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High Resolution Electron Microscopic Studies of the Atomistic Glide Processes in Semiconductors
K. Maeda, M. Inoue, K. Suzuki, H. Amasuga, M. Nakamura, E. Kanematsu
To cite this version:
K. Maeda, M. Inoue, K. Suzuki, H. Amasuga, M. Nakamura, et al.. High Resolution Electron Mi- croscopic Studies of the Atomistic Glide Processes in Semiconductors. Journal de Physique III, EDP Sciences, 1997, 7 (7), pp.1451-1467. �10.1051/jp3:1997199�. �jpa-00249657�
High Resolution Electron Microscopic Studies of the Atomistic Glide Processes in Semiconductors
K. Maeda (~~*), M. Inoue (~), K. Suzuki (~), H. Amasuga (~), M. Nakamura (~)
and E. Kanematsu (~)
(~) Department of Applied Physicsj Faculty of Engineering, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo l13, Japan
(~) Institute for Solid State Physics, The University of Tokyo, Roppongi, Minato-ku, Tokyo 106, Japan
(Received 3 October1996, revised 14 February1997, accepted 17 March 1997)
PACS 61.72 -y Defects and impurities in crystals; microstructure PACS.62.20.-x Mechanical properties of solids
PACS.61.18.-j Other methods of structure determination
Abstract. Direct observations of kinks and their motion on 30°-partial dislocations in Ge and GaAs have been for the first time attempted by using high resolution electron microscopy with the electron beam incident normal to the stacking fault plane separating the two partials.
Lattice fringe shift across the 30°-partials was used to locate the partial dislocation lines in an atomic resolution sufficient to identify kinks on them. Possible causes of kink migration and kink-pair formation observed in the images were discussed in light of available experimental and
theoretical information.
1. Introduction
The most prevalent view of dislocation glide in semiconductors is based on the theory of Hirth and Lothe iii or the kink diffusion model. This is owing to the belief that the kinks in covalent semiconductors are so abrupt that the barrier for kink diffusion may not be negligible, in contrast to kinks in metals and ionic crystals for which the smooth-kink model is more relevant.
Another common wisdom is to suppose that dislocations gliding in a dissociated form are in the so-called glide-set [2] in which a 60°-dislocation is split into a 90°-partial and a 30°-partial
and a screw dislocation into two 30°-partials, both separated by an intrinsic stacking fault.
Further, in analogy with surfaces in semiconductors, core atoms in the partial dislocations may be reconstructed to eliminate dangling bonds along the core. Theoretical calculations support this idea at least for 30°-partials in Si and Ge [3-6].
For dislocation glide in semiconductors, a large amount of experimental data has been accu- mulated and many theoretical considerations have been devoted to understand the microscopic
mechanisIn of the glide Inotion [2, 7]. In spite of that, there still reInain Inany uncertainties about the real process of dislocation glide. One of the controversies which seems not as yet
(*) Author for correspondence (e-mail: maeda@exp t.u-tokyo.ac.jp)
© Les (ditions de Physique 1997
settled is on the real magnitudes of the formation energy of a single kink and the migration
energy of the kink [8]. This fundamental problem is of crucial importance also in order to know the true mechanism of non-metallurgical effects such as the doping effect [2,9] and the
electronic excitation effect [10-12] widely observed in these crystals.
Many experimental efforts [13-21] have been made to measure the kink migration energy Em and the kink formation energy Fk separately. Most of the results commonly claimed that for Si [16,17,20-22] Em is as large as 1.3
+~ 1.8 eV whereas Fk is as small as 0.3
+~ 0.9 eV.
Theoretically, most of the calculations [23-27] have asserted that the experimental values are well reproduced, although there are different types of dislocations and different types of kinks,
as pointed out shortly in the next section.
Within the framework of the conventional view, however, some new experimental findings
are difficult to interpret, which led one of the present authors (Maeda) to propose a new model for dislocation dynamics in covalent crystals [8]. Recently, Bulatov and his coworkers [28]
extended atomistic calculations to a wider variety of defects that are possibly generated on
dislocation lines and could affect the dislocation glide in semiconductors. Their results are encouraging us to pursue the new model and look for more experimental evidences supporting
the underlying ideas.
A direct insight to the dislocation dynamics would be gained if one could directly observe the individual motion of kinks. Direct observations of an isolated kink, with dislocations viewed in the plan-view geometry in High Resolution Electron Microscopy (HREM), were attempted
in Si by Alexander and his coworkers [29] using forbidden reflections arising from stacking faults which separate partial dislocations. Recently Suzuki and his group [30] used the same
geometry and succeeded in obtaining good images of dislocations in Si which allowed them to extract 30°-partial dislocation lines. Most recently, we attempted to examine GaAs [31] in the plan-view HREM and have succeeded in m situ observing morphological, temporal changes of
dislocation lines in atomic resolution.
This paper first outlines the current knowledge of the magnitude of energy parameters
(Sect. 2) in order to illuIninate the points to which we had paid special attention. We then describe the principle of iInaging partial dislocations in atoInic resolution (Sect. 3), the experi-
mental procedure (Sect. 4), and new results of HREM observations obtained for Ge compared
with some previous results on GaAs (Sect. 5). Implications of the experimental findings are
discussed in Section 6.
2. The Magnitude of Energy Parameters
Table I summarizes the reported values of the kink formation energy Fk and the kink migration
energy Em deduced from various experiments on Si and Ge. The trend in Si that Em is large
and Fk is small is,also the case with Ge [18,19,22]. Among the experiments cited in Table II,
the Internal Friction (IF) measurements on Ge by Jendrich and Haasen [19j appears to be most persuasive. They assigned one IF peak to that due to migration of geometrical kinks and another to that due to double-kink formation. The evaluated values they obtained were Fk = 0.52 + 0.06 eV and Em = 1. ii + 0.01 eV for an intrinsic crystal and 0.7 + 0.I eV for n-type crystals. These values are consistent with the glide activation energy Q, that is to be given by Fk + Em provided that the long-range glide proceeds with kinks being1nutually annihilated
via kink-collision iii. The doping effect (Q
= 1.6 eV in intrinsic Ge and
" 1.2 eV in n+-Ge)
can be interpreted in terIns of the dependence of the kink1nigration energy on the doping
condition [19j.
As it is believed that Inobility of dissociated dislocations is iontrolled by 30°-partials, our
concern should be directed to the Inotion of this type of paitials (hence hereafter, unless
Table I. Experimental values reported for kink formation energy Fk and kink migration
energy Em in Si and Ge deduced from varioils measilrements.
Crystal Fk (eV) Em Experilnental Method
0.9 1.3 m siti1TEM (Louchet, 1993 [22])
0.44 1.5 Internal Friction (Gadaud, 1987 [17])
Si 0.5 1.6 Interlnittent Loading (Nikitenko, 1985 [16j)
<0.65 >1.45 Thin Hetero-Filln (Hull, 1993 [20j)
0.3 1.8 Loop Shrinkage (Gottshalk, 1993 [21j)
0.5 0.9 m siti1TEM (Louchet, 1988 [18j)
Ge 0.5 1. ii (intrinsic) Internal Friction (Jendrich, 1988 [19])
0.7 in-type) Internal Friction (Jendrich, 1988 [19])
Table II. Theoretical estimates of formation energies and battler heights of defects (ripper half) and defect reaction (lower half) on 30°-partials m St eva1ilated by var~oils atomistic
calcillations.
Defect Forlnation Motion
Energy (ev) Barrier (ev) Method
S EDB 0.15 K potential (Veth, 1983 [23])
0~81 0.17 SW potential (Bulatov, 1995 [28])
RK IA, 1.9 K potential (Jones, 1985 [25])
2.1+ 0.3 ab initio (Huang,1995 [27])
0.74 SW potential (Bulatov, 1995 [28])
LK 1.7, 1.9 K potential (Jones, 1985 [25])
0.82 SW potential (Bulatov, 1995 [28])
RKC 1.04 SW potential (Bulatov, 1995 [28])
LKC 0.22 SW potential (Bulatov, 1995
Forlnation Reaction
Reaction Energy of the Barrier (eV) Method
Products (eV)
0 ~ LK + RK I-I K potential (Marklund, 1984 [24])
0.9 K potential (Jones, 1985 [25])
1.60 2.88 SW potential (Bulatov, 1995 [28])
0 ~ S + S 1.62 1.79 SW potential (Bulatov, 1995 [28])
S ~ LK + RKC 0.66 1.65 SW potential (Bulatov, 1995 [28j)
S ~ LKC + RK 1.13 1.28 SW potential (Bulatov, 1995
S: Soliton, RK: Right Kink, LK: Left Kink, RKC. Right Kink soliton Complex, LKC: Left Kink soliton
Complex, 0: perfect site, SW potential Stillinger-Weber empirical potential, K potential: Keating potential, EDB: dangling bond energy
j
(al 16)
Fig. 1. Atomistic events that should occur (a) in the conventional double kink formation from a perfect site and (b) in the sohton-mediated double-kink formation from a soliton site
explicitly stated, 30°-partials are assuIned). Atolnistic calculations for 30°-partials in Si are, however, liInited to those listed in Table II. As the structure of kinks on 30°-partials is different froIn one sign to another, the kink formation energy and its migration energy may depend on
the sign of the kink. In Si, however, the calculations by Jones [25j using a modified Keating potential showed only a slight difference in Em: Em
= 1.8 + 0.I eV for kinks with a four- membered ring and Em
= 1.5 + 0.1 eV for kinks with a six-membered ring, both close to the
experimental values 11.4 +~ 1.8 eV). The theoretical values of double-kink formation energy by Jones [25j is
+~ 0.9 eV. If one neglects the possible difference in Fk between kinks of different signs, Fk will be given by half of the value (+~ 0.45 eV) which is in the range of experimental Fk (0.3 +~ 0.65 eV). Up to this stage, everything looks perfect. However, the real situation
may be more complex as shown in what follows.
Along the reconstructed core of partial dislocations, reconstruction defects (anti-phase de- fects or solitons) can be present thermally with a formation energy F~. Heggie and Jones [32j proposed a new model of glide processes in semiconductors noting the possible role of solitons in kink-pair formation and in kink migration. They supposed that kink-pairs are generated solely at solitons, and only the soliton-kink complex (Hirsch kink) can propagate along the dislocation line with a low activation energy. Figure I depicts the atomistic events that should
occur la) in the conventional double kink formation from a perfect site and 16) in the soliton-
mediated double«kink formation from a soliton site. Recently) the defect formation energies
and the defect motion barriers relevant to this soliton-mediating kink dynamics have been calculated for Si by Bulatov and his coworkers [28j using the Stillinger-Weber empirical poten- tial. Their results are included in Table II. As anticipated before [32j, the soliton formation
energy is large (F~
= 0.81 eV) but the barrier for soliton motion is very small (0.17 eV). The double-kink formation energy from a soliton site (0.66 eV or 1.13 eV, different depending on
the generated kink type) and the barrier height for the double-kink formation 11.28 eV) were
both much lower than those from a perfect site (1.60 eV and 2.88 eV, respectively). It is most remarkable that the left-right asymmetry in Em, which is not significant in the recon-
structed kink in their calculations as well, is very pronounced in the soliton-kink complexes.
The left-kink complex in their terminology, which stands for soliton-kink complex with a four- membered ring, has a very low activation barrier of Em
= 0.22 eV, whereas the right one,
which stands for soliton-kink complex with a six-membered ring, has a value of Em
= 1.04 eV,
even larger than the reconstructed kinks without solitons. According to the calculations by Bulatov et al. [28], therefore, the double kink formation takes place more easily at soliton sites, and when the soliton combines with a left kink, the soliton-kink complex can propagate very swiftly along the dislocation line. This is exactly what had been presumed in the soliton-kink
model of Heggie and Jones [32].
The soliton-kink model is appealing because it also allows us to understand the microscopic origin of the electronic effect [8]. A theoretical consideration [33] indicates that, for the excita- tion effect to be observed, enhancement of Smallest Double Kink (SDK) formation is required.
Therefore, there must be some sites on the straight part of dislocation lines that can act as
centers for non-radiative electron-hole recombination which leads to enhanced SDK formation.
Almost the only candidates for such sites in reconstructed dislocations are solitons. Thus, in this respect as well, it seems worthwhile examining the reality of the soliton-kink model once
again in more detail.
3. Atomistic Imaging of Partial Dislocations by Plan-View HREM
Although Transmission Electron Microscopy ITEM) is a powerful method to observe directly dislocations in crystals, even the weak-beam technique is not sufficient to resolve atomistic defects such as kinks on the dislocation lines. To image kinks on dislocations, the edge-on geometry adopted usually for observing dislocation lines in High Resolution Electron Mi- croscopy (HREM) would not be useful because it is almost impossible to know the depth of the kinks in the specimen film. However, when the dissociated dislocations are viewed nor-
mal to the stacking fault plane separating the two partials, we may be able to resolve the
shape of the part1al dislocation lines based on the following principles. The underlying two ba- sic ideas rely on the fact that structural images taken under appropriate conditions represent, in fairly good fidelity, projections of atomic arrangement in the specimen lattice viewed from the incident direction of the electron beam.
One of the ideas was first proposed by Alexander and his coworkers [29] for crystals of dia- 1nond or sphalerite structures. These crystals consist of two inter-penetrating face-centered cu- bic (fcc) sublattices which stack in the (111) directions with a sequence denoted by
ABCABC... The intrinsic Stacking Fault (SF) separating the two partials introduces near the SF plane a local stacking of hexagonal close-packed (hcp) structures denoted byABCA( CAB C...
Thus if one views the crystal norInal to the SF plane, one can see an atoInic projection
of the hcp structure viewed along the c-axis. The projection pattern of the hcp lattice
possesses a superlattice periodicity in the two-diInensional Wood's notation [34] of vi x vi R30°(~). Therefore, if the electron beaIn is incident norInal to the SF plane, forbidden reflec-
tions arise froIn the SF in the diffraction and in real space one is able to recognize the partial
dislocation lines as the periphery of the SF contrasts.
Another idea, first proposed by Suzuki and his coworkers [30], is based on a singularity in the atoInic alignInent across the 30°-partial dislocation line. The top drawing in Figure 2 shows the atoInic arrangeInent at the glide plane of a 60°-dislocation, in which one can see that the atoInic arrays norInal to the 30°-partial exhibit a displaceInent along the dislocation line whereas for the 90°-partial such a shift across the dislocation line is absent. Hence, if we
could get a plan-view HREM iInage representing this shift, we are able to detect the 30°-partial dislocation line by tracing the points where the lattice fringes exhibit a shift.
Ilnages siInulated for GaAs by the Inulti-sliceInethod are shown in the lower half of Figure 2.
Calculation details were described in our previous paper [35]. The vi x vi R30° superlat-
tice periodicity, though not proIninent under the Scherzer focus condition, is evident in the SF region. Systelnatic siInulations [35] show that the superperiodic pattern becoInes Inore distinct
when one uses an under-focus condition but the contrast becoInes weak when the speciInen is thicker than 10 nIn. These features found in GaAs were essentially the saIne for 30°-partial
dislocations in Ge. Figure 2 also indicates that the expected shift in the atomic alignment
can be seen across the computed image of the 30°-partial but not across the image of the
90°-partial. Since the atomic alignment shift arises froIn the screw component of the 30°-partials, one1nay suspect that the strain field deterInines the position of the iInage shift which Inight deviate froIn the real dislocation core. However, iInage siInulations indicate that positions where the iInage exhibits such shift coincide quite well with the dislocation core in the Inodel lattice, prooving the reliability of this approach for resolving the locations of kinks.
4. Experimental Procedures
We used two1naterials, undoped Ge (p = 50 Qcm) and Si-doped n-GaAs in
= 1x 10~~ cm~~).
One of the reasons for using GaAs as well as Ge was that GaAs is a typical mater1al which
exhibits a large electronic excitation effect [10] whereas Ge is another typical material which does not show any electronic excitation effect under the normal conditions [36]. Another reason
for using Ge was that reliable information of the kink formation energy and the kink migration
energy is available from the internal friction experiments [19] as already mentioned in Section 2.
The Ge crystals were uniaxially compressed in vacuum along a [123j single slip orientation at 505 °C up to 4.5% strain. The GaAs crystals were coInpressed along a [011] direction at 490 °C up to 5.1$i strain. Both deformed crystals were sliced along the ill1) main slip planes, mechanically thinned and ground with a dimpler machine. The final thinning was achieved by chemical etching at room temperature, with lvol HF +lvol H202 + 4vol H20 for Ge and
with lvol Br2 +10vol CH3 OH for GaAs. The final etching process was cruc1al to miniInize the
roughness of the specimen surfaces which could cause artifacts in the final images.
HREM observations were conducted at room temperature by using a Hitachi H-9000 (0.19 nm point resolution) with an electron beam, typically 8 nA and 1 pm in diameter, incident nor- mal to the (111) specimen plane. The objective aperture size was chosen so as to collect 18
diffraction spots up to (40T) indices. The acceleration voltage was reduced to 200 kV to avoid radiation damage in the specimens.
(~) vi x vi R30° expresses that the superlattice pattern is obtained by magnifiying both the two
primitive translation vectors of the fcc mother lattice by vi times in length and rotating them by 30°
around the axis normal to the projection plane.
~SF
.~w m~ +- 4w .-mmmw -
30°-partial 90°-partial
GaAs
Fig 2. Upper: Atomic arrangement at the glide plane of a 60°-dislocation, m which the atomic arrays normal to the 30°-partial are displaced along the dislocation line whereas in the 90°-partial
such a shift across the dislocation line is absent. Lower. Images simulated for GaAs by the multi-slice method.
The micrographs taken were digitized with a scanner and processed with an image analyzing
program. The main part of the image processing consists of two dimensional Fast Fourier Transform (FFT) of the original image and inverse FFT of selected spots in the diffraction pattern. Figure 3a schematically illustrates the procedure for extracting contrasts emphasizing Stacking Fhults (SF image).
One of the problems with this scheme is the arbitrariness of the intensity threshold which should be used to cut the diffuse tail in the contrast. In the present study, though, we adopted
such a threshold that the SF contrast develops with an average width equal to the separation of the two partials expected from the stacking fault energy.
Figure 3b illustrates the procedure to extract 30°-partial dislocation line shape according to the atomic alignment shift. As the dislocation is not necessarily oriented exactly in a (lT0)
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Fig 3. a) The procedure for extracting contrasts emphasizing stacking faults (SF image). b) The procedure to extract 30°-partial dislocation line shape from the binge shift (fringe-shift image) The method to determine the direction of the Burgers vector is also illustrated (see text). The circles in the FFT pattern indicate those spots used for inverse FFT.
Peierls potential valley, we first choose the (lT0) direction which is closest to the orientation of the dislocation segment. Then we select a pair of the (250) and (120) diffraction spots
which correspond to the lattice fringes crossing the dislocation segment and perform inverse Fourier transforInation of the selected pattern. Tracing along kinked points, if present, along the fringes, we get an iInage (fringe-shift iInage) which represents the 30°-partial dislocation
