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Lüders bands in deformed silicon crystals
OOOI-6160
LijDERS
BANDS
IN DEFORMED CRYSTALSt
79 0701.116SO?.W~O
SILICON
S. MAHAJAN and D. BRASEN Bell Laboratories.
Murray Hill, NJ 07974. U.S.A.
and P. HAASEN lnstitut fir Metallphysik. Universitlt (Receired
3 Nocember
Gottingen, West Germany 1978)
Abstract-The formation of Liiders bands in Czochralski and float-zone silicon crystals, oriented for single slip. has been investigated at 800. 900 and 1OOO’C.At 800°C. Liiders strain is observed in Czochralski crystals, whereas the situation is ill-defined in the case of float-zone crystals. However. the Liiders deformation observed at 8OOC can be eliminated by a double heat treatment consisting of a 4 h anneal at 700°C followed by a second anneal at 1OOOC for 30 h. Furthermore. on increasing the deformation temperature, the tendency for Liiders deformation progressively decreases, Arguments. based on Hahn’s postulates for nonuniform yielding. have been developed to rationalize the observed differences between Czochralski and float-zone crystals. influence of heat treatment and deformation temperature. The Liiders front is observed to lie close to the (iO1) plane. Microstructures at and behind the front have been investigated by transmission electron microscopy. An explanation involving strain compatibility between the deformed and undeformed regions is presented to explain the observed crystallography. R&nn&--Nous avons etudie la formation des bandes de Ltiders a 800.900 et 1000°C dans des monocristaux de silicium fabriques par les methodes de Czochralski et de la zone flottante et orient&s pour le glissement simple. A SOO’C,on observe la deformation de Liiders dans les cristaux de Crochralski, alors que la situation est ma1 dttinie dans les cas des cristaux de zone flottante. On peut cependant &miner la deformation de Liiders observee a 8OU”Cpar un double traitement thermique, qui consiste en un recuit de 4 h a 700°C suivi dun second recuit de 30 h a IOOOC. De plus, la tendance a une deformation de Liiders diminue progressivement lorsqu’on augments la temperature de deformation. Nous prCentons des arguments reposant sur les postulats de Hahn de la deformation non uniforme, afin d’expliquer les differences observees entre les cristaux de Czochralski et ceux de zone flottante, I’influence du traitement thermique et de la temperature de deformation. Zusammenf~ng-Die Ausbildung von Liidersblndern wurde bei 800, 900 und 1OOO’Can Crochalskiund ‘float-zone’-gezogenen Einkristallen mit Orientierung fur Einfachgleitung untersucht. Rei 800°C wird eine Liidersverformung in Crochalski-gezogenen Kristallen beobachtet, wohingegen die Lage bei den ‘float-zone’-gezogenen Kristallen uneinheitlich ist. Allerdings kann die Liidersverformung bei 800°C mit einer zweifachen WLmebehandlunz-Gliihuna 4 h bei 700°C und nachfolnend 30 h bei 1OOO”C-beseitigt werden. Des weiteren nimmt die Neigung zu;Liidersverformung mit anlteigender Verformungstemperatur ab. Mit Argumenten, die auf den Postulaten von Hahn iiber nichtgleichm%Biges FlieDen aufbauen. werden die beobachteten Unterschiede zwischen Crochalski- und ‘float-zone’-gezogenen Kristallen und dem EinfluD von Warmebehandlungen und Verformunsgtemperatur e&art.
1. INTBODUCTION The deformation behavior of elemental semiconductors has been investigated by many investigators [l-S]. Several interesting observations emerge from these studies. However, the most interesting one pertains to the yield drop behaviour observed in crystals having a very low grown-in dislocation density and oriented for single slip. This observation has been rationalized in terms of the Johnston-Gilman approach, originally developed to explain the origin of yield drops in ionic crystals [8,9]. t Work performed while S. Mahajan was on study leave at the Institut fur Metallphysik, Universitlt Giittingen, West Germany.
In the early stages of deformation, strain distribution is very inhomogeneous [6,7-j. Schroter et al. [6] have investigated this aspect in deformed germanium crystals by etch pitting. They observe that when the grown-in dislocation density is very low, the initial deformation is accomplished by the propagation of Luders bands. These bands originate from the specimen ends and propagate inwards. Their observations indicate that, even when the resolved shear stress reaches the lower yield point, the dislocation distribution as well as the local strain are very inhomogeneous over the specimen length. However, if the grown-in density is relatively high, this heterogeneity does not persist beyond the lower yield point. Two types of Liiders bands have been observed by
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MAHAJAN ef ~1.: LijDERS BANDS IN DEFORMED
1166
Schriiter et nl. [6]. In one situation the band front is parallel to the trace of the primary plane in the cross slip plane (G type band), whereas in the other case the front is normal to the trace (K type band). Subsequently, SiethofT [IO] investigated in detail G and K type bands in heavily doped float-zone silicon single crystals. Etching studies on the cross slip plane reveal a K type Liiders band front to be a typical kink band having a highly polygonized structure. Arguments have been developed as to how such structures evolve during deformation. In the present investigation the formation of Li.iders bands in Czochralski as well as float-zone silicon single crystals, oriented for single slip, has been investigated as a function of temperature. Dislocation distributions in sections parallel to the front have also been evaluated at, and behind, the K type front by transmission electron microscopy (TEM). In addition, dislocation arrangement around the band front observed on the cross slip plane has been studied. 2. EXPERIMENTAL
C~OCHRAL~KI CRYSTALS t
j
UNLOADED
44UR6 AT 700%
E
0:
FLOAT
0.2
0.6
1.0
-ZONE
1.4
CoYPR666lVE
CRYSTALS
1.6 STRAIN
2.2
2.6
3.0
W
Fig. 2. Representative stress-strain curves of FZ silicon crystals. oriented for single slip, at different temperatures.
DETAILS
Two types of dislocation-free silicon crystals were used in this investigation: crucible-grown Czochralski (CZ) and float-zone (FZ). As ascertained by infrared absorption measurements, the former crystals contained _ 5-8 x 10”/cm3 of dissolved oxygen, whereas in the latter the oxygen level was below the detectability limit. Shaped compression samples, _ 0.5 cm x 0.5 cm x 1.25 cm in size, were cut from the grown crystals with [i23] as the compression axis and (lil) and (54i) as the two side faces. The specimens were then ground and chemically polished in a solution consisting of 30 ml CH,COOH, 30 ml HF and 50ml HNOs. IO
9
SILICOX CRYSTALS
In order to study the influence of substructure on the formation of Liiders band, a set of CZ samples was annealed at 7WC for 4 h followed by a 30 h anneal at 1ooo”C under a hydrogen atmosphere. This heat treatment was chosen because it is known to result in the formation of precipitates and extrinsic stacking faults bounded by i( 111) Frank partials [7, 111. Chemically polished and heat treated samples were deformed in compression at temperatures between 800 and 1000°C and at a strain-rate of -6.7 x 10-‘/s; the protecting atmosphere was forming gas. The load was removed at the conclusion of a test, and the specimen was allowed to cool to ambient temperature. Deformed samples were evaluated by optical metallography and transmission electron microscopy. To prepare samples for electron microscopy, slices parallel to the Liiders band front as well as the (lil) cross slip plane were cut by a string saw. The Liiders slices were ground down and polished from both sides, while the (lil) section was finished only from one side. Thus the (111) deformed surface exhibiting the Liiders band front was preserved. Discs 3mm in dia. were trepanned from the polished sections. They were subsequently thinned in the aforementioned polishing solution. To examine substructure around the Liiders band front in the (111) plane, a thinning procedure was developed that permitted thinning at a preset location. Thinned discs were examined in a
0
0.4
0.6
1.2
1.6
CMPRESSIVE
2.0
2.4
2.6
3.2
67RAIN W
Fig. 1. Representative stress-strain curves of CZ silicon crystals, oriented for single slip, at different temperatures. Stress-strain curve of a heat-treated crystal, obtained at 8OO“C, is also included. Note the dramatic difference in the rcspons~ of asgrown and heat-treated crystals.
JEM 200 microscope operating at 200 kv. Taking [iOl]( 111) as the primary slip system. the upward normal of the region being examined and operating reflections were indexed in an internally consistent manner during examination from the Kikuchi line pattern superimposed on the spot pattern.
MAHMAN er &:
LGDERS BASDS 1% DEFOR%fED SILICON CRYSTALS
1167
Fis. 3. Slip lines observed
on the fgl) face of a CZ crystal deformed to a compressive strain of 3.2”,, at 8QOC. Note that near the sample edge. slip lines are coarse. deep and widely spaced.
Liiders deformation coincides with the obsened crease in stress after the lower yield point.
3. RESULTS
3.1 De~oormarion chracteristics Representative stress-strain curves of CZ and FZ crystals deformed at 800, 900 and IOOO’C and also of the heat treated CZ crystal deformed at 8OO’C are shown in Figs. 1 and 7. The principal observations are the following: (i) Both types of crystals exhibit yield drops at 8OWC. The magnitude of the drop progressively decreases with increasing deformation tem-
perature and the drop is absent at IOWC’. (ii) The yield stress
shows
L-cry strong
temperature
depen-
dence. (iii) CZ crystal deformed at 8WC exhibits a Liiders strain, whereas in the case of FZ crystal the situation is not very well delineated. (iv) In both types of crystals. a Liiders strain is virtually absent at 900 and lOOO’C, while in the heat treated CZ crystals Liiders strain is absent even at 800°C. It is implicit in the preceding assessment that the termination of
in-
32.1 CZ ctystds. Surfaces of deformed crystals were examined by optical metallography using the Nomarski interference contrast. and representative slip patterns observed on the (31) surfaces of samples deformed at WK. and at 900 and 1OOO’C.are reproduced as Figs. 3 and 4, respectively. It is clrar that slip occurs primarily on the (Ill) planes, i.e. the primary slip plane. but a few slip lines on the (ill1 planes are also seen in Figs. 3 and 4(a). Furthermore. comparing Figs. 3 and 4 it is evident that slip is distributed on a tiner scale in Fig. 4. However. a detailed comparison between these slip patterns is not possible because of the differences in imposed compressive strains (3”; at 8oO’C; l.J”, at 900 and 1OOO’C).
Fig. 4. Slip lines obserxzd on the (31) face of a CZ crystal deformed at (a) 9OO’C and (bj IOWC. .A one to one comparison with Fig. 3 is not possible because the str%n level is loner in Fig. 1.
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MAHZJAN
et af.:
LGDERS
BANDS
fN DEFORMED
SILICOX
Fig. 5. Optical micrograph showing Liiders band front observed on the deformed at YOO‘C. Xote that the Gout is fairly sharp towards the rig&. on the left. Al:.o the sharp portion in parallel to the [lil]
Surfaces of the heat-treated CZ crystal were also studied by optical metallography. Slip lines were not discernible, implying that slip is occurring on an extremely fine scale. The sample deformed at 8OO’C was examined across its whole length. In conformation with the observations of Schriiter er (I[.,[6] slip was found to be inhomogeneously distributed. In order to ascertain the crystallography of a Liiders band front. its endings in a sample deformed at SWC were examined on the (NT) and (iii) surfaces, and these results are shown in Figs. 5 and 6. On the (54i) surface, the front is fairly sharp at one end and becomes progressively diffuse in going towards the other end. In fact. slip activity ahead of the front in that region is fairly extensive. Furthermore, the sharper portion of the front tends to lie close to the [tilldirection. The front on the (flit plane is seen as a set of fringes running horizontally in Fig. 6 and is not as easily discernible as in the case of the (54i) surface. This may be due to the fact that the primary slip vector, +i[iOl], lies in the plane of the observation. Furthermore, the front lies normal to the [iOl] direction. Combining the preceding two assessments, it is inferred that the macroscopic habit-plane of the front is -(Tot). The K bands observed by Siethoff [lo] in heavily doped FZ silicon have the same crystallography.
CRYSTALS
(54il face of a CZ crystal --hereas it is quite direction.
diikse
Slip lines lying along the trace of the (I I1 1 plane are visible in Fig. 6. Since the primary slip vector does not produce any displacement on the plane of -the observation, i.e. the (11I) plane. the observed slip lines must be due to the activation of the coplanar. secondary slip systems. 3.2.2 FZ crystals. Figure 7 is a typical example of the slip pattern observed on the !ili)plane of a FZ crystal deformed to a compressive stram of 3.2:, at 800’C. Both coarse as well as fine slip lines, lying on the (111) planes. are seen. As argued previously, their visibility must be due to slip activity on the coplanar, secondary slip systems. Furthermore. the termination points of well-separated. coarse slip lines delineate a narrow band of parallel lines that is normal to the [iOl] direction. As depicted in Fig. 6, a very similar situation exists in the case of CZ crystals. although the observed slip distributions in the two cases differ. Slip lines seen on the (tit) and (31) surfaces of a FZ crystal, deformed to a compressive strain of 2.8”/ at 9OO’C, are reproduced in Figs. 8(a) and (b). respectively. In Fig. 8(a). fine slip lines are interspersed between the coarse ones. Furthermore. it is clear from Fig. 8(b) that, in addition to slip activity on the primary plane, slip lines on the (lil) and (ill) planes are also seen. An attempt was made to study the distribution of slip on a FZ crystal deformed at 1OOO’C.It proved
Fig. 6. The Liiders band shown in Fig. 5 is being examined on the (111) plane. i.e. the cross slip plane. The front is seen as a set of fringes running horizontally. Note that the primary slip vector, +![iOl]. lies in the [ilf) plane and thus the visibility of slip lines implies the activation of a coplanar, secondary slip vector.
M;\HAJAS
QZA:
tfDERS
BAXDS
14 DEFORMED
SILICON
CRYif.AU
Fig. 7. Slip lines observed on the (111) face of a FZ crystal deformed to a compressive X1”,, at So0 C. Note that the termination points of well-separated. coarse slip lines delineate band of parallel lines that is normal to the [il.)!] direction.
almost impossible to image these slip lines because the\; were too fine. 3.3 Dislocarion arrangement
close to rhe Liiders
band
fionr
Figure 9 depicts a representative example of the arrangement of dislocations observed by TEM either at or very close to a Liiders band front in a CZ crystal deformed at SWC. On the scale of our observations, the observed dislocation distribution in the (iOil section is inhomogeneous. In area A imperfections are fairly well clustered. whereas in other regions the den-
Fig. 8. Slip lines observed
1169
strain of a narrow
sity of dislocations
is very low. Moreover. dkkations are also absent in some portions of the crystal. In Figs. 9(c) and (d), the primary glide plane. till), is edge-on. and it is clear that the dislocation distribution is far from being characteristic of a sma!! angle tilt boundary lying in the (Tot) plans. In Fig. 91~) the plane of the micrograph is (lOi) and g = 102. and therefore the primary dislocations, t4[iOl]. shouid be in extinction or exhibit residual Gntrast. Comparing Fig. 9(c) with Figs. Y(a) and (b) it is apparent that the Burgers vector of the majority of the dislocations is +--[iOl]. but a few coplanar,
on the ia) (111) and Lb) (I’ll suriaces of a FZ crystal deformed to a comprw sive strain of 3.3”, at WWC.
1170
%fAfAHA_i.W et
of.: Li;DERS BANDS IN DEFOR.MED SILICOW CRYST.ALS
Fig. 9. Electron micrographs showing a typical dislocation arrangement observed in a iiN) section taken from an area at or close to a Liiders band front in a CZ crystal deljrmed at YOO~C.Planes of micrographs (a), (5). (c) and (.d) are ~(1 Ii). -(IIi), -(lOi) and -(Zii). respectiveI>-. (b) and (d) are weak-beam microFaphs taken under g. 3g condition. Note that dislocations are clustered in region A. Marker represents I pm.
secondary dislocations are aIso seen see area A in Fig. 9(a). This assessment is borne out by the optical metaliography observations discussed earlier. Furthermore, a portion of the debris is in the form of dipoles, see features exhibiting broad images. i.e. intense ‘inside’ contrast, in Fig. 9(b). This is consistent with the recent detailed study of Winter et al. [12] on faulted and unfaulted dipoles in deformed CZ crystals oriented for single slip. 3.4 Arrangement of dislocations away from the Likiers band front Variations in the observed dislocation arrangement in a (iO1) section, taken far away from a Ltiders band front in a CZ crystal deformed at 800°C. are illustrated in Figs. 10 and Il. In Fig. 10(a). the primary glide plane as well as the cross slip plane are edge-on, and g = 202 and 120 in (a) and (b), respectively. Comparing Figs. 10(a) and (b). it is apparent that slip is primarily accomplished by the glide of 2 i[iOl] dblocations on the primary as well as on the cross slip planes. In addition. slip activity w-ith a coplanar, secondary Burgers vector and secondary slip can also be seen. see region B in Fig. IO(a).
Two basic differences exist between the microstructures shown in Figs, 10 and 11. Firstly, dislocation segments lying on the cross slip plane are not observed in Fig. 11. compare Fig. lo(b) and II(a). Secondly, the majority of the debris is in the form of dipoles. Since g = 202 in Fig. 11(b) and dislocations exhibit a residual contrast, dipoles must belong to the primary slip system. It is emphasized that features similar to the ones shown in Fig. 11 were also observed in a thicker portion of the (iO1) section taken close to the Liiders band front. 3.5 Arrangement of dislocations obsersed Liiders band front on the cross glide plane
around a
On the scale of our observations the line of demarcation between the deformed and undeformed regioti was not sharp. and very long dipoles and isolated dislocations were observed to extend across the interface. Furthermore, in comparison with the (iO1) sections, the dislocation density in the (lil) section was lower. The contrast behaviour of deformation-induced microstructures observed in a region behind the macroscopic front was investigated in d&ii. and
MAHAJUAN er d:
LCDERS
BANDS
fN DEFORMED
SILICON
CRYSTALS
1171
arrangement observed in a (iO1) section taken from Fig. 10. Electron micrographs showing dislocation an area away from a Liiden band front in a CZ crystal deformed at 88o’C. Note that slip activity a;ith a coplanar. secondary Burgers vector and secondAry slip can be seen in region B in (a). Planes Marker represents I pm. of micrographs (a) and (b) are - (lOi) and - (11 I). respectively.
Fig. 1I. Electron micrographs showing another type of dislocation arrangement section taken lrom an area away from a Liiders band front in a CZ crystal Marker represents I pm.
observed deformed
in a (fO1) at 8OOT.
Fig. 11. Electron micrographs showing disloca:ion arrangement observed in a region behind the front; the section k parallel to the (Ii11 plane, i.e. the cross glide plane. The ptane of micrograph in each case is -itif,. Marker represents I pm.
I172
MAHAJAX
et al.:
LL’DERS
BANDS IN DEFORMED
results are reproduced as Fig. 13. Comparing Figs. 12(af, (bl and f& it is inferred that the Burgers vector of the majority of dislocations is &$[iOl]. These dislocations are fairly long and not very straight, implying that &s[iOl] screw se_qments undergo cross ghde. In addition, k+[Oli] dislocations are also in the field of view, and are steeply inclined. This result bears out an earher assessment that coplanar, secondary slip is occurring at the Liiders band front. 4. DISCUSSION Four interesting observations emerge from the present study. Firstly. a Liiders strain is observed in CZ crystals deformed at 8OO’C.whereas the situation is illdefined in the case of FZ crystals. Secondly, when the deformation temperature is raised to 900 or lOOO”C,Liiders band formation is virtually absent in both types of crystal. Thirdly, the Liiders strain observed in CZ crystals deformed at 8GO’C can be totally eliminated by a double heat treatment consisting of a 4 h anneal at 7OO’C, followed by a second anneal at 1OOO’Cfor 30 h. Fourthly. the macroscopic Liiders band front tends to lie parallel to the (TOI) plane, i.e. normal to the primary slip vector. Questions that need elucidation concern the growth of an embryonic Liiders band and its subsequent propagation into an undeformed portion of a crystal. Siethoff [lo] and Hahn [13] have considered these problems in detail. Siethoff visualizes that the propagation of a Liiders band front can be likened to the stress-induced migration of a small angle tilt boundary. Furthermore, the sideways growth of a band, i.e. growth in a direction normal to the primary slip plane, occurs by the operation of single-ended dislocation sources that could form as a result of image forces-induced cross slip of screw segments near crystal surfaces; such sources have been observed by Lohne and Rustad [14] in zone-refined aluminum single crystals. If Liiders deformation were to proceed in such an orderly way, it would be anticipated that: (i) edge dislocations comprising the front should be arranged in a regular manner, see Siethoffs Fig. 6(a); (ii) dislocations of one sign only should be observed at the front. However, these assessments are not borne out by the dislocation arrangement observed in a (iO1) section taken from an area close to or at a Liiders band front, see Fig. 9. Hahn [13] has postulated that the propagation of a Liiders band occurs by the injection of dislocations into undeformed areas adjoining a band front. Mechanistically it is not clear how this is done. However, if one assumes that the microscopic front is a bit ragged and screw segments near the front undergo cross slip, induced either by elastic interaction with other dislocations gliding on parallel planes or by image forces. mobile dislocations can be produced in the undeformed regions. Furthermore, the crystal would continue to yield nonuniformly. i.e. by Liiders
SILICON
CRYSTALS
deformation. as long as at a constant lower y-i&d stress, the contribution to strain of the material outside the band is substantially lower than that of the growing band. Experimental evidence presented in Figs. 10 and 12 suggests that, ev-en though the resolved shear stress on the cross slip plane is zero. cross slip occurs behind the front. In addition, dipoles observed in Fig. 9 could have formed due to jog dragging by screws. and jogs in turn could have resuhed from cross slip. It is known that FZ crystals contain A and B type clusters [is], and A clusters have been identified as large prismatic loops by transmission electron microscopy [16]. Features resembling A type clusters have also been observed in CZ crystals [17-j. but their density is considerably tower. It is therefore conceivable that when an undoped or a lightly doped FZ crystal is deformed, segments of large prismatic loops could act as dislocation sources and slip may start at various portions of the crystal: the slip distribution shown in Fig. 7 appears to bear this out. Thus the development of the strain condition conducive to nonuniform yielding is inhibited and the crystal deforms more or less in a uniform manner. However. A clusters could be pinned by dopant atoms in heavily doped FZ crystals and then Liiders deformation could develop. This assessment is compatible Gth Siethoffs observations on the presence of Ltidcrs bands in heavily doped FZ crystals [lo]. Pate1 [7] has shown that, in addition to extrinsic stacking faults, prismatically punched out dislocation loops are observed around precipitates that are produced in CZ crystals during the heat treatment used in this investigation. Since prismatic loops are distributed at random and can act as glide sources, the distribution of potential, equally potent dislocation sources is also at random. It is therefore envisaged that slip in the heat treated CZ crystal would be distributed on an extremely fine sccsle and it should undergo uniform yielding. This is indeed borne out by the experimental result. It is observed that, on raising the deformation temperature from SOO’Cto 900 or laoO;C. coarser and deeper slip lines are replaced by finer slip, see Figs. 3, 4, 7 and 8. Similar effects are observed in b.c.c. Ta-Re alloy single crystals in the temperature range where they are assumed to deform by the Peierls mechanism [IS]. The origin of this effect is not clear, but it could be that, with increasing deformation temperature more slip sources are activated. Thus slip distribution conducive to uniform yielding develops in preference to that for the Liiders deformation. It is ascertained that a macroscopic Liiders front tends to lie close to the (TOI) plane. see Figs. 5 and 6. Furthermore. in the present deformation experiments. the primary slip v-ector is also Ii[fOl]. It is therefore visualized that the observed crystallography may stem from the fact that in the present situation only the normal strain component has to be accommodated
MAHAJAN er al.:
LijDERS
BANDS IN DEFORMED
between the deformed and undeformed regions, and this may be done by the injection of primary dislocations into undeformed areas adjoining the front. In view of the fact that slip lines seen in Fig. 7 are fairly well separated and differ in the chronology of their formation, the observed tendency of the boundary to lie close to the (TOI) plane is remarkable. Again, strain compatibility arguments may be invoked to rationalize this observation. In comparison with the (iO1) sections, the dislocation density in the (lil) section is lower. This could be due to the fact that the area examine-d is bounded at the boundary
on one side by the original deformed surface to which dislocations can escape during deformation. This observation implies that the dislocation density in
the surface region is lower than that in the interior. This appears to confirm Fourie’s observation on the differences in dislocation content between the interior and surface regions of deformed copper single crystals [ 191. Ackmwledgemenrs-One of the authors (SM.) is grateful to the German Government for the award of a D.A.A.D. fellowship. In addition, the authors acknowledge fruitful discussions with G. Y. Chin and B. C. Wonsiewicz.
A.M.
27 7- f
SILICON CRYSTALS
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REFERENCES 1. C. J. Gallagher, P/IJX Rec. 88. 721 (1952). 2. L. Graf, H. R. LaCour and K. Seiler. Z. >Verallk. 44, I13 (1953). 3. J. R. Pate1 and B. H. Alexander, rlcra met& -1, 385 (1956). 4. W. D. Sylwestrowicz, Phil. &fag. 7, 1825 (19621. 5. R. L. Bell and W. Bonfield, Phil. Mag. 9, 9 (1964). 6. W. Schriiter, H. Alexander and P. Haasen, Ph.vs. Stat. Sol. 7, 983 (1964). 7. J. R. Patel, Discuss. Faraday Sm. 38, 201 (196-B. 8. H. Alexander and P. Haasen. Solitl State Ph.rs. 22, 28 (1968). 9. W. G. Johnston and J. J. Gilman. J. appl. Phys. 30, 129 (1959). IO. H. Siethoff, rlctu meral/. 21, 1523 (1973). II. G. A. Rozgonyi, S. Mahajan. M. H. Read and D. Brasen, Appl. Ph_rs. Lett. 29, 531 (1976). 12. A. T. Winter, S. Mahajan and D. Brasen, Phil. Mug. 37(A), 315 (1978). 13. G. T. Hahn. Acta metall. 10, 727 (1962). 14. 0. Lohne and 0. Rustad, Phil. &fog. 25, 529 (1972). 15. A. J. R. deKock, Philips Res. Rep. Suppl. 1. 43 (1973). 16. H. F611and B. 0. Kolhesen, Appl. Phys. 8. 319 (1975). 17. A. Staudinger, J. nppl. Phys. 49, 3870 (1978). 18. T. E. Mitchell and P. L. Raffo. Con. J. Phys. 45, 1047 (1967). 19. J. T. Fourie, Phil. Msg. 17. 735 (1968).
LijDERS
BANDS
IN DEFORMED CRYSTALSt
79 0701.116SO?.W~O
SILICON
S. MAHAJAN and D. BRASEN Bell Laboratories.
Murray Hill, NJ 07974. U.S.A.
and P. HAASEN lnstitut fir Metallphysik. Universitlt (Receired
3 Nocember
Gottingen, West Germany 1978)
Abstract-The formation of Liiders bands in Czochralski and float-zone silicon crystals, oriented for single slip. has been investigated at 800. 900 and 1OOO’C.At 800°C. Liiders strain is observed in Czochralski crystals, whereas the situation is ill-defined in the case of float-zone crystals. However. the Liiders deformation observed at 8OOC can be eliminated by a double heat treatment consisting of a 4 h anneal at 700°C followed by a second anneal at 1OOOC for 30 h. Furthermore. on increasing the deformation temperature, the tendency for Liiders deformation progressively decreases, Arguments. based on Hahn’s postulates for nonuniform yielding. have been developed to rationalize the observed differences between Czochralski and float-zone crystals. influence of heat treatment and deformation temperature. The Liiders front is observed to lie close to the (iO1) plane. Microstructures at and behind the front have been investigated by transmission electron microscopy. An explanation involving strain compatibility between the deformed and undeformed regions is presented to explain the observed crystallography. R&nn&--Nous avons etudie la formation des bandes de Ltiders a 800.900 et 1000°C dans des monocristaux de silicium fabriques par les methodes de Czochralski et de la zone flottante et orient&s pour le glissement simple. A SOO’C,on observe la deformation de Liiders dans les cristaux de Crochralski, alors que la situation est ma1 dttinie dans les cas des cristaux de zone flottante. On peut cependant &miner la deformation de Liiders observee a 8OU”Cpar un double traitement thermique, qui consiste en un recuit de 4 h a 700°C suivi dun second recuit de 30 h a IOOOC. De plus, la tendance a une deformation de Liiders diminue progressivement lorsqu’on augments la temperature de deformation. Nous prCentons des arguments reposant sur les postulats de Hahn de la deformation non uniforme, afin d’expliquer les differences observees entre les cristaux de Czochralski et ceux de zone flottante, I’influence du traitement thermique et de la temperature de deformation. Zusammenf~ng-Die Ausbildung von Liidersblndern wurde bei 800, 900 und 1OOO’Can Crochalskiund ‘float-zone’-gezogenen Einkristallen mit Orientierung fur Einfachgleitung untersucht. Rei 800°C wird eine Liidersverformung in Crochalski-gezogenen Kristallen beobachtet, wohingegen die Lage bei den ‘float-zone’-gezogenen Kristallen uneinheitlich ist. Allerdings kann die Liidersverformung bei 800°C mit einer zweifachen WLmebehandlunz-Gliihuna 4 h bei 700°C und nachfolnend 30 h bei 1OOO”C-beseitigt werden. Des weiteren nimmt die Neigung zu;Liidersverformung mit anlteigender Verformungstemperatur ab. Mit Argumenten, die auf den Postulaten von Hahn iiber nichtgleichm%Biges FlieDen aufbauen. werden die beobachteten Unterschiede zwischen Crochalski- und ‘float-zone’-gezogenen Kristallen und dem EinfluD von Warmebehandlungen und Verformunsgtemperatur e&art.
1. INTBODUCTION The deformation behavior of elemental semiconductors has been investigated by many investigators [l-S]. Several interesting observations emerge from these studies. However, the most interesting one pertains to the yield drop behaviour observed in crystals having a very low grown-in dislocation density and oriented for single slip. This observation has been rationalized in terms of the Johnston-Gilman approach, originally developed to explain the origin of yield drops in ionic crystals [8,9]. t Work performed while S. Mahajan was on study leave at the Institut fur Metallphysik, Universitlt Giittingen, West Germany.
In the early stages of deformation, strain distribution is very inhomogeneous [6,7-j. Schroter et al. [6] have investigated this aspect in deformed germanium crystals by etch pitting. They observe that when the grown-in dislocation density is very low, the initial deformation is accomplished by the propagation of Luders bands. These bands originate from the specimen ends and propagate inwards. Their observations indicate that, even when the resolved shear stress reaches the lower yield point, the dislocation distribution as well as the local strain are very inhomogeneous over the specimen length. However, if the grown-in density is relatively high, this heterogeneity does not persist beyond the lower yield point. Two types of Liiders bands have been observed by
1165
MAHAJAN ef ~1.: LijDERS BANDS IN DEFORMED
1166
Schriiter et nl. [6]. In one situation the band front is parallel to the trace of the primary plane in the cross slip plane (G type band), whereas in the other case the front is normal to the trace (K type band). Subsequently, SiethofT [IO] investigated in detail G and K type bands in heavily doped float-zone silicon single crystals. Etching studies on the cross slip plane reveal a K type Liiders band front to be a typical kink band having a highly polygonized structure. Arguments have been developed as to how such structures evolve during deformation. In the present investigation the formation of Li.iders bands in Czochralski as well as float-zone silicon single crystals, oriented for single slip, has been investigated as a function of temperature. Dislocation distributions in sections parallel to the front have also been evaluated at, and behind, the K type front by transmission electron microscopy (TEM). In addition, dislocation arrangement around the band front observed on the cross slip plane has been studied. 2. EXPERIMENTAL
C~OCHRAL~KI CRYSTALS t
j
UNLOADED
44UR6 AT 700%
E
0:
FLOAT
0.2
0.6
1.0
-ZONE
1.4
CoYPR666lVE
CRYSTALS
1.6 STRAIN
2.2
2.6
3.0
W
Fig. 2. Representative stress-strain curves of FZ silicon crystals. oriented for single slip, at different temperatures.
DETAILS
Two types of dislocation-free silicon crystals were used in this investigation: crucible-grown Czochralski (CZ) and float-zone (FZ). As ascertained by infrared absorption measurements, the former crystals contained _ 5-8 x 10”/cm3 of dissolved oxygen, whereas in the latter the oxygen level was below the detectability limit. Shaped compression samples, _ 0.5 cm x 0.5 cm x 1.25 cm in size, were cut from the grown crystals with [i23] as the compression axis and (lil) and (54i) as the two side faces. The specimens were then ground and chemically polished in a solution consisting of 30 ml CH,COOH, 30 ml HF and 50ml HNOs. IO
9
SILICOX CRYSTALS
In order to study the influence of substructure on the formation of Liiders band, a set of CZ samples was annealed at 7WC for 4 h followed by a 30 h anneal at 1ooo”C under a hydrogen atmosphere. This heat treatment was chosen because it is known to result in the formation of precipitates and extrinsic stacking faults bounded by i( 111) Frank partials [7, 111. Chemically polished and heat treated samples were deformed in compression at temperatures between 800 and 1000°C and at a strain-rate of -6.7 x 10-‘/s; the protecting atmosphere was forming gas. The load was removed at the conclusion of a test, and the specimen was allowed to cool to ambient temperature. Deformed samples were evaluated by optical metallography and transmission electron microscopy. To prepare samples for electron microscopy, slices parallel to the Liiders band front as well as the (lil) cross slip plane were cut by a string saw. The Liiders slices were ground down and polished from both sides, while the (lil) section was finished only from one side. Thus the (111) deformed surface exhibiting the Liiders band front was preserved. Discs 3mm in dia. were trepanned from the polished sections. They were subsequently thinned in the aforementioned polishing solution. To examine substructure around the Liiders band front in the (111) plane, a thinning procedure was developed that permitted thinning at a preset location. Thinned discs were examined in a
0
0.4
0.6
1.2
1.6
CMPRESSIVE
2.0
2.4
2.6
3.2
67RAIN W
Fig. 1. Representative stress-strain curves of CZ silicon crystals, oriented for single slip, at different temperatures. Stress-strain curve of a heat-treated crystal, obtained at 8OO“C, is also included. Note the dramatic difference in the rcspons~ of asgrown and heat-treated crystals.
JEM 200 microscope operating at 200 kv. Taking [iOl]( 111) as the primary slip system. the upward normal of the region being examined and operating reflections were indexed in an internally consistent manner during examination from the Kikuchi line pattern superimposed on the spot pattern.
MAHMAN er &:
LGDERS BASDS 1% DEFOR%fED SILICON CRYSTALS
1167
Fis. 3. Slip lines observed
on the fgl) face of a CZ crystal deformed to a compressive strain of 3.2”,, at 8QOC. Note that near the sample edge. slip lines are coarse. deep and widely spaced.
Liiders deformation coincides with the obsened crease in stress after the lower yield point.
3. RESULTS
3.1 De~oormarion chracteristics Representative stress-strain curves of CZ and FZ crystals deformed at 800, 900 and IOOO’C and also of the heat treated CZ crystal deformed at 8OO’C are shown in Figs. 1 and 7. The principal observations are the following: (i) Both types of crystals exhibit yield drops at 8OWC. The magnitude of the drop progressively decreases with increasing deformation tem-
perature and the drop is absent at IOWC’. (ii) The yield stress
shows
L-cry strong
temperature
depen-
dence. (iii) CZ crystal deformed at 8WC exhibits a Liiders strain, whereas in the case of FZ crystal the situation is not very well delineated. (iv) In both types of crystals. a Liiders strain is virtually absent at 900 and lOOO’C, while in the heat treated CZ crystals Liiders strain is absent even at 800°C. It is implicit in the preceding assessment that the termination of
in-
32.1 CZ ctystds. Surfaces of deformed crystals were examined by optical metallography using the Nomarski interference contrast. and representative slip patterns observed on the (31) surfaces of samples deformed at WK. and at 900 and 1OOO’C.are reproduced as Figs. 3 and 4, respectively. It is clrar that slip occurs primarily on the (Ill) planes, i.e. the primary slip plane. but a few slip lines on the (ill1 planes are also seen in Figs. 3 and 4(a). Furthermore. comparing Figs. 3 and 4 it is evident that slip is distributed on a tiner scale in Fig. 4. However. a detailed comparison between these slip patterns is not possible because of the differences in imposed compressive strains (3”; at 8oO’C; l.J”, at 900 and 1OOO’C).
Fig. 4. Slip lines obserxzd on the (31) face of a CZ crystal deformed at (a) 9OO’C and (bj IOWC. .A one to one comparison with Fig. 3 is not possible because the str%n level is loner in Fig. 1.
1168
MAHZJAN
et af.:
LGDERS
BANDS
fN DEFORMED
SILICOX
Fig. 5. Optical micrograph showing Liiders band front observed on the deformed at YOO‘C. Xote that the Gout is fairly sharp towards the rig&. on the left. Al:.o the sharp portion in parallel to the [lil]
Surfaces of the heat-treated CZ crystal were also studied by optical metallography. Slip lines were not discernible, implying that slip is occurring on an extremely fine scale. The sample deformed at 8OO’C was examined across its whole length. In conformation with the observations of Schriiter er (I[.,[6] slip was found to be inhomogeneously distributed. In order to ascertain the crystallography of a Liiders band front. its endings in a sample deformed at SWC were examined on the (NT) and (iii) surfaces, and these results are shown in Figs. 5 and 6. On the (54i) surface, the front is fairly sharp at one end and becomes progressively diffuse in going towards the other end. In fact. slip activity ahead of the front in that region is fairly extensive. Furthermore, the sharper portion of the front tends to lie close to the [tilldirection. The front on the (flit plane is seen as a set of fringes running horizontally in Fig. 6 and is not as easily discernible as in the case of the (54i) surface. This may be due to the fact that the primary slip vector, +i[iOl], lies in the plane of the observation. Furthermore, the front lies normal to the [iOl] direction. Combining the preceding two assessments, it is inferred that the macroscopic habit-plane of the front is -(Tot). The K bands observed by Siethoff [lo] in heavily doped FZ silicon have the same crystallography.
CRYSTALS
(54il face of a CZ crystal --hereas it is quite direction.
diikse
Slip lines lying along the trace of the (I I1 1 plane are visible in Fig. 6. Since the primary slip vector does not produce any displacement on the plane of -the observation, i.e. the (11I) plane. the observed slip lines must be due to the activation of the coplanar. secondary slip systems. 3.2.2 FZ crystals. Figure 7 is a typical example of the slip pattern observed on the !ili)plane of a FZ crystal deformed to a compressive stram of 3.2:, at 800’C. Both coarse as well as fine slip lines, lying on the (111) planes. are seen. As argued previously, their visibility must be due to slip activity on the coplanar, secondary slip systems. Furthermore. the termination points of well-separated. coarse slip lines delineate a narrow band of parallel lines that is normal to the [iOl] direction. As depicted in Fig. 6, a very similar situation exists in the case of CZ crystals. although the observed slip distributions in the two cases differ. Slip lines seen on the (tit) and (31) surfaces of a FZ crystal, deformed to a compressive strain of 2.8”/ at 9OO’C, are reproduced in Figs. 8(a) and (b). respectively. In Fig. 8(a). fine slip lines are interspersed between the coarse ones. Furthermore. it is clear from Fig. 8(b) that, in addition to slip activity on the primary plane, slip lines on the (lil) and (ill) planes are also seen. An attempt was made to study the distribution of slip on a FZ crystal deformed at 1OOO’C.It proved
Fig. 6. The Liiders band shown in Fig. 5 is being examined on the (111) plane. i.e. the cross slip plane. The front is seen as a set of fringes running horizontally. Note that the primary slip vector, +![iOl]. lies in the [ilf) plane and thus the visibility of slip lines implies the activation of a coplanar, secondary slip vector.
M;\HAJAS
QZA:
tfDERS
BAXDS
14 DEFORMED
SILICON
CRYif.AU
Fig. 7. Slip lines observed on the (111) face of a FZ crystal deformed to a compressive X1”,, at So0 C. Note that the termination points of well-separated. coarse slip lines delineate band of parallel lines that is normal to the [il.)!] direction.
almost impossible to image these slip lines because the\; were too fine. 3.3 Dislocarion arrangement
close to rhe Liiders
band
fionr
Figure 9 depicts a representative example of the arrangement of dislocations observed by TEM either at or very close to a Liiders band front in a CZ crystal deformed at SWC. On the scale of our observations, the observed dislocation distribution in the (iOil section is inhomogeneous. In area A imperfections are fairly well clustered. whereas in other regions the den-
Fig. 8. Slip lines observed
1169
strain of a narrow
sity of dislocations
is very low. Moreover. dkkations are also absent in some portions of the crystal. In Figs. 9(c) and (d), the primary glide plane. till), is edge-on. and it is clear that the dislocation distribution is far from being characteristic of a sma!! angle tilt boundary lying in the (Tot) plans. In Fig. 91~) the plane of the micrograph is (lOi) and g = 102. and therefore the primary dislocations, t4[iOl]. shouid be in extinction or exhibit residual Gntrast. Comparing Fig. 9(c) with Figs. Y(a) and (b) it is apparent that the Burgers vector of the majority of the dislocations is +--[iOl]. but a few coplanar,
on the ia) (111) and Lb) (I’ll suriaces of a FZ crystal deformed to a comprw sive strain of 3.3”, at WWC.
1170
%fAfAHA_i.W et
of.: Li;DERS BANDS IN DEFOR.MED SILICOW CRYST.ALS
Fig. 9. Electron micrographs showing a typical dislocation arrangement observed in a iiN) section taken from an area at or close to a Liiders band front in a CZ crystal deljrmed at YOO~C.Planes of micrographs (a), (5). (c) and (.d) are ~(1 Ii). -(IIi), -(lOi) and -(Zii). respectiveI>-. (b) and (d) are weak-beam microFaphs taken under g. 3g condition. Note that dislocations are clustered in region A. Marker represents I pm.
secondary dislocations are aIso seen see area A in Fig. 9(a). This assessment is borne out by the optical metaliography observations discussed earlier. Furthermore, a portion of the debris is in the form of dipoles, see features exhibiting broad images. i.e. intense ‘inside’ contrast, in Fig. 9(b). This is consistent with the recent detailed study of Winter et al. [12] on faulted and unfaulted dipoles in deformed CZ crystals oriented for single slip. 3.4 Arrangement of dislocations away from the Likiers band front Variations in the observed dislocation arrangement in a (iO1) section, taken far away from a Ltiders band front in a CZ crystal deformed at 800°C. are illustrated in Figs. 10 and Il. In Fig. 10(a). the primary glide plane as well as the cross slip plane are edge-on, and g = 202 and 120 in (a) and (b), respectively. Comparing Figs. 10(a) and (b). it is apparent that slip is primarily accomplished by the glide of 2 i[iOl] dblocations on the primary as well as on the cross slip planes. In addition. slip activity w-ith a coplanar, secondary Burgers vector and secondary slip can also be seen. see region B in Fig. IO(a).
Two basic differences exist between the microstructures shown in Figs, 10 and 11. Firstly, dislocation segments lying on the cross slip plane are not observed in Fig. 11. compare Fig. lo(b) and II(a). Secondly, the majority of the debris is in the form of dipoles. Since g = 202 in Fig. 11(b) and dislocations exhibit a residual contrast, dipoles must belong to the primary slip system. It is emphasized that features similar to the ones shown in Fig. 11 were also observed in a thicker portion of the (iO1) section taken close to the Liiders band front. 3.5 Arrangement of dislocations obsersed Liiders band front on the cross glide plane
around a
On the scale of our observations the line of demarcation between the deformed and undeformed regioti was not sharp. and very long dipoles and isolated dislocations were observed to extend across the interface. Furthermore, in comparison with the (iO1) sections, the dislocation density in the (lil) section was lower. The contrast behaviour of deformation-induced microstructures observed in a region behind the macroscopic front was investigated in d&ii. and
MAHAJUAN er d:
LCDERS
BANDS
fN DEFORMED
SILICON
CRYSTALS
1171
arrangement observed in a (iO1) section taken from Fig. 10. Electron micrographs showing dislocation an area away from a Liiden band front in a CZ crystal deformed at 88o’C. Note that slip activity a;ith a coplanar. secondary Burgers vector and secondAry slip can be seen in region B in (a). Planes Marker represents I pm. of micrographs (a) and (b) are - (lOi) and - (11 I). respectively.
Fig. 1I. Electron micrographs showing another type of dislocation arrangement section taken lrom an area away from a Liiders band front in a CZ crystal Marker represents I pm.
observed deformed
in a (fO1) at 8OOT.
Fig. 11. Electron micrographs showing disloca:ion arrangement observed in a region behind the front; the section k parallel to the (Ii11 plane, i.e. the cross glide plane. The ptane of micrograph in each case is -itif,. Marker represents I pm.
I172
MAHAJAX
et al.:
LL’DERS
BANDS IN DEFORMED
results are reproduced as Fig. 13. Comparing Figs. 12(af, (bl and f& it is inferred that the Burgers vector of the majority of dislocations is &$[iOl]. These dislocations are fairly long and not very straight, implying that &s[iOl] screw se_qments undergo cross ghde. In addition, k+[Oli] dislocations are also in the field of view, and are steeply inclined. This result bears out an earher assessment that coplanar, secondary slip is occurring at the Liiders band front. 4. DISCUSSION Four interesting observations emerge from the present study. Firstly. a Liiders strain is observed in CZ crystals deformed at 8OO’C.whereas the situation is illdefined in the case of FZ crystals. Secondly, when the deformation temperature is raised to 900 or lOOO”C,Liiders band formation is virtually absent in both types of crystal. Thirdly, the Liiders strain observed in CZ crystals deformed at 8GO’C can be totally eliminated by a double heat treatment consisting of a 4 h anneal at 7OO’C, followed by a second anneal at 1OOO’Cfor 30 h. Fourthly. the macroscopic Liiders band front tends to lie parallel to the (TOI) plane, i.e. normal to the primary slip vector. Questions that need elucidation concern the growth of an embryonic Liiders band and its subsequent propagation into an undeformed portion of a crystal. Siethoff [lo] and Hahn [13] have considered these problems in detail. Siethoff visualizes that the propagation of a Liiders band front can be likened to the stress-induced migration of a small angle tilt boundary. Furthermore, the sideways growth of a band, i.e. growth in a direction normal to the primary slip plane, occurs by the operation of single-ended dislocation sources that could form as a result of image forces-induced cross slip of screw segments near crystal surfaces; such sources have been observed by Lohne and Rustad [14] in zone-refined aluminum single crystals. If Liiders deformation were to proceed in such an orderly way, it would be anticipated that: (i) edge dislocations comprising the front should be arranged in a regular manner, see Siethoffs Fig. 6(a); (ii) dislocations of one sign only should be observed at the front. However, these assessments are not borne out by the dislocation arrangement observed in a (iO1) section taken from an area close to or at a Liiders band front, see Fig. 9. Hahn [13] has postulated that the propagation of a Liiders band occurs by the injection of dislocations into undeformed areas adjoining a band front. Mechanistically it is not clear how this is done. However, if one assumes that the microscopic front is a bit ragged and screw segments near the front undergo cross slip, induced either by elastic interaction with other dislocations gliding on parallel planes or by image forces. mobile dislocations can be produced in the undeformed regions. Furthermore, the crystal would continue to yield nonuniformly. i.e. by Liiders
SILICON
CRYSTALS
deformation. as long as at a constant lower y-i&d stress, the contribution to strain of the material outside the band is substantially lower than that of the growing band. Experimental evidence presented in Figs. 10 and 12 suggests that, ev-en though the resolved shear stress on the cross slip plane is zero. cross slip occurs behind the front. In addition, dipoles observed in Fig. 9 could have formed due to jog dragging by screws. and jogs in turn could have resuhed from cross slip. It is known that FZ crystals contain A and B type clusters [is], and A clusters have been identified as large prismatic loops by transmission electron microscopy [16]. Features resembling A type clusters have also been observed in CZ crystals [17-j. but their density is considerably tower. It is therefore conceivable that when an undoped or a lightly doped FZ crystal is deformed, segments of large prismatic loops could act as dislocation sources and slip may start at various portions of the crystal: the slip distribution shown in Fig. 7 appears to bear this out. Thus the development of the strain condition conducive to nonuniform yielding is inhibited and the crystal deforms more or less in a uniform manner. However. A clusters could be pinned by dopant atoms in heavily doped FZ crystals and then Liiders deformation could develop. This assessment is compatible Gth Siethoffs observations on the presence of Ltidcrs bands in heavily doped FZ crystals [lo]. Pate1 [7] has shown that, in addition to extrinsic stacking faults, prismatically punched out dislocation loops are observed around precipitates that are produced in CZ crystals during the heat treatment used in this investigation. Since prismatic loops are distributed at random and can act as glide sources, the distribution of potential, equally potent dislocation sources is also at random. It is therefore envisaged that slip in the heat treated CZ crystal would be distributed on an extremely fine sccsle and it should undergo uniform yielding. This is indeed borne out by the experimental result. It is observed that, on raising the deformation temperature from SOO’Cto 900 or laoO;C. coarser and deeper slip lines are replaced by finer slip, see Figs. 3, 4, 7 and 8. Similar effects are observed in b.c.c. Ta-Re alloy single crystals in the temperature range where they are assumed to deform by the Peierls mechanism [IS]. The origin of this effect is not clear, but it could be that, with increasing deformation temperature more slip sources are activated. Thus slip distribution conducive to uniform yielding develops in preference to that for the Liiders deformation. It is ascertained that a macroscopic Liiders front tends to lie close to the (TOI) plane. see Figs. 5 and 6. Furthermore. in the present deformation experiments. the primary slip v-ector is also Ii[fOl]. It is therefore visualized that the observed crystallography may stem from the fact that in the present situation only the normal strain component has to be accommodated
MAHAJAN er al.:
LijDERS
BANDS IN DEFORMED
between the deformed and undeformed regions, and this may be done by the injection of primary dislocations into undeformed areas adjoining the front. In view of the fact that slip lines seen in Fig. 7 are fairly well separated and differ in the chronology of their formation, the observed tendency of the boundary to lie close to the (TOI) plane is remarkable. Again, strain compatibility arguments may be invoked to rationalize this observation. In comparison with the (iO1) sections, the dislocation density in the (lil) section is lower. This could be due to the fact that the area examine-d is bounded at the boundary
on one side by the original deformed surface to which dislocations can escape during deformation. This observation implies that the dislocation density in
the surface region is lower than that in the interior. This appears to confirm Fourie’s observation on the differences in dislocation content between the interior and surface regions of deformed copper single crystals [ 191. Ackmwledgemenrs-One of the authors (SM.) is grateful to the German Government for the award of a D.A.A.D. fellowship. In addition, the authors acknowledge fruitful discussions with G. Y. Chin and B. C. Wonsiewicz.
A.M.
27 7- f
SILICON CRYSTALS
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REFERENCES 1. C. J. Gallagher, P/IJX Rec. 88. 721 (1952). 2. L. Graf, H. R. LaCour and K. Seiler. Z. >Verallk. 44, I13 (1953). 3. J. R. Pate1 and B. H. Alexander, rlcra met& -1, 385 (1956). 4. W. D. Sylwestrowicz, Phil. &fag. 7, 1825 (19621. 5. R. L. Bell and W. Bonfield, Phil. Mag. 9, 9 (1964). 6. W. Schriiter, H. Alexander and P. Haasen, Ph.vs. Stat. Sol. 7, 983 (1964). 7. J. R. Patel, Discuss. Faraday Sm. 38, 201 (196-B. 8. H. Alexander and P. Haasen. Solitl State Ph.rs. 22, 28 (1968). 9. W. G. Johnston and J. J. Gilman. J. appl. Phys. 30, 129 (1959). IO. H. Siethoff, rlctu meral/. 21, 1523 (1973). II. G. A. Rozgonyi, S. Mahajan. M. H. Read and D. Brasen, Appl. Ph_rs. Lett. 29, 531 (1976). 12. A. T. Winter, S. Mahajan and D. Brasen, Phil. Mug. 37(A), 315 (1978). 13. G. T. Hahn. Acta metall. 10, 727 (1962). 14. 0. Lohne and 0. Rustad, Phil. &fog. 25, 529 (1972). 15. A. J. R. deKock, Philips Res. Rep. Suppl. 1. 43 (1973). 16. H. F611and B. 0. Kolhesen, Appl. Phys. 8. 319 (1975). 17. A. Staudinger, J. nppl. Phys. 49, 3870 (1978). 18. T. E. Mitchell and P. L. Raffo. Con. J. Phys. 45, 1047 (1967). 19. J. T. Fourie, Phil. Msg. 17. 735 (1968).