can be neglected. Having a closer look on Fig. 6, strain relaxation seems to appear in sample (a), indicated by the drop of the linear slope during the growth of the first AlInN layer. Usually, this prevents the analysis of the layer composition, but nevertheless, strain is accumulated again in the following layers, so Stoney’s equation was applied for this sample as well. To control these results and to get a deeper understanding of the vertical strain state in the structures, reciprocal space mapping was performed around the (0 0 0 2) and (1,1,−2,4) reflection. From the asymmetric RSMs, the a- and c-lattice constants were determined so that the indium concentration could be compared to the in situ findings, as shown in Table 1. Astonishingly, the values show quite a good agreement, in spite of the simplifications. Considering the asymmetric RSMs in Fig. 7, for sample (b) and (c), the AlInN peak is aligned vertically above that of the GaN buffer implying a pseudomorphic growth of the DBR. However, in sample (a) the AlInN has a different in-plane lattice constant from the buffer. That means that lattice relaxation actually occurred, which is, however, not complete. The degree of lattice relaxation with
Fig. 8. In-plane lattice constants in dependence of the incoming angle ˛.
respect to the underlying GaN is: aAlInN − aGaN arelaxed − aGaN AlInN
=
3.172 − 3.183 = 48% 3.160 − 3.183
From grazing-incidence in-plane diffraction (GIID) the a-value of the structures was determined depth dependently. Through a stepwise increase of the incoming angle ˛, the penetration depth of the X-rays is changed, so that one first just gets a signal from the upper few nanometers and then one goes to depths of up to about 500 nm. Fig. 8 shows the a-values obtained from these depth-dependent measurements. The nearly lattice matched sample (b) shows one
Fig. 7. Reciprocal space maps around the symmetrical (0 0 0 2) and the asymmetrical (1,1,−2,4) reflection for the three samples, the red line in the asymmetrical RSM shows the positions on which reflections of fully relaxed AlInN are expected.
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Fig. 9. Grazing-incidence in-plane diffraction in comparison to X-ray transmission scattering. Fig. 10. X-ray reflectivity and X-ray standing wave measurements.
in-plane lattice parameter that stays constant within the DBR. Sample (c), with higher indium content, shows initially the same value, but then it becomes slightly larger, to decrease afterwards again. When the increase is registered for ˛ ≈ 0.4◦ , the X-rays are able to penetrate the first AlInN layer, which means that therein the aconstant becomes a little larger. With higher incoming angles, more information from the following GaN layer is gathered, and the lattice parameter in average becomes smaller again. In sample (a), the fitting of the diffractograms reveals two contributions which apparently belong to GaN and AlInN, respectively. Obviously the AlInN, which is tensely strained, also induces compressive strain to the GaN layers in the reflector and reduces its in-plane lattice constant. Hence, there is an interaction between the AlInN and GaN, which influence themselves mutually. That the AlInN already is seen at low incoming angles ˛, is explained by the rough surface of the sample, which allows the X-rays to advance deeper into the films. The effect of the AlInN on the GaN becomes also obvious in the comparison of the GIID with X-ray transmission scattering (XTS) measurements. In the latter method, the (1,0,−1,0) reflection was examined as well, with the difference that the beams now goes through the whole structure, including the substrate in Laue geometry. This is why the main part of the diffracted intensity comes from the thick GaN buffer. In Fig. 9, the comparison for the three samples is plotted, whereas for the GIID, a low ˛ has been chosen to see just the uppermost GaN layer. While sample (a) shows a clear difference between these two types of measurement, the GIID and XTS measurements for sample (b) and (c) are nearly the same, which is a strong indication that the AlInN is grown pseudomorphically. On the contrary, in sample (a), the GaN in the DBR has a lower a-lattice constant than in the GaN buffer, caused by induced compressive strain through the AlInN layers with insufficient indium. The distortion of GaN can be recognized in the asymmetric RSM too, where the GaN reflection is streched asymmetrically in the lower left direction, i.e., compressively strained GaN. Moreover, the superlattice fringes are arranged vertically in the RSM, which denotes that the DBR acts detached from the buffer. The smoothness of the interfaces and the homogeneity of the layer thicknesses was reviewed by X-ray reflection and X-ray standing wave (XSW) measurements. XSW is a technique, which is similar to XRR, but here X-ray source and detector are not arranged in a line, but rather the detector is positioned at the diffraction angle of the (1,0,−1,0) reflex. Hence, the method is a superposition of GIID and XRR. Only when the sample has smooth interfaces
and homogeneous layer thicknesses as well as a good crystalline quality without relaxation, the XSW scan should basically show the same Kiessig oscillations as the XRR scan. However, the presented samples show no well pronounced oscillations, as shown in Fig. 10. This behavior is indicative for a great roughness of the interfaces or for thickness fluctuations in the stack. This issue is mostly pronounced for the relaxed sample (a), marked through the steep decrease of the intensity. To corroborate these results, the samples were further investigated by AFM measurements. While sample (b) and (c) have comparable smooth surfaces with a RMS value of 6 nm (20 m× 20 m), sample (a) shows three-dimensional brainlike structures on the surface. Hence, this sample suffers from a strong inhomogeneity of the layer thicknesses, as observed in FE–SEM images. These pictures confirm the rough interfaces for all three samples as well, especially on the top of the AlInN layers, where dips with a seize of about 10 nm appear. Sample (d), a 10-fold DBR, which was grown earlier with thinner AlInN layers, has smoother interfaces and therefore exhibits stronger oscillations in the XRRand XSW-scan. This implies a deterioration of the interfaces with increasing AlInN thickness.
4. Summary The influence of the wafer anisotopy on the noise level in in situ curvature measurements was demonstrated. It was shown that, besides sapphire substrates, silicon substrates show a concave curvature when heated up as well, which leads to a larger vertical temperature gradient than in sapphire, explained through the higher emissivity of silicon. Furthermore it was shown with the example of the growth of AlInN/GaN DBRs that the bowing measurements can be corrected from the temperature-induced substrate bow to get only the curvature caused by strain. It was demonstrated that in situ measurements are very suitable to estimate the concentration in AlInN layers with an accuracy of approximately ±1%, if the layers are strained and do not exhibit cracks and if they are smooth enough to reflect the laser spots specularly. Consequently the method is a great addition or even an alternative to other ex situ experiments in order to control the strain and composition of thin films. For validation of the results and for a deeper insight into the structural properties of the structures, they were furthermore analyzed by various X-ray diffraction techniques.
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