GaAs heterostructures measured by low-loss electron energy-loss spectroscopy

Micron 37 (2006) 465–472 www.elsevier.com/locate/micron

Composition fluctuations in dilute nitride (Ga,In)(N,As)/GaAs heterostructures measured by low-loss electron energy-loss spectroscopy X. Kong *, A. Trampert, K.H. Ploog Paul-Drude-Institut fu¨r Festko¨rperelektronik, Hausvogteiplatz 5-7, D-10117 Berlin, Germany

Abstract We report on the investigation of composition fluctuations in epitaxially grown (Ga,In)(N,As) epilayers on GaAs(001) substrates by using electron energy-loss spectroscopy (EELS). The N and In concentrations are determined locally with a probe size of about 8 nm from the low-loss EELS measurements. We demonstrate that the small amount of N incorporating in dilute nitride alloys can be measured quantitatively by the plasmon energy shift with respect to a GaAs reference, and that the In content is analyzed simultaneously from the In 4d transitions, which have been isolated from the overlapping Ga 3d transitions. Our spatially resolved EELS results are utilized to discuss the origin of the inherent composition fluctuations and their influences on the morphological instabilities during epitaxial growth. q 2005 Elsevier Ltd. All rights reserved. PACS: 68.65.Fg; 68.55.Nq; 79.20Uv; 68.37.Lp Keywords: Electron energy-loss spectroscopy; (Ga, In)(N, As) epilayers; Composition fluctuation

1. Introduction The ternary and quaternary III–V semiconductor alloys are a class of materials that have received much attention due to their ability to continuously vary the band gap energy by changing the composition in a very controlled way (‘band gap engineering’). In this regard, the ‘dilute’ nitride alloys, in which a small N fraction of only a few percent is added into a conventional III–V semiconductor such as GaAs, GaInAs or GaP, show a strong band-gap reduction and thus open the way to several applications, for example to fabricate lasers operating in the telecommunication wavelength range (Kondow et al., 1997), or as high-efficiency solar cells (Friedman et al., 1998). However, due to the large miscibility gap and the phase separation tendency of the Ga–N–As systems (Ho and Stringfellow, 1997; Neugebauer and Van de Walle, 1995), composition fluctuations and morphological instabilities occur even if this kind of dilute nitride alloy is grown under metastable conditions. The situation is even more complex in the quaternary alloy, where two compositional degrees of freedom are present. Therefore, the elemental * Corresponding author. E-mail address: [email protected] (X. Kong).

0968-4328/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.micron.2005.11.008

distribution has to be analyzed on a local scale in more details in order to understand the origin of the inherent decompositions and their influences on the morphological instabilities during epitaxial growth. (Ga,In)(N,As) dilute nitride heterostructures are attractive systems for realizing GaAs-based laser diodes operating in the 1.3–1.55 mm optical fiber window (Kondow et al., 1996; Harris, 2002). However, when incorporating more than 2% N and 25% In as required for reaching the desired wavelength range, the structural quality of the resultant (Ga,In)(N,As) quantum wells (QWs) and epilayers deteriorates showing large composition fluctuations and interface roughnesses (Chauveau et al., 2003a; Trampert et al., 2004; Xin et al., 1999). Several tools including secondary ion mass spectroscopy (SIMS), X-ray photoelectron spectroscopy, medium energy ion scattering, transmission electron microscopy (TEM), as well as electron energy-loss spectroscopy (EELS) can be used to characterize elemental distributions. Among these techniques, the EELS in the TEM offers the unique combination of very high spatial resolution and the ability to provide information upon chemical bonding of conventional III–V semiconductors (Gutie´rrez-Sosa et al., 2002; Keast et al., 2002; Sanchez et al., 2004; Sanchez et al., 2005; Leifer, 1999). Presently however, there are only few studies in the literature concerning measurements of N and In concentrations of dilute nitrides with TEM and EELS (Gass et al., 2004; Grillo et al., 2001; Albrecht et al., 2002; Chauveau et al., 2003b; Litvinov et al.,

466

X. Kong et al. / Micron 37 (2006) 465–472

2004). The applied methods, which were used in all of these reports can be summarized in two categories: (i) the conventional (002) dark-field and high-resolution TEM methods (Grillo et al., 2001; Albrecht et al., 2002; Chauveau et al., 2003b; Litvinov et al., 2004), which can be used to investigate the N and In distribution along the growth direction, ([001] in most cases), and which require a rather homogeneous lateral elemental distribution relative to the TEM specimen thickness; (ii) the energy-filtered imaging method (Sanchez et al., 2004; Sanchez et al., 2005; Leifer, 1999; Gass et al., 2004), such as low-loss EELS combined with elemental mapping with the In 4d signal. However, the N content was not resolved and the In content has to be analyzed more carefully due to the overlapping Ga 3d signal in the low-loss region (Gass et al., 2004). Therefore, in the present study, we have further developed the low-loss EELS method in order to be able to quantify the N and In concentration simultaneously on the nanometer scale in the dilute nitride (Ga,In)(N,As) epilayers. In the first part of the paper, we describe the method used to analyze the local N, Ga and In concentrations from low-loss EEL spectra. It will be shown that this method is also feasible in the case of conventional and non-dedicated TEM equipments. In the second part, we present its application to quaternary (Ga,In)(N,As) QW structures and epilayers grown on GaAs substrates. Lateral fluctuations along the QWs with nominally high In and N content are observed indicating a favorable Ga–N and In–As configuration, respectively, in spite of a higher resulting local strain. A homogeneous In distribution in the epilayer keeps the growth surface smooth, i.e. two-dimensional (2D) growth mode predominantly, although large fluctuations in the N distribution are detected. 2. Experimental 2.1. Samples grown by molecular beam epitaxy The (Ga,In)(N,As) samples were grown on GaAs (001) substrates in a molecular beam epitaxy system equipped with conventional sources for the group-III elements as well as the As element, and with a rf-plasma source for N. First, a GaAs buffer layer was grown at about 580 8C. The growth temperature was then decreased to 400–430 8C for growing the Ga1KxInxNyAs1Ky QWs of about 10 nm thickness followed by a GaAs layer of about 3 nm. The remaining GaAs top barrier layer (w65 nm) was grown at 580 8C again. More details about the growth can be found in Tournie´ et al., (2003). Besides the QW structure, thick (Ga,In)(N,As) epilayers were grown under conditions necessary to guarantee 2D growth. The thickness of the films varies from 0.7 to 2.1 mm. During the epilayer growth, the surface retains the 2D growth mode thus providing a planar growth front, as monitored by the in situ reflection high-energy electron diffraction pattern. The samples studied in this paper are routinely characterized by photoluminescence (PL) and Raman spectroscopy, as well as by X-ray diffraction and conventional TEM (The studied samples are part of the European project).

2.2. Spectrum acquisition The cross-sectional TEM specimens used for the EELS analysis were prepared by the standard method of mechanical grinding and dimpling down to below 25 mm. The specimens were then thinned by an argon ion beam with an energy of 3 keV under an incident angle of 38 at room temperature in a Gatan precision ion polishing system. The TEM investigation was carried out in a JEOL 3010 microscope with LaB6 cathode operating at 300 kV. This microscope is equipped with a postcolumn Gatan Enfina parallel electron energy-loss spectrometer system. In the low-loss EEL spectra, the energy resolution is about 1.5 eV according to the full width at half maximum (FWHM) of the zero-loss peak. For the EELS measurements, the QWs were oriented parallel to the incident electron beam (‘end-on’) that the spectra taken from the QWs were not affected by overlapping GaAs regions. Under this orientation of the sample, the primary beam is at the center between the (002) and the (00-2) Kikuchi lines in the diffraction pattern. Only those areas of the sample with a thickness larger than half of the inelastic mean free path are studied to avoid the broadening and shift of the plasmon peak due to surface excitation. All spectra were collected using a dispersion of 0.05 eV/channel, as well as the diffraction mode with a collective semi-angle of about 3.25 mrad. The small collective angle ensures that the majority of energy loss transitions are around the momentum transfer jqjZ0. In order to minimize the drift of the electron beam and the sample, as well as to decrease the influence of irradiation damage and hydrocarbon contamination, typical acquisition times for each spectrum were set to about 1 s using a spot size of 5–8 nm diameter. Those experimental conditions are optimized based on the compromise between spatial resolution, acquisition time and signal-to-noise ratio. The reduction of spatial resolution due to the delocalization in the inelastic scattering process is estimated to be 2 nm (Egerton, 1996), which is believed to play a mirror effect on the determination of the plasmon energy in QWs with 10 nm thickness. Spectra were corrected for dark current and gain variations within the spectrometer. In order to remove the effect of multiple inelastic scattering and the multiple plasmon excitations, the standard Fourier-log deconvolution technique was applied to obtain a single scattering distribution (SSD) (Egerton, 1996). 3. Method: low-loss EELS According to our experimental equipment, we have applied the low-loss EELS for the quantitative determination of the N, Ga and In content because of the following reasons. (i) The high-energy N–K ionization edge, which is generally used to measure the N content due to a high degree of isolation from neighboring edges and the relatively accurate background subtraction, cannot be used here: this N–K edge can not attain sufficient intensity because of the very low concentration (!5%) in these Ga1KxInxNyAs1Ky quaternary alloys. (ii) Reflectivity measurements indicate that a small N fraction results in a large increase of the effective electron mass and

X. Kong et al. / Micron 37 (2006) 465–472

Single scattering distribution

Plasmon (~16eV)

In the energy-loss function, the most intense peak usually corresponds to the excitation of a collective oscillation of valence electrons, known as plasmons. The theory of the freeelectron gas has been found to give a good estimate of the plasmon excitation and its energy, even in semiconductors and insulators, where the valence electrons cannot be considered as free electrons. Following this theory, the energy-loss function can be given by (Egerton, 1996)

(Ga,In)(N,As) GaAs

In 4d (~18 eV) Ga 3d (~20 eV)


Im

0

10

20

30

40

50

467

60

Energy loss (eV) Fig. 1. Single scattering distributions in low-loss EEL spectra from GaAs and (Ga,In)(N,As).

a strong bowing effect on the band gap (Skierbiszewski et al., 2000). The variation of the band structure is sensitively reflected at very low energies (!1 eV) and the plasmon excitation in the low-loss region of the spectrum. (iii) Additionally, the low-loss EELS offers an improvement in the signal-to-noise ratio and a reduction in the sample drift as a result of the shorter acquisition times. Further, the increase in signal strength allows the incident probe intensity to be reduced, limiting the electron beam damage to the sample. Fig. 1 shows typical SSD spectra from GaAs and (Ga,In)(N,As) in the low-loss region of the EEL spectra reflecting two main characteristics: the plasmon excitation at about 16 eV, and a broad peak superimposed on the rapidly falling tail of the plasmon excitation, which includes the transitions from In 4d (above 18 eV) and the Ga 3d (above 20 eV) to the conduction band (Gass et al., 2004). Both features are utilized to quantitatively measure the N, Ga and In contents independently and simultaneously from one low-loss spectrum, as it will be demonstrated in the following. 3.1. Quantification of N content After appropriate removal of the zero-loss peak and the deconvolution of the plural scattering effects, the SSD, S(E), can be obtained. In the dielectric formulation, the SSD is proportional to the energy-loss function Im[K1/3(E)] and can be described as (Egerton, 1996) 
2 
 I0 t b K1 SðEÞ Z ln 1 C Im ; (1) qE 3ðEÞ pa0 m0 n2 where 3(E)Z31Ci32 is the dielectric response function of the material, I0 is the zero-loss intensity, t is the specimen thickness, n is the speed of incident electron beam, a0 is the Bohr radius, m0 is the electron rest mass, and b and qE are the collection semi-angle and the characteristic scattering angle, respectively.

 EðDEp ÞEp2 K1 ; Z 2 3ðuÞ E2 KEp2 C ðDEp EÞ2

(2)

where Ep is the energy of the plasmon excitation (Egerton, 1996): sffiffiffiffiffiffiffiffiffiffiffi ne2 : (3) Ep Z Z 30 m
In Eq. (3), n is the number of valence electrons per unit volume and m* is the effective electron mass. From this equation it follows that Ep depends on the density of electrons, i.e. as the lattice parameter, and on the effective electron mass, which is related to the band structure. A.M. Sa´nchez et al. (2005) have recently reported that in the case of strained (Ga,In)As semiconductor heterostructures, the change in the electron density via lattice parameter is the dominating factor determining the shift of plasmon peak, where changes due to the band structure are a second-order effect. Dilute nitrides, however, reveal a distinct behavior from these conventional semiconductor compounds. The incorporation of a few percent of nitrogen in GaAs and (Ga,In)As results in a huge reduction of the band gap (band gap ‘bowing’) (Vurgaftman et al., 2001). This is in contrast to the linear and small variation of the band gap with the composition of conventional III–V ternary alloys, like (Ga,In)As. Another distinct difference is the correlation between the band gap and the lattice constant: the addition of nitrogen in GaAs reduces the band gap while simultaneously reducing the lattice constant. As a consequence, quaternary (Ga,In)(N,As) alloys can be grown lattice matched to GaAs. Therefore, we can conclude that in (Ga,In)(N,As) the stain effect due to lattice parameter mismatch should play a minor role on the variation of Ep than the band structure. This conclusion is additionally supported by our results of welldefined reference samples as described in the following. In order to verify the dependency of Ep for Ga1KxInxNyAs1Ky, the plasmon energies were experimentally determined for two sets of reference samples containing three QWs with a systematic variations of the In and N concentrations, respectively. The three QWs in the reference sample A contain a constant N (2.5%) but increasing In content (23, 30, 40%), whereas the QWs in the reference sample B consists of a fixed In (35%) and variable N content (1, 2, 3.5%). The weak contrast variation in the chemically sensitive (002) dark-field image of the reference samples shown in the Fig. 2(a), indicates a relatively small composition fluctuation along the QWs.

468

X. Kong et al. / Micron 37 (2006) 465–472

(a) 50 nm

Plasmon energy E p (eV)

(b)

III

(Ga,In)(N,As) II g=(002)

In content (%) 10 20 30

0 16.1

40

GaAs

16.0

In 15.9 15.8

N

15.7

I

0

GaAs

1

2 N content (%)

3

4

Fig. 2. (a) Cross-sectional (002) dark-field TEM image of reference sample A: QW I [In]Z23%, II [In]Z30% and III [In]Z40%. (b) Experimental plasmon energies versus N and In content, obtained from reference samples A and B.

Line scans of low-loss EEL spectra (about 10 positions) were performed along every QW of these two reference samples. The corresponding average plasmon energies and their standard variations are summarized in Fig. 2(b). These experimental results demonstrate that, within the composition range of interest, Ep is sensitively depending on the N content but is almost independent on the In content. This result is in agreement to the above conclusion that, in dilute nitrides, Ep is more affected by the change in the effective electron mass via the band structure than by the strain variation due to the lattice mismatches. It is additionally remarkable that a 17% variation from 23 to 40% in the In content in (Ga,In)(N,As) doesn’t influence the plasmon energy, a result that is in contrast to the ternary (In,Ga)As case (Sanchez et al., 2005). However, these results become understandable, if we take into account that the incorporation of 2.5% N reduce the lattice mismatch to about 1–2%, and secondly, that effective electron mass variation (due to the band gap ‘bowing’) seems to compensate the change in the electron density caused by strain. Therefore, the N concentration can be quantitatively determined for our (Ga,In)(N,As) samples according to the shift of Ep relative to its position for the GaAs substrate. Finally, we have to note that in spite of the relative low energy resolution of 1.5 eV according to the FWHM of the zero-loss peak, the plasmon energy is defined with higher (a)

accuracy. In the original spectrum, Ep is determined with adequate resolution by fitting a Gaussian function and Eq. (2) to the zero-loss peak below the band gap at w1.2 eV and the plasmon peak in SSD spectrum, respectively. The typical fits in the (Ga,In)(N,As) alloy are shown as open circles in Fig. 3. It can be seen that excellent fits are obtained in the central parts of both peaks. The features on the right side of the plasmon peak due to In and Ga core transitions were not included in the fit. The standard deviation of the fitted plasmon energy is about 0.01 eV (The nonlinear least squares fitting is based on the Levenberg-Marquardt, LM algorithm). According to ten spectra from the substrate GaAs and (Ga,In)(N,As) reference QWs, respectively, the standard deviation of the variation in plasmon energy has been calculated to be between 0.03 and 0.05 eV. 3.2. Quantification of Ga and In contents The energy-loss function Im[K1/3(E)] contains the information about single electron intra- and interband excitations and collective plasmon oscillations, and even low core-shell transitions. Therefore, once the energy-loss function has been obtained, the real part of the dielectric response function Re[1/3(E)] is calculated by the use of the Kramers–Kronig transformations. The real and imaginary parts of the dielectric

(b)

0

10 Energy loss (eV)

20

SSD of (a) fit with eq.(3)

Intensity (arb. units)

Intensity (arb. units)

raw data Gaussian fit

0

10 20 30 40 Energy loss (eV)

50

Fig. 3. The fits of a Gaussian function and fit with Eq. (2) to the zero-loss peak (a) and the plasmon peak in SSD spectrum (b) of (Ga,In)(N,As) alloys.

X. Kong et al. / Micron 37 (2006) 465–472

function 31(E) and 32(E) are calculated by

the number of the group III atoms is proportional to the sample thickness:

3ðEÞ Z 31 ðEÞ C i32 ðEÞ Z

Re½1=3ðEÞ C iIm½K1=3ðEÞ : fRe½1=3ðEÞg2 C fIm½K1=3ðEÞg2

(4)

The imaginary part of the dielectric function 32(E) contains the information about the optical absorption of the material, including transitions from the d levels to the conduction band. Therefore, the In and Ga mole fractions of the (Ga,In)(N,As) alloy were analyzed from the integration of the In 4d and Ga 3d transition intensities in the 32 spectrum, in which the influence of the plasmon peak has been removed with an inverse power law allowing a better background fit, as shown in Fig. 4. However, it is difficult to get the real integrations of the In 4d and Ga 3d transition intensities, because these two ionization edges are lying close together and their transitions overlap almost completely. Therefore, in order to analyze quantitatively the Ga and In distribution, an isolation of the In and Ga contributions in the EEL spectra has to be carried out by applying the following method (Chapman et al., 1985; Thomas and Midgley, 2001). After subtracting the background, the edge intensities in the SSD spectrum of (Ga,In)(N,As) and GaAs can be expressed as ð GINA GINA GINA Iedge ðDEÞ Z I0 NGa dsGa ðEÞ GINA C I0GINA NIn

ð

dsIn ðEÞ;

(5a)

ð GaAs GaAs dsGa ðEÞ; ðDEÞ Z I0GaAs NGa Iedge

(5b)

GINA GaAs GINA where I0GINA and I0GaAs , NGa , NGa and NIn are the zeroloss intensities and the number of Ga and In atoms in (Ga,In)(N,As) and GaAs, respectively. Additionally,

0.6

(Ga,In)(N,As) GaAs

ε2 (E)

0.4

0.2

469

GINA GINA NGa C NIn tGINA Z GaAs NGa tGaAs

(6)

Combining Eqs. (5a,b) and (6), the Ga concentration can be calculated as xZ

ðF=CKKÞ ; 1KK

(7)

GINA GaAs where CZ I0GINA tGINA =ðI0GaAs tGaAs Þ, FZ Iedge ðDEÞ=Iedge ðDEÞ and K is the ratio between the integration of the Ga and In partial cross-sections for a certain energy window given by Ð dsIn ðEÞ ðF=CKxÞ Ð KZ : (8) Z 1Kx dsGa ðEÞ

If the ratio K is known, the Ga concentration x can be calculated according to Eq. (7). The ratio K was evaluated in the energy window of 18–35 eV before the As M45 edge (w42 eV) using the Ga and In partial cross-sections which are experimentally determined from the GaAs substrate and from reference samples with known In and Ga contents, respectively. Finally, the In concentration was determined by the simple relation Ga:InZx:(1Kx) which is generally applicable for III–V semiconductor compounds. The precision of these obtained Ga and In partial crosssections were checked by using a reference sample that consists of a laser structure with a (Ga,In)(N,As) QW in the center embedded between two GaAs barriers and (Al,Ga)As cladding layers. The nominal concentration were set to xInZ34% and yNZ1%. Along this QW, no contrast fluctuations are visible in the (002) dark-field micrograph of Fig. 5(a), indicating the high structural quality, which is in agreement to high PL efficiency (The studied samples are part of the European project). According to the corresponding PL peak position, the Ga and In concentrations can be estimated that is in agreement to the value determined by fitting the 32(E) after the back ground subtraction e.g. in Fig. 5(b) (Teukolsky et al., 1992). Furthermore, simulation of X-ray rocking curve confirms these results. The corresponding error bar of about 10% in the Ga and In contents mainly arises from the uncertainties of the concentrations in the reference samples determined from Ga L23 and In M45 edges, and from the background subtraction with the inverse power law (Chan and Williams, 1985).

4. Results and discussions

background removed

4.1. (Ga,In)(N,As) QWs on GaAs (001) substrate 0.0 16

20 24 Energy loss (eV)

28

Fig. 4. Imaginary part of dielectric functions, 32 (E) obtained from (Ga,In)(N,As) and GaAs used to isolate the overlapping transition intensities from Ga 3d and In 4d after subtracting the background with an inverse power law.

Based on the low-loss EELS method, we have investigated the element distribution in as-grown (Ga,In)(N,As) QWs. For this purpose, two samples were studied, which contain QWs with nominally identical compositions of about 3% N and 30% In, but which were grown at slightly different temperatures. For the QW grown at 430 8C, the cross-sectional (002) dark-field

470

X. Kong et al. / Micron 37 (2006) 465–472

Fig. 5. The (002) dark-field image of calibrated (Ga,In)(N,As) QW in laser structure (a), and the corresponding 32(E) and the linear fit with the Ga and In partial crosssections, (b).

TEM image in Fig. 6(a) reveals strong interface undulations and contrast modulations along the QW pointing to large composition fluctuations, whereas the QW grown at 410 8C (Fig. 7(a)) appears in uniform contrast with smooth interfaces. In order to analyze the element distribution along the QWs, an electron beam with about 8 nm spot size is generated that is smaller than the periodicity of the measured contrast modulation. A scan of low-loss EEL spectra along the QW is performed as indicated by the row of circles in Fig. 6(a). The appropriate plasmon energies shown in the inset of Fig. 6(a) indicate the inhomogeneous lateral distribution of N atoms. The maximal variation in Ep amounts to 0.4 eV, which corresponds to a wide fluctuation of the N content between 0 and 3.5%. The corresponding In content varies at these positions between 10 and 42%. These spatially resolved EELS results of the local In and N distribution along the QW 50 nm

16.0

Tg=430°C

15.9

Plasmon energy (eV)

Plasmon energy (eV)

16.1

are summarized in Fig. 6(b). The run of the curves reflecting the local elemental distributions shows a periodic oscillation similar to the contrast modulation in the dark-field TEM image. However, both curves follow an opposite trend, i.e. positions with high N content correspond to low In concentration and vice versa. Therefore, the contrast modulation seen in the darkfield image of Fig. 6(a) is not only the result of fluctuations in the N but also in the In composition. This result indicates that there are regions along the QW with preferred formation of Ga–N and In–As bond configurations, respectively, although these configurations lead to a higher local strain. On the other hand, the EELS results of the QW grown at lower temperature (410 8C), where uniform contrast and smooth interfaces are observed in the (002) dark-field image (cf. Fig. 7(a)), indicate less composition fluctuations for both elements within the error bars (see Fig. 7(b)). The ideal element distribution in a quaternary alloy, i.e. the nearest neighbor bond configuration, is determined by

15.8

15.7

Position (arb. units)

GaAs (Ga,In)(N,As)

50 nm

16.1 16.0

Tg=410°C

15.9 15.8 15.7 Position (arb. units)

g=(002)

GaAs (Ga,In)(N,As)

GaAs (a)

(b) 4

GaAs

(a)

20

1

10 0 0

N 3

40

2

30 20

1 In

0

In content (%)

30

2

50

(b) 4 N content (%)

40

3

In content (%)

N N content (%)

g=(002)

50 In

10 0

Position (arb. units) Position (arb. units) Fig. 6. Cross-sectional (002) dark-field TEM image of as-grown (Ga,In)(N,As) QW grown at 430 8C (a), and the corresponding N and In distribution (b) from a scan of low-loss EEL spectra marked by circles (inset: plasmon energy vs. position along the QW).

Fig. 7. Cross-sectional (002) dark-field TEM image of as-grown (Ga,In)(N,As) QW grown at 410 8C (a), and the corresponding N and In distribution (b) from a scan of low-loss EEL spectra marked by circles.

X. Kong et al. / Micron 37 (2006) 465–472

minimizing the alloy free energy, which includes local strain and cohesive bond energy terms. The local strain is produced by differences in bond lengths between the corresponding III– V atom combinations (Kim and Zunger, 2001). During the epitaxial growth, the physisorbed adatoms are able to relieve local strain toward the free surface. Therefore, the development of nearest neighbor configurations is more driven by maximizing the cohesive bond energy than minimizing the local strain. Taking into account the values for the cohesive energies of the various bond configurations (for GaN, InN, GaAs and InAs, being 2.24, 1.93, 1.63 and 1.55 eV per bond, respectively (Harrison, 1989)), the formation of Ga–N and In– As bonds should be favored inducing an inherent composition modulation near the growing surface. Lowering the growth temperature results in a reduction of the adatom mobilities, which is responsible to a lower probability of forming the favorable bonds. The composition modulation is hence suppressed, in agreement with our observation (Fig. 7(b)). On the other hand, the inherent composition modulation is associated with a strong increase of the epitaxial strain energy. The bond lengths of the Ga–N and In–As configurations lead to the higher epitaxial strain to the GaAs substrate compared to the case of Ga–As and In–N pairs (bond length for GaN, InN, ˚ , respectively GaAs and InAs, being 1.94, 2.15, 2.45 and 2.61 A (Harrison, 1989)). The elastic strain energy is accumulated during growth until elastic relaxation starts by surface roughening that initiates the 2D-to-3D growth mode transition. 4.2. (Ga,In)(N,As) Epilayer on GaAs substrate Figs. 8(a)–(c) display {110} cross-sectional dark-field TEM images with gZ(002), (004) and (220) taken from

a 0.7-mm-thick (Ga,In)(N,As) epilayer grown on GaAs that contains about 2% N and 20% In, respectively. The contrast variations are noticeable under the strain-sensitive (004) and (220) imaging conditions, which demonstrate that inhomogeneous surface relaxations and tetragonal lattice distortions, respectively, occur in the epilayer due to composition fluctuations. However, this composition fluctuation cannot be appropriately reflected in the chemically sensitive (002) darkfield image. According to the calculation of the dark-field intensity I200 in dependence of the compositions (Grillo et al., 2001; Chauveau et al., 2003b), we find that the present N and In concentrations are located at the broad minimum of the intensity, where variations in the composition cannot be reliably detected. Therefore, the small composition fluctuation in this epilayer cannot be observed in the (002) dark-field image. The combination of the (002) dark-field with highresolution TEM, as we mentioned in the introduction, is thus not suitable to analyze quantitatively the elemental distribution in this special case. In order to clarify the character and the amount of the composition fluctuation existing in the epilayer, a lateral scan of low-loss EEL spectra was performed in the same way as we did for the QWs. The results are summarized in Fig. 8(d) demonstrating that the In concentration keeps almost constant, however, the N concentration reflects large variations between 0 and 2.5%. Because of the small amount of N atoms (w2%) in the quaternary alloy, the variation from 0 to 2.5% in N content cannot further influence the surface morphology during growth, and thus, the epilayer surface retains atomically smooth as indicated in the RHEED pattern. These experimental results demonstrate that compositional modulation can take place even in the absence of morphological undulations if

(a)

40

6 In

5 N content (%)

(c)

(b)

30

4

20

3

10

2

0

1 0

In content (%)

(d)

471

N Position (arb. units)

Fig. 8. Cross-sectional (002) (a), (004) (b) and (220) (c) dark-field TEM images of (Ga,In)(N,As) epilayer grown on the GaAs substrate, and the corresponding lateral distributions of N and In concentrations.

472

X. Kong et al. / Micron 37 (2006) 465–472

the semiconductor alloy exhibits a driving force for phase separation and spinodal decomposition. 5. Conclusion In conclusion, the inherent composition fluctuations in epitaxially grown (Ga,In)(N,As) layers on GaAs(001) substrate were investigated by combining EELS and dark-field TEM. The local N and In concentrations are determined with a probe size of 8 nm from the low-loss EELS measurements. The small amount of N incorporated in dilute nitride alloys can be determined quantitatively by measuring the plasmon energy shift with respect to GaAs, and the In content can be analyzed simultaneously from the In 4d transitions that have been isolated from the overlapping Ga 3d transitions. Lateral fluctuations of the In and N concentration along the QWs are observed indicating favorable Ga–N and In–As bond configurations, respectively, in spite of a higher resultant local strain. These composition fluctuations are the driving force for morphological instabilities at the interfaces. The homogeneous In distribution in thick epilayers keeps the growth surface smooth and stabilizes 2D growth mode, although fluctuations in the N distribution exist between 0 and 2.5%. The main objective of this work was based on the measurement of local composition fluctuation of quaternary nitride dilute alloys with adequate accuracy in order to discuss the result with respect to morphological instabilities, which are critical for the understanding of the optical properties of quantum well devices. Self-evidently, compared to the present experimental results, further improvement would be obtained by using a FEG-STEM microscope. Applying those dedicated equipments, a higher spatial resolution can be achieved with smaller probe size, and the experimental errors can be reduced due to higher energy resolution and larger electron intensity. Additionally, the Ga and In concentrations can be proved independently by the energy-dispersive X-ray (EDX) spectroscopy. Acknowledgements The authors would like to thank Prof. Eric Tournie´ for providing the samples. This work was financially supported by the IST program of European Commission, project IST-200026478-GINA1.5. References Albrecht, M., Grillo, V., Remmele, T., Strunk, H.P., Egorov, A.Yu., Dumitras, Gh., Riechert, H., Kaschner, A., Heitz, R., Hoffmann, A., 2002. Appl. Phys. Lett. 81, 2719. Chan, H.M., Williams, D.B., 1985. Philos. Mag. B 52, 1019. Chapman, J.N., Chapman, J.N., Paterson, J.H., Titchmarsh, J.M., 1985. Inst. Phys. Conf. Ser. 78, 177.

Chauveau, J.-M., Trampert, A., Pinault, M.-A., Tournie´, E., Ploog, K.H., 2003a. Appl. Phys. Lett. 82, 3451. Chauveau, J.-M., Trampert, A., Pinault, M.-A., Tournie´, E., Du, K., Ploog, K.H., 2003b. J. Cryst. Growth 251, 383. Egerton, R.F., 1996. Electron Energy Loss Spectroscopy in the Electron Microscope, second ed. Plenum, New York. Friedman, D.J., Geisz, J.F., Kurtz, S.R., Olson, J.M., 1998. J. Cryst. Growth 195, 409. Gass, M.H., Papworth, A.J., Joyce, T.B., Bullough, T.J., Chalker, P.R., 2004. Appl. Phys. Lett. 84, 1453. Gass, M.H., Papworth, A.J., Bullough, T.J., Chalker, P.R., 2004. Ultramicroscopy 101, 257. Grillo, V., Albrecht, M., Remmele, T., Strunk, H.P., Egorov, A.Yu., Riechert, H., 2001. J. Appl. Phys. 90, 3792. Gutie´rrez-Sosa, A., Bangert, U., Harvey, A., Fall, C.J., Jones, R., Briddon, P.R., Heggie, M.I., 2002. Phys. Rev. B 66, 035302. Harris Jr., J.S., 2002. Semicond. Sci. Technol. 17, 880. Harrison, W.A., 1989. Electronic Structure and the Properties of Solids. Dover, New York, pp. 175–176. Ho, I., Stringfellow, B., 1997. J. Cryst. Growth 178, 1. Keast, V.J., Scott, A.J., Kappers, M.J., Foxon, C.T., Humphreys, C.J., 2002. Phys. Rev. B 66, 125319. Kim, K., Zunger, A., 2001. Phys. Rev. Lett. 86, 2609. Kondow, M., Uomi, K., Niwa, A., Kitatani, T., Watahiki, S., Yazawa, Y., 1996. Jpn. J. Appl. Phys. 35, 1273. Kondow, M., Kitatani, T., Nakatsuka, S., Larson, M.C., Nakahara, K., Yazawa, Y., Okai, M., Uomi, K., 1997. IEEE J. Selected Top. Quantum Electron 3, 719. Leifer, K., et al., 1999. Inst. Phys. Conf. Ser. 164, 27. Walther, T., et al., 1999. Phys. Rev. Lett. 86, 2381. Albrecht, M., et al., 1999. Inst. Phys. Conf. Ser. 169, 267. Sharma, N., et al., 1999. Inst. Phys. Conf. Ser. 169, 263. Walther, T., 1999. Proc. EMC2004 1, 251. Litvinov, D., Gerthsen, D., Rosenauer, A., Hetterich, M., Grau, A., Gilet, Ph., Grenouillet, L., 2004. Appl. Phys. Lett. 85, 3743. Neugebauer, J., Van de Walle, C., 1995. Phys. Rev. B 51, 10568. Sanchez, A.M., Gass, M., Papworth, A.J., Goodhew, P.J., 2004. Phys. Rev. B 70, 035325. Sanchez, A.M., Beanland, R., Gass, M.H., Papworth, A.J., Goodhew, P.J., Hopkinson, M., 2005. Phys. Rev. B 72, 075339. Skierbiszewski, C., Perlin, P., Wisniewki, P., Knap, K., Suski, T., Walukiewicz, W., Shan, W., Yu, K.M., Ager, J.W., Haller, E.E., Geisz, J.F., Olson, J.M., 2000. Appl. Phys. Lett. 76, 2409. Teukolsky, William H., Vetterling, Saul A., Flannery, William T., Flannery, Brian P., 1992. A Multiple-least-squares Procedure was used in the Fit, which was Performed with Programs Descried in Ch.15 of Numerical Recipes in Fortran. Cambridge University Press, Cambridge. Thomas, P.J., Midgley, P.A., 2001. Ultramicroscopy 88, 179. Tournie´, E., Pinault, M.-A., Lau¨gt, M., Chauveau, J.-M., Trampert, A., Ploog, K.H., 2003. Appl. Phys. Lett. 82, 1845. Trampert, A., Chauveau, J.-M., Ploog, K.H., Tournie´, E., Guzma´n, A., 2004. J. Vac. Sci. Technol., B 22, 2195. Vurgaftman, I., Meyer, J.R., Ram-Mohan, L.R., 2001. J. Appl. Phys. 89, 5815.Vurgaftman, I., Meyer, J.R., 2003. 94, 3675 (and references therein). Xin, H.P., Kavanagh, K.L., Zhu, Z.Q., Tu, C.W., 1999. J. Vac. Sci. Technol., B 17, 1649. Xin, H.P., Kavanagh, K.L., Zhu, Z.Q., Tu, C.W., 1999. J. Cryst. Growth 201/202, 419. The studied samples are part of the European project ‘GaInNAs-based semiconductor heterostructures for 1.5 mm opto-electronics’ (project IST2000-26478-GINA1.5). The nonlinear least squares fitting is based on the Levenberg-Marquardt (LM) algorithm, performed in the software OriginPro 7.0 (OriginLab Corporation, www.originlab.com).