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GaAs system
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ThinSolidFilms289 (1996) 261-266
A transmission electron microscopy study of interfacial reactions in the Fe/GaAs system M. Rahmoune, J.P. Eymery *, Ph. Goudeau, M.F. Denanot Laboratoire de MdtaUurgie Physique - lIRA 131 CNRS, Universit~ de Poitiers, Bd 3, Tdldport 2. BP 179, F.86960 Fumroscope Cedex. Frc~ce
Received30 November1995;accepted25 April 1996
Abstract The reaction between thin Fe films and gallium arsenide is studied using chiefly cross-sectional transmission electron microscopy. Fe films, 50--120 nm in thickness, were deposited onto (100) GaAs substrates by ion-beam sputtering and the Fe/GaAs couples were then annealed under vacuum at temperatures ranging between 400 and 550 °(2. The presence of a thin amorphous intermixed layer at the Fe/GaAs interface is pointed out in the as-deposited conditions; this layer consists of three elements Fe, Ga and As. The determination of the residual imemal stress in the as-deposited Fe films is also performed using the sin2Omethod and the result is of the order of - 2 GPa. Iron starts to react with GaAs at ~ 400 °C, producing a layered Fe/Fe3Ga/Fe2As + FeAs/GaAs structure. The sequence suggests that Fe diffuses into the GaAs and liberates Ga while forming iron arsenides. ARer annealing, the Fe/GaAs bimaterial also exhibits inteffacial undulations which arc discussed in terms of strain-energy relaxation. Keywords: Galliumarsenide;Interfaces;Iron;Transmissionelectronmicroscopy(TEM)
1. Introduction Considerable attention has been paid to the study ofmetalGaAs contacts in the past years in order to understand the mechanisms of contact formation and the effects ofinterfacial chemistry on the properties of the janctions. The aim of this research was to develop suitable metallization schemes for Schottky gates and Ohmic contact fabrication. For instance, titanium based metallizations are frequently used to form Schottky contacts in the fabrication of GaAs devices. Several recent studies, mainly performed by transmission electron microscopy (TEM), were concerned with the Ti/GaAs [ ! ], Ni/GaAs [2], Pt/GaAs [3] and Er/GaAs [4] systems. Besides the aforementioned application, the interest in Fe/ GaAs interfaces arises from the incorporation of magnetic elements into planar electronic structures. The properties of single-crystal films of iron grown by molecular-beam epitaxy or ion-beam sputtering (IBS) on GaAs substrates have been already investigated [5-8]. The focus in these studies was on the experimental conditions (substrate orientation and temperature, growth mode, etc.) required to yield good quality magnetic single-crystal films of bcc Fe on fcc GaAs sub~ strates. The magnetic properties of the films were mainly studied by measuring the saturation magnetization and ani. --* Correspondingauthor.T~l. (33) 49 49 67 35 - Fax: (33) 49 49 66 92 0040-60901961515.00@ 1996ElsevierScienceS.A. All rightsreserved PilS0040-6090(96)08912-2
sotropy field from a vibrating sample magnetometer or ferromagnetic resonance experiments. Here we report on a TEM study of the interfacial reactions in the Fe/GaAs system for which the deposition conditions are different from those in previous works [5-8]. In particular, we have grown by IBS polyorystalline Fe films with thicknesses ranging from 50 to 120 nm on (100) oriented GaAs substrates kept at room temperature. First we characterized the microstructure and reactions in the interfacial region of Fe/GaAs us-prepared couples. Since the knowledge of the stress state in the samples is of interest for understanding such physical phenomena as interface undulations, the residual stress in the Fe layers has also been determined using X-ray diffraction (XRD) data from previous work. Finally we studied the metallurgical reaction between Fe and GaAs in the temperature range 400-5.50 °(2, ~ main investigation technique being cross-sectional TEM. Some results concerning the magnetic properties of the ~s-deposited samples have been reported previously [9].
2. Experimental Iron films, 50-120 nm thick, were deposited onto (I00) GaAs substrates using an ion-beam sputtering technique. The sputtering system has already been described in reference
262
M. Rahmoune et al. I Thin Solid Filn:v289 (1996) 261-266
[ 10], so here we wil[ only give the conditions of deposition. The starting press~'e was 2x10 -4 Pa and during the deposition the pressure, was maintained at about I x 10- 2 Pa. An ion current of 70 mA for a beam diameter of 7.5 cm permitted a deposition rate of about 0.03 nm s - t with an Ar ion energy of 1.2 keV. Both deposition rate and film thickness were controlled by a quartz oscillator, he- ever the actual thickness of the as.deposited layers was determined with a DEKTAK 3030 profilometer. Before film deposition, the (100) GaAs substrates were polished with diamond paste and then etched for a short time ( ~ 5 s) in a solution of 0.2% Br (by volume) in methanol. During deposition, the substrates were mounted on a water-cooled sample holder so that the wafer temperature could not exceed 80 °C. For isochronal annealing studies, the samples were annealed in vacuum (10 -4 Pa) for 1 h at temperatures ranging between 400 and 550 °C. Structural analyses were performed by XRD in order to determine the residual stresses in the Fe films developed during the deposition process. The experiments were performed at LURE (Laboratoire pour l'Utilisation du Rayonnement Electromagn~tiqne, Orsay, France) using a home-made set-up especially adapted for nanocrystalline thin film analysis [11]. It was designed for working with an intense X-ray source and allowed the spectra to be recorded with a position sensitive detector; both incident and diffracted X-ray paths were placed under vacuum in order to optimize the signal to noise ratio. The wavelength was taken as 0.2137 nm in order to avoid K-Fe fluorescence. We selected the {211 } diffracting plane family for stress estimations since the shift of the peak position caused by stresses is more important at large diffraction angles. The method used to determine the residual stresses is known as the sin2tp method [ 12], which is a particular application of X-ray diffraction. Assuming that stresses are both planar and isotropic, the residual internal stress or may be calculated with the help of the equation: Ln( I/sin0hra) ----1/2S2crsin21p+ 2Sto" + L n ( 1/sin0o)
JEOL 200 CX electron microscope operating at 200 kV or JEOL 3010 microscope operating at 300 kV. The chemical composition of each region studied by microdiffraction was analysed concurrently by using an energy dispersive spectrometer (EDS) attached to the latter microscope. Finally, let us mention that, before thinning, some TEM samples were capped by a ~ 200 nm thick Si overlayer in order to facilitate the observations at low tilt angles.
3. Results and discussion 3.1. As-sputtered state 3.1.1. TEM experiments
A dark-field cross-sectional TEM image of an as-deposited Fe/GaAs sample is presented in Fig. l ( a ) . The boundary between the 120 nm thick Fe film and the (100) GaAs substrate appears fiat. The microstructure indicates columnar Fe grains growing normal to the GaAs surface, the grain diameters being between 18 and 40 nm.
( 1)
where 0h~ stands for the diffraction angle of the (hki) plane, 00 is the stress-free diffraction angle and ~b is the angle between the surface normal and the diffracting-plane normal. Let us note that E~!. (1) was obtained using the rational definition of strain: e=Ln(sin0o/0)
(2)
The St, 1/2S2 X-ray elasticity constants for lattice plane
(hkl) may be expressed as a function of Young's modulus E and Poisson's ratio v according to: SI=-v/E
1/2S2=(1+v)/E
Concerning the cross-sectional TEM experiments, the Fe layers were glued together face-to-face in a sandwich structure and then cut in vertical sections which were first thinned by mechanical polishing to a thickness of about 80 tzm. Final thinning to electron transparency was achieved by Ar + ionbeam milling. The observations were performed in either
Fig. !. Dark-fieldTEM cross-sectionmicrographsof u-depositedFe/OaAs samples:a) microstracturoof a 120 nm Fe filmgrownat roomtemperature on a (100) GaAssubstrate;notethatthe interfaceis fiat;b) intermixedlayer alongthe interfacebetweenFe (50 nm thick) and GaAs.
M. Rahmoune et aL I Thin Solid Films289 (1996) 261-266
Iron reacts readily with GaAs during deposition. The reacted layer, which cannot be clearly pointed out in Fig. 1(a), was however evidenced using a greater magnification in the 50 nm thick Fe film. The corresponding darkfield image is shown in Fig. l(b). The interfacial zone, 7 9 nm thick, is found to be iron rich ( ~ 80 at.%) and mainly amorphous. Indeed, complementary high resolution experiments have shown that the band contrast was typical of an amorphous material with, however, from place to place, some evidence of crystallinity. The effects of the reacted zone on the magnetic properties of the Fe films were already presented in [9]. The average magnetization and STFe hyperfine field decreased with decreasing Fe thickness; moreoveranin-plane uniaxial anisotropy was pointed out in the thinnest films. Ko and Sinclair [3] have also observed that a thin amorphous intermixed layer was present at the Pt/GaAs interface in the as-deposited conditions. This interlayer was quite uniform in the sample, with an average thickness of 3 nm. The interlayer formation was assumed to be assisted by the latent heat released from metal condensation during the deposition process. For the Fe/GaAs system, we suggest the same explanation, though the latent heat of sublimation for iron (399 kl mol - i ) is less than that for platinum (564 kJ mol- ~). The formation of a thin amorphous intermixed layer at the Fe/GaAs interface is then clearly evidenced for the first time. It may be regarded as an intermediate step to the thermal reaction between Fe and GaAs, which will be reported in Section 3.2. 3.1.2. X R D experiments
The value of the internal residual stress or was determined using Eq. (1). The experimental variations in Ln(1/sin0) as a function of sin2~bare presented in Fig. 2 for a 120 nm thick Fe film deposited onto a (100) GaAs substrate. A straight line clearly appears, the slope of which allows or to be estimated. Owing to the selectivity of the X-ray interference process, the St and 1/2S2 constants were calculated using a model for crystallite coupling known as KrOner-Eshelby selfconsistent method [13], and taken as 5.8x10 -3 and - 1. l x l 0 - 3 G P a - i respectively. The residual stress is then found to be or -- - 1.9 GPa which indicates that the film is in o., ~.....~
}0.-i
0.094--, 0
owl
Q
i
I
I
0.2
0.4 sin~
0.6
5/
---4 0.8
Fig. 2. Variationsin Ln ( 1/sin0) as a functionof sin2~ : the slopeallows the residualstress to be estimated.Both 0 and 0 anglesare definedin the text. wp-and ~p+denotenegativeand positivevaluesof~#,respectively.
263
a high compressive state. The ao stress-free lattice may also be calculated using Eq. (1). The result is ao ffi0.2879 nm, i.e. somewhat greater than bulk a-Fe lattice parameter of 0.2866 nm. The uncertainties in or and a~ values are 0.2 GPa and 0.0003 nm respectively. The lattice expmv sion may be attributed to energetic particle during deposition, as discussed in the following. Concerning the residual stress, a similar result was also obtained with a 120nm thick Fe film deposited onto a (100) Si wafer wilh or = - 2.1 GPa. Evidence is then found that the influence of substrate nature on stress magnitude is r m l w weak. This high residual compressive stress, at around 1% of the Yotmg's modulus of bulk a-Fe, is to be connected to the preparation mode. Similar orders of magnitude of stress were already found in 304 stainless steel films having the bec structure and prepared using the same method [ 14]. The two models that have been used in the litemtme to account for comp~ssive stresses in sputtered films are impurities and atomic peening [ 15]. The impurity model is based on the concept of lattice distortion produced by the iucotporation of atoms having a different size from the host. In particular, since sputtered films are known to contain some amount of the sputtering gas, the compressive stresses are often attributed to inert gas entrapment. However, they may be also caused by energetic particles bombarding the film during the deposition process (atomic peening). In ourexperiments, the energy distribution of the sputtered atoms tmghes a maximom at around 10 eV and then deereases accmding to a power law [ 16]. Thus 10% of the spottered Fe atoms arrive on the substrate with an energy around a few hundredelectrou volts. These energetic atoms then produce a film densification which leads to an increase in the lattice parameter as well as to compressive stresses. 3.2. Thermal reactions 3.2.1. Film and interface morphologies
Fe films were found to react with the GaAs substrates at ---400 °C. A series of cross-sectional TEM observations was then performed on the isochroaally annealed samples (450, 500 and 550 °C for I h). The results are presented with reference to Fig. 3 which is a dark-field image taken from a sample annealed at 500 °C for I h; the initial thickness of the Fe layer was 120 nm. Let us also mention that, since the F e Ga--As ternary phase diagram is unknown, the final reaction products cannot be simply predicted. The observations indicate several morphological changes. Apparently the initial reacted layer, depicted in Section 3.1.1., has been completely consumed in the thermal reaction. Moreover the total thickness of the metallic layer increases with increasing temperature; starting from 120nm, it reaches ~ 250 nm after 1 h at 500 °(2. We suggest that the reaction between Fe and GaAs involves the exchange of Fe and Ga across the original interface since the TEM micrographs clearly show both substrate consumption and an increase in the total thickness of the metallic layer. The boundary
264
M. Rahmoune et al. /Thin Solid Films 289 (1996) 261-266
Fig. 3. Cross-sectionalTIEMdark-fieldimage of a 120 nm thick Fe film annealed for I h at 500 °C. showing a layered structure (Fe3Ga/Fe~As x = 1,2/GaAs) as wellas modulationsat the Fe,As/GaAsinterface. between the latter layer and the semiconductor is no longer fiat but develops undulations; this morphology is well depicted on the left side of Fig. 3. The interracial undulations will be discussed in terms of the strain-energy relaxation in Section 3.2.2. The TEM observations also show the growth of a layered structure at the interface. Two distinct Fe-As and Fe-Ga layers have formed, the former being closest to the GaAs substrate. This layering phenomenon may also be understood in terms of atomic diffusion. Because arsenic has a relatively low mobility, an iron-arsenide layer is formed adjacent to the GaAs, with an iron gallide on top. At this stage of the study, we suggest a layered structure of the type Fe/Fe-Ga/Fe-As/GaAs. The upper Fe layer, which is still visible after I h at 450 °C, has been apparently consumed in the reaction after I h at 500 °C. As far as the iroo-gallide layer is concerned, the Fe3Ga disordered phase (bcc structure) is identified in all cases from microdiffraction and EDS microanalysis experiments. The atomic concentration of As is found to be as low as 4%. No crystallographic relationship between the layer itself and the adjacent ones was detected. Moreover, high resolution micrographs, which we do not include here, reveal that the average grain size of the Fe3Ga phase is very small ( ~ 3 nm). On the contrary, the morphology of the iron-arsenide layer is somewhat more complex. First, the grain size is quite large since, after 1 h at 500 °C, we can notice an increase in size by a factor of four with respect to the as-deposited conditions. However, the grains remain nearly columnar, their axes being normal to the substrate boundary. The atomic concentration of Ga does not exceed 2-3% throughout the layer. Second, the phase identification in this region has indicated the formation of at least two Fe-As compounds. The CuSb-type Fe2As phase is identified within = 60% of the grains; the microdiffraction pattern presented in Fig. 4(a) corresponds to the tetragonal Fe2As structure. Detailed analysis of this phase with microdiffraction yields a tetragonal structure (a = 0.363 nm and c = 0.598 nm), which corresponds to the known bulk Fe2As phase. Similarly, the MnP-type FeAs phase can be detected in -- 20% of the grains; a typical microdiffraction pattern is also shown in Fig. 4(b). The analysis
Fig.4. Microdiffractionpatternstakenfromthe iron-arsenidelayerobtained after I h at 500 °C:a) Fe.zAsgrain; [ ! l I ] zoneaxisof a tetragonaistructure; b) FeAsgrain; [ f32] zoneaxis of an orthorhombicstructure. indicates an orthorhombic structure with parameters a = 0.544 nm, b-- 0.337 nm, and c ffi0.603 nm, in agreement with the bulk FeAs phase. The 20% remaining grains yield an As atomic composition in the range 33-50% and the analysis of the corresponding microdiffraction patterns has proven to be problematic since it was not possible to associate the patterns with any known phase. In summary, the results from the Fe-As layer indicate that this area mainly contains both Fe2As and FeAs phases, the former being in the majority. It is to be recalled here that the formation enthalpies (AH) for those two compounds are close to each other, namely A H = - 38 kJ mol- t for Fe2As and A H = - 4 0 kJ tool- i for FeAs. Hence, from the microdiffraction and microanalysis results, we suggest that the layered microstructure of the heat treated Fe/GaAs samples is described by the sequence Fe/Fe3Ga/Fe2As +FeAs + unknown phase/GaAs. The unknown phase will be omitted in the following in order to shorten the sequence. Further details may also be evidenced from the selected area diffraction patterns; in particular, they indicate the existence of crystallographic relationships between Fe2As and GaAs such as (110) Fe2As//( 100)GaAs and (101) Fe2As//( 111 )GaAs. Finally, let us mention that
M. Rahmouneet al./Thin Solid Films289 (1996)261-266
some modifications in the interface morphology happen when the anneal temperature reaches 550 °(2; for example, the aforementioned interracial undulations and crystallographic relationships between the metallic film and the substrate slowly disappear. All these observations are consistent with recent studies of several other metal/gallium arsenide systems by Sands et al. [2] and Kim et al. [ 1]. The authors concluded that layered growth morphologies were the consequence of the relative immobility of As during the initial stages of the reaction. The Fe-Ga-As system can be classified as a type IV phase diagram according to the classification scheme proposed by Beyers ct al. [ 17]. In this case, the elemental metal M reacts with GaAs and forms M-Ga and M-As compounds. The system under study would be assigned to type V, which may be regarded as a subset of type IV, if a ternary phase with the stoichiometry FexGaAs could be detected after annealing at temperatures lower than 400 °(2; such a phase was unsuccessfully researched at 350 °C. 3.2.2. Observation o f interfacial undulations
The aim of this section is to summarize and discuss the observations of interfacial fluctuations in the heat-treated Fe/ GaAs system. Surface and int,erface fluctuations can be created by elastic and plastic deformation or by bulk and interface atomic diffusion. The free surface ofamateriai submitted to either internal or external stresses is not stable and becomes stabilized by the formation of roughness. From a theoretical point of view, Srolovitz [ 18 ] has presented a simple linear stability analysis which demonstrates that the nominally flat surface of an elastically stressed body was unstable with respect to the growth of perturbations with wavelengths greater than a critical value. The predicted wavelength of the instability was consistent with observations of thin InGaAs films grown on GaAs. Experimentally, when thin, strained Sii-xGex alloy layers were grown on (001) Si substrates, Cuilis et al. [ 19] have shown that topographical undulations were formed upon the layer surface under specific circumstances. The results showed that the ratio of the undulation amplitude to the square of the wavelength was constant for a given Ge fraction. Similar phenomena may happen at the interface of stressed bi- or muitimaterials. However, in this case, the results are less numerous in the literature. Ponchet et al. [20] have shown lateral thickness modulations in alternate tensile-compressive strained GaInAsP multilayers grown by gas source molecular beam epitaxy. The undulations were strongly anisotropic with a periodicity of about 50 nm along the [ 110] direction, while no modulation occurred along the [ 110] direction. The phenomenon was assumed to he controlled by partial elastic relaxation of the tensile layers. As reported in Section 3.2.1, we have observed modulations at the Fe-arsenides/GaAs interface after 1 h annealing at 500 °(2. This morphology is clearly evidenced on the left side of Fig. 3 where the wavelength A and peak-to-valley amplitude t of the ripples (see also Fig. 5) are determined as
265
Fig. 5. Schematicdiagramfor sinusoidalfluctuationsat the irgerfaceof A/B bimaterial. 300 and 75 nm respectively. Other quantitative measurements of A and t values were also performed from several TEM images of annealed Fe/GaAs couples. A clear pattern which emerges from this study is that all experimental A valees lie in the range 300-600 nm while the t/A ratio decreases with increasing period from about 0.25 to 0.10. Let us also mention the existence of few voids visible at the Fearsenides/GaAs interface; they probably relate to the Ga diffusing species. A similar rippling phenomenon may also be evidenced from the article by Sands et al. [2] who studied the reaction between (100) GaAs and near-noble metals such as Ni, Pd and Pt using TEM. Emphasis was placed on the evolution of the phase distributions, film compositions and interface morphologies during annealing at temperatures up to 480 o(2. Though the undulations were not investigated in detail, the following may be drawn from the published micrographs. For the Ni/GaAs system heated at 480 °(2, interface modulations with a periodicity of 140 nm are clearly visible while the tlA ratio ranges between 0.15 and 0.25. As far :.s the Pd/ GaAs system is concerned, the reaction is somewhat more complicated since intermediate-phase layers grew in the interfacial zone; however ripples with various wavelengths are detected. The interpretation of the modulations in Fig. 3 is not simple since during solid phase reaction, the interface morphology will depend upon a number of factors such as interface cleanliness, the microstructure of the deposited layer, the reaction path and stress in the reacting layers. We suggest here that the initial stress in the as-deposited Fe film plays an important role for modulating the interface roughness in the annealed Fe/GaAs system, the strain-energy relaxation occurring by large scale interdiffusion. In summary, we have pointed out interracial undulations, the period values of which compare well to those available in the literature from experimental studies.
4. Summary Interracial reactions have been investigated in Fe/GaAs couples for which the Fe layers were deposited on (100) GaAs substrates using an ion-beam sputtering technique. The conclusions drawn from this study are the following.
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1. Fe reacts readily with GaAs during deposition. The reacted layer, 7 - 9 nm thick, is both iron rich and mainly amorphous. Its formation is assumed to be assisted by the latent heat released from metal condensation during deposition. 2. The level o f residual stress o" in the as-deposited Fe film was determined using the so-called sin2O method. The results (o- ~- - 2 GPa) indicate that the film is in a high compressive state due to the preparation mode. 3. Fe is shown to react extensively with GaAs at temperatures above 400 °C. The reaction is diffusion controlled and involves the exchange o f Fe and Ga across the original interface, the arsenic being relatively immobile. Moreover it produces a layered structure o f the type Fe/Fe3Ga/ F e 2 A s + F e A s / G a A s . The F e - G a and F e - A s layers exhibit fine grains and coarse grains respectively. 4. After annealing, the interfacial zone ofthe F e / G a A s bimaterial exhibits an undulating morphology. The wavelength o f the periodic roughness is measured between 300 and" 600 nm. The modulation phenomena are analysed in terms o f strain-energy relaxation.
References [ I ] K.B Kim, M. Kniffin, R. Sinclair and C.R. Helms, J. Vac. Sci. Technol.. A6 (3) (1988) 1473.
[2] T. Sands, V.G. Keramidas, AJ. Yu, K.M. Yu, R. Gmnsky and J. Washburn,J. Mater. Res., 2 (2) (1987) 262. [3] D.H. Ko and R. Sinclair,Appl. Phys. Lett., 58 (17) ( 1991) 1851. [4] S. D~putier,A. Guivarc'h,J. Canlet, M. Minierand R. Gu~rin,J. Phys. Iil France, 4 (1994) 867. [5 ] G.A. Prinz and J.J. Krebs,Appl. Phys. Lett., 39 ( 1981) 397. [6] S.B. Quadri, M. Goldenberg,G.A. Prinz and J.M. Ferrari,J. Vac. Sci. Technol., B3 (1985) 718. [7] JJ. Krebs,B.T. Jonkerand G.A. Prinz,J. Appl. Phys., 61 ( 1987) 2596. [8] R.W. Tustison,T. Varitimos,J. Van Hook and E. Schloemann, Appl. Phys. Lett., 51 (1987) 285. [9] M. Rahmouneand J.P. Eymery,J. Phys. !11 France, 4 (1994) 859. [ 10] M. Janlin, G. Laplanche,J. Delafond and S. Pimbert-Michanx,Surf. Coat. Technol, 37 (1989) 225, [ 11] K.F. Badawi, A. Decldmy,A. Naudon and Ph. Goudeau,J. Phys. !11 France, 2 (1992) 1741. [ 12] G. Maeder.Chemica Scrota, 26,4 (1986) 23, [ 13] L. Castex,J.L. Lebrun,G. Maederand J.M. Spmuel,Publ. Sci. Techn., BNSAM, Paris, 1981, p. 81. [ 14] B. Boubeker, J.P. Eymery, Ph. Goudeau, K. Bouslykhane and J.P. Villain,Ann. Chim. Fr., 19 (1994) 377. [15] H. Windischmann,Critical Reviews in Solid State and Materials Sciences, 17 (6) (1992) 547. [ 16] C. Pellet, C. Desgranges,C. Schwebeland J. Aubert, Appl. Phys. A, 55 (1992) 359. [17] R. Beyers, K.B. Kim and R. Sinclair,J. Appl. Phys., 61 (6) (1987) 2195. [ 18] DJ. Srolovitz,Acta Metall., 37 (2) (1989) 321. [ 19] A.G. Cullis, DJ. Robbins, A.J. Pidduck and P.W. Smith, J. Crystal Growth, 123 (1992) 333. [20] A. Ponchet,A. Rocher,J.Y. Emery,C. Stasckand L. Goldstein,Mater. Sci. Eng., B21 (1993) 241.
ThinSolidFilms289 (1996) 261-266
A transmission electron microscopy study of interfacial reactions in the Fe/GaAs system M. Rahmoune, J.P. Eymery *, Ph. Goudeau, M.F. Denanot Laboratoire de MdtaUurgie Physique - lIRA 131 CNRS, Universit~ de Poitiers, Bd 3, Tdldport 2. BP 179, F.86960 Fumroscope Cedex. Frc~ce
Received30 November1995;accepted25 April 1996
Abstract The reaction between thin Fe films and gallium arsenide is studied using chiefly cross-sectional transmission electron microscopy. Fe films, 50--120 nm in thickness, were deposited onto (100) GaAs substrates by ion-beam sputtering and the Fe/GaAs couples were then annealed under vacuum at temperatures ranging between 400 and 550 °(2. The presence of a thin amorphous intermixed layer at the Fe/GaAs interface is pointed out in the as-deposited conditions; this layer consists of three elements Fe, Ga and As. The determination of the residual imemal stress in the as-deposited Fe films is also performed using the sin2Omethod and the result is of the order of - 2 GPa. Iron starts to react with GaAs at ~ 400 °C, producing a layered Fe/Fe3Ga/Fe2As + FeAs/GaAs structure. The sequence suggests that Fe diffuses into the GaAs and liberates Ga while forming iron arsenides. ARer annealing, the Fe/GaAs bimaterial also exhibits inteffacial undulations which arc discussed in terms of strain-energy relaxation. Keywords: Galliumarsenide;Interfaces;Iron;Transmissionelectronmicroscopy(TEM)
1. Introduction Considerable attention has been paid to the study ofmetalGaAs contacts in the past years in order to understand the mechanisms of contact formation and the effects ofinterfacial chemistry on the properties of the janctions. The aim of this research was to develop suitable metallization schemes for Schottky gates and Ohmic contact fabrication. For instance, titanium based metallizations are frequently used to form Schottky contacts in the fabrication of GaAs devices. Several recent studies, mainly performed by transmission electron microscopy (TEM), were concerned with the Ti/GaAs [ ! ], Ni/GaAs [2], Pt/GaAs [3] and Er/GaAs [4] systems. Besides the aforementioned application, the interest in Fe/ GaAs interfaces arises from the incorporation of magnetic elements into planar electronic structures. The properties of single-crystal films of iron grown by molecular-beam epitaxy or ion-beam sputtering (IBS) on GaAs substrates have been already investigated [5-8]. The focus in these studies was on the experimental conditions (substrate orientation and temperature, growth mode, etc.) required to yield good quality magnetic single-crystal films of bcc Fe on fcc GaAs sub~ strates. The magnetic properties of the films were mainly studied by measuring the saturation magnetization and ani. --* Correspondingauthor.T~l. (33) 49 49 67 35 - Fax: (33) 49 49 66 92 0040-60901961515.00@ 1996ElsevierScienceS.A. All rightsreserved PilS0040-6090(96)08912-2
sotropy field from a vibrating sample magnetometer or ferromagnetic resonance experiments. Here we report on a TEM study of the interfacial reactions in the Fe/GaAs system for which the deposition conditions are different from those in previous works [5-8]. In particular, we have grown by IBS polyorystalline Fe films with thicknesses ranging from 50 to 120 nm on (100) oriented GaAs substrates kept at room temperature. First we characterized the microstructure and reactions in the interfacial region of Fe/GaAs us-prepared couples. Since the knowledge of the stress state in the samples is of interest for understanding such physical phenomena as interface undulations, the residual stress in the Fe layers has also been determined using X-ray diffraction (XRD) data from previous work. Finally we studied the metallurgical reaction between Fe and GaAs in the temperature range 400-5.50 °(2, ~ main investigation technique being cross-sectional TEM. Some results concerning the magnetic properties of the ~s-deposited samples have been reported previously [9].
2. Experimental Iron films, 50-120 nm thick, were deposited onto (I00) GaAs substrates using an ion-beam sputtering technique. The sputtering system has already been described in reference
262
M. Rahmoune et al. I Thin Solid Filn:v289 (1996) 261-266
[ 10], so here we wil[ only give the conditions of deposition. The starting press~'e was 2x10 -4 Pa and during the deposition the pressure, was maintained at about I x 10- 2 Pa. An ion current of 70 mA for a beam diameter of 7.5 cm permitted a deposition rate of about 0.03 nm s - t with an Ar ion energy of 1.2 keV. Both deposition rate and film thickness were controlled by a quartz oscillator, he- ever the actual thickness of the as.deposited layers was determined with a DEKTAK 3030 profilometer. Before film deposition, the (100) GaAs substrates were polished with diamond paste and then etched for a short time ( ~ 5 s) in a solution of 0.2% Br (by volume) in methanol. During deposition, the substrates were mounted on a water-cooled sample holder so that the wafer temperature could not exceed 80 °C. For isochronal annealing studies, the samples were annealed in vacuum (10 -4 Pa) for 1 h at temperatures ranging between 400 and 550 °C. Structural analyses were performed by XRD in order to determine the residual stresses in the Fe films developed during the deposition process. The experiments were performed at LURE (Laboratoire pour l'Utilisation du Rayonnement Electromagn~tiqne, Orsay, France) using a home-made set-up especially adapted for nanocrystalline thin film analysis [11]. It was designed for working with an intense X-ray source and allowed the spectra to be recorded with a position sensitive detector; both incident and diffracted X-ray paths were placed under vacuum in order to optimize the signal to noise ratio. The wavelength was taken as 0.2137 nm in order to avoid K-Fe fluorescence. We selected the {211 } diffracting plane family for stress estimations since the shift of the peak position caused by stresses is more important at large diffraction angles. The method used to determine the residual stresses is known as the sin2tp method [ 12], which is a particular application of X-ray diffraction. Assuming that stresses are both planar and isotropic, the residual internal stress or may be calculated with the help of the equation: Ln( I/sin0hra) ----1/2S2crsin21p+ 2Sto" + L n ( 1/sin0o)
JEOL 200 CX electron microscope operating at 200 kV or JEOL 3010 microscope operating at 300 kV. The chemical composition of each region studied by microdiffraction was analysed concurrently by using an energy dispersive spectrometer (EDS) attached to the latter microscope. Finally, let us mention that, before thinning, some TEM samples were capped by a ~ 200 nm thick Si overlayer in order to facilitate the observations at low tilt angles.
3. Results and discussion 3.1. As-sputtered state 3.1.1. TEM experiments
A dark-field cross-sectional TEM image of an as-deposited Fe/GaAs sample is presented in Fig. l ( a ) . The boundary between the 120 nm thick Fe film and the (100) GaAs substrate appears fiat. The microstructure indicates columnar Fe grains growing normal to the GaAs surface, the grain diameters being between 18 and 40 nm.
( 1)
where 0h~ stands for the diffraction angle of the (hki) plane, 00 is the stress-free diffraction angle and ~b is the angle between the surface normal and the diffracting-plane normal. Let us note that E~!. (1) was obtained using the rational definition of strain: e=Ln(sin0o/0)
(2)
The St, 1/2S2 X-ray elasticity constants for lattice plane
(hkl) may be expressed as a function of Young's modulus E and Poisson's ratio v according to: SI=-v/E
1/2S2=(1+v)/E
Concerning the cross-sectional TEM experiments, the Fe layers were glued together face-to-face in a sandwich structure and then cut in vertical sections which were first thinned by mechanical polishing to a thickness of about 80 tzm. Final thinning to electron transparency was achieved by Ar + ionbeam milling. The observations were performed in either
Fig. !. Dark-fieldTEM cross-sectionmicrographsof u-depositedFe/OaAs samples:a) microstracturoof a 120 nm Fe filmgrownat roomtemperature on a (100) GaAssubstrate;notethatthe interfaceis fiat;b) intermixedlayer alongthe interfacebetweenFe (50 nm thick) and GaAs.
M. Rahmoune et aL I Thin Solid Films289 (1996) 261-266
Iron reacts readily with GaAs during deposition. The reacted layer, which cannot be clearly pointed out in Fig. 1(a), was however evidenced using a greater magnification in the 50 nm thick Fe film. The corresponding darkfield image is shown in Fig. l(b). The interfacial zone, 7 9 nm thick, is found to be iron rich ( ~ 80 at.%) and mainly amorphous. Indeed, complementary high resolution experiments have shown that the band contrast was typical of an amorphous material with, however, from place to place, some evidence of crystallinity. The effects of the reacted zone on the magnetic properties of the Fe films were already presented in [9]. The average magnetization and STFe hyperfine field decreased with decreasing Fe thickness; moreoveranin-plane uniaxial anisotropy was pointed out in the thinnest films. Ko and Sinclair [3] have also observed that a thin amorphous intermixed layer was present at the Pt/GaAs interface in the as-deposited conditions. This interlayer was quite uniform in the sample, with an average thickness of 3 nm. The interlayer formation was assumed to be assisted by the latent heat released from metal condensation during the deposition process. For the Fe/GaAs system, we suggest the same explanation, though the latent heat of sublimation for iron (399 kl mol - i ) is less than that for platinum (564 kJ mol- ~). The formation of a thin amorphous intermixed layer at the Fe/GaAs interface is then clearly evidenced for the first time. It may be regarded as an intermediate step to the thermal reaction between Fe and GaAs, which will be reported in Section 3.2. 3.1.2. X R D experiments
The value of the internal residual stress or was determined using Eq. (1). The experimental variations in Ln(1/sin0) as a function of sin2~bare presented in Fig. 2 for a 120 nm thick Fe film deposited onto a (100) GaAs substrate. A straight line clearly appears, the slope of which allows or to be estimated. Owing to the selectivity of the X-ray interference process, the St and 1/2S2 constants were calculated using a model for crystallite coupling known as KrOner-Eshelby selfconsistent method [13], and taken as 5.8x10 -3 and - 1. l x l 0 - 3 G P a - i respectively. The residual stress is then found to be or -- - 1.9 GPa which indicates that the film is in o., ~.....~
}0.-i
0.094--, 0
owl
Q
i
I
I
0.2
0.4 sin~
0.6
5/
---4 0.8
Fig. 2. Variationsin Ln ( 1/sin0) as a functionof sin2~ : the slopeallows the residualstress to be estimated.Both 0 and 0 anglesare definedin the text. wp-and ~p+denotenegativeand positivevaluesof~#,respectively.
263
a high compressive state. The ao stress-free lattice may also be calculated using Eq. (1). The result is ao ffi0.2879 nm, i.e. somewhat greater than bulk a-Fe lattice parameter of 0.2866 nm. The uncertainties in or and a~ values are 0.2 GPa and 0.0003 nm respectively. The lattice expmv sion may be attributed to energetic particle during deposition, as discussed in the following. Concerning the residual stress, a similar result was also obtained with a 120nm thick Fe film deposited onto a (100) Si wafer wilh or = - 2.1 GPa. Evidence is then found that the influence of substrate nature on stress magnitude is r m l w weak. This high residual compressive stress, at around 1% of the Yotmg's modulus of bulk a-Fe, is to be connected to the preparation mode. Similar orders of magnitude of stress were already found in 304 stainless steel films having the bec structure and prepared using the same method [ 14]. The two models that have been used in the litemtme to account for comp~ssive stresses in sputtered films are impurities and atomic peening [ 15]. The impurity model is based on the concept of lattice distortion produced by the iucotporation of atoms having a different size from the host. In particular, since sputtered films are known to contain some amount of the sputtering gas, the compressive stresses are often attributed to inert gas entrapment. However, they may be also caused by energetic particles bombarding the film during the deposition process (atomic peening). In ourexperiments, the energy distribution of the sputtered atoms tmghes a maximom at around 10 eV and then deereases accmding to a power law [ 16]. Thus 10% of the spottered Fe atoms arrive on the substrate with an energy around a few hundredelectrou volts. These energetic atoms then produce a film densification which leads to an increase in the lattice parameter as well as to compressive stresses. 3.2. Thermal reactions 3.2.1. Film and interface morphologies
Fe films were found to react with the GaAs substrates at ---400 °C. A series of cross-sectional TEM observations was then performed on the isochroaally annealed samples (450, 500 and 550 °C for I h). The results are presented with reference to Fig. 3 which is a dark-field image taken from a sample annealed at 500 °C for I h; the initial thickness of the Fe layer was 120 nm. Let us also mention that, since the F e Ga--As ternary phase diagram is unknown, the final reaction products cannot be simply predicted. The observations indicate several morphological changes. Apparently the initial reacted layer, depicted in Section 3.1.1., has been completely consumed in the thermal reaction. Moreover the total thickness of the metallic layer increases with increasing temperature; starting from 120nm, it reaches ~ 250 nm after 1 h at 500 °(2. We suggest that the reaction between Fe and GaAs involves the exchange of Fe and Ga across the original interface since the TEM micrographs clearly show both substrate consumption and an increase in the total thickness of the metallic layer. The boundary
264
M. Rahmoune et al. /Thin Solid Films 289 (1996) 261-266
Fig. 3. Cross-sectionalTIEMdark-fieldimage of a 120 nm thick Fe film annealed for I h at 500 °C. showing a layered structure (Fe3Ga/Fe~As x = 1,2/GaAs) as wellas modulationsat the Fe,As/GaAsinterface. between the latter layer and the semiconductor is no longer fiat but develops undulations; this morphology is well depicted on the left side of Fig. 3. The interracial undulations will be discussed in terms of the strain-energy relaxation in Section 3.2.2. The TEM observations also show the growth of a layered structure at the interface. Two distinct Fe-As and Fe-Ga layers have formed, the former being closest to the GaAs substrate. This layering phenomenon may also be understood in terms of atomic diffusion. Because arsenic has a relatively low mobility, an iron-arsenide layer is formed adjacent to the GaAs, with an iron gallide on top. At this stage of the study, we suggest a layered structure of the type Fe/Fe-Ga/Fe-As/GaAs. The upper Fe layer, which is still visible after I h at 450 °C, has been apparently consumed in the reaction after I h at 500 °C. As far as the iroo-gallide layer is concerned, the Fe3Ga disordered phase (bcc structure) is identified in all cases from microdiffraction and EDS microanalysis experiments. The atomic concentration of As is found to be as low as 4%. No crystallographic relationship between the layer itself and the adjacent ones was detected. Moreover, high resolution micrographs, which we do not include here, reveal that the average grain size of the Fe3Ga phase is very small ( ~ 3 nm). On the contrary, the morphology of the iron-arsenide layer is somewhat more complex. First, the grain size is quite large since, after 1 h at 500 °C, we can notice an increase in size by a factor of four with respect to the as-deposited conditions. However, the grains remain nearly columnar, their axes being normal to the substrate boundary. The atomic concentration of Ga does not exceed 2-3% throughout the layer. Second, the phase identification in this region has indicated the formation of at least two Fe-As compounds. The CuSb-type Fe2As phase is identified within = 60% of the grains; the microdiffraction pattern presented in Fig. 4(a) corresponds to the tetragonal Fe2As structure. Detailed analysis of this phase with microdiffraction yields a tetragonal structure (a = 0.363 nm and c = 0.598 nm), which corresponds to the known bulk Fe2As phase. Similarly, the MnP-type FeAs phase can be detected in -- 20% of the grains; a typical microdiffraction pattern is also shown in Fig. 4(b). The analysis
Fig.4. Microdiffractionpatternstakenfromthe iron-arsenidelayerobtained after I h at 500 °C:a) Fe.zAsgrain; [ ! l I ] zoneaxisof a tetragonaistructure; b) FeAsgrain; [ f32] zoneaxis of an orthorhombicstructure. indicates an orthorhombic structure with parameters a = 0.544 nm, b-- 0.337 nm, and c ffi0.603 nm, in agreement with the bulk FeAs phase. The 20% remaining grains yield an As atomic composition in the range 33-50% and the analysis of the corresponding microdiffraction patterns has proven to be problematic since it was not possible to associate the patterns with any known phase. In summary, the results from the Fe-As layer indicate that this area mainly contains both Fe2As and FeAs phases, the former being in the majority. It is to be recalled here that the formation enthalpies (AH) for those two compounds are close to each other, namely A H = - 38 kJ mol- t for Fe2As and A H = - 4 0 kJ tool- i for FeAs. Hence, from the microdiffraction and microanalysis results, we suggest that the layered microstructure of the heat treated Fe/GaAs samples is described by the sequence Fe/Fe3Ga/Fe2As +FeAs + unknown phase/GaAs. The unknown phase will be omitted in the following in order to shorten the sequence. Further details may also be evidenced from the selected area diffraction patterns; in particular, they indicate the existence of crystallographic relationships between Fe2As and GaAs such as (110) Fe2As//( 100)GaAs and (101) Fe2As//( 111 )GaAs. Finally, let us mention that
M. Rahmouneet al./Thin Solid Films289 (1996)261-266
some modifications in the interface morphology happen when the anneal temperature reaches 550 °(2; for example, the aforementioned interracial undulations and crystallographic relationships between the metallic film and the substrate slowly disappear. All these observations are consistent with recent studies of several other metal/gallium arsenide systems by Sands et al. [2] and Kim et al. [ 1]. The authors concluded that layered growth morphologies were the consequence of the relative immobility of As during the initial stages of the reaction. The Fe-Ga-As system can be classified as a type IV phase diagram according to the classification scheme proposed by Beyers ct al. [ 17]. In this case, the elemental metal M reacts with GaAs and forms M-Ga and M-As compounds. The system under study would be assigned to type V, which may be regarded as a subset of type IV, if a ternary phase with the stoichiometry FexGaAs could be detected after annealing at temperatures lower than 400 °(2; such a phase was unsuccessfully researched at 350 °C. 3.2.2. Observation o f interfacial undulations
The aim of this section is to summarize and discuss the observations of interfacial fluctuations in the heat-treated Fe/ GaAs system. Surface and int,erface fluctuations can be created by elastic and plastic deformation or by bulk and interface atomic diffusion. The free surface ofamateriai submitted to either internal or external stresses is not stable and becomes stabilized by the formation of roughness. From a theoretical point of view, Srolovitz [ 18 ] has presented a simple linear stability analysis which demonstrates that the nominally flat surface of an elastically stressed body was unstable with respect to the growth of perturbations with wavelengths greater than a critical value. The predicted wavelength of the instability was consistent with observations of thin InGaAs films grown on GaAs. Experimentally, when thin, strained Sii-xGex alloy layers were grown on (001) Si substrates, Cuilis et al. [ 19] have shown that topographical undulations were formed upon the layer surface under specific circumstances. The results showed that the ratio of the undulation amplitude to the square of the wavelength was constant for a given Ge fraction. Similar phenomena may happen at the interface of stressed bi- or muitimaterials. However, in this case, the results are less numerous in the literature. Ponchet et al. [20] have shown lateral thickness modulations in alternate tensile-compressive strained GaInAsP multilayers grown by gas source molecular beam epitaxy. The undulations were strongly anisotropic with a periodicity of about 50 nm along the [ 110] direction, while no modulation occurred along the [ 110] direction. The phenomenon was assumed to he controlled by partial elastic relaxation of the tensile layers. As reported in Section 3.2.1, we have observed modulations at the Fe-arsenides/GaAs interface after 1 h annealing at 500 °(2. This morphology is clearly evidenced on the left side of Fig. 3 where the wavelength A and peak-to-valley amplitude t of the ripples (see also Fig. 5) are determined as
265
Fig. 5. Schematicdiagramfor sinusoidalfluctuationsat the irgerfaceof A/B bimaterial. 300 and 75 nm respectively. Other quantitative measurements of A and t values were also performed from several TEM images of annealed Fe/GaAs couples. A clear pattern which emerges from this study is that all experimental A valees lie in the range 300-600 nm while the t/A ratio decreases with increasing period from about 0.25 to 0.10. Let us also mention the existence of few voids visible at the Fearsenides/GaAs interface; they probably relate to the Ga diffusing species. A similar rippling phenomenon may also be evidenced from the article by Sands et al. [2] who studied the reaction between (100) GaAs and near-noble metals such as Ni, Pd and Pt using TEM. Emphasis was placed on the evolution of the phase distributions, film compositions and interface morphologies during annealing at temperatures up to 480 o(2. Though the undulations were not investigated in detail, the following may be drawn from the published micrographs. For the Ni/GaAs system heated at 480 °(2, interface modulations with a periodicity of 140 nm are clearly visible while the tlA ratio ranges between 0.15 and 0.25. As far :.s the Pd/ GaAs system is concerned, the reaction is somewhat more complicated since intermediate-phase layers grew in the interfacial zone; however ripples with various wavelengths are detected. The interpretation of the modulations in Fig. 3 is not simple since during solid phase reaction, the interface morphology will depend upon a number of factors such as interface cleanliness, the microstructure of the deposited layer, the reaction path and stress in the reacting layers. We suggest here that the initial stress in the as-deposited Fe film plays an important role for modulating the interface roughness in the annealed Fe/GaAs system, the strain-energy relaxation occurring by large scale interdiffusion. In summary, we have pointed out interracial undulations, the period values of which compare well to those available in the literature from experimental studies.
4. Summary Interracial reactions have been investigated in Fe/GaAs couples for which the Fe layers were deposited on (100) GaAs substrates using an ion-beam sputtering technique. The conclusions drawn from this study are the following.
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M. Ralunoune et al. / Thin Solid Films 289 (I 996) 261-266
1. Fe reacts readily with GaAs during deposition. The reacted layer, 7 - 9 nm thick, is both iron rich and mainly amorphous. Its formation is assumed to be assisted by the latent heat released from metal condensation during deposition. 2. The level o f residual stress o" in the as-deposited Fe film was determined using the so-called sin2O method. The results (o- ~- - 2 GPa) indicate that the film is in a high compressive state due to the preparation mode. 3. Fe is shown to react extensively with GaAs at temperatures above 400 °C. The reaction is diffusion controlled and involves the exchange o f Fe and Ga across the original interface, the arsenic being relatively immobile. Moreover it produces a layered structure o f the type Fe/Fe3Ga/ F e 2 A s + F e A s / G a A s . The F e - G a and F e - A s layers exhibit fine grains and coarse grains respectively. 4. After annealing, the interfacial zone ofthe F e / G a A s bimaterial exhibits an undulating morphology. The wavelength o f the periodic roughness is measured between 300 and" 600 nm. The modulation phenomena are analysed in terms o f strain-energy relaxation.
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[2] T. Sands, V.G. Keramidas, AJ. Yu, K.M. Yu, R. Gmnsky and J. Washburn,J. Mater. Res., 2 (2) (1987) 262. [3] D.H. Ko and R. Sinclair,Appl. Phys. Lett., 58 (17) ( 1991) 1851. [4] S. D~putier,A. Guivarc'h,J. Canlet, M. Minierand R. Gu~rin,J. Phys. Iil France, 4 (1994) 867. [5 ] G.A. Prinz and J.J. Krebs,Appl. Phys. Lett., 39 ( 1981) 397. [6] S.B. Quadri, M. Goldenberg,G.A. Prinz and J.M. Ferrari,J. Vac. Sci. Technol., B3 (1985) 718. [7] JJ. Krebs,B.T. Jonkerand G.A. Prinz,J. Appl. Phys., 61 ( 1987) 2596. [8] R.W. Tustison,T. Varitimos,J. Van Hook and E. Schloemann, Appl. Phys. Lett., 51 (1987) 285. [9] M. Rahmouneand J.P. Eymery,J. Phys. !11 France, 4 (1994) 859. [ 10] M. Janlin, G. Laplanche,J. Delafond and S. Pimbert-Michanx,Surf. Coat. Technol, 37 (1989) 225, [ 11] K.F. Badawi, A. Decldmy,A. Naudon and Ph. Goudeau,J. Phys. !11 France, 2 (1992) 1741. [ 12] G. Maeder.Chemica Scrota, 26,4 (1986) 23, [ 13] L. Castex,J.L. Lebrun,G. Maederand J.M. Spmuel,Publ. Sci. Techn., BNSAM, Paris, 1981, p. 81. [ 14] B. Boubeker, J.P. Eymery, Ph. Goudeau, K. Bouslykhane and J.P. Villain,Ann. Chim. Fr., 19 (1994) 377. [15] H. Windischmann,Critical Reviews in Solid State and Materials Sciences, 17 (6) (1992) 547. [ 16] C. Pellet, C. Desgranges,C. Schwebeland J. Aubert, Appl. Phys. A, 55 (1992) 359. [17] R. Beyers, K.B. Kim and R. Sinclair,J. Appl. Phys., 61 (6) (1987) 2195. [ 18] DJ. Srolovitz,Acta Metall., 37 (2) (1989) 321. [ 19] A.G. Cullis, DJ. Robbins, A.J. Pidduck and P.W. Smith, J. Crystal Growth, 123 (1992) 333. [20] A. Ponchet,A. Rocher,J.Y. Emery,C. Stasckand L. Goldstein,Mater. Sci. Eng., B21 (1993) 241.