Study of strain variation in LEC-grown GaAs bulk crystals by synchrotron radiation X-ray topography

Applied Surface Science 50 (1991) 1-8 North-Holland

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Study of strain variation in LEC-grown GaAs bulk crystals by synchrotron radiation X-ray topography Junji M a t s u i Research and Development Group, NEC Corporation, 34 Miyukigaoka, Tsukuba 305, Japan Received 27 November 1990; accepted for publication 7 January 1991

Lattice distortions in LEC-grown semi-insulating GaAs bulk crystals are studied mainly by synchrotron X-ray topography. Besides the macroscopic lattice orientation and lattice parameter variations relating to the dislocation generation by thermal stress after growth, microscopic variation of the lattice parameter in a single cell is observed, which may be intrinsic due to some interaction of excess arsenic atoms with the entangled dislocations forming the cell walls.

1. Introduction

2. Experimental procedure

It has been generally agreed that the dislocation density in GaAs bulk crystals grown by the liquid encapsulated Czochralski (LEC) method affects the characteristics of FET's fabricated using a direct ion-implantation technique [1]. There have been many publications reporting dislocation features, such as slips and cellular structures, and also optical properties of the dislocations, e.g., photoluminescence and infrared absorption especially in terms of the so-called EL2 deep level in GaAs. Although lattice distortion (especially, lattice parameter variation) measurement is thought to be useful to evaluate the stoichiometry in the bulk crystal [1-16], there has been a lack of unique description with respect to its relationship with the dislocation distribution so far, since the bulk crystals include residual stresses which may have an influence on the lattice parameter being independent of the stoichiometry. This paper reviews our studies of the lattice distortion distribution in GaAs by means of precise X-ray topography, not only macroscopically in a whole wafer but also microscopically, even in a single cell.

(001)-oriented, undoped, LEC-grown GaAs wafers of 2 inches in diameter with different dislocation densities were investigated by X-ray topography [17-20]. Prior to the X-ray measurement, both surfaces of the cut wafers were mechanochemically polished. C u K a I X-rays from a rotating anode were used for ( + , - ) doublecrystal reflection topography. For a more precise measurement of the intensity distribution, we used a monochromatized X-ray beam (~ = 0.7 ,~) from the 2.5 GeV storage ring of the Photon Factory at Tsukuba. In the latter case, the Bragg condition is only satisfied at a narrow line-shaped part on the specimen, as an iso-Bragg contour, because of the highly parallel incident X-ray beam which can be regarded as a plane wave [21]. A series of topographs was taken successively by rotating the specimen wafer with an angular step of 10 seconds of arc around the axis normal to the X-rays and lying in the wafer surface. After that, the wafer was rotated by 180 ° about the normal to the (001) surface, and then, another series of topographs was taken in the same way. In

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J. Matsui / Strain variation in LEC-grown GaAs bulk crystals a

a

Fig. 1. Crystal arrangement for angle-resolved plane-wave X-ray topography. Crystals used in the present case are: (A) (111) Si giving a 111 reflection as a monochromator; (B), (C) (111) Si, 553 reflection, as collimators; (D) (001) GaAs sample, 008 reflection; (E) (553) Si, 553 reflection as an analyzer.

either case, a superimposed pattern was obtained by putting another plate simultaneously in the plate holder. Based on those two superimposed patterns, it is possible to separate the lattice parameter variation from the lattice inclination quantitatively [22]. To image directly the distribution of the lattice parameter change, equi-lattice-parameter mapping topography was performed [23]. The diffraction geometry employs a ( + , - , + ) triple-crystal system, the first being a collimator (noted as C in fig. 1), the second a specimen (D in fig. 1) and the third an analyzer crystal (E in fig. 1). The system is useful for studying the topology of reciprocallattice points [24-26].

b I

D

3. Results and discussion

3.1. Macroscopic lattice distortion Dislocation distributions of the <001)-pulled LEC-grown GaAs bulk crystals usually exhibited typical four-fold symmetry [27] with a high concentration in the regions near the periphery and around the pulling axis, as shown in fig. 2a, which was taken by the anomalous transmission technique with M o K a x radiation. Fig. 2b shows a superimposed pattern of the plane-wave topographs taken at each angular position of the sample around the vertical axis lying in the plane of the paper for the same specimen as in fig. 2a. The crystal arrangement consists of (111) Si giving a 553 asymmetric reflection as a collimator and (001) GaAs sample giving a 008 symmetric reflection, since the lattice spacings for Si(553) and GaAs(008) are very close to each other. We can

C

C ~

.......................

~,,C' I

! ! 1 I

Fig. 2. (a) Anomalous transmission topograph with M o K a : radiation, 220 reflection and (b) the superimposed iso-Bragg contour map taken for (001) undoped LEC-grown high-dislocation-density GaAs of 2 inches in diameter with use of the synchrotron X-rays and the ( + , - ) crystal arrangement consisting of (111) Si giving a 553 asymmetric reflection as a collimator and (001) GaAs sample giving a 008 symmetric reflection. The angular step is 10 seconds of arc. (c) The sectional scheme of the lattice inclination (indicated by sofid lines) along the lines A - A ' , B - B ' , C - C ' and D - D ' in (b).

J. Matsui

/ Strain variation in LEC-grown GaAs bulk crystals

Fig. 3. Enlarged double-crystal reflection topographs of a part including a few ceils, being taken with the angular separation of three seconds of arc.

calculate the distribution of the lattice inclination and the lattice parameter with a combination of fig. 2b and another superimposed pattern taken after a 180 ° rotation around [001]. It was found that those iso-Bragg contours were mainly due to lattice inclination. In fig. 2c, the lattice inclination features along the horizontal lines, such as A - A ' , B - B ' , C - C ' and D - D ' , on the wafer surface are shown schematically. At the lineages along the (110~ diameters which are easily seen in fig. 2a, the lattice planes are abruptly tilted, as for line B - B ' in fig. 2c, by a maximum value of 40 seconds of arc [28]. Besides the macroscopic lattice inclination variation shown in fig. 2c, a small lattice tilt of less than a few seconds of arc was also observed at the cell walls, as shown in figs. 3a and 3b, which are topographs taken at different angles by three seconds of arc. Thus, the lattice orientation variation along the lines in fig. 2c is a connection of small segments of the lattice plane, inclined from each

cell wall.~

r

/--- GaAs wafer surface ,I ~ ~y/", )'~ i if' i i i J i !

'

' 1

cell interior

other between the neighboring cells, as shown schematically in fig. 4. In In-doped GaAs where the dislocation density has been much reduced [29], the lattice inclination feature is slightly different from that including the cell structures. Slip dislocations are generated in the vicinity of the wafer edge, where the screw dislocation components lie in a row,

~ l

,

s s

lattice plane

,

, ,¢

i

s i

r i[ I

i

, r

¢

i ~

,

lineage

Fig. 4. Schematic drawing of the wafer section showing local lattice inclinations at the cell walls.

Fig. 5. Superimposed iso-Braggcontour map for (001) In-doped LEC-grown low-dislocation-densityGaAs of 2 inches in diameter taken in a similar way to the case of fig. 2b.

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J. Matsui / Strain oariation in LEC-grown GaAs bulk crystals

Fig. 6. Equi-lattice-parameter (a(001)) mapping topographs for (001) undoped LEC-grown high-dislocation-density GaAs with use of the synchrotron X-rays and the ( + , - ) crystal arrangement consisting of Si giving a 553 asymmetric reflection as a collimator and (001) GaAs sample giving a 008 symmetric reflection and (553) Si giving a 553 symmetric reflection as an analyzer. The difference of the analyzer angle positions between fig. 6a and 6b is 3 seconds of arc.

giving rise to a very local lattice tilt [30]. An iso-Bragg contour map reflecting mostly equi-inclination of the lattice planes is also shown in fig. 5 for a low-dislocation-density wafer. Those local lattice tilts form an approximate eight-fold-symmetric pattern of iso-Bragg contours, regardless of In dope or non-dope as long as the crystals have a low dislocation density (less than 3 × 103 cm-3). Kitano et al. have demonstrated that dislocation generation is preferable at the eight-fold strain fields between {110} and {100} radii of the (001}-pulled crystal [20]. In order to obtain more direct information on the lattice parameter (a(001}) distribution in a single (001) wafer, irrespective of the lattice inclination, equi-lattice-parameter mapping topographs were taken by the triple-crystal arrangement with the third analyzer crystal [31]. Figs. 6a and 6b show the two topographs of a semicircular wafer which have been taken by rocking the sample crystal around the Bragg-peak position at several fixed angles of the analyzer. The difference of the analyzer angle positions between fig. 6a and

fig. 6b is 3 seconds of arc. The diffraction condition for the analyzer crystal is satisfied at the peripheral part in fig. 6a or at the central part in fig. 6b. Thus, it has been clarified that the lattice parameter a(001) at the peripheral part is larger than that at the central part by Ad/d-~ 1 x 10 -s. Okada and Orito also reported larger lattice parameters a(001} in the peripheral region of a (001) GaAs wafer by means of the Bond method [16]. On the other hand, for a (100) slice cut parallel to the pulling axis, they observed relatively small lattice parameters ao00> in the vicinity of the ingot circumference. It should be noted that the lattice parameters ad0o) measured in this way are those along the tangential direction of the ingot. This suggests that the unit cell around the ingot periphery expands in the pulling direction and shrinks in the plane normal to the pulling axis. It was also recognized that the lattice parameter a(001> became uniform within a very small variation (less than 1.5 x ]0 -6) after cutting the specimen into pieces of 10 x 10 mm 2 in size. These facts imply that the lattice parameter variation is caused by some elastic deformation after growth, rather than local changes of the stoichiometry. Fig. 7 shows a possible explanation for the elastic deformation of the (001) wafer. First of all, a

b

c

ingot

tensile stress

i

slip generallon

j

~

~=2tzz

cell formation

~

lattice plane

Fig. 7. Possible procedures of the lattice inclination (below) for the (001)-pulled GaAs ingot: (a) tensile stresses are exerted along the circumference of the ingot during cooling after growth being followed by (b) the generation of slip dislocations (in the In-dope case), or by (c) the formation of lineages and cellular structures (in the non-dope case).

J. Matsui / Strain variation in LEC-grown GaAs bulk crystals

top view 1

iI

11 k

J

J

s"

[~ [~

sectional .view.

b

-.

1

/

,

•

3

Fig. 8. Schematic drawings of the elastic deformation of the crystal in (b) the ingot, (c) the wafer cut out from the ingot and (d) the divided semicircular wafer. Circumference shrinks in this model as labeled 1-3 in (a) after each process.

a tensile stress is exerted on the crystal along the tangential direction, due to a radial thermal gradient (fig. 7a). This may cause generation of slip dislocations from the ingot edge as shown schematically in fig. 7b. The thermal stresses are partially relaxed by the dislocation generation, but not fully relaxed during usual cooling. An average length of the ingot circumference m a y shrink by slip dislocation generation (in the In-doping case) and also by the formation of cells as shown in figs. 4 and 7c (in the non-doping case). After cutting the wafers from the ingot, there are free surfaces on both sides, as shown schematically in fig. 8. Consequently, if the residual in-plane stress is tensile, especially at the peripheral part of the wafer, it is easy for the wafer to deform elastically in such a way that the unit cell would expand in the direction normal to the wafer surface, as shown in figs. 8a and 8c (labeled 2). The unit cell deformation may be more significant at the peripheral part than at half-radii parts of the wafer, permitting larger lattice parameters a(ool ) in the pulling direction at the peripheral part of the wafer. The relatively smaller lattice parameters a, as observed b y O k a d a and Orito [16], in the tangential direction normal to the slice surface are consistent with the present idea. In figs. 6a and 6b which are the topographs of the semicircular wafer, it is noted that larger lattice parameters a<001> are observed not only at the

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peripheral region but also in the vicinity of the straight cut line. This could be explained as in fig. 8d, that is, by cutting the circular wafer into two halves, a new tensile stress arises along the cut line due to the already existing tensile stress along the wafer periphery. Thus, the circumference of the semicircular wafer shrinks again in a similar way to that stated previously, giving rise to another wafer deformation as shown in figs. 8a and 8d (labeled 3). 3.2. M i c r o s c o p i c lattice distortion

In spite of the advantage in using the analyzer crystal as stated above, it still seems difficult to image equi-lattice-parameter maps for small areas including several cell structures of a few hundred /~m in size, since the image contrast thus obtained is determined not solely by the Bragg condition but also by the intensity priority between dynamical and kinematical diffraction effects at each position [31]. The former effect expands isotropically in a reciprocal lattice space to a large distance from the reflection point when the crystal quality is poor (e.g., with a high dislocation density), while the latter one expands anisotropically (almost unidirectionally in the diffraction vector direction) when the crystal is ideally perfect [26].

ko,,/'N~ ',"..

,'% ,l kh~'

=

,~

q× Fig. 9. Diffraction geometry of the angle-resolved plane-wave X-ray topography in the reciprocal lattice space, k 0 and k h are incidence and diffraction vectors, respectively.Deviation of the scattering vector h = k h - k o is expressed in the (qx, qy) coordinates.

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J. Matsui / Strain variation in LEC-grown GaAs bulk crystals

At the cell walls, where the crystal perfection is inferior because of the entangled dislocations, the kinematical effect on the integrated intensity obtained during rocking the sample is stronger than the dynamical one and vice versa inside the cell, where the crystal is nearly perfect. This is why the black-and-white contrasts on a equi-lattice-param-

8 =

eter map image should be checked carefully for the crystal including both the perfect and imperfect regions. In order to overcome this difficulty, the topographic images were angularly analyzed by varying the angular position of the analyzer crystal in the triple-crystal arrangement shown in fig. 1. The

/9=

°'~i

i !i

7!¸

:

Fig. 10. Two series of the angle-resolved plane-wave X-ray topographs taken at different deviation angles fl of the analyzer for the two fixed deviation 2 angles a = - 0 . 5 second of arc (left) and ct = 0.5 second of arc (right) of the sample. Note that the black (diffraction enhancement) and white contrasts appear in a different way at a certain angle of a between the cell walls and the cell interior.

J. Matsui / Strain variation in LEC-grown GaAs bulk crystals

crystal arrangement consists of (111) Si giving a 553 asymmetric reflection as a collimator, (001) GaAs sample giving a 008 symmetric reflection and (553) Si giving a 553 symmetric reflection (the lattice spacings for Si(553) and GaAs(008) have similar Bragg angles). This scheme is called angleresolved plane-wave X-ray topography [32]. A series of topographs is taken at each deviation angle a of the sample crystal from the Bragg condition, by stepwise rotation of the analyzer crystal with various deviation angles fl from the Bragg condition. Fig. 9 shows a diffraction geometry in the reciprocal lattice space for the present measurement. With careful inspection of those topographs taken in the (a, r ) matrix (being related to (qx, qy) in the reciprocal lattice space coordinates as qx = fl cos 0 J h and qy = ( 2 a fl)sin 0B/h), microscopic lattice strain around the cell walls as well as in the inner region of the cell is separated in the reciprocal lattice space into two factors; lattice parameter variation and lattice inclination variation [33]. The lattice inclination in this case is quoted as a projected angle in the plane of fig. 9. Fig. 10 shows, for example, two series of angle-resolved topographs which are taken at a = - 0 . 5 and 0.5 second of arc. In almost dislocation-free cell interior regions (like B in the drawing), black contrast (diffraction enhancement) is observed near the Bragg condition. By inspecting black-and-white contrasts observed in the series of topographs taken at different a and/3 and also by mapping the intensity in the (qx, qy) coordinates, it can be estimated how the lattice parameter a<0m> varies in the wafer. Although the detailed analysis procedure will be given in a separate paper [33], it is determined that the lattice parameter a<0ol> near the cell walls is smaller than the average value by about 3 x 10 - 6 and that in regions away from the cell walls it is larger than the average value by 1 × 10 6. Thus, the lattice parameter variation usually depends on the dislocation features. Otoki et al. reported interesting results that infrared scattering images from arsenic precipitates in the dislocation-free cell interiigr region appeared after low-temperature annealing as misty zones of scattering and that some denuded zones

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of the misty scatter were observed near the cell wall [34]. They concluded that the misty scatter in the cell interior region is due to the condensation of excess arsenic atoms over the limit of saturation solubility. It is understood that the large lattice parameter a<0m> in the dislocation-free cell interior region is related to the existence of the dissolved excess arsenic atoms. Meanwhile, the entangled dislocation at the cell wall is thought to act as a sink for the excess arsenic atoms, giving smaller lattice parameters a<0m> there. Interaction of the excess atoms with the dislocations might be followed by formation of the denuded zone and dislocation climb [35].

4. Conclusion It was studied by means of synchrotron X-ray topography that macroscopic lattice distortion in LEC-grown semi-insulating GaAs crystals is contributed mainly by lattice inclination. The elastic expansion of the lattice along the pulling axis is observed in the peripheral region, which may be caused by thermal stress after growth and slip dislocation generation. By cutting the ingot into wafers, the additional deformation occurs by residual stress. Consequently, measurement of the lattice parameter for studying stoichiometry should be carefully carried out by taking the elastic deformation of lattice into account. Besides the macroscopic deformation, intrinsic lattice parameter variation, even in a single cell, is observed probably due to some interaction of excess arsenic atoms with the entangled dislocations at the cell wall.

Acknowledgements The author would like to thank his colleagues, Dr. T. Kitano in N E C Corporation and Professor T. Ishikawa in Tokyo University for their contribution to the studies presented in this review paper. He also expresses his acknowledgement to many workers in N E C Corporation and the P h o ton Factory for their discussion and assistance.

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J. Matsui / Strain variation in LEC-grown GaAs bulk crystals

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