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Dislocations in dendritic web silicon
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Journal of Crystal Growth 213 (2000) 288}298
Dislocations in dendritic web silicon S.L. Morelha o *, J. HaK rtwig, D.L. Meier Instituto de Fn& sica, Universidade de SaJ o Paulo, CP 66318, 05315-970 SaJ o Paulo, SP, Brazil European Synchrotron Radiation Facility, BP 220, F-38043 Grenoble, France EBARA Solar, Inc., 811 Route 51 South, Large, PA 15025, USA Received 27 May 1999; accepted 1 February 2000 Communicated by M.S. Goorsky
Abstract Due to its peculiar laminated structure, dendritic web silicon presents one of the most interesting con"gurations of dislocations in Si crystals. On the way to growing dislocation-free Si webs, X-ray di!raction topography techniques were used to visualize the dislocations in the material. The results and the analysis of dislocation reactions reported here provide information on the mechanisms involved in the formation of dislocation networks in the material. Also, the applicability of synchrotron radiation white-beam topography for a rapid characterization of dislocations is investigated and discussed. 2000 Elsevier Science B.V. All rights reserved.
1. Introduction The dendritic web silicon (DWS) growth process provides the basic material for manufacturing lowcost high-e$ciency solar cells. In the actual process, silicon web crystals are obtained as ribbons of several meters in length, a few centimeters in width, and an ideal thickness of about 100 lm. The aims of all growers of DWS are the continuous growth of the ribbon and web crystals free of defects. The defects, dislocations plus impurities, strongly limit the photovoltaic conversion e$ciency of the solar cells [1,2]. The web surface is parallel to (1 1 1), and the axis of the ribbon, the growth direction, is [1 1 2 ]. In a cross section the web is laminated, consisting of layers of about 50 lm thickness at each surface, separated by an odd number of twin planes in
* Corresponding author.
a very thin layer (&5 lm). Since the twin planes are parallel to the web surface, (1 1 1), the two thick surface layers are twin-related. Recently, an X-ray topography study of the growth process [3] has correlated the evolution of the dislocation networks in web crystals with growth interruptions. Several mechanisms playing roles in the evolution of dislocation networks were described. It has been observed that the (1 1 1) twin planes, present over the whole area of most crystals, limit the movement of dislocations, trapping them inside the material. It gives rise to long dislocation lines as well as a high probability for dislocation reactions to occur. For instance, Lomer dislocations [4] have been identi"ed and they could be generated by dislocation reactions. This type of dislocations do not glide, and they can a!ect sti!ness and viscoplastic behavior at high temperature, which can lead to deformation of the ribbons as well as to their poor crystalline quality. One of the most dominant factors causing the cessation of
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growth has been observed to be the formation of polycrystalline silicon [5]. Low angle boundaries [6], stringers observed at the center of the ribbons and along the growth direction, made up of edge-dislocation lines have been correlated to materials with low minority carrier di!usion length [3,5]. A dislocation reaction has been suggested as a possible source of such edge dislocations. Crystallographically, the DWS crystals can be described by two Thompson's tetrahedrons with the d face, (1 1 1)-twin plane, in common for both. They are represented in Fig. 1a, by the tetrahedrons with vertices ABCD and ABCD . Several types of dislocations have been identi"ed in web crystals [3,6]. According to Thompson's notation, the dislocations with Burgers vectors, $a/2[1 0 1], $a/2[0 1 1], and $a/2[1 1 0], out of the web plane (d plane) are named DA(b, c), DB(a, c), and DC(a, b), respectively. a, b, and c in parentheses indicate the possible slip planes of these dislocations. They can occur on either side of the web crystals, for instance as D A, D B, and D C dislocations in their respective a , b , and c slip planes. These dislocations do not cross the twin boundary because their Burgers vectors (or slip directions) are not parallel to the slip planes on both sides. Only dislocations with in-plane Burgers vector, BA(c, c , d), CA(b, b , d), and CB(a, a , d), do not have their movement limited by the twin boundaries. DA and DB are the notation for Lomer
dislocations that have often been identi"ed in web crystals. Table 1 summarizes the Burgers vector, b, of the dislocations as well as the Bragg re#ections, or the di!raction vector u, for which they are invisible (b ) u"0). In this article, we report several results in order to further describe the unique nature of the dislocations in DWS. The results were obtained by X-ray di!raction techniques, such as monochromatic transmission topography using symmetric and asymmetric re#ections and synchrotron radiation white-beam topography. The images recorded by
The Thompson's tetrahedron is formed by the 1 1 1 planes of the cubic system. The a, b, c, and d faces represent the (1 1 1 ), (1 1 1 ), (1 1 1), and (1 1 1) planes, respectively.
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Fig. 1. (a) The crystallography of the web crystals represented by two twin-correlated Thompson's tetrahedron, with the d face as the twin plane. The ABCD and ABCD tetrahedrons are the back and front sides of web, respectively. (b) In-plane di!raction vectors used for transmission topography of symmetric re#ections.
these techniques contain many dislocations, extensive stacking faults, and exhibit interesting reactions which de"ne most of the networks along the ribbons. They provide experimental evidence of the reactions involved in the formation of Lomer dislocations, which can be related to the presence of
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Table 1 Burgers vector of the dislocations in the normal Thompson tetrahedron notation, and the re#ections for which b ) u"0. Only 2 0 2 , 0 2 2 , 2 2 0, 2 2 4 , and 1 1 1 re#ections have been used in this study Dislocation
Burgers vector (b)
Re#ections
DA DB DC BA CA CB Da Db Dc Ad Bd Cd
a/2[1 0 1] a/2[0 1 1] a/2[1 1 0] a/2[1 1 0] a/2[0 1 1] a/2[1 0 1] a/6[1 2 1] a/6[2 1 1] a/6[1 1 2] a/6[1 2 1 ] a/6[2 1 1 ] a/6[1 1 2]
2 0 2 0 2 2 2 2 0 2 2 4 4 2 2 2 4 2 2 0 2 0 2 2 2 2 0 2 0 2 0 2 2 2 2 0
1 1 1 1 1 1 1 1 1
1 1 1
the stringers (BA edge dislocations). Based on this evidence, a mechanism explaining the occurrence of the immense stacking faults, already observed in these materials in the past [7], is also proposed. The use of the double-contrast image criterion [8] of a dislocation line, in white-beam topographs, for identi"cation of dislocations in DWS is discussed.
2. Experimental details A standard topographic Lang camera and a Rigaku X-ray generator with a Mo target were used to perform transmission topography measurements (Lang topography [9]). The X-ray beam was collimated in the incident plane (horizontal plane) to about three minutes of arc. The vertical beam size and the horizontal maximum scan range limit the size of the analyzed area to 18;26 mm, respectively. The nuclear plates, or high-resolution "lms, were set parallel to the web surface in order to keep the distance between imaged features independent of the re#ections used. The average exposure times were 8 h. Transmission topography of symmetric-Bragg re#ections is used to produce di!raction images of the dislocations. Symmetric re#ections for trans-
mission di!raction are those illustrated in Fig. 1b, with the reciprocal lattice vector (di!raction vector) in the d plane of the web crystal. Since the back and front sides, or in other words, the two thick surface layers of the web are twin-related crystals, symmetric re#ections are common for both sides, and they provide di!raction images from the total thickness of the material. Images of one-half of the thickness, i.e., an image of only one side or the other, are obtained using asymmetric re#ections. An example of asymmetric re#ections are those with a di!raction vector out of the d plane, such as the 1 1 1 and 1 1 1 re#ections, i.e., transmission di!ractions from the c and c Bragg planes, respectively. Synchrotron radiation white-beam topographs were recorded at the ID19 &topography and highresolution di!raction' beamline at the ESRF [10]. The beamline has an experimental station outside the ring building, which gives a source-to-sample distance of 145 m. It provides a spectrally and spatially homogenous beam at the sample position, with dimensions of &40 (horizontal);14 (vertical) mm. The geometrical resolution is (1 lm even for a sample-to-"lm distance as great as 1 m. A high photon #ux assures exposure times of the order of a few seconds. Direct, or kinematical, image condition (lt(1) is achieved by using high-energy photons ('50 keV), thus 2h is (73 for the imaged re #ections. It allows the "lm to be placed normal to the incident-white beam without signi"cantly affecting the image width through projection e!ects. The use of high energies also drastically reduces the harmonic contamination due to the extended spectrum of the synchrotron radiation. The topographs were recorded on Kodak Industrex synchrotron radiation "lms (grain size 1}2 lm), and the images were digitized from "lms using a CCD camera (with linear intensity response) coupled to a microscope.
3. Results 3.1. Symmetric reyections High-resolution transmission topographs for 0 2 2 , 2 0 2 , 2 2 0, and 2 2 4 re#ections are shown in
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Fig. 2. They were taken from the same as-grown Si web analyzed in Fig. 5 of Ref. [3]. The 603 dislocations DA(b), DB(a), and DC(a, b) are most of the lines presented in the images. A few Lomer dislocations, DB , are also seen, for example, between
the points marked with numbers 1 and 3. The complexity of the network in these topographs is basically due to two types of dislocation reactions, DC(a)#DB(a)"Da#aC#Da#aB"3Da, DC(b)#DA(b)"Db#bC#Db#bA"3Db,
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since aC#aB"Da and bC#bA"Db. In this type of reaction, the unit dislocations are dissociated into Shockley partials and the node is formed by subsequent rearrangement of the partials [11]. Fig. 3 illustrates how these attractive reactions increase the complexity of the network, and how it is seen when imaged by di!erent re#ections. The hypothetical network in this "gure is similar to the one observed in the area around the number 2 in Fig. 2. On the right-hand side of the topographs (Fig. 3), arrays of DC(b) and DA(b)
Fig. 2. High-resolution transmission topographs of a #at web crystal. The same network is imaged using four di!erent symmetric re#ections.
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Fig. 3. The network formed by DA(b), DB(a), and DC(a, b) dislocation lines plus their reactions, as seen on the 0 2 2 , 2 0 2 , 2 2 0, and 2 2 4 topographs. The network is similar to the one observed at the center of Fig. 2.
dislocation lines are running along the [0 1 1 ] direction. Near the intersection with DB(a) lines, parallel to the [0 1 1 ] direction, the DC(b) lines move towards these lines due to their mutual attraction. Before reaching the DB(a) lines, the DC(b) ones "rst react with the DA(b) lines to form 3Db nodes. Then, they cross-slip to the a slip system, becoming DC(a) lines, and the reaction DC(a)# DB(a)"3Da takes place. All dislocation lines and nodes are visible in the 2 2 4 topograph, and the DB(a), DA(b), and DC(a, b) lines are invisible only in the 0 2 2 , 2 0 2 , 2 2 0 topographs, respectively (see Table 1). Experimental evidence of the reactions involved in the generation of Lomer dislocations is also observed in Fig. 2. The DB Lomer dislocation,
with its endpoints at 1 and 3, is the resultant dislocation of the reactions which occur at these points. The dislocation lines involved in these reactions are shown in Fig. 4, as seen in the topographs. At point 1, DC(b)#CB(d)"Db#bC#Cd#dB "Db#bd#dB"DB
and at point 3, DA(b)#AB(d)"Db#bA#Ad#dB "Db#bd#dB"DB
Fig. 4. Schematic of the contrast observed in the four topographs of Fig. 2, for the dislocation lines in the reactions at points 1 and 3. The DB "Db#bd#dB, DA, DC, and AB
dislocations are invisible for the 0 2 2 , 2 0 2 , 2 2 0, and 2 2 4 re#ections, respectively. The inset illustrates the arrangement of the dislocations involved.
The unit dislocations in these reactions are dissociated into partials on the b and d slip planes. The partials react at the intersection of the planes to form the bd dislocation (stair rod dislocation or Cottrel}Lomer dislocation). Since it lies on both planes (inset of Fig. 4), the dislocation line must be along the [0 1 1 ] direction, which is common to both planes. In such a con"guration, this type of dislocation is completely sessile, i.e., it cannot move either by glide or by climb without creating surfaces or very bad mis"t. The faults bounded by the partials cannot be resolved by X-ray topography.
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Then, the total Burgers vector, which determines the visibility of the dislocation, is the same as a DB line (b"$a/2[0 1 1]). However, the slip plane that contains the line direction and Burgers vector has the [1 0 0] normal direction. In the Lomer dislocation observed in Fig. 2, it should be noted that the bd dislocation is introduced by the reaction of one pair of partials, and it can split into another pair of partials; i.e., bC#CdPbdPbA#Ad. 3.2. Asymmetric reyections The transmission topographs of asymmetric re#ections show contrasts of large stacking faults parallel to the web surfaces, or to d planes. Figs. 5a}c show the 1 1 1, 1 1 1 , and 2 2 4 topographs, respectively. The #at Si web sample has been annealed at 8503C for 1 h, followed by slow cooling to 6003C at a rate of 1C/min. Unfortunately, no Xray topographs were taken before annealing. The DA and DB lines are invisible for the 1 1 1 and 1 1 1 asymmetric re#ections, and all lines are visible in the 2 2 4 topograph. For these asymmetric re#ections, the extrinsic faults on d planes, d faults, introduce phase shifts of 2p/3 between the X-ray wave"eld di!racted below and above them. As a consequence, the recorded intensity decreases, and the faults are seen in the topographs as white areas. In the analyzed sample, such d faults are seen only on one side of the web crystal, i.e., only in the 1 1 1 topograph. The contrast of the extensive stacking faults in annealed Si web has been studied more than three decades ago [7]. Due to the higher density of grown-in dislocations in the material obtained by the growth process at that time, overlapping of extensive faults produced contrast of extrinsic, intrinsic, and nonfaulted regions. However, &there was no evidence as to how the faults were formed, whether from Lomer dislocation reactions or from the generation and movement of partials from a dislocation source'.
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The images of three spots, topographs, due to symmetrical re#ections obtained simultaneously in an exposure time of about 1 s, are shown in Fig. 6. While the dislocation lines present single contrast in the 2 0 2 topograph (Fig. 6a), double contrast of the lines is a feature clearly visible in the 2 2 0 and 2 4 2 topographs, Figs. 6b and c, respectively. The double contrast is related to the distorted regions around the dislocation core, where the two misorientation contours contribute separately [12,13]. And, it is nearly always observed because of the experimental condition at ID19 beamline [8]: good geometrical resolution, large sample to "lm distance, and high photon energy. In order for double contrast to be observed, a non-zero projection of the edge component (b ) of the Burgers vector into the di!raction vector direction is required, i.e., b . uO0. Also, the angle c between the dislocation line direction and the incidence plane must be near 90. The double-contrast conditions in terms of b ) u and c values are summarized in Table 2. Near the center of the topographs, an array of DB(a) and DC(a) dislocation lines along the [1 0 1 ] direction is observed. A few lines are reacting and climbing out of their a planes to run along the growth direction. Since DC lines along the growth direction have b perpendicular to the web face, all symmetrical re#ections produce lines of single contrast (Table 2). Therefore, by analyzing only the 2 4 2 topography (Fig. 6c), it is possible to identify the lines along the growth direction as DB lines. The DC lines are those lines with very weak contrast in the 2 2 0 topograph, Fig. 6b. DB(a) and DC(a) dislocations produce single-contrast lines for di!raction vectors that are also in the a plane. It is observed in the 2 0 2 topograph, Fig. 6a. Although in this topograph, b ) u and c are not zero for the DB lines along the growth direction, they are also seen with single-contrast, just a little darker.
4. Discussion 3.3. Synchrotron radiation white-beam topography The white-beam topographic method (Laue method) is used to provide several di!raction spots (images) of the sample on the photographic "lm.
Standard two-dimensional thermal stress models [14], assume that the thickness components of stress vanish in comparison with the in-plane ones. As a result, the coe$cients of resolved shear stress
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Fig. 5. Transmission topography of asymmetric, 1 1 1, 1 1 1 , and symmetric 2 2 4 re#ections. They reveal the occurrence of stacking faults of d planes only on one side of the web crystal, and the di!erences between the networks on each side.
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Fig. 6. Synchrotron radiation white-beam topographs from three symmetrical re#ections: (a) 2 0 2 , (b) 2 2 0, and (c) 2 4 2.
for the d slip systems are zero. Although the CA(d), CB(d), and BA(d) dislocations should not occur, their existence is revealed by the reactions involved in the formation of the DB (Fig. 4) and
DA Lomer dislocations. The defects type
stringers [5] in DWS also reveal the existence of BA edge dislocations, which are BA dislocations with the line parallel to the growth direction. In
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Table 2 Double-contrast conditions for DA, DB and DC dislocation lines in white-beam topographs of symmetrical re#ections: b ) u is the cosine of the angle between the edge component, b , of the Burgers vector and the di!raction vector u, and c is angle of the dislocation line direction, L, with the incidence plane Re#ection
L"[0 1 1 ]
L"[1 0 1 ] c
b )u
2 2 0 2 0 2 0 2 2 2 2 4 2 4 2 4 2 2
DA
DC
0.29 * 0 0.17 0.17 !0.33
* 0.29 0 0.17 0.17 !0.33
60 60 0 30 30 90
L"[1 1 2 ] c
b )u DB
DC
!0.29 0 * 0.17 !0.33 0.17
* 0 !0.29 0.17 !0.33 0.17
Fig. 7. Example of the suggested mechanism for generating large d faults in DWS. The CA(b) dislocation, attracted by the DC(a)"Da#aC line, cross-slips to the d slip plane and dissociates into Cd and dA partials. The aC and Cd partials react to form the ad stair rod dislocation. Then, the large d fault is introduced when the dA partial moves apart from the stair rod.
order to explain the three dislocations, on the d slip systems, in the material, and consequently the occurrence of Lomer dislocations, the following mechanism is suggested: the thermal stresses e$ciently introduce CB(a) and CA(b) dislocations [14]. Since they are not trapped by the d twin boundaries, the lines of such dislocations should be
60 0 60 30 90 30
c
b )u DA
DB
DC
0.52 * !0.26 0 0.45 !0.45
!0.52 !0.26 * 0 !0.45 0.45
* 0 0 0 0 0
90 30 30 0 60 60
very short, of the order of the web thickness. It is in agreement with the length of the CB line observed at point 1 of Fig. 2 (see also Fig. 4). The CB(a) and CA(b) dislocations, due to eventual interactions with the network of DX dislocations (X"A, B or C), would cross-slip to d slip planes, react with the DC(a, b) ones and give rise to the Lomer dislocations. Therefore, the probability for Lomer dislocations being introduced in the material strongly depends on the complexity of the network along the ribbon as well as on how the network evolves during crystal cooling in the growth process, or during subsequent annealing. As also observed in Fig. 2, and illustrated in Fig. 3, the attractive reactions between DC(a) and DB(a) dislocations, or DC(b) and DA(b) dislocations, play an important role for increasing the network dynamism and complexity. In the above-suggested mechanism, the BA(d) dislocations are introduced when the Lomer dislocations split, as seen at point 3 in Fig. 2. It could be another source of BA dislocations, besides the already proposed mechanism that involves reactions between DA(c) and DB(c) dislocations [3,4]. The d faults observed in Fig. 5a , 1 1 1 topograph, are other features correlated with the activity on the d slip systems. Such faults are bounded by partial dislocations, which are introduced when a unit dislocation, BA(d), CB(d), or CA(d), dissociates into the partials, for instance CA(d)" Cd#dA. The small size of the stacking faults, or
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distance between the partials, expected for Si [7,11] is below the resolution of the X-ray di!raction imaging techniques. In DWS, when this type of dissociation happens near the solid}liquid interface of the growing crystal, i.e., near the growth front, strips of grown-in faults are introduced. If the bounding partials of a strip interact with other dislocations, or walls of dislocations, or any other crystal defects, they will not move parallel to each other. Then at high temperature, whether during growth or during annealing, the distance between the two partials can be signi"cantly increased. Examples of such stacking-fault strips are clearly observed on the left-hand side of the topograph in Fig. 5a. This argument is used here, in order to understand the wide strips, of more than 500 lm, that remain locked in the Si web at room temperature in spite of the large stacking-fault energy. A similar argument is used to explain the immense stacking faults recorded in the topograph of Fig. 5a. In this case, the large faults are part of or even start at Lomer dislocations. Each of them is bounded by a stair rod and a partial dislocation. The stair rod determines straight contours well aligned along the [0 1 1 ] or [1 0 1 ] direction, as seen for several faults in the topograph. One possible situation is exempli"ed in the illustration of Fig. 7. The CA(b) dislocation, introduced by thermal stresses, cross-slips to the d plane, dissociates into partials, and reacts with the DC(a) line to form the Da and dA partials, and the ad stair rod dislocation. The large d faulted area is generated at high temperature when the dA partial moves apart from the stair rod, which is completely sessile. Releasing of residual stresses by sample annealing signi"cantly changed the structure of dislocations of Si webs grown in the past [7]. The thermal environment of the actual growth process has been optimized during the last 30 years in order to produce wide ribbons, as long as possible, and with minimum residual stresses. Whether the extensive d faults reported here were generated in the growth process or during the annealing, was not examined. In either case, the free partial dislocations on the d plane must move away from the stair rod, whether by viscoplastic #ow or restructuring of the network after annealing. Moreover, the low density of dislocations in the analyzed Si web contributes in
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increasing the size of the faulted areas and in avoiding their overlap. In the analysis of DWS by synchrotron radiation white-beam topographs, the double-contrast is very useful for identifying dislocation line character. Since dislocations along the growth direction are one of the major reasons for increasing the dislocation density during crystal growth, the rapid identi"cation of their character is important for quality control. The 2 2 0, 2 0 2 , and 0 2 2 re#ections will not allow a rapid identi"cation since one of the DX dislocations (X"A, B or C) is always invisible for each of these re#ections. Further, based on the calculated values in Table 2, the 2 2 4 re#ections do not provide double contrast for the DX lines along 1 1 2 because the line is parallel to the incidence plane, c"0. However, by using the 2 4 2 or 4 2 2 re#ections all lines are visible, and the double contrast discriminates the DC line from the DA and DB lines. In the example reported here, the lines along the growth direction, in the topographs of Fig. 6, were identi"ed as DB dislocations by analyzing only the 2 4 2 topograph (Fig. 6c).
5. Conclusions The results reported here are consistent with introduction of Lomer dislocations in DWS from reactions between two types of dislocations generated by the thermal stresses. One that is trapped at the twin boundaries and another that is not. Although the web is a very thin crystal, the con"guration of the defects on each side of the twins is not the same. The existence of large stacking faults is a consequence of the sti!ness of the stair rod at the Lomer dislocations plus viscoplastic #ow at high temperature, during growth or annealing. The double-contrast of the dislocation lines in synchrotron radiation white-beam topographs allows faster identi"cation of the character of the dislocation lines along the growth directions.
Acknowledgements The authors would like to thank Prof. S. Mahajan for very helpful discussions about dislocation
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reactions during the beginning of the work with DWS. The "rst author also acknowledges the partial "nancial support of the Brazilian agency CNPq. References [1] D.L. Meier, R.H. Ropkins, R.B. Campbell, J. Propulsion 4 (1988) 586. [2] K. Joardar, C.O. Jung, S. Wang, D.K. Schoder, S.J. Krause, G.H. Schwuttke, D.L. Meier, IEEE Trans. Electron Devices 35 (1988) 911. [3] S.L. Morelha o, S. Mahajan, J. Crystal Growth 177 (1997) 41. [4] S. O'Hara, G.H. Schwuttke, J. Appl. Phys. 36 (8) (1965) 2475.
[5] B. Ingram, B. Bathey, D.L. Meier, S. Mahajan, Seventh NREL Defects Workshop 1997, unpublished. [6] S. O'Hara, J. Appl. Phys. 35 (1964) 409. [7] E.S. Meieran, I.A. Blech, J. Appl. Phys. 38 (9) (1967) 3495. [8] F. Zontone, L. Mancini, R. Barrett, J. Baruchel, J. HaK rtwig, Y. Epelboin, J. Synchrotron Rad. 3 (1996) 173. [9] A.R. Lang, Acta Crystallogr. 12 (1959) 249. [10] P. RejmaH nkovaH , J. Baruchel, Nucl. Instr. and Meth. B 97 (1995) 518. [11] S. Mahajan, Metall. Trans. 6A (1975) 1877. [12] J. Miltat, D.K. Bowen, J. Appl. Crystallogr. 8 (1975) 657. [13] B.K. Tanner, D. Midgley, M. Safa, J. Appl. Crystallogr. 10 (1977) 281. [14] J.A. Spitznagel, R.G. Seidensticker, S.Y. Lien, J.P. McHugh, R.H. Hopkins, J. Crystal Growth 82 (1987) 39.
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Dislocations in dendritic web silicon S.L. Morelha o *, J. HaK rtwig, D.L. Meier Instituto de Fn& sica, Universidade de SaJ o Paulo, CP 66318, 05315-970 SaJ o Paulo, SP, Brazil European Synchrotron Radiation Facility, BP 220, F-38043 Grenoble, France EBARA Solar, Inc., 811 Route 51 South, Large, PA 15025, USA Received 27 May 1999; accepted 1 February 2000 Communicated by M.S. Goorsky
Abstract Due to its peculiar laminated structure, dendritic web silicon presents one of the most interesting con"gurations of dislocations in Si crystals. On the way to growing dislocation-free Si webs, X-ray di!raction topography techniques were used to visualize the dislocations in the material. The results and the analysis of dislocation reactions reported here provide information on the mechanisms involved in the formation of dislocation networks in the material. Also, the applicability of synchrotron radiation white-beam topography for a rapid characterization of dislocations is investigated and discussed. 2000 Elsevier Science B.V. All rights reserved.
1. Introduction The dendritic web silicon (DWS) growth process provides the basic material for manufacturing lowcost high-e$ciency solar cells. In the actual process, silicon web crystals are obtained as ribbons of several meters in length, a few centimeters in width, and an ideal thickness of about 100 lm. The aims of all growers of DWS are the continuous growth of the ribbon and web crystals free of defects. The defects, dislocations plus impurities, strongly limit the photovoltaic conversion e$ciency of the solar cells [1,2]. The web surface is parallel to (1 1 1), and the axis of the ribbon, the growth direction, is [1 1 2 ]. In a cross section the web is laminated, consisting of layers of about 50 lm thickness at each surface, separated by an odd number of twin planes in
* Corresponding author.
a very thin layer (&5 lm). Since the twin planes are parallel to the web surface, (1 1 1), the two thick surface layers are twin-related. Recently, an X-ray topography study of the growth process [3] has correlated the evolution of the dislocation networks in web crystals with growth interruptions. Several mechanisms playing roles in the evolution of dislocation networks were described. It has been observed that the (1 1 1) twin planes, present over the whole area of most crystals, limit the movement of dislocations, trapping them inside the material. It gives rise to long dislocation lines as well as a high probability for dislocation reactions to occur. For instance, Lomer dislocations [4] have been identi"ed and they could be generated by dislocation reactions. This type of dislocations do not glide, and they can a!ect sti!ness and viscoplastic behavior at high temperature, which can lead to deformation of the ribbons as well as to their poor crystalline quality. One of the most dominant factors causing the cessation of
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growth has been observed to be the formation of polycrystalline silicon [5]. Low angle boundaries [6], stringers observed at the center of the ribbons and along the growth direction, made up of edge-dislocation lines have been correlated to materials with low minority carrier di!usion length [3,5]. A dislocation reaction has been suggested as a possible source of such edge dislocations. Crystallographically, the DWS crystals can be described by two Thompson's tetrahedrons with the d face, (1 1 1)-twin plane, in common for both. They are represented in Fig. 1a, by the tetrahedrons with vertices ABCD and ABCD . Several types of dislocations have been identi"ed in web crystals [3,6]. According to Thompson's notation, the dislocations with Burgers vectors, $a/2[1 0 1], $a/2[0 1 1], and $a/2[1 1 0], out of the web plane (d plane) are named DA(b, c), DB(a, c), and DC(a, b), respectively. a, b, and c in parentheses indicate the possible slip planes of these dislocations. They can occur on either side of the web crystals, for instance as D A, D B, and D C dislocations in their respective a , b , and c slip planes. These dislocations do not cross the twin boundary because their Burgers vectors (or slip directions) are not parallel to the slip planes on both sides. Only dislocations with in-plane Burgers vector, BA(c, c , d), CA(b, b , d), and CB(a, a , d), do not have their movement limited by the twin boundaries. DA and DB are the notation for Lomer
dislocations that have often been identi"ed in web crystals. Table 1 summarizes the Burgers vector, b, of the dislocations as well as the Bragg re#ections, or the di!raction vector u, for which they are invisible (b ) u"0). In this article, we report several results in order to further describe the unique nature of the dislocations in DWS. The results were obtained by X-ray di!raction techniques, such as monochromatic transmission topography using symmetric and asymmetric re#ections and synchrotron radiation white-beam topography. The images recorded by
The Thompson's tetrahedron is formed by the 1 1 1 planes of the cubic system. The a, b, c, and d faces represent the (1 1 1 ), (1 1 1 ), (1 1 1), and (1 1 1) planes, respectively.
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Fig. 1. (a) The crystallography of the web crystals represented by two twin-correlated Thompson's tetrahedron, with the d face as the twin plane. The ABCD and ABCD tetrahedrons are the back and front sides of web, respectively. (b) In-plane di!raction vectors used for transmission topography of symmetric re#ections.
these techniques contain many dislocations, extensive stacking faults, and exhibit interesting reactions which de"ne most of the networks along the ribbons. They provide experimental evidence of the reactions involved in the formation of Lomer dislocations, which can be related to the presence of
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Table 1 Burgers vector of the dislocations in the normal Thompson tetrahedron notation, and the re#ections for which b ) u"0. Only 2 0 2 , 0 2 2 , 2 2 0, 2 2 4 , and 1 1 1 re#ections have been used in this study Dislocation
Burgers vector (b)
Re#ections
DA DB DC BA CA CB Da Db Dc Ad Bd Cd
a/2[1 0 1] a/2[0 1 1] a/2[1 1 0] a/2[1 1 0] a/2[0 1 1] a/2[1 0 1] a/6[1 2 1] a/6[2 1 1] a/6[1 1 2] a/6[1 2 1 ] a/6[2 1 1 ] a/6[1 1 2]
2 0 2 0 2 2 2 2 0 2 2 4 4 2 2 2 4 2 2 0 2 0 2 2 2 2 0 2 0 2 0 2 2 2 2 0
1 1 1 1 1 1 1 1 1
1 1 1
the stringers (BA edge dislocations). Based on this evidence, a mechanism explaining the occurrence of the immense stacking faults, already observed in these materials in the past [7], is also proposed. The use of the double-contrast image criterion [8] of a dislocation line, in white-beam topographs, for identi"cation of dislocations in DWS is discussed.
2. Experimental details A standard topographic Lang camera and a Rigaku X-ray generator with a Mo target were used to perform transmission topography measurements (Lang topography [9]). The X-ray beam was collimated in the incident plane (horizontal plane) to about three minutes of arc. The vertical beam size and the horizontal maximum scan range limit the size of the analyzed area to 18;26 mm, respectively. The nuclear plates, or high-resolution "lms, were set parallel to the web surface in order to keep the distance between imaged features independent of the re#ections used. The average exposure times were 8 h. Transmission topography of symmetric-Bragg re#ections is used to produce di!raction images of the dislocations. Symmetric re#ections for trans-
mission di!raction are those illustrated in Fig. 1b, with the reciprocal lattice vector (di!raction vector) in the d plane of the web crystal. Since the back and front sides, or in other words, the two thick surface layers of the web are twin-related crystals, symmetric re#ections are common for both sides, and they provide di!raction images from the total thickness of the material. Images of one-half of the thickness, i.e., an image of only one side or the other, are obtained using asymmetric re#ections. An example of asymmetric re#ections are those with a di!raction vector out of the d plane, such as the 1 1 1 and 1 1 1 re#ections, i.e., transmission di!ractions from the c and c Bragg planes, respectively. Synchrotron radiation white-beam topographs were recorded at the ID19 &topography and highresolution di!raction' beamline at the ESRF [10]. The beamline has an experimental station outside the ring building, which gives a source-to-sample distance of 145 m. It provides a spectrally and spatially homogenous beam at the sample position, with dimensions of &40 (horizontal);14 (vertical) mm. The geometrical resolution is (1 lm even for a sample-to-"lm distance as great as 1 m. A high photon #ux assures exposure times of the order of a few seconds. Direct, or kinematical, image condition (lt(1) is achieved by using high-energy photons ('50 keV), thus 2h is (73 for the imaged re #ections. It allows the "lm to be placed normal to the incident-white beam without signi"cantly affecting the image width through projection e!ects. The use of high energies also drastically reduces the harmonic contamination due to the extended spectrum of the synchrotron radiation. The topographs were recorded on Kodak Industrex synchrotron radiation "lms (grain size 1}2 lm), and the images were digitized from "lms using a CCD camera (with linear intensity response) coupled to a microscope.
3. Results 3.1. Symmetric reyections High-resolution transmission topographs for 0 2 2 , 2 0 2 , 2 2 0, and 2 2 4 re#ections are shown in
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Fig. 2. They were taken from the same as-grown Si web analyzed in Fig. 5 of Ref. [3]. The 603 dislocations DA(b), DB(a), and DC(a, b) are most of the lines presented in the images. A few Lomer dislocations, DB , are also seen, for example, between
the points marked with numbers 1 and 3. The complexity of the network in these topographs is basically due to two types of dislocation reactions, DC(a)#DB(a)"Da#aC#Da#aB"3Da, DC(b)#DA(b)"Db#bC#Db#bA"3Db,
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since aC#aB"Da and bC#bA"Db. In this type of reaction, the unit dislocations are dissociated into Shockley partials and the node is formed by subsequent rearrangement of the partials [11]. Fig. 3 illustrates how these attractive reactions increase the complexity of the network, and how it is seen when imaged by di!erent re#ections. The hypothetical network in this "gure is similar to the one observed in the area around the number 2 in Fig. 2. On the right-hand side of the topographs (Fig. 3), arrays of DC(b) and DA(b)
Fig. 2. High-resolution transmission topographs of a #at web crystal. The same network is imaged using four di!erent symmetric re#ections.
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Fig. 3. The network formed by DA(b), DB(a), and DC(a, b) dislocation lines plus their reactions, as seen on the 0 2 2 , 2 0 2 , 2 2 0, and 2 2 4 topographs. The network is similar to the one observed at the center of Fig. 2.
dislocation lines are running along the [0 1 1 ] direction. Near the intersection with DB(a) lines, parallel to the [0 1 1 ] direction, the DC(b) lines move towards these lines due to their mutual attraction. Before reaching the DB(a) lines, the DC(b) ones "rst react with the DA(b) lines to form 3Db nodes. Then, they cross-slip to the a slip system, becoming DC(a) lines, and the reaction DC(a)# DB(a)"3Da takes place. All dislocation lines and nodes are visible in the 2 2 4 topograph, and the DB(a), DA(b), and DC(a, b) lines are invisible only in the 0 2 2 , 2 0 2 , 2 2 0 topographs, respectively (see Table 1). Experimental evidence of the reactions involved in the generation of Lomer dislocations is also observed in Fig. 2. The DB Lomer dislocation,
with its endpoints at 1 and 3, is the resultant dislocation of the reactions which occur at these points. The dislocation lines involved in these reactions are shown in Fig. 4, as seen in the topographs. At point 1, DC(b)#CB(d)"Db#bC#Cd#dB "Db#bd#dB"DB
and at point 3, DA(b)#AB(d)"Db#bA#Ad#dB "Db#bd#dB"DB
Fig. 4. Schematic of the contrast observed in the four topographs of Fig. 2, for the dislocation lines in the reactions at points 1 and 3. The DB "Db#bd#dB, DA, DC, and AB
dislocations are invisible for the 0 2 2 , 2 0 2 , 2 2 0, and 2 2 4 re#ections, respectively. The inset illustrates the arrangement of the dislocations involved.
The unit dislocations in these reactions are dissociated into partials on the b and d slip planes. The partials react at the intersection of the planes to form the bd dislocation (stair rod dislocation or Cottrel}Lomer dislocation). Since it lies on both planes (inset of Fig. 4), the dislocation line must be along the [0 1 1 ] direction, which is common to both planes. In such a con"guration, this type of dislocation is completely sessile, i.e., it cannot move either by glide or by climb without creating surfaces or very bad mis"t. The faults bounded by the partials cannot be resolved by X-ray topography.
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Then, the total Burgers vector, which determines the visibility of the dislocation, is the same as a DB line (b"$a/2[0 1 1]). However, the slip plane that contains the line direction and Burgers vector has the [1 0 0] normal direction. In the Lomer dislocation observed in Fig. 2, it should be noted that the bd dislocation is introduced by the reaction of one pair of partials, and it can split into another pair of partials; i.e., bC#CdPbdPbA#Ad. 3.2. Asymmetric reyections The transmission topographs of asymmetric re#ections show contrasts of large stacking faults parallel to the web surfaces, or to d planes. Figs. 5a}c show the 1 1 1, 1 1 1 , and 2 2 4 topographs, respectively. The #at Si web sample has been annealed at 8503C for 1 h, followed by slow cooling to 6003C at a rate of 1C/min. Unfortunately, no Xray topographs were taken before annealing. The DA and DB lines are invisible for the 1 1 1 and 1 1 1 asymmetric re#ections, and all lines are visible in the 2 2 4 topograph. For these asymmetric re#ections, the extrinsic faults on d planes, d faults, introduce phase shifts of 2p/3 between the X-ray wave"eld di!racted below and above them. As a consequence, the recorded intensity decreases, and the faults are seen in the topographs as white areas. In the analyzed sample, such d faults are seen only on one side of the web crystal, i.e., only in the 1 1 1 topograph. The contrast of the extensive stacking faults in annealed Si web has been studied more than three decades ago [7]. Due to the higher density of grown-in dislocations in the material obtained by the growth process at that time, overlapping of extensive faults produced contrast of extrinsic, intrinsic, and nonfaulted regions. However, &there was no evidence as to how the faults were formed, whether from Lomer dislocation reactions or from the generation and movement of partials from a dislocation source'.
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The images of three spots, topographs, due to symmetrical re#ections obtained simultaneously in an exposure time of about 1 s, are shown in Fig. 6. While the dislocation lines present single contrast in the 2 0 2 topograph (Fig. 6a), double contrast of the lines is a feature clearly visible in the 2 2 0 and 2 4 2 topographs, Figs. 6b and c, respectively. The double contrast is related to the distorted regions around the dislocation core, where the two misorientation contours contribute separately [12,13]. And, it is nearly always observed because of the experimental condition at ID19 beamline [8]: good geometrical resolution, large sample to "lm distance, and high photon energy. In order for double contrast to be observed, a non-zero projection of the edge component (b ) of the Burgers vector into the di!raction vector direction is required, i.e., b . uO0. Also, the angle c between the dislocation line direction and the incidence plane must be near 90. The double-contrast conditions in terms of b ) u and c values are summarized in Table 2. Near the center of the topographs, an array of DB(a) and DC(a) dislocation lines along the [1 0 1 ] direction is observed. A few lines are reacting and climbing out of their a planes to run along the growth direction. Since DC lines along the growth direction have b perpendicular to the web face, all symmetrical re#ections produce lines of single contrast (Table 2). Therefore, by analyzing only the 2 4 2 topography (Fig. 6c), it is possible to identify the lines along the growth direction as DB lines. The DC lines are those lines with very weak contrast in the 2 2 0 topograph, Fig. 6b. DB(a) and DC(a) dislocations produce single-contrast lines for di!raction vectors that are also in the a plane. It is observed in the 2 0 2 topograph, Fig. 6a. Although in this topograph, b ) u and c are not zero for the DB lines along the growth direction, they are also seen with single-contrast, just a little darker.
4. Discussion 3.3. Synchrotron radiation white-beam topography The white-beam topographic method (Laue method) is used to provide several di!raction spots (images) of the sample on the photographic "lm.
Standard two-dimensional thermal stress models [14], assume that the thickness components of stress vanish in comparison with the in-plane ones. As a result, the coe$cients of resolved shear stress
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Fig. 5. Transmission topography of asymmetric, 1 1 1, 1 1 1 , and symmetric 2 2 4 re#ections. They reveal the occurrence of stacking faults of d planes only on one side of the web crystal, and the di!erences between the networks on each side.
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Fig. 6. Synchrotron radiation white-beam topographs from three symmetrical re#ections: (a) 2 0 2 , (b) 2 2 0, and (c) 2 4 2.
for the d slip systems are zero. Although the CA(d), CB(d), and BA(d) dislocations should not occur, their existence is revealed by the reactions involved in the formation of the DB (Fig. 4) and
DA Lomer dislocations. The defects type
stringers [5] in DWS also reveal the existence of BA edge dislocations, which are BA dislocations with the line parallel to the growth direction. In
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Table 2 Double-contrast conditions for DA, DB and DC dislocation lines in white-beam topographs of symmetrical re#ections: b ) u is the cosine of the angle between the edge component, b , of the Burgers vector and the di!raction vector u, and c is angle of the dislocation line direction, L, with the incidence plane Re#ection
L"[0 1 1 ]
L"[1 0 1 ] c
b )u
2 2 0 2 0 2 0 2 2 2 2 4 2 4 2 4 2 2
DA
DC
0.29 * 0 0.17 0.17 !0.33
* 0.29 0 0.17 0.17 !0.33
60 60 0 30 30 90
L"[1 1 2 ] c
b )u DB
DC
!0.29 0 * 0.17 !0.33 0.17
* 0 !0.29 0.17 !0.33 0.17
Fig. 7. Example of the suggested mechanism for generating large d faults in DWS. The CA(b) dislocation, attracted by the DC(a)"Da#aC line, cross-slips to the d slip plane and dissociates into Cd and dA partials. The aC and Cd partials react to form the ad stair rod dislocation. Then, the large d fault is introduced when the dA partial moves apart from the stair rod.
order to explain the three dislocations, on the d slip systems, in the material, and consequently the occurrence of Lomer dislocations, the following mechanism is suggested: the thermal stresses e$ciently introduce CB(a) and CA(b) dislocations [14]. Since they are not trapped by the d twin boundaries, the lines of such dislocations should be
60 0 60 30 90 30
c
b )u DA
DB
DC
0.52 * !0.26 0 0.45 !0.45
!0.52 !0.26 * 0 !0.45 0.45
* 0 0 0 0 0
90 30 30 0 60 60
very short, of the order of the web thickness. It is in agreement with the length of the CB line observed at point 1 of Fig. 2 (see also Fig. 4). The CB(a) and CA(b) dislocations, due to eventual interactions with the network of DX dislocations (X"A, B or C), would cross-slip to d slip planes, react with the DC(a, b) ones and give rise to the Lomer dislocations. Therefore, the probability for Lomer dislocations being introduced in the material strongly depends on the complexity of the network along the ribbon as well as on how the network evolves during crystal cooling in the growth process, or during subsequent annealing. As also observed in Fig. 2, and illustrated in Fig. 3, the attractive reactions between DC(a) and DB(a) dislocations, or DC(b) and DA(b) dislocations, play an important role for increasing the network dynamism and complexity. In the above-suggested mechanism, the BA(d) dislocations are introduced when the Lomer dislocations split, as seen at point 3 in Fig. 2. It could be another source of BA dislocations, besides the already proposed mechanism that involves reactions between DA(c) and DB(c) dislocations [3,4]. The d faults observed in Fig. 5a , 1 1 1 topograph, are other features correlated with the activity on the d slip systems. Such faults are bounded by partial dislocations, which are introduced when a unit dislocation, BA(d), CB(d), or CA(d), dissociates into the partials, for instance CA(d)" Cd#dA. The small size of the stacking faults, or
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distance between the partials, expected for Si [7,11] is below the resolution of the X-ray di!raction imaging techniques. In DWS, when this type of dissociation happens near the solid}liquid interface of the growing crystal, i.e., near the growth front, strips of grown-in faults are introduced. If the bounding partials of a strip interact with other dislocations, or walls of dislocations, or any other crystal defects, they will not move parallel to each other. Then at high temperature, whether during growth or during annealing, the distance between the two partials can be signi"cantly increased. Examples of such stacking-fault strips are clearly observed on the left-hand side of the topograph in Fig. 5a. This argument is used here, in order to understand the wide strips, of more than 500 lm, that remain locked in the Si web at room temperature in spite of the large stacking-fault energy. A similar argument is used to explain the immense stacking faults recorded in the topograph of Fig. 5a. In this case, the large faults are part of or even start at Lomer dislocations. Each of them is bounded by a stair rod and a partial dislocation. The stair rod determines straight contours well aligned along the [0 1 1 ] or [1 0 1 ] direction, as seen for several faults in the topograph. One possible situation is exempli"ed in the illustration of Fig. 7. The CA(b) dislocation, introduced by thermal stresses, cross-slips to the d plane, dissociates into partials, and reacts with the DC(a) line to form the Da and dA partials, and the ad stair rod dislocation. The large d faulted area is generated at high temperature when the dA partial moves apart from the stair rod, which is completely sessile. Releasing of residual stresses by sample annealing signi"cantly changed the structure of dislocations of Si webs grown in the past [7]. The thermal environment of the actual growth process has been optimized during the last 30 years in order to produce wide ribbons, as long as possible, and with minimum residual stresses. Whether the extensive d faults reported here were generated in the growth process or during the annealing, was not examined. In either case, the free partial dislocations on the d plane must move away from the stair rod, whether by viscoplastic #ow or restructuring of the network after annealing. Moreover, the low density of dislocations in the analyzed Si web contributes in
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increasing the size of the faulted areas and in avoiding their overlap. In the analysis of DWS by synchrotron radiation white-beam topographs, the double-contrast is very useful for identifying dislocation line character. Since dislocations along the growth direction are one of the major reasons for increasing the dislocation density during crystal growth, the rapid identi"cation of their character is important for quality control. The 2 2 0, 2 0 2 , and 0 2 2 re#ections will not allow a rapid identi"cation since one of the DX dislocations (X"A, B or C) is always invisible for each of these re#ections. Further, based on the calculated values in Table 2, the 2 2 4 re#ections do not provide double contrast for the DX lines along 1 1 2 because the line is parallel to the incidence plane, c"0. However, by using the 2 4 2 or 4 2 2 re#ections all lines are visible, and the double contrast discriminates the DC line from the DA and DB lines. In the example reported here, the lines along the growth direction, in the topographs of Fig. 6, were identi"ed as DB dislocations by analyzing only the 2 4 2 topograph (Fig. 6c).
5. Conclusions The results reported here are consistent with introduction of Lomer dislocations in DWS from reactions between two types of dislocations generated by the thermal stresses. One that is trapped at the twin boundaries and another that is not. Although the web is a very thin crystal, the con"guration of the defects on each side of the twins is not the same. The existence of large stacking faults is a consequence of the sti!ness of the stair rod at the Lomer dislocations plus viscoplastic #ow at high temperature, during growth or annealing. The double-contrast of the dislocation lines in synchrotron radiation white-beam topographs allows faster identi"cation of the character of the dislocation lines along the growth directions.
Acknowledgements The authors would like to thank Prof. S. Mahajan for very helpful discussions about dislocation
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reactions during the beginning of the work with DWS. The "rst author also acknowledges the partial "nancial support of the Brazilian agency CNPq. References [1] D.L. Meier, R.H. Ropkins, R.B. Campbell, J. Propulsion 4 (1988) 586. [2] K. Joardar, C.O. Jung, S. Wang, D.K. Schoder, S.J. Krause, G.H. Schwuttke, D.L. Meier, IEEE Trans. Electron Devices 35 (1988) 911. [3] S.L. Morelha o, S. Mahajan, J. Crystal Growth 177 (1997) 41. [4] S. O'Hara, G.H. Schwuttke, J. Appl. Phys. 36 (8) (1965) 2475.
[5] B. Ingram, B. Bathey, D.L. Meier, S. Mahajan, Seventh NREL Defects Workshop 1997, unpublished. [6] S. O'Hara, J. Appl. Phys. 35 (1964) 409. [7] E.S. Meieran, I.A. Blech, J. Appl. Phys. 38 (9) (1967) 3495. [8] F. Zontone, L. Mancini, R. Barrett, J. Baruchel, J. HaK rtwig, Y. Epelboin, J. Synchrotron Rad. 3 (1996) 173. [9] A.R. Lang, Acta Crystallogr. 12 (1959) 249. [10] P. RejmaH nkovaH , J. Baruchel, Nucl. Instr. and Meth. B 97 (1995) 518. [11] S. Mahajan, Metall. Trans. 6A (1975) 1877. [12] J. Miltat, D.K. Bowen, J. Appl. Crystallogr. 8 (1975) 657. [13] B.K. Tanner, D. Midgley, M. Safa, J. Appl. Crystallogr. 10 (1977) 281. [14] J.A. Spitznagel, R.G. Seidensticker, S.Y. Lien, J.P. McHugh, R.H. Hopkins, J. Crystal Growth 82 (1987) 39.