Lattice spacings of LEC-grown and MLEC-grown GaAs crystals

600

Journal of Crystal Growth 100 (1990) 600—604 North-Holland

LATTICE SPACINGS OF LEC-GROWN AND MLEC-GROWN GaAs CRYSTALS S. YASUAMI and K. USUDA Research and Development Center, Toshiba Corporation, 1, Komukai, Toshiba-cho, Saiwai-ku, Kawasaki 210, Japan

Y. HIGASHI Applied Sciences, National Laboratory for High Energy Physics, i-i, Oho, Tsukuba 305, Japan

and H. KAWATA and M. ANDO Photon Factory, National Laboratory for High Energy Physics, 1-1, Oho, Tsukuha 305, Japan Received 26 August 1989

Lattice spacings (d) were measured with an accuracy of 5.9 X 10—6 in terms of zld/d, using a diffractometer with a Si monolithic 2 order of dislocation density, the lattice spacing varied in the iO~ order of monochromator. For crystals with 10~—10~ cm magnitude. This variation was attributed to the residual strains in the crystals. There was no definite evidence to prove that lattice spacings depend either on initial melt compositions or on dislocation density.

1. Introduction Lattice spacing is a possible measure for the nondestructive detection of composition shifts from stoichiometry in compound crystals. Absolute measurements on GaAs have been carried out [1—4]by the Bond method [5],while a relative measurement was accomplished by Takano et al. [6] with some modifications to the Bond method, both using conventional X-ray sources. However, the composition dependence of the lattice spacings resulting from undoped liquid encapsulated Czochralski (LEC)-grown and magnetic field applied LEC (MLEC)-grown crystals is inconsistent among these data. The lattice spacing is reported by Nakajima et al. [2] and Takano et al. [6] to increase as the initial melt composition becomes As-rich, whereas the result reported by Kuwamoto and Holmes [3] is entirely the opposite. Furthermore, Okada et al. [4] reported that the lattice spacings exhibited no appreciable cornposition dependence. 0022-0248/90/$03.50 © Elsevier Science Publishers B.V. (North-Holland)

Reviewing these studies suggests that there are two principal issues to be taken into consideration: various strains distorting crystal lattices and the precision with which the lattice spacings are measured. First, crystals grown by the LEC or MLEC method contain a number of dislocations and thermally induced elastic strains, in addition to an assumed-to-be weak strain due to point defects caused by composition shift from stoichiometry. For extracting the composition dependence of the lattice spacings, every aspect of the lattice distortion should be examined. However, it is unrealistic to segregate the effects by the respective strains for an actual crystal. Therefore, a variety of crystals were used for statistically extracting meaningful results in this study. Second, a lattice spacing(d) has to be measured with at least 106 order precision in terms of ~d/d, since the various strains described before seem to be in this order. A lattice spacing is simply determined from the Bragg relation

S. Yasuami et a!.

/ Lattice spacings of LEC-grown

2d sin °B X, where ~I3 is the Bragg angle and A the wavelength of the incident X-rays. Accordingly, its variation follows d/d A/A L1O cot 9J3. The precision of the lattice spacings is thus limited by the angular divergence zlO and wavelength dispersion z~Aof the incident X-ray beam. The values achieved by the Bond method are iO~ rad and iO~ A, respectively. For the further improvement in both factors, the (+, +) alignment should be employed for monochromators. One of the difficulties involved in implementing this lay-out is that wavelengths available with significant intensity are limited to those with characteristic lines; when another difficulty is an extreme decrease in the X-ray intensity incident on samples, even then a conventional X-ray source is used. In this study, these problems were solved by constructing a diffractometer using synchrotron X-radiation at the Photon Factory, National Laboratory for High Energy Physics. This diffractometer enables one to determine lattice spacings with precision of zX d/d ~o 6 [7]. =

~

—

=

~

—

—

—

2. Experimental 2.1. Diffractometer

601

and MLEC-grown GaAs crystals

the horizontal plane. The diffractometer was installed in a room in which temperature fluctuation was kept within 0.1°C during one measurement for one sample. Each crystal was mounted on a goniometer, Huber 410 for the 1st and 2nd, and Huber 420 for the 3rd. These goniometers were driven by pulse motors with a minimum angular step of iO~ deg, whose angular positions were monitored by rotary encoders which read i0~ deg for the 2nd and 3rd crystals (Heidenhain ROD 800), while it read 10 arc sec for the 1st one (Nikon RMH-100). White X-rays radiated from the storage ring are led to a (111) channel-cut Si crystal. This crystal extracts a certain width of energy band around the wavelength to be used for the lattice spacing measurement, and then eliminates the lower energy part of the spectrum, which is detrimental for the following monochromator. The second Si crystal is a monolithic monochromator [7], designed for complying with the requirement for precision in the lattice spacing, already described in the previous section. This monochromator provides a couple of net planes, (335) and (535), composing a (+, +) arrangement. An X-ray beam consecutively reflected by these net-planes should have a wavelength centered on 1.3536 A. The angular divergence and wavelength dispersion, calculated assuming the gaussian profile for both rocking curves, are zXO 3.2 X 10~rad and AX/A 1.7 x 106, respectively. To calibrate the wavelength, the 444 reflection was taken for a reference Si crystal in the place of samples (the 3rd crystal), regarding its lattice spacing being 5.4310652 A, the value derived by =

Fig. 1 illustrates a plan view of the present experimental set-up. X-ray beams run through in

l8O°~2~

=

Deslattes and Henins [8]. The achieved precision in ~A/X is better than 5.5 x 106. Hence the racy better than 5.9 x 2

Fig. 1. Experimental set-up for lattice spacing measurement, SR: storage ring; C: (111) channel-cut Si crystal (1st crystal); M: (335-535) monolithic Si monochromator (2nd crystal); S: sample (3rd crystal); Sc 1, ~2 scintillation counters; S1—S3: slits,

106

in terms of z.~d/dfor

the 800spacing lattice reflection should of GaAs~samples. be determined with an accu2.2. Samples Undoped GaAs crystals were pulled in the [100] direction from melts with varied compositions by the LEC and MLEC methods. From head, middle and tail parts of each crystal, (100) oriented wafers were fabricated perpendicular to the pulling direc-

602

S. Yasuami et a!.

/ Lattice spacings of LEC-grown and MLEC-grown

tion. In fig. 2, the wafers obtained from the head, middle and tail parts of 9 crystals were used, whereas those obtained from the head parts were used in figs. 3, 4 and 5. These wafers were diced into samples measuring 7.5 by 7.5 mm to minimize residual grown-in elastic strain within the wafers. The etch-pit (dislocation) density (EPD) was measured over a 1 x 1 mm2 area at the sample center. 2.3. Data acquisition

For each sample, the lattice spacing was measured for the 1 X 1 mm2 area at the sample center. The entire procedure for the data collection was monitored with a computer, which drives pulse motors for the goniometers, records actual angular positions read by the encoders, counts X-ray intensities, and saves these data in its memory. To derive the Bragg angles ~ the peak positions for the rocking curves were obtained through curve fitting procedures, assuming that the ideal rocking curve has the Cauchy distribution profile. After that, correction for the refraction effect was made, the Lorentz-polarization effect being safely neglected in this study. Finally, all the lattice spacings thus obtained were normalized to their values at 298 K, using a linear thermal expansion coefficient of 5.8 X iO~ K” at 298 K [4].

3. Results and discussion

565380

565375

565370

04

06

0.8 0 L21.4 EPD (XJOScm2)

[6

Fig. 2. A plot ofinch lattice spacing versus etch pit density for 3 diameter MLEC crystals

However, lattice spacings occasionally exhibit a seeming correlation with dislocation density. Such an example is shown in fig. 3: the lattice parameter and EPD distribution across a diameter of the wafer which exhibited the largest lattice spacing variation over the three samples at the wafer center among the wafers examined in fig. 2, being mdicated by an arrow in fig. 2. The lattice spacing varies by much the same amount for even lower variations in the dislocation density than in fig. 2. However, this in-wafer variation in the lattice spacings, 1.5 x io~A, is less than 2.3 X iO~ A as observed by Stoakes et al. [9], probably because the grown-in strain is partially relieved by dicing the wafer into pieces [10]. The (100) lattice spacing expands, where the dislocation density is low, and vice versa, for this wafer. If such is always the case, fig. 2 would also show a gradual decrease in the lattice spacing as

3.1. Dislocation and residual strain effects on the lattice spacing

Fig. 2 shows lattice spacings plotted against EPDs, obtained for 9 crystals (3 inch diameter) grown with an MLEC puller. Each lattice spacing value was averaged over those obtained from three samples at the wafer center, while the etch pits were counted for the sample at the wafer center. The data points lie in a band with zXd= 1.5 x i0~ A width, as indicated, without having any appreciable functional variation within it. This result proves that no direct effects exist for dislocations with density 0.5 through 1.5 X io~cm2 to vary the lattice spacing.

GaAs crystals

~65380

°.~ 0’

o a

(.5 I

-

S

0

5.65375

0

a5.65370

05 -4

-3

-2

-I

0

I

2

3

4

(Center) Position (IS mm Pitch)

Fig. 3. Across-the-diameter distribution of lattice spacings (•) and EPDs (x) for the same wafer used for obtaining the data indicated by an arrow in fig. 2. This wafer exhibited maximum lattice spacing variation among the wafers examined in fig. 2.

S. Yasuami eta!. ~65380

~

/ Lattice spacings of LEC-grown

—

A S

a

603

The dislocation density is incidentally lower in the crystal denoted by B: the higher the dislocation density, the larger the lattice spacing. This lattice spacing tendency toward dependence on

I I

and MLEC-grown GaAs crystals

sB 5.65375-

in

565370

—~

I I

050

052

0.51

Arsenic-Atom Fraction in Row Material )At%)

Fig. 4. Lattice spacing vanation obtained for 3 inch diameter MLEC crystals, grown from varied raw material compositions. B was grown under different magnetic field strengths than A.

dislocation density is just the opposite to that observed in fig. 3. Hence, the conclusion is drawn that the strain field varies either relevantly or irrelevantly to dislocation density as a result of stress relaxation. This situation seems likely to develop the misunderstanding that lattice spacing would be a funclion of the dislocation density, whichever case was taken.

the dislocation density increases. This in-wafer variation in the lattice spacing is hence hardly considered really associated with the strain accompanying dislocation itself. It seems more likely that the lattice spacing is affected by another kind of strain, if this lattice spacing variation is meaningful at all. It is possible that grown-in thermal strain is still left in a crystal after it has been partly relieved by introducing dislocations, Fig. 4 shows another example implying that residual strain might be the dominant cause of lattice spacing variations in a crystal. Although the composition shift seems to vary the lattice spacing slightly, magnetic field strength, which relates to temperature fluctuation at the liquid— solid interface, is much more influential (compare A and B). The different growth conditions should correspond to the different strain field created in the crystal. 5.65380-~ I

S

I

I

•

~

5

0

U

5.65375 OA Category

0 -J

SB Category 5.65370

~

047 048 0.49 050 051 052 053

Arsenic—Atom Fraction in Initial Melt lAt%l

Fig. 5. Lattice parameter variation obtained for 2 inch diameter LEC crystals, grown from various initial melt compositions. (0) A and (S) B category crystals were grown with different LEC and MLEC pullers at different institutes, respectively,

3.2. Effect of initial melt composition on lattice spacing

Fig. 5 shows variations in the lattice spacings for 2 inch diameter crystals grown from initial melts with varied compositions. The crystals in the A category were grown with the usual LEC puller, while those in the B category were grown with another MLEC puller in a different institute. The lattice spacing variations are in obvious contrast with each other. For the A category crystals, the lattice spacing increases as the initial melt cornposition becomes more As-rich, whereas, in the B category crystals, the lattice spacing seems almost irrelevant to the initial melt composition, except being somewhat lower for the stoichiometric melt. In fig. 4, already shown in the previous section, however, the lattice spacing exhibited a slight increase as the As fraction in the melt increases. Dislocation density coincidentally increases as the initial melt composition becomes more As-rich in the A category crystals, while it remains on the same level in the B category crystals. There are two possibilities to ascribe these lattice spacing variations to the composition shifts in the initial melts. In the first case, the crystal composition may vary distinctively in the three sets of crystals, despite the shifts in the composition of the initial melts in the same manner. Second, composition-dependent point defects, such as VA5 As, or Ga,, discussed by Stoakes et al. [9], may generate differently for the three sets, because of different thermal histories that these crystals underwent.

604

S. Yasuami eta!.

/ Lattice spacings of LEC-grown

However, if the result obtained in the previous section is additionally taken into account, it is more reasonable to ascribe most of this difference in the seeming dependence of the lattice spacing on the initial melt composition to the different behavior of the residual strain. Such seems to be the case also for another Ill—V material, GaN, although lattice spacing measurements were made on epitaxial films. Data obtained from different measurements on different samples which are nominally of the same composition, scatter significantly [11]. Seifert et al. concluded that reasons other than composition-related microdefects are responsible for this, on the basis of the lattice spacing dependence on growth rate but not on growth temperature. Attention to crystallographic imperfections was suggested [12]. For obtaining the authentic composition effect on lattice spacings, it might be required to obtain crystals with extremely low dislocation density and with low residual strain. However, even if crystals meeting these requirements were realized, the question would still remain as to whether the composition in the crystals really varies depending on that in initial melts. Circumstantial evidence, such as crystal appearance, suggests that crystal composition varies somehow when initial melt composition varies. Nevertheless, few means are available of substantially proving the existence of composition shift in the crystals to date.

4. Conclusion For LEC- and MLEC-grown GaAs crystals, the lattice spacing variations due to residual strain were revealed to be in the order of 106 in terms of ~d/d. No definite dependences of lattice spacings on initial melt composition were found. The composition-dependent variations in the lattice spacing are hence expected to be in the order of 106 at most, if any. Thus, it is concluded that lattice spacing variations in the order of iO~due

and MLEC-grown GaAs crystals

to composition shifts in initial melts, so far reported, are possibly due to differences in residual strain in crystals.

Acknowledgements The authors wish to express their gratitude to Mr. T. Fujii and Dr. Terashima for supplying crystals. They also thank Dr. M. Nakajima, Matsushita Electric Industrial Co., Ltd., for valuable discussions and Dr. K. Ishida, NEC Corporation, and Dr. Y. Okada, Electrotechnical Laboratory, for useful information. Finally, they would like to thank Dr. A. Hojo for continual encouragement.

References [1] A.F.W. Willoughby, C.M.H. Driscoll and BA. Bellamy, J. Mater. Sci. 6 (1971) 1389.

[21Appl. M. Nakajima, T. Sato, T. Inada, T. Fukuda Phys. Letters 49 (1986) 1251.

and K. Ishida,

[3] H. Kuwamoto and D.E. Holmes, J. Appi. Phys. 59 (1986) 656.

[4] Y. Okada, Y. Tokumaru and Y. Kadota, Appl. Phys. Letters 48 (1986) 975. [5] W.L. Bond, Acta Cryst. 13 (1960) 814. [6] Y. Takano, T. Ishiba, N. Matsunaga and N. Hashimoto,

Japan. J. Appi. Phys. 24 (1985) L239. Ando, Y. Higashi, K. Usuda, S. Yasuami and H. Kawata, Rev. Sci. Instr. 60 (1989) 2410. [8] RD. Deslattes and A. Henins, Phys. Rev. Letters 31

[71M.

(1973) 972. [9] R.C. Stoakes, A.F.W. Willoughby and I.R. Grant, in:

Semi-Insulating Ill—V Materials, Eds. H. Kukimoto and S. Miya.zawa (Ohmsha, Tokyo, 1986) p. 231. [10] Y. Okada and Y. Tokumaru, in: Semi-Insulating Ill—V Matenals, Eds. H. Kukimoto and S. Miyazawa (Ohmsha, Tokyo, 1986) p. 175.

[11] 0. Lagerstedt and B. Monemar, Phys. Rev. 19 (1979) 3064. [12] W. Seifert, H.-G. Bruehl and G. Fitzl, Phys. Status Solidi (a) 61(1980) 493.