Nitrogen-enhanced indium segregation in (Ga,In)(N,As)/GaAs multiple quantum wells grown by molecular-beam epitaxy

Transmission electron microscopy (TEM) is used to determine the composition of quaternary (Ga,In)(N,As) quantum wells (QWs). Through a combined analysis of the chemically sensitive (002) dark-field (DF) images and the lattice-resolving high-resolution TEM images, the local distributions of nitrogen and indium in the growth direction are determined. In particular, we are able to directly detect the existence of indium segregation in (Ga,In)(N,As) QWs. A comparison with the indium distribution profile in the nitrogen-free (In,Ga)As QWs, grown under similar conditions, revealed that incorporating N into the alloy enhanced indium segregation.


Introduction
Dilute III-V-N heterostructures are of considerable research interest from both a fundamental and technological point of view [1,2]. In particular, for the (Ga,In)(N,As) alloy, the huge band gap bowing by the introduction of N and the resulting strong redshift of the band gap, make it very attractive for application in GaAs-based laser diodes operating in the 1.3-1.55 µm optical fibre windows [3]- [5]. However, the mechanisms controlling the incorporation of In (35-40%) and N (2-5%) required for reaching the desired wavelength range are still not well understood [6]. It is accepted that the structural perfection of the alloy deteriorates dramatically with increasing N content due to the large miscibility gap and the phase separation tendency [7,8]. As a consequence, composition fluctuations and interface undulations are generally developed, that can only be avoided by the growth at low temperatures (T g 460 • C) using techniques like molecular-beam epitaxy (MBE) [1]. On the other hand, realization of atomically flat and abrupt heterointerfaces is a matter of greatest concern. However, it is well known that during heteroepitaxial growth of (In,Ga)As, a considerable amount of indium atoms segregate to the surface [9]. As a consequence, spatially varying composition profiles appear that exert an undesirable influence on the optical and transport properties of superlattices and quantum wells (QWs) as they modify the intended potential profile and energy levels of the confined states [10]. Despite the fact that good performance (Ga,In)(N,As)-based lasers have been fabricated [6,11], indium segregation in (Ga,In)(N,As) is a subject largely unexplored so far. Recently, it has been put forward that the presence of N in the alloy enhances In segregation [12]. This suggestion, however, is based on the data obtained from indirect experiments [12].
In this paper, we present direct experimental evidence of indium segregation in MBEgrown (Ga,In)(N,As) multiple-QWs by using transmission electron microscopy (TEM). MQWs are required to improve the performance of (Ga,In)(N,As) devices. In particular, the In and N compositions, [In] and [N], studied across the QWs were locally determined by a combined evaluation of the tetragonal lattice distortion of coherently strained structures and the contrast analysis of the chemically sensitive (002) dark-field (DF) TEM images [13]. The obtained profiles are then compared to those taken from nitrogen-free (In,Ga)As/GaAs QWs grown under similar conditions. For the T g considered, we found that In segregation is undetectable in the (In,Ga)As MQWs, contrary to the (Ga,In)(N,As) case, where the presence of nitrogen promotes indium surface segregation.

Experimental
Ten 7-nm wide (Ga,In)(N,As) QWs with 30-nm thick GaAs potential-energy barriers were grown on GaAs(001) substrates under As-rich conditions in a MBE system equipped with a rf nitrogen plasma source. Prior to the growth of the (Ga,In)(N,As) MQWs, a 100 nm thick GaAs buffer layer was grown at 580 • C. The samples were prepared at two different growth temperatures T g = 420 and 460 • C, measured by a thermocouple. For the growth of the MQW, the fluxes of all the elements were fixed throughout this study. Finally, a 100 nm GaAs cap layer was grown on top of the samples at the same temperature as the MQWs [14]. Growth took place in a layer-by-layer mode, as monitored by in situ reflection high-energy electron diffraction (RHEED). We examined two sets of samples. One of them contained (Ga,In)(N,As) QWs; the other contained QWs without nitrogen. The samples containing (Ga,In)(N,As) QWs are labelled G420 (T g = 420 • C) and G460 (T g = 460 • C). The corresponding (In,Ga)As samples are labelled I420 and I460. In all cases, we investigate the as-grown samples. Prior to the analysis by TEM, the samples were characterized by x-ray diffraction (XRD) and photoluminescence.
Cross-sectional TEM foils were prepared in the [110] and [110] projections, using mechanical thinning followed by Ar-ion milling. The TEM investigation was carried out using a Jeol JEM 3010 microscope operating at 300 kV, equipped with a GATAN CCD camera.
In classical ternary alloys (e.g. InGaAs and AlGaAs) there are two well-established techniques based on TEM to determine the composition: (i) measurement of the tetragonal lattice distortion from experimental high-resolution TEM (HR-TEM) or (ii) imaging and analysis of the intensity of the chemically sensitive (002) reflection from DF images. In the case of quaternary alloys, using only one of these methods give ambiguous results since a whole set of In and N concentrations leads to the same tetragonal distortion or DF intensity. Grillo et al [13] showed that the combined use of both methods solves the problem thus leading to an unambiguous and independent determination of the In and N content.
In III-V alloys, the diffracted intensity of the (002) reflection is proportional to the square of the (002) structure factor F 002 , which depends on the difference in the atomic scattering factors, f , of the elements III and V [15]. In the case of the Ga 1−x In x N y As 1−y alloy, the kinematically diffracted intensity I 002 can then be written as: In order to avoid the necessity of measuring absolute intensities, the scattered intensity I 002 of the (Ga,In)(N,As) QW is normalized to GaAs of the same thickness. The ratio R 002 of the intensities of (Ga,In)(N,As) and GaAs is then a quadratic function of x and y: On the other hand, the coherent strain in the Ga 1−x In x N y As 1−y QWs, which depends on the composition as well [a ⊥ = f (x, y)], produces a tetragonal distortion of the cubic unit cells that can directly be determined from the HR-TEM images. In our case, we use the LADIA program package [16] to evaluate the strain distribution. In short, this method is based on the local measurement of lattice spacing in HR-TEM micrographs, where the intensity maxima are identified related to the positions of atomic columns. The positions of these maxima are determined with respect to a reference lattice on the same micrograph. In our case, we use the GaAs barriers as a reference. The tetragonal lattice distortion of the layer is then the derivative of 4 the displacement between the atomic positions and the reference lattice [17]. The composition of the layer can then be calculated from the tetragonal distortion assuming Vegard's law, i.e. the tetragonal distortion depends linearly on the composition. The tetragonal lattice distortion of a (Ga,In)(N,As) layer on GaAs(001) is then: where c (Ga,In)(N,As) i j are the elastic constants of the quaternary system, and a (Ga,In)(N,As) 0 and a GaAs 0 are the lattice constants of the bulk alloy and substrate, respectively, which are obtained from the lattice parameter of the constituents (GaAs, GaN, InAs and InN) [18] assuming the validity of Vegard's law: Estimates of the coefficients c i j for (Ga,In)(N,As) are obtained from the corresponding binary constituents [18] assuming a linear interpolation: The combination of both techniques, the DF intensity and tetragonal distortion, i.e. solving equations (1)-(5) point by point across the QW, thus gives an unambiguous measurement of [In] and [N] as a function of the well depth. For the (In,Ga)As samples, [In] was directly determined from the analysis of the (002) DF images. In the analysis of the (002) images we took into account the atomic scattering factors given by Doyle and Turner [19], while influences of electron redistribution due to the bonding of atoms, local structural distortions and thin-foil surface relaxation [20]- [23] are not considered here. The analysis of the intensity of the (002) DF images is performed using the Digital Micrograph software (Digital Micrograph tm Gatan, Inc.). For the determination of the intensity profile across the QW (Digital Micrograph) as well as of the strain distribution along the growth direction (LADIA) we performed several linescans averaged over an area 20 × 20 nm perpendicular to the QW. We then average the data of these averaged-linescans in order to further reduce the noise. We average the data coming from the same QW, but do not average the data coming from different QWs. The examination of several QWs confirms however that the results found are reproducible and do not depend on the selected QW. Figure 1(b) shows an averaged linescan of the contrast in the (002) DF images across a QW ( figure 1(a)), the intensity being already normalized to that of GaAs. The average deviation of I 002 /I GaAs 002 (R 002 ) in the GaAs barriers is ∼0.015 and this represents an estimate of the noise associated with this measurement. On the other hand, figure 1(c) shows the strain map obtained from the analysis of the HR-TEM images with LADIA, together with the strain distribution across a QW ( figure 1(d)). In this case, the average deviation of the strain value in the GaAs barrier is ∼0.002, representing the estimated noise of this technique. indicated by the two dark lines on both sides of each QW, and laterally homogeneous overall composition. The origin for the two dark lines defining the interfaces is based upon the functional dependence of the intensity of the (002) reflection on the In and N concentrations [13,24]. For a given N concentration, the (002) reflection intensity in kinematic approximation shows a parabolic behaviour with a minimum located in the range between 15 and 25% of In (the minimum of the parabola shifts with increasing N values to lower In concentration [13] While the In distribution inside the QW is rather homogeneous for G420, it has a pronounced asymmetry for G460, characteristic of segregation effects; i.e. the local indium concentration gradually increases inside the QW, as growth proceeds. However, after the growth of the QW, hence after closing the indium shutter, we do not detect significant segregated indium into the upper GaAs barrier layer, which results in a rather symmetric distribution at the interfaces. Similar indium profiles are also found for other (Ga,In)(N,As) QWs [26]. The [N] profile of G460 exhibits a pronounced asymmetry, too. The areas of lower [N] correspond to the areas of higher [In], which is a well-known phenomenon caused by the preferred formation of Ga-N and In-As bonds with an increase in T g , due to the phase separation tendency of the alloy [27]. For G460, the fluctuations in [N] are strong amounting to a difference of 1.6% between the minimum and maximum values in the QW. For G420 with reduced T g , the fluctuations in [N] are only 0.8%.

Indium segregation in (Ga,In)(N,As)
The indium content across the (Ga,In)(N,As) QWs grown at 420 • C is homogeneous with a symmetric distribution profile, which can be well fitted by the error functions that describe diffusion processes ( figure 3(a)): the composition profile is characterized by an interface roughness parameter, L [28]; x 0 is the nominal indium mole fraction, N w is the well width in monolayers (ML), and n denotes the position along the growth direction.
The raise of T g to 460 • C promotes a gradual increase in [In] from 36 to 40%, characteristic of In segregation. The question of how this increase in the In content with its consequent increase in strain might affect critical layer thickness (h c ) then arises. We have estimated the critical thickness using the Matthews and Blakeslee model [29] for 40% In and 3% N (the experimental In and N contents resulting from In segregation) and get h c ∼ 19 nm. This value is much lower than that obtained assuming 36% In and 4.6% N (before segregation), h c ∼ 28 nm. However, in spite of the reduction in h c as a result of In segregation, our 7-nm wide QWs are still well below the estimated limit for plastic relaxation. This is in agreement with the experiments. We have evidence that the relaxation of epitaxial strain does not yet occur since no misfit dislocations were observed in the TEM investigations and the XRD data can be very well simulated assuming a coherently strained layer structure. Finally, it should be mentioned that, for a fixed indium content, the addition of nitrogen to the (In,Ga)As alloy compensates the high strain, thus increasing h c as shown by Tomić and O'Reilly [30].
It is known that T g is the growth parameter mainly controlling segregation and that increasing T g increases indium segregation in (In,Ga)As [10]. We have found, however, that the impact of higher growth temperatures on In segregation in the (Ga,In)(N,As) QWs is partly masked by an increase in surface roughening and the appearance of lateral composition fluctuations [31]. Therefore, due to the phase separation tendency of (Ga,In)(N,As), the range of T g to be explored is kept rather limited: on one side, the growth at higher T g leads to severe morphological instabilities; and on the other, the lower the growth temperature is, the higher the point defects density and the larger the degradation of the optical properties.
In addition to the gradual increase in [In] inside the QW, the growth at T g = 460 • C broadens the interfaces, if compared to G420 ( figure 3). This can be explained by the enhanced thermally activated diffusion at the interfaces due to the increase of T g . Similarly to G420, error functions also provide a good description at the interfaces of sample G460, as seen in figure 3(b), but in this case the [In] profile inside the QW clearly deviates from the symmetric fit.
Surface segregation of atoms is often described and quantified by a segregation efficiency factor, R, which defines the fraction of the topmost-layer atoms that move to the next layer. According to Muraki et al's phenomenological model for segregation [10], the indium  concentration in the n-th ML is given by: (1 n N w ; well) In G460, a fit to Muraki's model for segregation (figure 4) yields R = 0.81; i.e. indium segregation is remarkable. For (In,Ga)As QWs, from the analysis of RHEED oscillations during MBE growth, Martini et al [32] found R = 0.72 at the same T g = 460 • C; while a similar R of 0.8 has been reported for (In,Ga)As QWs grown at T g = 535 • C by lattice fringe analysis in the TEM by Litvinov et al [33]. Judging from our observations (figure 4), Muraki's model for segregation describes well the distribution of indium in the QW, but there is a discrepancy at the upper interface. As already mentioned, no significant 'tail' of indium atoms penetrates into the GaAs layer. Thus, it seems to be that interfaces act as a 'barrier' for segregation in this special material system.

Nitrogen-enhanced indium segregation
In order to explore the influence of nitrogen on indium segregation, we compared the In distribution obtained for the (In,Ga)As QWs grown under similar conditions (same T g and element fluxes, but without N supply). We found that when growing them at 420 • C T g 460 • C, indium segregation was undetectable, as shown in figure 5, and the [In] distribution is characterized by a diffusion-like symmetric profile. This is to say that indium segregation in the nitrogen-free QWs occurs at higher T g 's only. Figure 6 shows that [In] remains, indeed, constant at 39% across the QW (for I460), in contrast with the gradual increase in [In] for the sample with N in the QW (G460).
As deduced from the experiments, it is clear that the presence of nitrogen in the quaternary alloy enhances indium segregation. We attribute this effect to the increase in the driving force for segregation, i.e. higher elastic and bonding energy gradients [9], as a consequence of the introduction of nitrogen in (In,Ga)As. Due to the specific properties of the N atoms (small size and electronegativity), there are large differences in the bond lengths and cohesive energies between the arsenide-like and nitride-like 'environments' constituting the (Ga,In)(N,As) alloy [34] that makes the elastic and bonding energy gradients more pronounced than in the (In,Ga)As case.  Finally, according to the [In] and [N] distribution shown in figure 2(d), the strong N accumulation at the interfaces would increase In segregation there. The question whether the phase separation tendency affects indium segregation or whether it is indium segregation that affects the phase separation tendency then arises. Preliminary experiments performed on samples grown at constant T g but under different As fluxes, show that the As pressure has no detectable effect on the morphological instabilities associated with the composition modulations [27,31] but controls indium surface segregation. Thus, the element distribution would be determined by surface segregation, the latter affecting the phase separation tendency. A similar influence of surface segregation on phase separation has been already reported for the metastable In(As,Sb) and (In,Ga)N systems [35,36]. At present, additional work is in progress to further clarify this point.

Conclusions
We found for the first time direct evidence that the presence of nitrogen in the (Ga,In)(N,As) QW enhances indium segregation when compared to the nitrogen-free (In,Ga)As QW grown under similar conditions in the T g range from 420 to 460 • C. As a consequence of the phase separation tendency, this asymmetry in indium distribution produces strong fluctuations in the nitrogen content. The occurrence of In segregation in (Ga,In)(N,As) QWs should be considered in the design of devices based on this alloy, as it critically influences the potential profile and therefore the energy levels and corresponding emission wavelength.