- Email: [email protected]
Si interface
Physica B 273}274 (1999) 593}597
Atomic resolution EELS analysis of a mis"t dislocation at a GeSi/Si interface P.E. Batson* IBM Thomas J. Watson Research Center, Yorktown Heights, NY 10598, USA
Abstract A dissociated 603 mis"t dislocation at the substrate interface of a Si/Ge Si heterojunction has been examined x (1~x) using EELS and ADF imaging. New spectra are obtained at the intrinsic stacking fault, at the dislocation cores and in the strained regions on either side of the stacking fault. A splitting of the L conduction band due to symmetry breaking at 1 the stacking fault is observed. Near edge conduction band states are veri"ed at the partial dislocation cores, but not at the stacking fault. ( 1999 Elsevier Science B.V. All rights reserved. Keywords: Dislocations; Electronic structure; EELS; GeSi
1. Introduction
2. Experimental details and description of the dislocation
When the thickness of a thin "lm exceeds the Matthews}Blakeslee limit for pseudomorphic growth, mis"t dislocations are introduced at the underlying heterojunction [1]. In the case for Si growth on the (0 0 1) surface of Ge Si , the mis"t takes the form of a 603 dislocation x (1~x) dissociated into 303 (P30) and 903 (P90) partial dislocations separated by an intrinsic stacking fault (ISF). These structures also occur in heavily deformed silicon, and are believed to support electrically active states within 0.1 eV of the conduction band (CB) minimum [2]. TEM and luminescence studies have con"rmed optical activity near the defect, but the atomic structure that gives rise to the activity is not yet known [3}5]. Optical activity has also been detected associated with mis"t structures [4]. Theoretical work for the stacking fault [6], and for straight partial dislocations [7}9] have found that defect structures often reconstruct to clear the gap of electronic states. On the other hand, there has been some theoretical evidence for the existence of shallow valence band states [10].
I report here experiments using spatially resolved electron energy loss spectroscopy (EELS) to probe small regions of dissociated mis"t dislocations in a strained Si quantum well imbedded in Ge Si . Atomic column 0.35 0.65 positions in the [1 1 0] projection, and the spatial location for the spectral results are obtained using annular dark "eld (ADF) imaging [11,12] in the VG microscopes scanning transmission electron microscope (STEM), modi"ed to operate at 120 kV to obtain a 0.2 nm diameter electron probe. In prior work with GeSi alloys, it has been shown that very detailed conduction band (CB) information is obtainable using high resolution, spatially resolved EELS measurements of the Si 2p core ab3@2 sorption edge [13,14]. The EELS spectrometer was a Wien Filter design with an energy resolution of &200 meV and an absolute calibration of $20 meV [15]. Numerical deconvolution of the 0.3 eV wide "eld emission yielded a spectral resolution of 0.20}0.25 eV limited by statistical considerations [16]. The mis"t dislocation was of the 603 type located at the substrate interface of a 15 nm Si quantum well structure [17] Fig. 1 shows an annular dark "eld (ADF) image of the [1 !1 0] projection of the structure at high magni"cation. The Si well is at the bottom left, below the dashed line. The dislocation is extended about 3 nm in the [1 1 !2] direction away from the Si interface. Since the
* Tel.: 914-945-2782; fax: 914-945-2141. E-mail address: [email protected] (P.E. Batson)
0921-4526/99/$ - see front matter ( 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 0 0 7 8 - 2
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P.E. Batson / Physica B 273}274 (1999) 593}597
Fig. 1. ADF image of a second mis"t dislocation structure. Detailed EELS results were obtained from the locations marked a}f.
inter-column distance in the [0 0 1] direction in this projection is about 0.135 nm, this distance is not resolved using the 0.2 nm probe size. Instead, for each pair of columns, we see one spot, elongated in either the [0 0 1] direction in the bulk or in the [!2 !2 1] direction in the ISF. The measured distance between the two partial dislocations is 3.3 nm, or 10 `dumbbella units. This distance was found in other simple mis"t structures elsewhere in this sample. The P30 core is well de"ned, but the P90 core appears indistinct, probably due to kinks occurring along its length [18,19]. However, it can be located by considering continuity of (1 1 !1) type atomic planes as they cross the ISF. This "gure de"nes several unique locations for EELS analysis: (a) the bulk, relaxed GeSi alloy several tens of nm away from the defect, (b) the regions of tension and (c) compression within two (1 1 1) plane spacings on either side of the ISF, (d) the ISF itself, (e) the P30 dislocation core and (f ) the P90 core.
3. Experimental results Si 2p core absorption spectra are processed to remove a slowly varying background, to sharpen the energy resolution by deconvolution of the incident beam energy distribution, and to remove the 2p PCB intensity. 1@2 The shape of the remaining intensity is due to transitions to the s- and d-projected CB local density of states (LDOS). A model spectrum is made from a trial LDOS, using an inelastic scattering theory including core excitonic interactions, lifetime broadening and instrumental resolution. The model LDOS consists of parabolic e!ective mass contributions for the s-like band edges at * , L , and a saddle point at the d-like point L . These 1 1 3
Fig. 2. Spatially resolved EELS results for the Si 2p PCB 3@2 absorption edge for various locations within the structure summarized in Fig. 1. There appear to be unoccupied electron states below the CB within the dislocation cores, but not within the ISF.
contributions are terminated linearly at the p-like points ! and ! in the center of the Brillouin zone. The 1,5 2{ model positions for the important band edges * and 1 L are then adjusted to "t the experimental data. Finally, 1 there is a small contribution to the L intensity due to 1 a Ge-like saddle point in the " band. 1 In Fig. 2 there are spectral results for each of the regions described above. Each spectrum includes the processed data, a trial LDOS and the "tted spectrum. The spectra are aligned on an absolute energy scale relative to the 2p core level. This level has been shown 3@2 to be a constant for the relaxed alloy series [14], but it does shift with the addition of crystal strain [20]. 3.1. Bulk relaxed and strained alloy areas The bulk alloy results in Fig. 2 match the prior results closely for the alloy composition Ge Si [13]. The four 35 65 usual CB features, * , L , L , and " , are required to 1 1 3 1 fully explain the measured data. In the regions of tension and compression, the most notable change is to shift the spectra lower or higher in energy. A secondary di!erence is an apparent broadening of the L contribution in the 1 compressed region. In order to understand these results, we need to consider both volume and uniaxial strain in [1 1 1] type directions. The experimental data show a * shift of !0.085 eV 1 for the region in tension and #0.10 eV in compression. These shifts are opposite to those expected for the CB and so we expect a large core level shift. Within a couple (1 1 1) lattice planes on either side of the ISF, inspection of the image shows that this 10 unit ISF has 10 atomic planes on one side and 11 planes on the other, occupying roughly 10.5 bulk lattice units, giving a lattice strain of
P.E. Batson / Physica B 273}274 (1999) 593}597
$5% on either side. The deformation potential for the Si 2p core level is about!6 eV [20] giving a core level 3@2 shift of !0.3 eV at 5% tension and #0.3 eV in compression. Therefore these measurements place the * CB at 1 #0.22 eV at (b) in tension, and !0.20 eV at (c) in compression, relative to the bulk alloy. The band o!set in the Si well in this case is about !0.28 eV so this is a signi"cant perturbation of a desired device quantity. The deformation potential for * is #4 eV, [20] and therefore 1 provides a satisfying consistency to the interpretation. The uniaxial strain is somewhat more di$cult to deal with in that it results in splitting of the eight-fold degenerate L bands into two-fold/six-fold combinations. Again, 1 inspection of the image suggests that the uniaxial strain is about $5% within a (1 1 1) plane, but oriented in a [1 1 2] type of direction. The appropriate deformation potential for this process appears to be NL and is 6 15}16 eV [20]. The shifts are expressed relative to the strain e "1/3(e !e )+0.1e for this case, leading xy M @@ 111 to a shift of two-fold part of the band by about 0.15 eV and the six-fold part by 0.05 eV in the opposite direction. An experimental determination of these quantities is made di$cult by the disparity in degeneracy, making the two-fold contribution di$cult to identify. In Fig. 2 the total splitting for the best "t to the data is indicated by the dotted lines attached to the L point in the bulk 1 results. In tension, the two-fold edge falls over the edge of the * contribution, giving a spectrum that appears to 1 have only one, less intense, L peak. In compression, the 1 two-fold piece shifts upwards in energy, where the underlying * contribution is #at, leading to an apparent 1 broadening of the L peak. This modeling arrives at a 1 total splitting of 0.26 eV, compared with 0.20 eV expected from the deformation potential.
595
bors at each end. In the bulk, the six end atoms transform into each other by a two-fold screw axis oriented along the `dumbbella. In the ISF, this screw axis is replaced by a mirror plane. I model the band splitting that results from this by introducing a gap in the L band, labeling the upper and 1 lower branches, !` and !~, following the notion that the band is projected into the 2-D zone center and split into symmetric and anti-symmetric parts by the third-neighbor interaction. This splitting is calculated to be about 1.5 eV for Si, while the lower band is calculated to shift about 0.25 eV down from the L minimum in the bulk. 1 These predictions strongly resemble the observed behavior. That work also predicts that the X CB in the bulk 1 lattice, for which * is the band minimum, becomes the 1 !}M band in the hexagonal ISF BZ and is not a!ected by the change in local symmetry at the ISF. Again this is re#ected in the data of Fig. 2, which shows no change at the ISF * onset relative to the bulk alloy. 1 This experimental result argues against the presence of in-gap empty states near the CB at the ISF. It obviously does not address the possibility of states near the valence band edge, although it indirectly supports that possibility because they are predicted within the Mathiess and Patel work, which appears consistent with these results in areas where it can be checked. 3.3. Dislocation cores P30 spectral results in Fig. 2 show L splitting that is 1 very similar to that at the ISF. Referring to the model structure in Fig. 3a, we see, in the parent lattice, the
3.2. Intrinsic stacking fault Spectral results from position (d), the ISF, show a splitting of the L peak, with no other apparent shifts or 1 changes. In particular, there appears to be no shift or change in shape of the onset at * . The splitting can be 1 understood using the calculations for Si of Mattheiss and Patel [21]. They predicted that the L branch is a!ected 1 in two ways. First, it is projected into the center of the 2-D hexagonal ISF Brillouin zone (BZ) by two-dimensional nature of the fault. Then it is split into two components by mixing of Si sp3 orbitals from third-neighbor atoms on either side of the glide-cut plane. In the parent crystal, third-neighbor atoms occupy positions on either end of a structure commonly referred to as a `chaira. In the ISF structure, as a consequence of the 1803 rotation of the structure about the [1 1 1] direction, the thirdneighbors form a `boata structure, moving from their normal 0.45 nm distance apart to nearly the second neighbor distance of 0.38 nm. This structure can also be visualized as a two atom `dumbbella with three neigh-
Fig. 3. P30 (a) and P90 (b) model structures. Note that the P30 resembles the ISF structure.
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P.E. Batson / Physica B 273}274 (1999) 593}597
Fig. 4. EELS analysis for the P30 (a) and P90 (b) partial dislocation cores. The solid line reproduces the "t to the ISF data on the left and the bulk data on the right. There is extra intensity coincident with the CB onset in both cases.
two-fold screw operation for the bulk. In the ISF, this is replaced by a structure supporting a quasi-mirror plane. The P30 core structure is very similar to that in the ISF, although it has to be admitted that the mirror symmetry is not exact in the P30 case, either. Interestingly, the orientation of the core structure is in a [1 1 0] type direction rather than in a [1 1 1] direction as it is in the ISF. It appears that the reconstructed P30 core is consistent with the "nding of splitting in the L band at the 1 dislocation core. This result is supported by a statistical analysis of the structure of the relaxed core to be reported elsewhere. Examination of the P30 near edge structure at * , 1 summarized in Fig. 4a, shows near edge gap states at the dislocation core. For everywhere except near * , the ISF 1 model "t is a very good match to the data. When this "t is subtracted from the P30 data, a peak remains centered at the * onset. It's width is close to the instrumental 1 resolution of 0.2 eV. In addition, excess intensity remains near the L peak. It is known that this peak is symmetry 3 compatible with * so that it shifts in a similar manner 1
under the in#uence of strain [13]. Therefore, it is reasonable that any distortion in the crystal that splits o! states into the gap from * should also shift states downwards 1 from L . 3 The P90 core EELS results present an interesting problem because they do not show the L splitting. Fig. 1 3b shows the single period (SP90) reconstructed P90 structure. This consists of 5}7-fold rings joined across the core. In this model structure third-neighbor pairs (for instance, labeled a) mimic the ISF con"guration, so it would seem that this structure might not be consistent with the spectral results. A new model for the P90, recently suggested by Bennetto et al. [9] introduces a double period (DP90) reconstruction at the core through the addition of kinks in the plane of the ISF. Viewed in the [1 1 1] direction, these have the e!ect of creating 5}7-fold rings along the dislocation core. The model is interesting in the present context because the introduction of kinks reduces the number of ISF-like third-neighbor interactions. In fact, introducing many kinks within an extended core structure can completely eliminate ISF third-neighbor interactions near the P90 core. This would be more likely, therefore, to produce a spectrum that resembles the bulk result. Fig. 4b shows the EELS analysis for the P90 core. In this case the "tted model for the bulk result has been subtracted from the data to reveal that a peak exists about 80 meV below the onset of * . Also in this case, a 1 second peak exists near L , as it must if the near edge 3 peak is actually due to the splitting of states from the CB edge. These two results, together with the results from the ISF and strained regions above, suggest that optical activity involving empty states near the CB is likely to be con"ned to the dislocation cores. Electrical activity may also be associated with the regions of strain on either side of the ISF, since 200 meV peaks and valleys in the CB o!set are certainly present there.
4. Conclusions This report describes the EELS and atomic structure of the dissociated 603 mis"t dislocation. Splitting of the L CB peak is almost certainly due to local symmetry 1 breaking by the presence of ISF-like atomic structure. Near edge gap states are found at the partial dislocation cores, leading one to surmise that optical activity exists at these locations. No information about near valence band (VB) edge states can be obtained from these results, so the possibility of optical activity near the ISF due to excitations from a shallow VB state remains. Future work on these structures will be undertaken using improved EELS and imaging capabilities that are currently under development.
P.E. Batson / Physica B 273}274 (1999) 593}597
Acknowledgements Model structures for this work were relaxed by Y. Tu at IBM. I also acknowledge discussion with P.M. Mooney, F.K. LeGoues, and K. Ismail during this work. R.W. Nunes kindly provided atomic coordinates for the DP structure.
References [1] J.W. Matthews, A.E. Blakeslee, J. Crystal Growth 27 (1974) 118. [2] L.C. Kimerling, H.J. Leamy, J.R. Patel, Appl. Phys. Lett. 30 (1977) 217. [3] H. Alexander, J. Phys. Coll. Paris 40 (1979) 1. [4] Kai Shum, P.M. Mooney, J.O. Chu, Phys. Rev. Lett. 71 (1997) 1074. [5] H. Alexander, J.C.H. Spence, D. Shindo, H. Gottschalk, N. Long, Philos. Mag. A 53 (1986) 627. [6] M.Y. Chou, M.L. Cohen, S.G. Louie, Phys. Rev. B 32 (1985) 7979. [7] J.R. Chelikowsky, Phys. Rev. Lett. 49 (1982) 1569.
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[8] J.R. Chelikowsky, J.C.H. Spence, Phys. Rev. B 30 (1984) 694. [9] J. Bennetto, R.W. Nunes, David Vanderbilt, Phys. Rev. Lett. 79 (1997) 245. [10] F. Liu, M. Mosteller, V. Millman, M.F. Chisholm, T. Kaplan, Phys. Rev. B 51 (1995) 17192. [11] S.J. Pennycook, L.A. Boatner, Nature 336 (1988) 565. [12] R.F. Loane, E.J. Kirkland, J. Silcox, Acta. Crystallogr. A 44 (1988) 912. [13] P.E. Batson, J.F. Morar, Appl. Phys. Lett. 59 (1991) 3285. [14] J.F. Morar, P.E. Batson, J. Terso!, Phys. Rev. B 47 (1993) 4107. [15] P.E. Batson, Rev. Sci. Instr. 57 (1986) 43. [16] P.E. Batson, D.W. Johnson, J.C.H. Spence, Ultramicroscopy 41 (1992) 137. [17] K. Ismail, F.K. LeGoues, K.L. Saenger, M. Arafa, J.O. Chu, P.M. Mooney, B.S. Meyerson, Phys. Rev. Lett. 73 (1994) 3447. [18] A. Olsen, J.C.H. Spence, Philos. Mag. A 43 (1981) 945. [19] Y.M. Huang, J.C.H. Spence, O.F. Sankey, Phys. Rev. Lett. 74 (1995) 3392. [20] C.G. Van de Walle, Phys. Rev. B 39 (1989) 1871. [21] L.F. Matheis, J.R. Patel, Phys. Rev. B 23 (1981) 5384.
Atomic resolution EELS analysis of a mis"t dislocation at a GeSi/Si interface P.E. Batson* IBM Thomas J. Watson Research Center, Yorktown Heights, NY 10598, USA
Abstract A dissociated 603 mis"t dislocation at the substrate interface of a Si/Ge Si heterojunction has been examined x (1~x) using EELS and ADF imaging. New spectra are obtained at the intrinsic stacking fault, at the dislocation cores and in the strained regions on either side of the stacking fault. A splitting of the L conduction band due to symmetry breaking at 1 the stacking fault is observed. Near edge conduction band states are veri"ed at the partial dislocation cores, but not at the stacking fault. ( 1999 Elsevier Science B.V. All rights reserved. Keywords: Dislocations; Electronic structure; EELS; GeSi
1. Introduction
2. Experimental details and description of the dislocation
When the thickness of a thin "lm exceeds the Matthews}Blakeslee limit for pseudomorphic growth, mis"t dislocations are introduced at the underlying heterojunction [1]. In the case for Si growth on the (0 0 1) surface of Ge Si , the mis"t takes the form of a 603 dislocation x (1~x) dissociated into 303 (P30) and 903 (P90) partial dislocations separated by an intrinsic stacking fault (ISF). These structures also occur in heavily deformed silicon, and are believed to support electrically active states within 0.1 eV of the conduction band (CB) minimum [2]. TEM and luminescence studies have con"rmed optical activity near the defect, but the atomic structure that gives rise to the activity is not yet known [3}5]. Optical activity has also been detected associated with mis"t structures [4]. Theoretical work for the stacking fault [6], and for straight partial dislocations [7}9] have found that defect structures often reconstruct to clear the gap of electronic states. On the other hand, there has been some theoretical evidence for the existence of shallow valence band states [10].
I report here experiments using spatially resolved electron energy loss spectroscopy (EELS) to probe small regions of dissociated mis"t dislocations in a strained Si quantum well imbedded in Ge Si . Atomic column 0.35 0.65 positions in the [1 1 0] projection, and the spatial location for the spectral results are obtained using annular dark "eld (ADF) imaging [11,12] in the VG microscopes scanning transmission electron microscope (STEM), modi"ed to operate at 120 kV to obtain a 0.2 nm diameter electron probe. In prior work with GeSi alloys, it has been shown that very detailed conduction band (CB) information is obtainable using high resolution, spatially resolved EELS measurements of the Si 2p core ab3@2 sorption edge [13,14]. The EELS spectrometer was a Wien Filter design with an energy resolution of &200 meV and an absolute calibration of $20 meV [15]. Numerical deconvolution of the 0.3 eV wide "eld emission yielded a spectral resolution of 0.20}0.25 eV limited by statistical considerations [16]. The mis"t dislocation was of the 603 type located at the substrate interface of a 15 nm Si quantum well structure [17] Fig. 1 shows an annular dark "eld (ADF) image of the [1 !1 0] projection of the structure at high magni"cation. The Si well is at the bottom left, below the dashed line. The dislocation is extended about 3 nm in the [1 1 !2] direction away from the Si interface. Since the
* Tel.: 914-945-2782; fax: 914-945-2141. E-mail address: [email protected] (P.E. Batson)
0921-4526/99/$ - see front matter ( 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 0 0 7 8 - 2
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P.E. Batson / Physica B 273}274 (1999) 593}597
Fig. 1. ADF image of a second mis"t dislocation structure. Detailed EELS results were obtained from the locations marked a}f.
inter-column distance in the [0 0 1] direction in this projection is about 0.135 nm, this distance is not resolved using the 0.2 nm probe size. Instead, for each pair of columns, we see one spot, elongated in either the [0 0 1] direction in the bulk or in the [!2 !2 1] direction in the ISF. The measured distance between the two partial dislocations is 3.3 nm, or 10 `dumbbella units. This distance was found in other simple mis"t structures elsewhere in this sample. The P30 core is well de"ned, but the P90 core appears indistinct, probably due to kinks occurring along its length [18,19]. However, it can be located by considering continuity of (1 1 !1) type atomic planes as they cross the ISF. This "gure de"nes several unique locations for EELS analysis: (a) the bulk, relaxed GeSi alloy several tens of nm away from the defect, (b) the regions of tension and (c) compression within two (1 1 1) plane spacings on either side of the ISF, (d) the ISF itself, (e) the P30 dislocation core and (f ) the P90 core.
3. Experimental results Si 2p core absorption spectra are processed to remove a slowly varying background, to sharpen the energy resolution by deconvolution of the incident beam energy distribution, and to remove the 2p PCB intensity. 1@2 The shape of the remaining intensity is due to transitions to the s- and d-projected CB local density of states (LDOS). A model spectrum is made from a trial LDOS, using an inelastic scattering theory including core excitonic interactions, lifetime broadening and instrumental resolution. The model LDOS consists of parabolic e!ective mass contributions for the s-like band edges at * , L , and a saddle point at the d-like point L . These 1 1 3
Fig. 2. Spatially resolved EELS results for the Si 2p PCB 3@2 absorption edge for various locations within the structure summarized in Fig. 1. There appear to be unoccupied electron states below the CB within the dislocation cores, but not within the ISF.
contributions are terminated linearly at the p-like points ! and ! in the center of the Brillouin zone. The 1,5 2{ model positions for the important band edges * and 1 L are then adjusted to "t the experimental data. Finally, 1 there is a small contribution to the L intensity due to 1 a Ge-like saddle point in the " band. 1 In Fig. 2 there are spectral results for each of the regions described above. Each spectrum includes the processed data, a trial LDOS and the "tted spectrum. The spectra are aligned on an absolute energy scale relative to the 2p core level. This level has been shown 3@2 to be a constant for the relaxed alloy series [14], but it does shift with the addition of crystal strain [20]. 3.1. Bulk relaxed and strained alloy areas The bulk alloy results in Fig. 2 match the prior results closely for the alloy composition Ge Si [13]. The four 35 65 usual CB features, * , L , L , and " , are required to 1 1 3 1 fully explain the measured data. In the regions of tension and compression, the most notable change is to shift the spectra lower or higher in energy. A secondary di!erence is an apparent broadening of the L contribution in the 1 compressed region. In order to understand these results, we need to consider both volume and uniaxial strain in [1 1 1] type directions. The experimental data show a * shift of !0.085 eV 1 for the region in tension and #0.10 eV in compression. These shifts are opposite to those expected for the CB and so we expect a large core level shift. Within a couple (1 1 1) lattice planes on either side of the ISF, inspection of the image shows that this 10 unit ISF has 10 atomic planes on one side and 11 planes on the other, occupying roughly 10.5 bulk lattice units, giving a lattice strain of
P.E. Batson / Physica B 273}274 (1999) 593}597
$5% on either side. The deformation potential for the Si 2p core level is about!6 eV [20] giving a core level 3@2 shift of !0.3 eV at 5% tension and #0.3 eV in compression. Therefore these measurements place the * CB at 1 #0.22 eV at (b) in tension, and !0.20 eV at (c) in compression, relative to the bulk alloy. The band o!set in the Si well in this case is about !0.28 eV so this is a signi"cant perturbation of a desired device quantity. The deformation potential for * is #4 eV, [20] and therefore 1 provides a satisfying consistency to the interpretation. The uniaxial strain is somewhat more di$cult to deal with in that it results in splitting of the eight-fold degenerate L bands into two-fold/six-fold combinations. Again, 1 inspection of the image suggests that the uniaxial strain is about $5% within a (1 1 1) plane, but oriented in a [1 1 2] type of direction. The appropriate deformation potential for this process appears to be NL and is 6 15}16 eV [20]. The shifts are expressed relative to the strain e "1/3(e !e )+0.1e for this case, leading xy M @@ 111 to a shift of two-fold part of the band by about 0.15 eV and the six-fold part by 0.05 eV in the opposite direction. An experimental determination of these quantities is made di$cult by the disparity in degeneracy, making the two-fold contribution di$cult to identify. In Fig. 2 the total splitting for the best "t to the data is indicated by the dotted lines attached to the L point in the bulk 1 results. In tension, the two-fold edge falls over the edge of the * contribution, giving a spectrum that appears to 1 have only one, less intense, L peak. In compression, the 1 two-fold piece shifts upwards in energy, where the underlying * contribution is #at, leading to an apparent 1 broadening of the L peak. This modeling arrives at a 1 total splitting of 0.26 eV, compared with 0.20 eV expected from the deformation potential.
595
bors at each end. In the bulk, the six end atoms transform into each other by a two-fold screw axis oriented along the `dumbbella. In the ISF, this screw axis is replaced by a mirror plane. I model the band splitting that results from this by introducing a gap in the L band, labeling the upper and 1 lower branches, !` and !~, following the notion that the band is projected into the 2-D zone center and split into symmetric and anti-symmetric parts by the third-neighbor interaction. This splitting is calculated to be about 1.5 eV for Si, while the lower band is calculated to shift about 0.25 eV down from the L minimum in the bulk. 1 These predictions strongly resemble the observed behavior. That work also predicts that the X CB in the bulk 1 lattice, for which * is the band minimum, becomes the 1 !}M band in the hexagonal ISF BZ and is not a!ected by the change in local symmetry at the ISF. Again this is re#ected in the data of Fig. 2, which shows no change at the ISF * onset relative to the bulk alloy. 1 This experimental result argues against the presence of in-gap empty states near the CB at the ISF. It obviously does not address the possibility of states near the valence band edge, although it indirectly supports that possibility because they are predicted within the Mathiess and Patel work, which appears consistent with these results in areas where it can be checked. 3.3. Dislocation cores P30 spectral results in Fig. 2 show L splitting that is 1 very similar to that at the ISF. Referring to the model structure in Fig. 3a, we see, in the parent lattice, the
3.2. Intrinsic stacking fault Spectral results from position (d), the ISF, show a splitting of the L peak, with no other apparent shifts or 1 changes. In particular, there appears to be no shift or change in shape of the onset at * . The splitting can be 1 understood using the calculations for Si of Mattheiss and Patel [21]. They predicted that the L branch is a!ected 1 in two ways. First, it is projected into the center of the 2-D hexagonal ISF Brillouin zone (BZ) by two-dimensional nature of the fault. Then it is split into two components by mixing of Si sp3 orbitals from third-neighbor atoms on either side of the glide-cut plane. In the parent crystal, third-neighbor atoms occupy positions on either end of a structure commonly referred to as a `chaira. In the ISF structure, as a consequence of the 1803 rotation of the structure about the [1 1 1] direction, the thirdneighbors form a `boata structure, moving from their normal 0.45 nm distance apart to nearly the second neighbor distance of 0.38 nm. This structure can also be visualized as a two atom `dumbbella with three neigh-
Fig. 3. P30 (a) and P90 (b) model structures. Note that the P30 resembles the ISF structure.
596
P.E. Batson / Physica B 273}274 (1999) 593}597
Fig. 4. EELS analysis for the P30 (a) and P90 (b) partial dislocation cores. The solid line reproduces the "t to the ISF data on the left and the bulk data on the right. There is extra intensity coincident with the CB onset in both cases.
two-fold screw operation for the bulk. In the ISF, this is replaced by a structure supporting a quasi-mirror plane. The P30 core structure is very similar to that in the ISF, although it has to be admitted that the mirror symmetry is not exact in the P30 case, either. Interestingly, the orientation of the core structure is in a [1 1 0] type direction rather than in a [1 1 1] direction as it is in the ISF. It appears that the reconstructed P30 core is consistent with the "nding of splitting in the L band at the 1 dislocation core. This result is supported by a statistical analysis of the structure of the relaxed core to be reported elsewhere. Examination of the P30 near edge structure at * , 1 summarized in Fig. 4a, shows near edge gap states at the dislocation core. For everywhere except near * , the ISF 1 model "t is a very good match to the data. When this "t is subtracted from the P30 data, a peak remains centered at the * onset. It's width is close to the instrumental 1 resolution of 0.2 eV. In addition, excess intensity remains near the L peak. It is known that this peak is symmetry 3 compatible with * so that it shifts in a similar manner 1
under the in#uence of strain [13]. Therefore, it is reasonable that any distortion in the crystal that splits o! states into the gap from * should also shift states downwards 1 from L . 3 The P90 core EELS results present an interesting problem because they do not show the L splitting. Fig. 1 3b shows the single period (SP90) reconstructed P90 structure. This consists of 5}7-fold rings joined across the core. In this model structure third-neighbor pairs (for instance, labeled a) mimic the ISF con"guration, so it would seem that this structure might not be consistent with the spectral results. A new model for the P90, recently suggested by Bennetto et al. [9] introduces a double period (DP90) reconstruction at the core through the addition of kinks in the plane of the ISF. Viewed in the [1 1 1] direction, these have the e!ect of creating 5}7-fold rings along the dislocation core. The model is interesting in the present context because the introduction of kinks reduces the number of ISF-like third-neighbor interactions. In fact, introducing many kinks within an extended core structure can completely eliminate ISF third-neighbor interactions near the P90 core. This would be more likely, therefore, to produce a spectrum that resembles the bulk result. Fig. 4b shows the EELS analysis for the P90 core. In this case the "tted model for the bulk result has been subtracted from the data to reveal that a peak exists about 80 meV below the onset of * . Also in this case, a 1 second peak exists near L , as it must if the near edge 3 peak is actually due to the splitting of states from the CB edge. These two results, together with the results from the ISF and strained regions above, suggest that optical activity involving empty states near the CB is likely to be con"ned to the dislocation cores. Electrical activity may also be associated with the regions of strain on either side of the ISF, since 200 meV peaks and valleys in the CB o!set are certainly present there.
4. Conclusions This report describes the EELS and atomic structure of the dissociated 603 mis"t dislocation. Splitting of the L CB peak is almost certainly due to local symmetry 1 breaking by the presence of ISF-like atomic structure. Near edge gap states are found at the partial dislocation cores, leading one to surmise that optical activity exists at these locations. No information about near valence band (VB) edge states can be obtained from these results, so the possibility of optical activity near the ISF due to excitations from a shallow VB state remains. Future work on these structures will be undertaken using improved EELS and imaging capabilities that are currently under development.
P.E. Batson / Physica B 273}274 (1999) 593}597
Acknowledgements Model structures for this work were relaxed by Y. Tu at IBM. I also acknowledge discussion with P.M. Mooney, F.K. LeGoues, and K. Ismail during this work. R.W. Nunes kindly provided atomic coordinates for the DP structure.
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