Furuday Discuss. Chem. SOC., 1990, 89, 191-200 X-Ray Scattering from Semiconductor Interfaces J. E. Macdonald Physics Department, University of Wales College of Cardifl P.O. Box 913, CardifCFl 3TH, UK X-ray diffraction has been used to determine the structure of surfaces over the past decade or so. The concepts involved in surface structure determina- tion may be extended to the study of buried interfaces. A formalism for the determination of the structure of epitaxial interfaces is outlined, together with its application to the NiSiJSi(111) interface. The use of a grazing incidence diffraction geometry to investigate strain relaxation in lattice- mismatched epilayers on the monolayer scale is discussed. The technique has been employed to monitor strain relaxation in thin Ge overlayers on Si(OO1) substrates with greater sensitivity than is attainable using other techniques.The results indicate that strain relaxation in this system relates primarily to islanding on the surface rather than the formation of misfit dislocations. For several decades, X-ray diffraction has been a powerful tool for determining the structure of bulk materials. The advent of intense synchrotron sources has led to the application of X-ray diffraction (XRD) to determine the detailed atomic structure of reconstructed surfaces. The comparatively low count rates obtained with X-rays are compensated by the applicability of the kinematic approximation, which assumes single- scattering processes in contrast to electron diffraction techniques. The surface scientist indeed possesses a range of experimental techniques giving structural information, both as direct images and in a more indirect manner, such as diffraction. These include electron diffraction and microscopy, atomic diffraction and inelastic scattering, X-ray diffraction, ion scattering, scanning tunnelling microscopy and surface-extended X-ray absorption fine structure spectroscopy (SEXAFS). Techniques based on diffraction are primarily suited to the study of the ordered regions of the surface, since disordered regions give rise to much weaker diffuse scattering between Bragg peaks.Tunnelling microscopy provides a localised, direct image of ordered and disordered regions thus providing a very powerful tool. However, the precision of the resulting atomic coordin- ates is low and the technique is insensitive to sub-surface relaxations.Ion scattering primarily probes ordered regions of the surface, but is more sensitive than diffraction to the presence of disorder, and gives information in direct space without resort to the use of reciprocal space. SEXAFS gives the coordination number and bond lengths of neighbouring atoms for specific atomic species. Electron spectroscopy can also be used to indicate the bonding between atoms and thus gives more indirect information on their structure. Thus a range of complementary techniques may be brought to bear on a particular problem. Despite the intense study of the structure of surfaces over recent years, there remains a paucity of information on the structural properties of interfaces.This is largely due to the fact that buried interfaces are inaccessible to many of the above surface-science techniques which have limited penetration. XRD would appear to be a suitable candidate for such studies owing to the variable penetration of the incident beam with angle of incidence and its sensitivity to scattering from a single monolayer. Most of the principles which have formed the basis of the use of XRD for the study of reconstructed surfaces 191192 X - Ray Scattering from Semiconductor interfaces may be applied directly to the study of buried interfaces, particularly where the overlayer is amorphous. Here we recap briefly the concepts involved in XRD studies of surfaces and of interfaces under amorphous overlayers. We then extend these ideas to the study of crystalline epitaxial interfaces and to the investigation of strain in lattice-mismatched systems, illustrating their use with suitable examples.Structure of Surface and Crystalline-Amorphous Interfaces Following the initial work of Marra and Eisenberger on the Ge(001) 2 x 1 surface,' XRD has been used to determine the detailed atomic structure of many reconstructed surfaces, particularly for semiconducting materiak2 The fractional-order peaks, which arise from the surface periodicity being a multiple of that for the underlying crystal, are uncontaminated by bulk scattering and thus may be used to determine the structure of the reconstructed unit cell. By measuring the variation of the fractional order peak intensity with wavevector normal to the surface the relaxation induced in deeper atoms by the surface reconstruction may also be probed.' In systems where the lateral registry of the reconstructed structure onto the bulk structure is unclear, the coherent interference between scattering from the surface and the bulk may be exploited.For instance, the structure of the GaSb( 11 1) 2 x 2 reconstruction was determined from the fractional-order peaks, as described above. Since the bulk structure is known the structure factors, and hence amplitudes, of the scattering from bulk and surface could be calculated. By considering the scattering in regions of reciprocal space where both components con- tribute, the resulting interference pattern could be compared with the calculated scatter- ing for different models of the r e g i ~ t r y .~ These ideas are extended to the investigation of epitaxial interfaces below. Similar measurements have been used to investigate the Si( 11 1)/a-Si interface. The stacking fault and dimers of the 7 x 7 reconstruction of the clean Si surface5 were found to be preserved under the amorphous layer.' Similarly, measurements of crystal truncation rods, used for determining surface roughness, may also be applied to the roughness of buried interfaces.' Structure of Epitaxial Interfaces A detailed knowledge of the atomic structure of interfaces is crucial to the understanding of interfacial electronic states. In the case of a fully coherent, epitaxial, crystalline overlayer deposited on a substrate, the diffracted amplitudes for both the substrate and the film may be calculated separately provided their unit cell structures are known.The observed diffracted-intensity distribution will then be the square of the magnitude of the total scattered amplitude. This total amplitude is given by summing coherently the diffracted amplitudes for the substrate and film, taking into account the phase shift due to the displacement of the origin of the unit cell of the epilayer relative to that of the substrate. This displacement is governed by the bonding at the interface. The same principle has been used to deduce the registry of a reconstructed unit cell onto the underlying bulk crystal, as noted above. A simple optical analogy of this situation is that of the diffraction pattern for a pair of overlapping diffraction gratings of known spacing.If one grating is moved with respect to the other, the diffraction pattern changes. Thus the observed diffraction pattern may be used to determine the relative displacements of the gratings. Consider a substrate having direct unit-cell parameters a l s , a2s and a3s, with corre- sponding reciprocal lattice vectors 6, , 6, and 6?, and an epitaxial film having unit-cell parameters a , , , a,, and a3,. For the case of a coherent epitaxial film we can take a , , = a , , = a , and = a,, = a,. We can also take a? = a?, and all to be normal to the surface, with = ~ a , . Let the displacement vector between the unit cells of the substrate and film at the interface be A = Ala, +A,a,+A,a, (fig. 1). The finite penetration of theJ.E. Macdonald 193 Fig. 1. A schematic diagram of the unit cells of the substrate and film. The displacement vector, A, describing the bond distance and lateral registry at a coherent epitaxial interface is shown. X-ray beam may be represented by a l / e penetration depth, A. Then the scattered amplitude for the substrate is A, = F, C exp (iQ - n ~ ) C exp (iQ * n2a2) 1 exp (iQ - n3a3) exp ( - n 3 a 3 / A ) " I " 2 "3 ( 1 ) 1 1 - exp (- iQl - a3) exp (- a3/A)' = (27-r)'N1 N2FsS( QII - H ) Here the scattering vector Q = QII + QI where QiI = Q , b , + Q2b2 and Q1 = Q3b3 are the components parallel and perpendicular to the interface respectively and H is an in-plane reciprocal lattice vector. The summation over n3 extends in the negative direction since we sum over unit cells extending into the bulk whereas u3 is directed towards the surface.N1 N2 is the number of illuminated unit cells on the surface. The structure factor, F,, is given by the usual summation over atoms j in the unit cell having position rJ and Debye- Waller factor, WJ F, =Cf; ~ X P (iQ * r,) exp(- W,>- (2) J Eqn (1) describes the scattered amplitude for a sharply terminated surface of a crystal. The scattering is sharp in Qil around a reciprocal lattice point but falls off approximately as QI' normal to the surface from the Bragg peak. This amplitude profile is usually referred to as a crystal truncation rod.8*9 We can write the corresponding equation for the film as where the film is of thickness Nf unit cells. The scattered intensity is then given by I = /A, + exp( iQ*A)Al-12.(4) Thus, since A, and A,- may be calculated for a given structure, the displacement vector, A, may be determined. In principle, additional contributions from modifications to the structure at the interface and at the uppermost reconstructed surface may be included. These would be A, = F, and A, = F, for the interface and reconstructed surface, respec- tively, the structure factors given by corresponding expressions to (2), together with appropriate displacement vectors A, and A,. Eqn (4) is then replaced by ( 5 ) I = IA,+ exp( iQ - A)A,.+ exp( iQ - A,)A, + exp( iQ - Ar)Arl'.194 X-Ray Scattering from Semiconductor interfaces 1- ' 0.8 0.9 1.0 1.1 1.2 1.3 Q3 (r.1.u.) Fig. 2. ( a ) The calculated intensity for differing values of the interfacial separation, d, for NiS&/Si(lll).d/a,= 1.0(- - - ) 1.05 (- -), 1.1(-). ( b ) The integrated intensity ofthe (O,O, Q3) rod, corresponding to the ( 1 1 1 ) bulk cubic direction. The result of the four-parameter fit, involving a scale factor and the parameters Nr, d and r,~, is shown as a solid line. However, such an expression contains too many parameters to be of general use and simplified expressions containing two or three of these terms would be used in practice. In all such expressions care must be taken in the choice of consistent unit-cell parameters. The above formalism is a generalised form of that presented by Robinson et al. in a study of the interface structure of Nisi,/%( 1 1 l).'" This is an ideal test system in that the two materials are well lattice-matched, enabling the growth of high-quality layers, and the interface structure has also been well characterised using X-ray standing-wave fluorescence yield measurements,' ' ion scattering" and high-resolution electron micro- scopy." Samples were prepared by evaporating 20A of Ni onto the cold substrate, followed by an anneal at 550 "C.The film was capped with amorphous Si, allowing the experiment to be performed in air using a standard 4-circle diffractometer at Stanford Synchrotron Radiation Laboratory. Measurements of the (0, 0, Q3) truncation rod, corresponding to the ( 1 1 1 ) direction in the usual cubic notation, were used to determine the height of the Ni atomic planes relative to the substrate Si atoms, d, and the ratio of the epilayer lattice parameter to that of the substrate, 77.Scans were performed by varying QI. across the rod to obtain the integrated intensity at each point along the rod, thus accounting for thermal diffuse contributions to the background. The resulting data are shown in fig. 2 together with model calculations for various values of the interfacialJ. E. Macdonald 195 separation. The data were fitted with a four-parameter model which gave values of d = (1.10 f 0.02)a, and 77 = 0.996 f 0.003, where a , is the spacing between (1 11) planes in Si. These values are in reasonable, though not exact, agreement with those obtained from the other techniques. The ideal interface, with bulk bonds throughout and no relaxation, has d/a, = 9/8 and hence the resulting value corresponds to a contraction at the interface.The above study demonstrated the usefulness of this interference technique for determining interface structures. Similar measurements using several truncation rods, having different values of QII, would enable the determination of the lateral registry of the film onto the substrate. This would be useful, for instance, to resolve the current disagreement concerning the structure of the CaF,/Si( 11 1) i n t e r f a ~ e . ’ ~ ” ~ By increasing the measured range in QI the layer structure may also be characterised. However, the sensitivity of the technique does entail the need for high-structural-quality interfaces and epilayers. Care must be taken in dealing with surface and interface morphology and it may well be that the number of systems studied using this interference technique will be limited by the structural quality of samples.Relaxation of Strained Interfaces There has been extensive interest in recent years in the growth of heavily strained layers, involving materials having a large lattice mismatch, in order to exploit the in-built strain to modify the electronic or optical properties of the material.16 As the thickness of the overlayer is increased the strain energy increases until it is relieved by the formation of misfit dislocations. Most studies of strain relief have concentrated on thick films having comparatively low lattice-mismatch values. For monolayer-scale films, the surface energy becomes relatively more important and the role of islanding in strain relief must also be considered.Here an XRD study of thin Ge films on Si(OO1) substrates is described to illustrate the use of a grazing incidence geometry for investigation of strain relief near an interface.”.” For a strained, unrelaxed layer, the lattice parameter of the epilayer and the substrate are identical in the plane of the interface thus causing a tetragonal distortion of the epilayer unit cell. As the layer relaxes, its in-plane lattice parameter increases towards its bulk value and the tetragonal distortion is reduced thus changing a3f, as illustrated in fig. 3. Conventional XRD studies of strained layers involve scans along QL with QII being small or zero. Consequently strain relaxation is detected as a shift in the epilayer peak as the tetragonal distortion is relieved.In the grazing-incidence geometry both incident and diffracted beams are close to the plane of the interface and thus QI == 0. The strain distribution is probed by scanning radially outwards in reciprocal space (the so-called S/2S scan) through the region around a substrate Bragg peak. The peak from an unrelaxed epilayer coincides with that of the substrate as a result of their identical in-plane lattice spacings. Any relaxed material having an in-plane spacing different from the substrate value gives rise to a separate peak and thus relaxation in small localised regions of the epilayer may be detected, even when the rest of the layer is fully strained. The grazing-incidence geometry also benefits from a much narrower intrinsic peak width for the epilayer owing to the much larger extent of the film parallel to rather than normal to the interface.The scattering from the substrate crystal truncation rod, which can obscure the epilayer peak in the conventional geometry, may also be resolved entirely and consequently does not obscure the epilayer scattering. The limited beam penetration of the grazing-incidence geometry also suppresses the background owing to thermal diffuse scattering from the bulk. The experiments were performed at the Synchrotron Radiation Source in Daresbury ( U K ) using unfocused radiation from the superconducting Wiggler beamline. The equipment consists of a large 5-circle diff ractometer, coupled to an ultrahigh-vacuum196 X-Ray Scattering from Semiconductor interfaces 0 0 0 0 0 0 0 0 0 0 0 0 ( a ) 0 0 0 0 0 0 e o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .0 0 0 0 0 0 0 0 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ( b ) 0 0 0 0 0 0 0 0 8 2 xo x o x x x x x x x x 0 0 0 0 x x x x 8 9 9 9 8 P .o x o %-+ 8 --@- @ QL rn - x o a// relaxed layer Q// strained layer Fig. 3. A schematic side-view of ( a ) direct space ( b ) reciprocal space for a fully strained and partially relaxed layer. In ( a ) the open and filled circles denote substrate and. epilayer atoms, respectively. In ( b ) the open circles and crosses denote substrate reciprocal lattice points and the peak position for the substrate and a fully relaxed epilayer, respectively. A radia! scan at grazing incidence is denoted as an arrow.chamber having in situ MBE growth facilities as well as standard surface-science analytical techniques.'' A monochromatic beam of wavelength 0.8 8, was incident at an angle of 0.09" onto the physical surface, just below the critical angle of 0.12", corresponding to a penetration depth of 100 8, in a flat Si crystal. The detector subtended an angle at the sample of 0.10" normal to the surface at a mean take-off angle of 0.13". The real unit-cell vectors were related to the conventional bulk cubic real cell vectors by a, = (1, 1, O)cubic, a2 = (1, -1, O)cubic and aj = (0, 0, 1/4)cubic. The Si(OO1) substrates were cleaned by light sputtering with 800eV'r Ar' ions for 60s followed by an anneal for 3 min at 1060 "C. Deposition of Ge was performed using a Knudsen effusion cell which gave a deposition rate of 1 monolayer (ML) per 18 min f lo%, calibrated by Rutherford backscattering.For Ge/Si(001), 1 ML corresponds to a thickness of 1.41 A. The substrate was held at 550°C during deposition and immediately cooled to room temperature before measurement. This procedure was repeated after deposition of each monolayer. Radial scans (along Q , ) through the (2,0,0) Bragg peak were performed at grazing incidence at each coverage in order to give the distribution of lattice spacings parallel to the interface (fig. 4). The resolution along Q , was 0.02 reciprocal lattice units (r.1.u.) as determined by the detector aperture slits and the illuminated surface area. The peak profile remains unchanged for a coverage 8 s 3 ML owing to the coherent epitaxial nature of the Ge layer.The wings of the peak are not substantially broadened indicating the high crystalline quality of the overlayer. At 4 ML, a weak shoulder appears on the i.1 e V = 1.602 18x 10 "'J.J. E. Macdonald 197 1.85 1.90 1.95 2-00 2.05 2.10 1.85 1.90 1.95 2.00 2.05 2.10 Q, (r.1.u.) Q, (r.1.u.) 5000 .- Y 4 0 0 0 C f 4 3000 a v .- 3 2000 v) C 0 * c 1000 .C 0 3000 40001 ( g ) 0 0 0 i 0 0 1 1.85 1.90 1.95 2.00 2.05 2.10 Q, (r.1.u.) 0 0 1.85 1.90 1.95 2.00 2.05 2.10 Q, (r.1.u.) Fig. 4. Radial scans as a function of coverage for sample I. The intensity is plotted on an arbitrary scale. On this scale the Bragg peak intensity is CQ. lo5. For 0 = 11 ML, circles denote data for angles of incidence and exit p = 0.09", p' = 0.13", respectively, and triangles represent the same scan with p = 0.07", p' = 0.05", leading to a reduced effective penetration depth.A (a) Clean Si, ( b ) 1.6 ML Ge, ( c ) 3.2 ML Ge, ( d ) 3.9 MLGe. (e) 4.7 ML Ge, (f) 5.5 ML Ge, (8) 7.1 ML Ge, ( h ) 11.0 ML Ge.198 X-Ray Scattering from Semiconductor interfaces Bragg peak owing to the onset of strain relaxation. Upon further deposition the shoulder develops as the layer relaxes further. At a coverage of 11 ML the peak from the overlayer occurs at Q, = 1.925 r.1.u. which is close to that expected for bulk Ge (Q, = 1.920 r.1.u.). This gradual shift shows that the strain is relaxed gradually after exceeding the critical thickness, which is 3-4 ML in this case. Strain relief is incomplete even after deposition of 11 ML of Ge.A further striking feature of the radial scan for sample I is the ‘plateau’ of scattering between the bulk values of Ge and Si. This indicates that the strain is not constant in the epilayer, but rather that there is a distribution of intermediate values of strain. The question arises whether the strain is distributed laterally across the layer or as a function of height above the interface. Consequently, the scan was repeated with the angle of both incident and scattered beams being below the critical angle. The effective penetration depth was thus reduced from 100 to 40 8, and led to the scan profile denoted by triangles in fig. 4. Here the scattering from the plateau in the region Q1 = 1.95-2.00 r.1.u. suffers more severe attenuation than the peak at Q1 = 1.925 r.1.u.This indicates that the atomic layers closest to the interface are still strained while the uppermost layers are almost fully relaxed. Note that the values of the penetration depth quoted above are difficult to interpret in view of the islanding that occurs at this coverage, as discussed later. A significant fraction of the beam may be totally externally reflected from the tops of islands thus shadowing parts of the surface. Several studies have shown that growth and annealing conditions affect strain relaxation in thick layers and that relaxation is a kinetically driven Con- sequently, the above measurements were repeated on a similar sample which was maintained at 520 “C during deposition and measurements. The onset of strain relaxation was found to occur at 3 ML and subsequent relaxation was more rapid.Samples prepared by MBE at a much faster growth rate of 0.5 8, s-I onto substrates at 400* 50 “C and capped with amorphous silicon (supplied by C. Gibbings, British Telecom Research Laboratories) again showed the onset of strain relief at 4 ML. In general, the coverage at which strain relief sets in has been found consistently to be 3 or 4 ML but the details of the strain distribution as a function of coverage are dependent on the growth procedure. We thus conclude that the critical thickness for the onset of strain relief in Ge/Si(001) is 3-4 ML. In contrast, the values of critical thickness for strain relief reported using reflection high-ener y electron diffraction (RH EED).?’, low-energy electron diffractionz3 and ion scattering2’is 6 ML.As seen from fig. 4 the amount of relaxed Ge increases rapidly at ca. 5-6 ML indicating that the epilayer is only partially relaxed for 6 =: 3-5 ML. Raman scattering and ion scattering are less sensitive to partial relaxation of the epilayer and thus yield the higher value for the critical thickness. Thus the high resolution and dynamic range of XRD yields considerable sensitivity to strain relaxation in thin epilayers. Electron microscopy studies of Ge layers, using similar growth conditions, show that islands form on the Ge surface at a coverage of 3-4 ML, and that these islands cluster with annealing time25 in good qualitative correspondence with the above results for strain relaxation. Ge layers deposited at room temperature form islands upon heating above 250°C for coverages greater than 3 ML.’6 Thus the critical thickness at which islands form and the critical thickness for the onset of strain relaxation coincide.There are no current data for the critical thickness for dislocation formation or migration, but calculations using equilibrium model^''^^^) and using energy minimisation for empirical potentials”T3’ yield values in the range 7-15 ML. These comparisons indicate that the initial relaxation of strain is closely related to islanding of the surface rather than to the formation of dislocations, as is the case for thicker films. This would appear to be a reasonable conclusion in view of the larger relative effect of the surface in monolayer- thick films than in thicker films which are not so heavily strained.The grazing-incidence geometry has also been used for a similar study of the initial stages of growth of GaAs on Si(O01).33 In contrast to Ge/Si(001), a mismatch of 1.55%J. E. Macdonald 199 was observed for the lowest measured coverage of 1.5 ML (1 ML=2.8 8, for GaAs/ Si( 001)) and the amount of relaxed material increases approximately linearly with the deposited amount, indicating that the interface is not fully coherent. The average lattice parameter for the overlayer increased gradually with layer thickness up to 20 ML. By varying the angle of incidence, a lattice parameter gradient could be detected, corresponding to a mismatch of 3.8% for the surface region and an average value for the complete overlayer of 3.3570, for a layer thickness of 15 ML. Thus the growth of GaAs on Si(OO1) is confirmed to be of a Volmer-Weber growth mode, in which the epilayer forms islands immediately on deposition.This islanding process is again accompanied by strain relaxation. Conclusions The concepts involved in the use of X-ray diffraction to the determination of reconstruc- ted surface structures may also be applied to the study of interfaces. In contrast with reconstructed surfaces, there is no region in reciprocal space where scattering from the interface is totally uncontaminated by bulk scattering. However, the coherent interfer- ence between scattering from the epilayer and the bulk may be exploited to probe the interfacial structure. Rod scans of the scattered intensity between Bragg peaks normal to the surface may, in principle, be used to study the structure of the interface and epilayer together with the strain normal to the interface.This technique has been applied to the Nisi,/%( f l l ) interface to determine the interfacial separation and the epilayer lattice parameter normal to the interface. Further work is required to determine the practical limitations, such as sample quality. The grazing incidence geometry, for which the momentum transfer is almost entirely in the plane of the interface, is most suited to studies of strain parallel to the interface. It benefits from several advantages over the conventional geometry for strain relaxation studies of ultra-thin films. The lateral strain distribution is measured directly and the measurements are very sensitive to small amounts of relaxed material.Depth information about the strain distribution may be obtained by varying the angle of incidence around the critical angle for total reflection. The results for Ge/Si(001) show that strain relaxation sets in at a coverage of 3-4 ML and proceeds gradually with increasing coverage. At a coverage of 11 ML the strain distribution displays two components, corresponding to almost fully relaxed Ge and a region having intermediate strain values. The results indicate that strain relaxation accompanies the onset of islanding on the surface. C. Norris, J. F. van der Veen and several workers from Leicester University and the FOM Institute, Amsterdam are thanked for a pleasant collaboration. Helpful discussions with I .K. Robinson and R. Feidenhans’l are also gratefully acknowledged. 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