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X-ray topographic observation of dislocation structure in sapphire single crystal grown by temperature gradient technique
Journal of Crystal Growth 108 (1991) 377—384 North-Holland
377
X-ray topographic observation of dislocation structure in sapphire single crystal grown by temperature gradient technique Zhang Qiang, Deng Peizhen and Gan Fuxi Shanghai Institute of Optics and Fine Mechanics, Academia Sinica, P.O. Box 8216, Shanghai, People’s Rep. of China
Received 12 September 1989; manuscript received in final form 3 August 1990
The characteristic triangular cross-grid dislocation structure in sapphire single crystals grown in [0001] direction by temperature gradient technique (TGT) has been investigated by means of X-ray diffraction topography. Dislocations lie on (0001) basal planes and pnmarily appear as three parallel groups of straight dislocation lines. At high temperature these dislocation lines can move easily on the slip planes and form different dislocation configurations due to pinning, climbing and interacting. The analysis of Burgers vector and image width of dislocation lines confirmed that three parallel groups of straight dislocation lines are pure edge type having <1120) type Burgers vector, and a few dislocation reactions are of the type of [11201+[1210]+[2110] = 0. A simple model of basal slip of the type of (0001)<1120) is used to explain these dislocations.
I. Infroduction Sapphire single crystal is an important crystal material, used for a number of high technology applications. As an optical material, sapphire single crystal has wide transmission, spanning the ultra-violet, visible and infra-red bands. It has, therefore, been used as an optical window material. For this purpose large diameter, zero birefnngence and [0001] orientation sapphire single crystals have been grown by the heat exchanger method (HEM) [1] and the temperature gradient technique (TGT) [2]. Generally, it is difficult to grow sapphire single crystal along [0001] direction because this orientation was not preserved in the grown crystal [3], due to the weakening action of the main slip system [4]. Therefore, the dislocation structure in as-grown sapphire single crystals may be quite different from that in the other orientation grown crystals reported by Caslavsky and Gazzara [5]. The present paper reports the X-ray transmission topographic results of the dislocation distribution and behaviour, which clearly displayed the characteristic triangular cross-grid dislocation structure consisting of three parallel groups of 0022-0248/91/$03.50 © 1991
—
straight dislocation lines. The effect of doping and growth direction on the dislocation structure is also considered.
2. Experimental procedure In the present investigation, high quality sapphire single crystals, 56 mm in diameter, were grown in [00011 seeding direction by TGT [3]. Samples 1* and 2* were cut from sapphire and 0.1 wt% Ti3~doped sapphire single crystals respectively. For comparison purpose, sample 3* was cut from a [1102] orientation sapphire single crystal. All of the samples are (0001) wafers of thickness 1 mm. After lapping and polishing mechanically, the wafers were chemically polished and thinned in molten borax (950~10500C). At least 100 ~tm of the surface was removed to ensure that no surface effects would be recorded. The orientation of the wafers deviated I from the (0001) plane. The chemical etching was also carried out in molten borax (850—900°C)for about 15 mm. All of the topographs displayed here were ohtamed by X-ray transmission topographic method.
Elsevier Science Publishers B.V. (North-Holland)
0450
378
Zhang Qiang et a!.
/ X-ray
topographic observation ofdislocation structure in sapphire
The diffraction planes were {1120} and {3300} prism planes which are perpendicular to the (0001) basal plane. The Ag K~1X-ray diffraction image was recorded on an X-ray film with 1 jim emulsion particle size. The exposure time was 0.3—0.6 h/mm scan length. The indices used in this paper were based on the crystallographic hexagonal Xray unit cell with a 4.758 A and c 12.991 A [61. =
=
3. Results and discussion 3.1. Location of dislocation
Fig. 1 illustrates typical X-ray topographs which displayed the characteristic triangular cross-grid dislocation structure. Five pictures were taken from sample I * by successive rotations of 30° in the plane of the wafer and oriented with the [1100] vertical. The pronounced feature in the topographs is the appearance of three parallel groups of straight dislocation lines; three such systems marked I, II and III are 60°or 120° apart respeclively. The group I system runs along [1100], the group II dislocation system and group III run along [IO1OLand [0110], respectively. In the reflection of {1120}, three groups of dislocation lines appeared (figs. lb and ld) in which the group of dislocation lines perpendicular to the diffraction vector was generally darker in contrast and the image width of these dislocation lines was approximately twice that of other two groups. While in the reflection of {3300}, only two groups of dislocation lines which display the same contrast and the same image width of dislocation lines appeared (figs. la, ic and ie), the group of dislocation lines parallel to the diffraction vector vanished totally. The dependence of the contrast and the image width of the dislocation line on the diffraction vector implicated that three parallel groups of dislocation lines lay on the (0001) basal planes. Further experimental evidence for this dislocation distribution could be obtained by thinning the wafer again in molten borax for about 20 mm. The prolonged polishing has led to a slightly beveled edge of the wafer. Figs. if and ig show the
topographs. In comparison with figs. Ic and id, a lot of dislocation lines vanished together with removal of the surfaces, and the segments of dislocation lines near the margin, labelled A, B and C, disappeared due to the formation of the beveled edge. In addition, the fact of relatively few dislocation etch pits visible on the surfaces of the wafer in an optical microscope, which corresponds to the outcrops of dislocations, also confirmed that almost all of the dislocations lay on the (0001) basal planes. Also noticeable are the pendellosung fringes appearing as three dark fringes marked 1, 2 and 3 in fig. if, and one labeled 1 in fig. Ig at the beveled edge of the wafer, which indicate the high degree of the perfection of the sapphire single crystal investigated. Fig. 2 shows enlarged pictures of the area marked M in fig. 1 a; different dislocation configurations, such as 600 kinked dislocation lines E and D, edge type of dislocation dipole F, spinal dislocation turns G and H, and dislocation reaction nodes 0 and Q were clearly displayed. Some of these dislocations, i.e. the kinked dislocation ltne D, has undergone a slip movement along its Burgers vector direction due to the chemical stress during chemical polishing. Other dislocations, i.e. the spinal dislocation turn H, has undergone a climbing along the direction normal to (0001) basal plane. 3.2. Determinatton of Burgers vector
A useful feature of X-ray transmission topography is the readiness with which the Burgers vector of the dislocation can be determined. In case of low X-ray absorption, the direct image of dislocation is very dense and the quantity q b is a reasonable measure of its strength. According to the principle, the contrast of a given dislocation line is determined by the relative orientation of diffraction vector g, Burgers vector b, and dislocation line vector 1 [7]. Pure screw dislocation is invisible in the reflections for which the scalar product g~b 0. Pure edge dislocations only vanish in the reflections from the plane for which the scalar products g b 0 and g b x 1 0. A mixed dislocation does not vanish. In the present paper the vectors g and 1 are normal to [00011 direction (i.e. lie on the (0001) planes). hence the =
.
=
=
Zhang (jian,g ci al
A—rat tupographu obccrt anon of dubs ation ctruc turc in copplure
--
37q
~~1
~:
~.-
—
/
~‘j5 ~
-‘
.-.
-
,
r
‘
.
/ -
.~.:i
o
,
~~—2<-~ ~:ST’~-..” -
.~•
::-J
~-t-
-
.
-
____
Fig. I. Topograph of sample 1 * sho~ing the characteristic triangular cross—grid dislocation structure: (a). tht. (el. (dl and Ce) are iii the reflections (0330). (1120). (1010). (2110) and (3300). respectisels and t = 3l~pm: (f) and Ig) are in the reflections (33001 and (21101 and t 203 p.nt.
380
Zhang Qiang et al
/ X-ray
topographic observation of dislocation Structure in sapphire
I
__
,
~
64
(a)
~(c)
,,
“.~.
•.‘: ~
‘h
k
(i)
(d)
~
•
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~
0
G
Fig. 2. Enlarged topographs of the area M in fig. I showing different dislocation configurations: D and F are 60° kinked dislocations, F is edge dislocation dipole, G and H are helical dislocation turns, and 0 and Q are dislocation reaction nodes; (a), (b). (c) and (d) are in the reflections (2110), (3030), (0330) and (3300).
Burgers vector of these dislocation lines can be determined unambiguously from the presence of contrast (g b = 1) or absence of contrast (g b = 0). Consider first the group I dislocation lines which progress vertically across the topographs; they display high contrast in (1120) reflection (fig. ib) and vanish in (3300) reflection (fig. le), and therefore the [1120] Burgers vector is justified. In the same manner, the dislocation groups II and III can be substantiated to have the [2110] and [1210] Burgers vectors respectively. Because the Burgers vector b is perpendicular to the dislocation line vector 1, these parallel groups of straight dislocation lines are all pure edge type having (1120) type Burgers vectors. The dislocation structure on .
the (0001) basal plane with the relevant dislocation identified is shown schematically in fig. 3. Examine next the dislocation lines labeled A, B and C in fig. 2. Three dislocation lines converged at the point 0 and displayed different contrast in different_reflections, the dislocation A which ran along [1210] showed strong contrast in (1i20} reflection and vanished totally in (3030) reflection. With conformity to g• b = 0, the Burgers vector for dislocation A is justified to be in [1120] direction. As the Burgers vector b is parallel to the dislocation line vector 1, dislocation A is a pure screw dislocation line. If the same criterion is applied to the dislocation lines B andC, because they are extinct in the (3030) and (3300) reflections respectively, the Burgers vectors for disloca-
Zhang Qiang et al
/ X-ray
1700
2710
1210
1070
1120
1f20
iii
a = [ imo i a = [7110]
ii
alTo 1
o=
7010
20j
11
7270
7110
tions B and C are determined to be parallel to the [2110] and [1120] directions respectively. Obviously, the point 0 has to be a singular dislocation reaction node where three dislocations, whose sum of Burgers vectors equals zero, meet and interaction terminates inside the crystal. The corresponding dislocation reaction is the type of [1120] + [1210] + [2110] = 0. Similarly, the point Q is also a dislocation reaction node with the same type of 1710
0_flu
1-1-00
~—_~
=
Talc
b=[1120 = [12101
1170
3.3. Image width of dislocation
Further experimental evidence for the character of these parallel groups of straight dislocation lines can be obtained from the image widths of dislocation lines in topographs. The present case, when a pure screw dislocation or a pure edge dislocation lies on the (0001) basal plane, is viewed in a reflection whose diffraction vector is perpendicular or at a certain angle to the Burgers vector of dislocation; the image width of dislocalion varies with the quantityg. b. The direct image width W~,for a pure screw dislocation, and ~We, for a pure edge dislocation, are given by the formulas [8] = ~g(g• b)/2~r, (1) (2)
W~=0.88~g(g.b)/ir, 0
2710
7110
1100
0170
dislocation reaction. A schematic representation of the dislocation reaction is shown in fig. 4. Careful examination of the topographs has revealed that nearly all of the dislocation configurations exhibit a similar behavior in contrast, they show the strong contrast and loss contrast in different reflections. Regardless of the dislocation character, the Burgers vectors of these dislocation configurations can be identified to be in the (1120) direction according to the invisibility rule g~b = 0. Hence it is highly probable that these different dislocation configurations originate from the parallel groups of straight dislocation lines by a series of dislocation movement.
noo Fig. 3. Schematic diagram of the characteristic triangular cross-grid dislocation structure. Three groups of dislocation lines, I, II and III, are properly oriented with respect to the (0001) stereographic projection; the Burgers vectors are represented by the arrows.
010
381
topographic observation of dislocation structure in sapphire
1270
Fig. 4. Schematic representation of the dislocation reaction, The dislocations are properly oriented with respect to the (0001) stereograph; the Burgers vectors are represented by the arrows,
where the extinction distance
~g’
under the dif-
fraction conditions of Laue symmetrical geometry, is described by [9] ~g= J’~CosGB/reXCF, (3) where ~ is the volume of the unit cell, ~ is the classical radius of the electron, A is the X-ray wavelength, C is the polarization factor, F is the structure factor and 9B is the Bragg angle. The structure factors F for the {1120} and {3300} reflections are calculated to be 59 and 135, the corresponding extinction for Ag Kct 1 radia—
tion, according to formula (3), are 88 and 40 jim, respectively. The measured extinction distance
382
Zhang Qiang ci at.
/ X-ray topographic
Table I Companson between calculated and measured image widths of pure screw and pure edge dislocations in different pnsm refleclions Reflection
1210 2110 1120 3300 0330 3030
observation of dislocation structure in sapphire
interior due to thermal stress [12], were held at both ends by an unspecified barrier which may he .
.
.
.
.
-
Width of dislocation (pm)
dislocatton tntersecttons or nodes, composite Jogs and pricipitates, etc. These pinned dislocations act as the dislocation multiplication course, such as
Measured
the well-known Frank—Read source [13]. This dis-
Calculated
~i~dg~
~creo
~
37 22 23 28 28 0
28 13 14 18 19 0
38 19 19 27 27 0
22 11 11 15 15 0
based on the position of the pendellosung fringes in the beveled edge of the wafer are about 97 and 46 jim for the (1120} and {3300} reflections, respectively, A comparison between the calculated and the measured image widths of the pure screw and the pure edge dislocations in different prism reflections is listed in table 1. The good correspondence between the values offers further experimental cvidence that these parallel groups of straight dislocation lines can_be considered to be pure edge type having (1120) type of total Burgers vector (~ b = a = 4.758 A).
location multiplication process is regenerative and rapidly proceeds in the action of symmetrical therma! stress. A series of characteristic hexagonal dislocation loops which tend to lie along sp~cific directions are formed [14]; then these dislocation loops continue to expand on their slip planes. break and finally form the three parallel groups of straight dislocation lines during the plastical deformation of the (0001)(1120) basal slip. Similar dislocation configuration appearing as pure edge type of straight dislocation lines and dipoles has been observed by transmission electron microscope in the (0001) sample of deformed sapphire single crystal, which was compressively loaded at elevated temperature [15]. Thus, from the following results concerning the distribution, configuralion and character of the dislocations in as-grown sapphire single crystals. it can be concluded that three parallel groups of straight dislocation lines originate from the dislocation multiplication by Frank—Red source and are_formed by the plastic deformation of (000i)(1120) basal slip during crystal cooling process due to symmetrical thermal
3.4. Formation of dislocation
stress.
In the TGT growth method, the crystal is subjected to a radially compressive stress located at the crystal periphery. This symmetrical thermal stress parallel to the growth interface is caused by the temperature difference between the crystal surface and the interior, and the crucible wall during crystal cooling. From the point of view of crystallography and crystal structure, the (0001) (1120) basal slip system has the lowest critical resolved shear stress (CRSS) in all the slip systems of the sapphire single crystal [10]. At high temperature (T> 1800°C). the basal slip system could be easily initiated by the thermal stress (CRSS < 100 kg/cm2) [11]. In the early stage of crystal cooling few dislocations, such as the grown-in dislocation originating from the seed crystal or the dislocation generated by nucleating in the crystal
To assess the effect of doping and growth orientation on the dislocation structure, sample 2* cut from 0.1 wt% Ti3 doped sapphire and sample 3* from the [1102] orientation grown sapphire single crystals were examined. Fig. 5 shows the topograph of sample 2* which displays the dislocation structure much similar to that shown in 6g. 1, the characteristic dislocation structure is not related to the dopant or impurity. Fig. 6 illustrates the topograph of sample 3* which displays the tangle dislocation structure consisting of dense clusters of highly curved dislocation lines. This dislocation structure is much similar to that reported by Caslavski and Gazzara [5]. The same results have been observed in other orientation grown sapphire single crystals. In this case, the thermal stress applied to the crystal can initiate not only the (0001 )(1120) basal slip, hut also the
Zhang Qiang et al.
/ X-ray topographic observation ofdislocation
________________ ______
______
___________________
-
________ _____
__2__. -
.
Fe. 5. I opograph of sample 2 * from a (1.1 n t~c Ui doped sapphire showing the similar dislocation structure: (0330) reflection and t = 312 pm.
(1102)(OiIl) pyramidal slip, although the_critical resolved shear stress (CRSS) for (1102)(0111) slip system is much higher than that for (000i)(112) slip system [16]. As the deformation proceeds, through cross-slip or climbing, the multiplicating dislocations originating from the Frank—Read source meet and interact, and a number of dislocation reaction nodes shown as in fig. 2 are formed. These dislocation nodes act as the obstacle to the multiplicating dislocations or slip dislocations and cause them to bent and form the tangle disloca-
-s
,
p 04’
.
383
tion structure. It is apparent that the characteristic triangular cross-grid dislocation structure is closely related to the growth orientation of the sapphire single crystals.
4. Conclusion
_______
‘is,
structure in sapphire
(/
I
,
Characteristic triangular cross-grid dislocation structure in [0001] orientation sapphire single crystal grow by TGT has been investigated by X-ray transmission topography. The results can be summanzed as follows: .
.
-
(1) The dislocations primarily appeanng as parallel groups of straight dislocation lines lie on the (0001) basal slip planes. They are all pure edge type of slip dislocation with the (1120) type of total Burgers vectors. These slip dislocation lines originate from the dislocation multiplication of the Frank—Read source and are formed by the plastical deformation of the (0001)(1120) basal slip due to symmetrical thermal stress set up in the sapphire during crystal cooling process. (2) The sapphire single crystals grown by TGT growth method have a high degree of perfection with lower densities of dislocations. At high ternperature the dislocations can move quite easily on their slip planes and form different dislocation configurations by interacting or climbing. A few dislocation reactions can be described by the equation: [1120] + [1210] + [2110] = 0. Such a reaction represents self-pinning of dislocations and influences the mobility of dislocations. (3) With the variation of the growth orientation, the dislocation structure changes greatly; a tangle dislocation structure consisting of dense clusters of dislocation lines appears. The characteristic dislocation structure is closely related to the growth orientation of the sapphire single crystal and is not connected with the doping or impurities.
Acknowledgements G
Fig 6. Topograph of sample 3* from a 111021 orientation grown sapphire showing the tangle dislocation structures; (3030) reflection and i = 198 pm.
The authors express their thanks to Qiang Zhenying and Hu Bing of our laboratory for valuable discussions on this investigation.
384
Zhang Qiang et at.
/
X-ray topographic observation of dislocation structure in sapphire
References [1] F. Schmid and C.P. Khattak. Laser Focus/Electron Optics 19 (9) (1983) 147. [2] Cui Fengzhu and Zhou Yongzhong, J. Chinese Silicate Soc. 8 (1980) 109. [3] Kh.S. Bagdasarov et al.. Soviet Phys-Cryst. 18 (1973) 242. [41M,V Klassen-Neklyudova Ct al.. Phys Status Solidi 39 (1970) 679. [5] J L Caslavsky and C.P. Gazzara, Phil. Mag. 26 (1972) 961. [6] ML. Kronberg. Acta Met. 5 (1957) 508. [7] R.F. Bell, J. Am. Ceram. Soc. 50 (1967) 591. [8] Xu Shunshen and Feng Duan, X-Ray Diffraction Topography (Science Press, Beijing, 1987) p 86.
[9] B.K. Tanner, X-Ray Diffraction Topography (Pergamon. Oxford, 1976) p. 118. [101 J.D. Snown and A.H. Hener, J. Am. Ceram. Soc. 56 (1973) 185. [11] K.C. Radford and P.L. Pratt, Proc. Brit. Ceram. Soc. 15 (1970) 185. [121 P. Penning, Philips Res. Rept. 12 (1958) 79. [131 H. Pernek. Introduction to Dislocations (Pergamon. Oxford, 1975) p. 183. [14] H. Pernek, Introduction to Dislocations (Pergamon. Oxford, 1975) p. 184. [15] B.J. Pletka and T.E. Mitchell. J. Am. Ceram. Soc. 57 (1974) 390. [16] W.D. Kingery, H.K. Bowen and D.R. Uhlmann, Introduction to Ceramics (Wiley. New York. 1976) p. 735.
377
X-ray topographic observation of dislocation structure in sapphire single crystal grown by temperature gradient technique Zhang Qiang, Deng Peizhen and Gan Fuxi Shanghai Institute of Optics and Fine Mechanics, Academia Sinica, P.O. Box 8216, Shanghai, People’s Rep. of China
Received 12 September 1989; manuscript received in final form 3 August 1990
The characteristic triangular cross-grid dislocation structure in sapphire single crystals grown in [0001] direction by temperature gradient technique (TGT) has been investigated by means of X-ray diffraction topography. Dislocations lie on (0001) basal planes and pnmarily appear as three parallel groups of straight dislocation lines. At high temperature these dislocation lines can move easily on the slip planes and form different dislocation configurations due to pinning, climbing and interacting. The analysis of Burgers vector and image width of dislocation lines confirmed that three parallel groups of straight dislocation lines are pure edge type having <1120) type Burgers vector, and a few dislocation reactions are of the type of [11201+[1210]+[2110] = 0. A simple model of basal slip of the type of (0001)<1120) is used to explain these dislocations.
I. Infroduction Sapphire single crystal is an important crystal material, used for a number of high technology applications. As an optical material, sapphire single crystal has wide transmission, spanning the ultra-violet, visible and infra-red bands. It has, therefore, been used as an optical window material. For this purpose large diameter, zero birefnngence and [0001] orientation sapphire single crystals have been grown by the heat exchanger method (HEM) [1] and the temperature gradient technique (TGT) [2]. Generally, it is difficult to grow sapphire single crystal along [0001] direction because this orientation was not preserved in the grown crystal [3], due to the weakening action of the main slip system [4]. Therefore, the dislocation structure in as-grown sapphire single crystals may be quite different from that in the other orientation grown crystals reported by Caslavsky and Gazzara [5]. The present paper reports the X-ray transmission topographic results of the dislocation distribution and behaviour, which clearly displayed the characteristic triangular cross-grid dislocation structure consisting of three parallel groups of 0022-0248/91/$03.50 © 1991
—
straight dislocation lines. The effect of doping and growth direction on the dislocation structure is also considered.
2. Experimental procedure In the present investigation, high quality sapphire single crystals, 56 mm in diameter, were grown in [00011 seeding direction by TGT [3]. Samples 1* and 2* were cut from sapphire and 0.1 wt% Ti3~doped sapphire single crystals respectively. For comparison purpose, sample 3* was cut from a [1102] orientation sapphire single crystal. All of the samples are (0001) wafers of thickness 1 mm. After lapping and polishing mechanically, the wafers were chemically polished and thinned in molten borax (950~10500C). At least 100 ~tm of the surface was removed to ensure that no surface effects would be recorded. The orientation of the wafers deviated I from the (0001) plane. The chemical etching was also carried out in molten borax (850—900°C)for about 15 mm. All of the topographs displayed here were ohtamed by X-ray transmission topographic method.
Elsevier Science Publishers B.V. (North-Holland)
0450
378
Zhang Qiang et a!.
/ X-ray
topographic observation ofdislocation structure in sapphire
The diffraction planes were {1120} and {3300} prism planes which are perpendicular to the (0001) basal plane. The Ag K~1X-ray diffraction image was recorded on an X-ray film with 1 jim emulsion particle size. The exposure time was 0.3—0.6 h/mm scan length. The indices used in this paper were based on the crystallographic hexagonal Xray unit cell with a 4.758 A and c 12.991 A [61. =
=
3. Results and discussion 3.1. Location of dislocation
Fig. 1 illustrates typical X-ray topographs which displayed the characteristic triangular cross-grid dislocation structure. Five pictures were taken from sample I * by successive rotations of 30° in the plane of the wafer and oriented with the [1100] vertical. The pronounced feature in the topographs is the appearance of three parallel groups of straight dislocation lines; three such systems marked I, II and III are 60°or 120° apart respeclively. The group I system runs along [1100], the group II dislocation system and group III run along [IO1OLand [0110], respectively. In the reflection of {1120}, three groups of dislocation lines appeared (figs. lb and ld) in which the group of dislocation lines perpendicular to the diffraction vector was generally darker in contrast and the image width of these dislocation lines was approximately twice that of other two groups. While in the reflection of {3300}, only two groups of dislocation lines which display the same contrast and the same image width of dislocation lines appeared (figs. la, ic and ie), the group of dislocation lines parallel to the diffraction vector vanished totally. The dependence of the contrast and the image width of the dislocation line on the diffraction vector implicated that three parallel groups of dislocation lines lay on the (0001) basal planes. Further experimental evidence for this dislocation distribution could be obtained by thinning the wafer again in molten borax for about 20 mm. The prolonged polishing has led to a slightly beveled edge of the wafer. Figs. if and ig show the
topographs. In comparison with figs. Ic and id, a lot of dislocation lines vanished together with removal of the surfaces, and the segments of dislocation lines near the margin, labelled A, B and C, disappeared due to the formation of the beveled edge. In addition, the fact of relatively few dislocation etch pits visible on the surfaces of the wafer in an optical microscope, which corresponds to the outcrops of dislocations, also confirmed that almost all of the dislocations lay on the (0001) basal planes. Also noticeable are the pendellosung fringes appearing as three dark fringes marked 1, 2 and 3 in fig. if, and one labeled 1 in fig. Ig at the beveled edge of the wafer, which indicate the high degree of the perfection of the sapphire single crystal investigated. Fig. 2 shows enlarged pictures of the area marked M in fig. 1 a; different dislocation configurations, such as 600 kinked dislocation lines E and D, edge type of dislocation dipole F, spinal dislocation turns G and H, and dislocation reaction nodes 0 and Q were clearly displayed. Some of these dislocations, i.e. the kinked dislocation ltne D, has undergone a slip movement along its Burgers vector direction due to the chemical stress during chemical polishing. Other dislocations, i.e. the spinal dislocation turn H, has undergone a climbing along the direction normal to (0001) basal plane. 3.2. Determinatton of Burgers vector
A useful feature of X-ray transmission topography is the readiness with which the Burgers vector of the dislocation can be determined. In case of low X-ray absorption, the direct image of dislocation is very dense and the quantity q b is a reasonable measure of its strength. According to the principle, the contrast of a given dislocation line is determined by the relative orientation of diffraction vector g, Burgers vector b, and dislocation line vector 1 [7]. Pure screw dislocation is invisible in the reflections for which the scalar product g~b 0. Pure edge dislocations only vanish in the reflections from the plane for which the scalar products g b 0 and g b x 1 0. A mixed dislocation does not vanish. In the present paper the vectors g and 1 are normal to [00011 direction (i.e. lie on the (0001) planes). hence the =
.
=
=
Zhang (jian,g ci al
A—rat tupographu obccrt anon of dubs ation ctruc turc in copplure
--
37q
~~1
~:
~.-
—
/
~‘j5 ~
-‘
.-.
-
,
r
‘
.
/ -
.~.:i
o
,
~~—2<-~ ~:ST’~-..” -
.~•
::-J
~-t-
-
.
-
____
Fig. I. Topograph of sample 1 * sho~ing the characteristic triangular cross—grid dislocation structure: (a). tht. (el. (dl and Ce) are iii the reflections (0330). (1120). (1010). (2110) and (3300). respectisels and t = 3l~pm: (f) and Ig) are in the reflections (33001 and (21101 and t 203 p.nt.
380
Zhang Qiang et al
/ X-ray
topographic observation of dislocation Structure in sapphire
I
__
,
~
64
(a)
~(c)
,,
“.~.
•.‘: ~
‘h
k
(i)
(d)
~
•
~
~
0
G
Fig. 2. Enlarged topographs of the area M in fig. I showing different dislocation configurations: D and F are 60° kinked dislocations, F is edge dislocation dipole, G and H are helical dislocation turns, and 0 and Q are dislocation reaction nodes; (a), (b). (c) and (d) are in the reflections (2110), (3030), (0330) and (3300).
Burgers vector of these dislocation lines can be determined unambiguously from the presence of contrast (g b = 1) or absence of contrast (g b = 0). Consider first the group I dislocation lines which progress vertically across the topographs; they display high contrast in (1120) reflection (fig. ib) and vanish in (3300) reflection (fig. le), and therefore the [1120] Burgers vector is justified. In the same manner, the dislocation groups II and III can be substantiated to have the [2110] and [1210] Burgers vectors respectively. Because the Burgers vector b is perpendicular to the dislocation line vector 1, these parallel groups of straight dislocation lines are all pure edge type having (1120) type Burgers vectors. The dislocation structure on .
the (0001) basal plane with the relevant dislocation identified is shown schematically in fig. 3. Examine next the dislocation lines labeled A, B and C in fig. 2. Three dislocation lines converged at the point 0 and displayed different contrast in different_reflections, the dislocation A which ran along [1210] showed strong contrast in (1i20} reflection and vanished totally in (3030) reflection. With conformity to g• b = 0, the Burgers vector for dislocation A is justified to be in [1120] direction. As the Burgers vector b is parallel to the dislocation line vector 1, dislocation A is a pure screw dislocation line. If the same criterion is applied to the dislocation lines B andC, because they are extinct in the (3030) and (3300) reflections respectively, the Burgers vectors for disloca-
Zhang Qiang et al
/ X-ray
1700
2710
1210
1070
1120
1f20
iii
a = [ imo i a = [7110]
ii
alTo 1
o=
7010
20j
11
7270
7110
tions B and C are determined to be parallel to the [2110] and [1120] directions respectively. Obviously, the point 0 has to be a singular dislocation reaction node where three dislocations, whose sum of Burgers vectors equals zero, meet and interaction terminates inside the crystal. The corresponding dislocation reaction is the type of [1120] + [1210] + [2110] = 0. Similarly, the point Q is also a dislocation reaction node with the same type of 1710
0_flu
1-1-00
~—_~
=
Talc
b=[1120 = [12101
1170
3.3. Image width of dislocation
Further experimental evidence for the character of these parallel groups of straight dislocation lines can be obtained from the image widths of dislocation lines in topographs. The present case, when a pure screw dislocation or a pure edge dislocation lies on the (0001) basal plane, is viewed in a reflection whose diffraction vector is perpendicular or at a certain angle to the Burgers vector of dislocation; the image width of dislocalion varies with the quantityg. b. The direct image width W~,for a pure screw dislocation, and ~We, for a pure edge dislocation, are given by the formulas [8] = ~g(g• b)/2~r, (1) (2)
W~=0.88~g(g.b)/ir, 0
2710
7110
1100
0170
dislocation reaction. A schematic representation of the dislocation reaction is shown in fig. 4. Careful examination of the topographs has revealed that nearly all of the dislocation configurations exhibit a similar behavior in contrast, they show the strong contrast and loss contrast in different reflections. Regardless of the dislocation character, the Burgers vectors of these dislocation configurations can be identified to be in the (1120) direction according to the invisibility rule g~b = 0. Hence it is highly probable that these different dislocation configurations originate from the parallel groups of straight dislocation lines by a series of dislocation movement.
noo Fig. 3. Schematic diagram of the characteristic triangular cross-grid dislocation structure. Three groups of dislocation lines, I, II and III, are properly oriented with respect to the (0001) stereographic projection; the Burgers vectors are represented by the arrows.
010
381
topographic observation of dislocation structure in sapphire
1270
Fig. 4. Schematic representation of the dislocation reaction, The dislocations are properly oriented with respect to the (0001) stereograph; the Burgers vectors are represented by the arrows,
where the extinction distance
~g’
under the dif-
fraction conditions of Laue symmetrical geometry, is described by [9] ~g= J’~CosGB/reXCF, (3) where ~ is the volume of the unit cell, ~ is the classical radius of the electron, A is the X-ray wavelength, C is the polarization factor, F is the structure factor and 9B is the Bragg angle. The structure factors F for the {1120} and {3300} reflections are calculated to be 59 and 135, the corresponding extinction for Ag Kct 1 radia—
tion, according to formula (3), are 88 and 40 jim, respectively. The measured extinction distance
382
Zhang Qiang ci at.
/ X-ray topographic
Table I Companson between calculated and measured image widths of pure screw and pure edge dislocations in different pnsm refleclions Reflection
1210 2110 1120 3300 0330 3030
observation of dislocation structure in sapphire
interior due to thermal stress [12], were held at both ends by an unspecified barrier which may he .
.
.
.
.
-
Width of dislocation (pm)
dislocatton tntersecttons or nodes, composite Jogs and pricipitates, etc. These pinned dislocations act as the dislocation multiplication course, such as
Measured
the well-known Frank—Read source [13]. This dis-
Calculated
~i~dg~
~creo
~
37 22 23 28 28 0
28 13 14 18 19 0
38 19 19 27 27 0
22 11 11 15 15 0
based on the position of the pendellosung fringes in the beveled edge of the wafer are about 97 and 46 jim for the (1120} and {3300} reflections, respectively, A comparison between the calculated and the measured image widths of the pure screw and the pure edge dislocations in different prism reflections is listed in table 1. The good correspondence between the values offers further experimental cvidence that these parallel groups of straight dislocation lines can_be considered to be pure edge type having (1120) type of total Burgers vector (~ b = a = 4.758 A).
location multiplication process is regenerative and rapidly proceeds in the action of symmetrical therma! stress. A series of characteristic hexagonal dislocation loops which tend to lie along sp~cific directions are formed [14]; then these dislocation loops continue to expand on their slip planes. break and finally form the three parallel groups of straight dislocation lines during the plastical deformation of the (0001)(1120) basal slip. Similar dislocation configuration appearing as pure edge type of straight dislocation lines and dipoles has been observed by transmission electron microscope in the (0001) sample of deformed sapphire single crystal, which was compressively loaded at elevated temperature [15]. Thus, from the following results concerning the distribution, configuralion and character of the dislocations in as-grown sapphire single crystals. it can be concluded that three parallel groups of straight dislocation lines originate from the dislocation multiplication by Frank—Red source and are_formed by the plastic deformation of (000i)(1120) basal slip during crystal cooling process due to symmetrical thermal
3.4. Formation of dislocation
stress.
In the TGT growth method, the crystal is subjected to a radially compressive stress located at the crystal periphery. This symmetrical thermal stress parallel to the growth interface is caused by the temperature difference between the crystal surface and the interior, and the crucible wall during crystal cooling. From the point of view of crystallography and crystal structure, the (0001) (1120) basal slip system has the lowest critical resolved shear stress (CRSS) in all the slip systems of the sapphire single crystal [10]. At high temperature (T> 1800°C). the basal slip system could be easily initiated by the thermal stress (CRSS < 100 kg/cm2) [11]. In the early stage of crystal cooling few dislocations, such as the grown-in dislocation originating from the seed crystal or the dislocation generated by nucleating in the crystal
To assess the effect of doping and growth orientation on the dislocation structure, sample 2* cut from 0.1 wt% Ti3 doped sapphire and sample 3* from the [1102] orientation grown sapphire single crystals were examined. Fig. 5 shows the topograph of sample 2* which displays the dislocation structure much similar to that shown in 6g. 1, the characteristic dislocation structure is not related to the dopant or impurity. Fig. 6 illustrates the topograph of sample 3* which displays the tangle dislocation structure consisting of dense clusters of highly curved dislocation lines. This dislocation structure is much similar to that reported by Caslavski and Gazzara [5]. The same results have been observed in other orientation grown sapphire single crystals. In this case, the thermal stress applied to the crystal can initiate not only the (0001 )(1120) basal slip, hut also the
Zhang Qiang et al.
/ X-ray topographic observation ofdislocation
________________ ______
______
___________________
-
________ _____
__2__. -
.
Fe. 5. I opograph of sample 2 * from a (1.1 n t~c Ui doped sapphire showing the similar dislocation structure: (0330) reflection and t = 312 pm.
(1102)(OiIl) pyramidal slip, although the_critical resolved shear stress (CRSS) for (1102)(0111) slip system is much higher than that for (000i)(112) slip system [16]. As the deformation proceeds, through cross-slip or climbing, the multiplicating dislocations originating from the Frank—Read source meet and interact, and a number of dislocation reaction nodes shown as in fig. 2 are formed. These dislocation nodes act as the obstacle to the multiplicating dislocations or slip dislocations and cause them to bent and form the tangle disloca-
-s
,
p 04’
.
383
tion structure. It is apparent that the characteristic triangular cross-grid dislocation structure is closely related to the growth orientation of the sapphire single crystals.
4. Conclusion
_______
‘is,
structure in sapphire
(/
I
,
Characteristic triangular cross-grid dislocation structure in [0001] orientation sapphire single crystal grow by TGT has been investigated by X-ray transmission topography. The results can be summanzed as follows: .
.
-
(1) The dislocations primarily appeanng as parallel groups of straight dislocation lines lie on the (0001) basal slip planes. They are all pure edge type of slip dislocation with the (1120) type of total Burgers vectors. These slip dislocation lines originate from the dislocation multiplication of the Frank—Read source and are formed by the plastical deformation of the (0001)(1120) basal slip due to symmetrical thermal stress set up in the sapphire during crystal cooling process. (2) The sapphire single crystals grown by TGT growth method have a high degree of perfection with lower densities of dislocations. At high ternperature the dislocations can move quite easily on their slip planes and form different dislocation configurations by interacting or climbing. A few dislocation reactions can be described by the equation: [1120] + [1210] + [2110] = 0. Such a reaction represents self-pinning of dislocations and influences the mobility of dislocations. (3) With the variation of the growth orientation, the dislocation structure changes greatly; a tangle dislocation structure consisting of dense clusters of dislocation lines appears. The characteristic dislocation structure is closely related to the growth orientation of the sapphire single crystal and is not connected with the doping or impurities.
Acknowledgements G
Fig 6. Topograph of sample 3* from a 111021 orientation grown sapphire showing the tangle dislocation structures; (3030) reflection and i = 198 pm.
The authors express their thanks to Qiang Zhenying and Hu Bing of our laboratory for valuable discussions on this investigation.
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X-ray topographic observation of dislocation structure in sapphire
References [1] F. Schmid and C.P. Khattak. Laser Focus/Electron Optics 19 (9) (1983) 147. [2] Cui Fengzhu and Zhou Yongzhong, J. Chinese Silicate Soc. 8 (1980) 109. [3] Kh.S. Bagdasarov et al.. Soviet Phys-Cryst. 18 (1973) 242. [41M,V Klassen-Neklyudova Ct al.. Phys Status Solidi 39 (1970) 679. [5] J L Caslavsky and C.P. Gazzara, Phil. Mag. 26 (1972) 961. [6] ML. Kronberg. Acta Met. 5 (1957) 508. [7] R.F. Bell, J. Am. Ceram. Soc. 50 (1967) 591. [8] Xu Shunshen and Feng Duan, X-Ray Diffraction Topography (Science Press, Beijing, 1987) p 86.
[9] B.K. Tanner, X-Ray Diffraction Topography (Pergamon. Oxford, 1976) p. 118. [101 J.D. Snown and A.H. Hener, J. Am. Ceram. Soc. 56 (1973) 185. [11] K.C. Radford and P.L. Pratt, Proc. Brit. Ceram. Soc. 15 (1970) 185. [121 P. Penning, Philips Res. Rept. 12 (1958) 79. [131 H. Pernek. Introduction to Dislocations (Pergamon. Oxford, 1975) p. 183. [14] H. Pernek, Introduction to Dislocations (Pergamon. Oxford, 1975) p. 184. [15] B.J. Pletka and T.E. Mitchell. J. Am. Ceram. Soc. 57 (1974) 390. [16] W.D. Kingery, H.K. Bowen and D.R. Uhlmann, Introduction to Ceramics (Wiley. New York. 1976) p. 735.