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Perfection and laser performances of Nd: YAG crystals grown by Temperature Gradient Technique (TGT)
276
Journal of Crystal Growth 92 (1988) 276—286 North-Holland, Amsterdam
PERFECTION AND LASER PERFORMANCES OF Nd:YAG CRYSTALS GROWN BY TEMPERATURE GRADIENT TECHNIQUE (TGT) DENG Peizhen, QIAO Jingwen, HU Bing, ZHOU Yongzong and ZHANG Meithen Shanghai Institute of Optics and Fine Mechanics, Academia Sinica, P.O. Box 8211, Shanghai, People’s Rep. of China Received 27 September 1987; manuscript received in final form 15 June 1988
The formation and development of defects in the Nd: YAG crystal grown by the temperature gradient technique (TGY) have been systematically studied. The morphology of the submicron-defects in the crystal samples are clearly shown by high resolution dark-field and phase contrast microscopy. The distribution of the different defects in some crystals revealed that the growth process can be considered as consisting of three parts, of which, the intermediate one yields very high quality crystals. An analysis of the defect forming mechanism enabled the enlargement of high quality part via the modification of the growth parameters. The TEM~ and single-axial-mode laser operations have been obtained from transversally-cut high Nd 203 doping (Nd203 >1 wt%) and with high optical homogeneity (4N = ix 10—6) rod. Nonuniform intensity of growth striations that always occur during crystal growth, cause an inhomogeneity along the growth direction. Sometimes, the refractive index inhomogeneity ~n is up to lx iO~, as measured by a Zygo interferometer. The effects of such an inhomogeneity on laser beam quality and on the threshold of a disk laser are also reported.
1. Introduction The temperature gradient technique (TGT) has been used to grow perfect Nd : YAG single crystals with high Nd-doping concentrations, with 75 X 130 mm diameter and weight of 2 kg [1,2]. Good TEM~ and single-axial-mode laser operations have been carried out with laser rods transverally cut from such crystals [3,4]. A pulse laser output with 0.6% efficiency from the Nd: YAG disk, laser was also obtained [5]. In this paper, we pay most of our attention to the morphology, properties and ditribution of defects in the crystals grown by TGT. While preparing the crystals, we have systematically examined the defect type and distribution in each crystal, and found that the formation and distribution of defects are generally dependent upon both material structural properties and growth parameters. The types of defects found in the TGT grown Nd: YAG crystals were metal particles, three-dimensional’ point defect clusters, dislocation loops, helical and zigzag dislocations, straight edge dislocations, cracks, foreign phase inclusions due to constitutional supercooling and non-uniform growth
striations. According to the distribution of the defects, it is possible to devide the crystal into three parts with different crystal quality. An analysis of mechanisms of defect formation in the crystal enabled us to effectively decrease the area with defects and to increase the perfect area via the modification of the growth parameters. We have also quantitatively measured the optical path difference (PV) at the defect area in the crystal with Zygo Mark III interferometer, and the refractive index inhomogeneity (L~n) was calculated. The effects of defects on the quality of the laser beam and on the laser threshold could be deduced from the laser near field pattern of a disk laser. These studies are highly useful for the optimization of the quality of Nd : YAG laser material prepared from the TGT crystals. 2. Experimental 2.1. Sample preparation In order to examine the general optical inhomogeneity and the stresses caused by crystal de-
0022-0248/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
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fects, we first cut off the seed and the bottom part of boules perpendicularly to the growth direction, and then grind and polish the cut surfaces of both end. The obtained crystal boule is further cut into several slabs in parallel to the growth direction, for revealing the morphology and the general distribution of crystal defects.
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2.2. Evaluation procedures (1) To observe the submicron-defects in crystals, a Leitz wide field microscope was used. Its resolution is 0.2 ,.Lm for conventional transmission or reflection [6], several microns for optical birefringence topography with polarized microscopy [7] and as high as 40 A (diffraction effect) for dark field [8] and high contrast effect for phase contrast microscopy [9]. (2) Laser light scattering topography with 100—400 A resolution (scattering effect) [10,11] is carried out to observe and distinguish the decorated and undecorated dislocations. (3) EDS and EPMA were used to analyze the composition of the inclusions in crystals. (4) X-ray transmission topography is employed to show the space distribution of defects and identify the characteristics of dislocations in crystals. (5) A Mark II Zygo interferometer was used to quantitatively determine the optical homogeneity of the crystals. (6) A Nd : YAG disk pulse laser was fabricated in order to study the effect of the defects in the crystals on laser performances. (7) Laser rods were evaluated for their lasing performance and the results were published elsewhere [3,4].
3. Results and aflalYsiS The perfection of the TGT Nd YAG crystal was studied from two viewroints: defect distribution/ characteristics and optical homogeneity. 3.1. Defect distribution and characteristics The examination of typical longitudinal segements from crystal reveals the distribution of
Fig. i. Schematic distribution of defects in TGT Nd:YAG crystal boules: (1) the first part contains point-defect clusters, small size dislocation loops, helices and zigzag dislocations; (2) the second part with less scattering centers and dislocations, and with high quality; (3) the third part (last to freeze section), with macroscopic defects and dislocations both produced by constitutional supercooling. G = growth direction.
crystal defects through the whole crystals. This, and a closer inspection of the defects enable conclusions on the factors affecting the formation and evolution of these defects. Fig. 1 schematically shows the distribution of different defects along a longitudinal section of a crystal boule (sample No. 1) as revealed by different methods. In general, the crystals can be divided into three parts according to the defect’s nature and distribution. The first part consists of the area from the seed to the shouldering zone. There is a variety of defects in this part, e.g. scattering partides, point-defect clusters, dislocation loops, different kinds of dislocations and cracks. The second part is the best quality part, where less dislocations or scattering centers can be found. It extends from zone to somewhere below the topthe of shouldering the crystal sometimes at about 87% of the crystal height. The third part consists of the last portion of the growth, and hence contains macro-defects and dislocation lines due to constitutional supercooling. In the following, the details of the observations performed on the defects in the different parts will be described.
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Fig. 2. (a) Optical hirefringence image of ~strings~’ and of scattering centers (under crossed poladzers(. (b) The strong stress field caused by a “string”, ~ n = (6—8) x 10
3.1.1. The first part of the crystal Many scattering centers and “strings” are revealed in the first part of sample No. 1 when it is illuminated by a He—Ne laser beam. The optical birefringence topography is a good technique to show the photoelastical pattern induced by defects in isotropic crystals with larger lattice parameter such as GGG and Nd : YAG [12,13]. The birefrmgence pattern of “strings” and of some scattering centers are obtained with crossed polarizers (fig. 2a). Some of the “strings” are zigzag-shaped. The optical birefringence image of scattering centers looks like a petal with four- or two-fold symmetry. Due to the resolution limit of optical birefringence topography (about several microns), the details of these scattering centers and some of the “strings” cannot be resolved. It is possible, however, to reveal large strains correlated with some “strings”, as shown in fig. 2b. The refractive index inhomogeneity within this area was measured with a tilting compensator and was found to be (6—8) x 10 This amount of inhomogeneity is surely harmful to the optical quality of the crystals. All the defects were decorated by impurities or point defects which deposited from the melt during crystal growth [14]. The size of the decorated defec’ts is too small to reveal them by scanning electron microscopy (resolution of 100 A). However, their details can successfully be revealed by dark field and phase contrast microscopy due to ~.
diffraction effects. These indicate that the scattering centers are three-dimensional point-defect clusters (fig. 3a) and small dislocation loops and also that the “strings” are zigzag or helical dislocations caused by jogging, kinking, glinding or climbing motions. The helical dislocations are shown in fig. 4. Fig. 4a shows two helical dislocations which look like “springs” and there are no precipitated particles at the centers of the helical loops. This kind of helix probably originates from dislocation climbing which is forced by the supersaturation of point defects in the crystal melt. Fig. 4b shows the helix originating from an edge dislocation line and the entrapment of inclusions by the climbing motion. Another kind of dislocations is the zigzag ones, formed by jogging, gliding or kinking of formerly straight dislocation lines. Fig. 5 shows the zigzag dislocations, and the theoretical explanation of their formation is illustrated in fig. 6 [16]. It seems that when there is a supersaturation of point defects in the melt, straight dislocation lines can jog, then glide into zigzag lines. At the same time, vacancies of interstial atoms can be emitted or absorbed. In conclusion, the appearances of point defect clusters, dislocation loops and various dislocation lines reveal that all the occur due to the existence of supersaturated point defects in a primary growth step. Since no second phase precipitates are found in this part of the crystal sample, it is proposed that the su-
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Fig. 3. Details of the scattering centers revealing point-defect clusters and small size dislocation loops (phase contrast microscopy): (a) point-defect clusters with different shapes; (b) small dislocation loops with different shapes.
persaturation of point defects resulted from a slight deviation from stoichiometry that can thermodynamically resolve itself by formation of crystal defects rather than by precipitation of a second phase [17]. The metal particles found in the crystal appear to be with cubic or hexagonal symmetry, and they are identified by EDS and EPMA to be molybdenum which is introduced via reactions/ volatilization of the charge and of the crucible material. When the vaccum degree in the melting
b
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Fig. 4. The two kinds of helical disloctions in TGT Nd: YAG crystals (phase contrast microscopy): (a) spring-shaped helices; (b) helix, containing large inclusions in the center of each loop,
container increased, the content of the metal partides clearly decreases. In this part of the crystal sample, cracks are also observed. Some of them appear when the dislocation lines start or stop forming (fig. 7). It is necessary for the formation of the cracks that
200iim Fig. 5. A mixed zigzag dislocation formed by jogging and gliding motions from straight dislocation lines (dark field microscopy).
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laser performances of Nd: YAG crystals
larger than the theoretical elastic limit
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3.1.2. The second part of the crystal In this part of the crystal, there are fewer dislocations, and fewer scattering centers. It can be assumed that at the beginning of the growth,
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•i o ~ b\ Fig. 6. The theoretical model of the formation mechanism of the mixed dislocation in fig. 5. A jogged left-handed screw dislocation which produces vacancies when it moves to the right; b = Burgers vector, I = ghding length, h = jogging height.
there is a central area of higher local stress which might be caused by local supercooling, precipitates, pile-up of dislocations or by grain boundaries. When the tensile stress causing cracks meets the following equation [18]: a’t2r/btl/Sjs, (1) where r is the surface energy, ~t is the shear modulus, b is the Burgers vector, and a’ is the tensile stress. It is indicated that a’ has been
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thermal fluctuations (due to fluctuations in the cooling water and thermal field) cause non-equilibrium growth defects and thatare with progress of the growth, these fluctuations being damped out because of insulating effect of already-grown crystal part. In this part, the above mentioned defects such as point defect clusters, dislocation loops, helical and zigzag dislocations reduced gradually because the melt has got into an equilibrium of stoichiometry. This part is of the highest quality of all the three parts, and it is the part which is often used to produce good laser rods or slabs. In this part, nd3 + doping concentration is 1.0—1.7 wt% and fluorescence lifetime is 190—200 ~ts from the bottom to the top of this part. 3.1.3. The third part of the crystal The third part is crystallized in the latter or close-to-end period of growth. In this part, a large number of bubbles, trail tracks of solute, second-phase precipitates, as well as straight and zigzag dislocation lines appear (fig. 1). The tomography and distribution of straight dislocation lines are observed with laser light scattering tomography (fig. 8), and taking the advantage of X-ray transmission topography, we confirm these dislocations to be undecorated edge dislocations [19].
As iswhen well known constitutional occurs G/V< mCL( the Kfollowing equationsupercooling is satisfied [20]: where G is the0temperature 1)/DK0, gradient at the interface in the melt, V is the growth rate, D is the diffusion coefficient of the solute, m is the slope of liquidus, K0 is equilibrium dopant distribution —
Fig. 7. Cracks formed on helices (dark field microscopy): (a) crack formed on the initial part and (b) crack formed on the final part of a helix,
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Perfection and laser performances of Nd: YA G crystals
coefficient, and CL is the dopant equilibrium concentration in the melt. Due to the small distribution coefficient of Nd3~in YAG, the Nd3~concentration in the melt remarkably increases as the crystallization is near to completion, and it is therefore easy to meet the condition of constitutional supercooling at this stage. However, this process can be delayed if the temperature gradient at the growth interface is modified according to the relationship between composition and melting point temperature [21]: RT2 m
(~H *
(1 _K*)X.~~,
)F A
.
I
.
(3)
I
.
L
.
where K. is effective distnbution coefficient, X, the concentration of i (solute) in the melt, RT,~/ (i~Hm ~ a constant for the decrease in the solidification point A, and i.~T the temperature gradient at the interface in the melt. From eq. (3), we can see that when L~Tis increased along with the increment in X,’, the constitutional supercooling area can be ~n~-
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-
.
Fig. 9. Optical homogeneity of a cross section of a crystal boule (sample No. 2, cross-section 50 x 25 mm); PV = 0.312X, RMS=0.073X ~n=0.7X105.
mized. Experimentally it was found possible to reduce the area with constitutional supercooling effects to as low as 20 mm at the end of the growth. 3.2. Optical homogeneity of Nd. YAG crystals grown by TGT the crystal samples were taken from part 2 of All the crystal boules. 3.2.1. Cross sections of the crystal boules Fig. 9 gives the interference fringe pattern with the calculated values of PV for a 25 mm thick cross section of crystal sample No. 2. Three facets which are located at the peripheral edge of crystal are observed. Most of the section if of high optical homogeneity and the ~ n within it is calculated to be 0.7 x iO~. A laser rod, sample No. 3, which was transversally cut from such a region of this crystal, reveals a PV of 0.097X and z~nof 1 X 106 (fig. 10). This is probably due to the high homogeneity and also because there are few dislocations and scattering centers inside. The optical quality
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rod is competible with that of Nd-doped
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10 Ohm Fig. 8. A number of undecorated edge and zigzag lines produced at the end ofcrystal boules (taken by laser light scattering tomography); G = growth direction, S = incident direction.
3.2.2. Optical homogeneity in longitudinal direction of the crystal boules .
.
.
There is often some nonumform intensity distribution of growth striations (under crossed
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hg. 10. High-quality laser rod (sample No. 3. Nd- concentration =1—2 wt%), PV= 0.097X. RMS = 0.024X, L~n=1 X106.
polarizers) in the longitudinal segment parallel to the growth direction. Fig. 11 illustrates the optical birefringence pattern of the longitudinal segment of sample No. 4. Fig. 12 shows the interference fringe pattern and the measured PV value of sample No. 4, which indicates that the inhomogeneity caused by growth striations has considerably distorted the interference fringe pattern and deteriorated the optical quality of the crystal. The /.~nof sample No. 4 is 1
x iO~.
3.3. Laser performances experiments There are two remarkable virtues for the Nd : YAG crystals grown by TGT: one is that there is a large area of high optical quality in the
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laser performances of Nd: YAG crystals
Fig. 12. The optical homogeneity of a longitudinall~cut slab 4. (sampleNo. 4); PV= 0.95X, RMS=0.136X ~n =1X10
cross section of the crystal, so it is easy to cut high optically homogeneous laser rods transversally. The second virtue is the relatively high doping concentration of Nd3 + about 0.7 2.3 wt% from the lowest part to the end of the crystal boules. This ensures a lower laser threshold and higher efficiency, so as to meet the requirement for TEM~ and single-axial-mode lasers. —
3.3.1. The TEM 00 and single-axial-mode laser operations Laser operations have been successfully carried out with such laser rod, sample No. 2 (cross section 5 x 50 mm) transversally cut from part 2 of the crystal boules. Fig. 13a shows the arrangement of TEM0Ø laser device. The laser is Q-switched by a LiF crystal and mode-selected by a hole of 0.81 mm diameter. No optical elastical distortion can be observed from the crystal rod because there are fewer micron-defects such as inclusions or dislocations, hence a fairly homogeneous far field laser pattern is exhibited. Fig. 13b exhibits the very uniform field pattern taken 8 m after from the cavity. This figure clearly indicates that the crystal is of high optical quality. Fig. 13c shows the field distribution of the TEM~ laser output and in comparison with theoretical Gaussian curve I = I~exp( r/r0), the two curves are in good agreement. lasers demand higher quality Single-axial-mode rods than TEM~lasers do. This is because (1) the rods should have higher optical homogeneity, otherwise, the single-axial-mode can not be —
200jm -
-
-
Fig. 11. The strong stress-field caused h~ growth striations (under crossed polarizers),
—
a
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oscillators with quasi-cw prelase or pulsed prelase have been developed successfully and have been used in a big laser fusion system with high quality Nd : YAG laser rods grown by TGT by Cao Weilou [4].
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laser performances of Nd: YA G crystals
3.3.2. The disk laser operation During the past years, much efforts have been made on developing high average powder solid state lasers. Due to the limitation of the cross area of rod and slab lasers, the output power was limited. Using the large size Nd : YAG crystals grown by TGT, a 40 mm clear aperture Nd : YAG disk laser has been successfully built. The schematic diagram of the Nd : YAG disk laser oscillator is shown in fig. 14a. Two Nd—YAG disks with dimensions of 6 x 40 X 80 mm3 were mounted at a Brewster angle to the laser beam and surrounded by four flash lamps. Surface pumping and surface cooling made a temperature gradient along the propagation direction of the laser beam. The heat deposited in the disks could be easily removed by the coolant due to its high thermal conductivity and small thickness. The laser output energy versus pumping power density is shown in fig. 14b. When the reflectivity R 91%, the laser pulse efficiency can be achieved to ~ 0.6%. The laser output energy is about 6J for each shot and the repetition rate could be up to 100 Hz. From the above mentioned results and calculations, four pieces of disks could provide 1000 W average laser power which is very useful for laser ranging, laser processing lithography, laser fusion, laser plasma, X-ray (LPX) and military systems. In order to evaluate the effects of nonuniform =
=
0
1
Fig. 13. The TEM~ laser experimental results of a transversally cut laser rod (sample No. 3). (a) Arrangement diagram of the TEM~laser: (1) LiF Q switch; (2) Nd: YAG crystal rod; (3) 0.81 mm hole. (b) The uniform laser far field pattern (8 m) of the laser rod. (c) The field distribution of the TEM~laser output: ( ) experimental values; (— — —) theoretical values,
selected due to existence of many other modes; (2) the doping concentration of Nd3 + in the same cross section of the rods should be homogeneous in order to get the same laser gain through the whole rod; (3) there should be no single-axial-mode laser disturbance caused by the interference of the original laser wavefronts with scattered laser wavefronts arising from the scattering centers within the rods. The long duration 100% singleaxial-mode Q-switched Nd : YAG and Nd : YLF
growth striations on laser performance, the pulse performance such as the quality of near field laser pattern of a disk laser with slabs No. 4 and No. 5 was checked. The inhomogeneity of the growth striations obviously affects the quality of the laser beam and the laser threshold. Fig. 14b shows a different near field pattern with variable input power from which we can conclude that the inhomogeneity of the growth striation in the samples, No. 4 and No. 5 is corresponding to that of nonuniform intensity distribution of near field patterns. From the above-mentioned experimental results, it is shown that although a good laser
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Perfection and laser performances of Nd: YAG crystals
~~Ø2222Z’22/’i
__
-
__
1cm
E
(0,0)
R=91.67%
(j)
0.5
i.0
E
(kj)
Fig. 14. Laser experiment of disk laser, (a) Diagram of the Nd: YAG disk laser: (1) xenon flash lamp; (2) Nd: YAG slabs (samples No. 4 and No. 5); (3) glass window; (4) filters, (5) laser output beam. (b) Laser output energy versus pumping power; R = reflectivity of coupling mirror.
operation was achieved with laser rods that were transversally cut from TGT crystals, it was difficult to achieve a very good slab and disk laser longitudinally cut from the crystal. This is because of the existence of nonuniform growth striations in such slabs. It is therefore essential to improve the growth process in order to reduce the nonumform growth striations or to enlarge the dimension
of crystal boules to get slabs transversally cut from the crystal boules.
4. Conclusion Due to the complicated effects of various factors, it is almost impossible to grow a large piece
DengPeizhen et a!. / Perfection and laser performances of Nd: YA G crystals
605j
585j
626j
564j
648j
692j
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Fig. 15. The laser near field pattern obtained with different input energies and with a disk laser operation.
of Nd : YAG crystal without any defect. That is just the same as the occurrence of Swirl defects in free-dislocation silicon single crystal [22]. Our goal is, of course, to decrease the area with defects and to increase the area of qualified material achieved by TGT. As we have shown, the existence of the defects mentioned above, heavily depends on Nd : YAG crystal-structure properties and on the growth parameters of TGT. There are three main mechanisms for the formation of crystal defects: (a) Due to constitutional supercooling, a large number of defects such as bubbles, tunnels, second-phase compounds and dislocations are formed. Constitutional supercooling and the resulting defects also occurred in Nd : YAG crystals that were grown by the heat exchange method [23]. This must be avoided for the primary step growth, and we have successfully done that by designing a suitable thermal field and keeping a very slow growth rate. (b) The dislocation lines which are caused by thermal stresses can extent through the whole length of the crystal if the solid—liquid interface is nearly flat. In our experi-
ments the solid—liquid interface is slightly convex and some of the dislocations grow out of the crystals [24]. (c) Small point defect clusters and dislocation loops, helical and zigzag dislocations, cracks and so are caused by the supersaturation of the point defects and originated from slight deviations from stoichiometry and from local supercooling. These defects can be gradually reduced when the melt gets into a better equilibrium of stoichiometry and the local supercooling region is eliminated by modifying the thermal field at the lowest part of the crucible. This is done by carefully controlling the flow or cooling water and controlling the gradients and growth rates. Besides, the point defect clusters and dislocation loops are closed-type defects and therefore cannot propagate into subsequent growing crystal portions. Also, the helical and zigzag dislocations can be reduced by stoping the climbing and jogging motion when the supersaturation degree of point defects in the melts is decreased. Thus, by studying the mechanisms of defect formation and modifying the growth parameters
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at different stages, we effectively reduced the formation of crystal defects and enlarged the high quality crystal fraction.
Acknowledgement We wish to thank Professor Cao Weilo for his sincere help in the lasing experiments. We are also grateful to Professor Deng Ximing for valuable suggestions.
References [1] Zhou Yongzong, Deng Peizhen and Qiao Jinwen, J. Chinese Silicate Soc. 11(1983) 357. [2] Zhou Yongzong, J. Crystal Growth, 78 (1986) 31. [3] Zhang Meizhen and Li Chengfu, Chinese J. Lasers 11 (1984) 665. [4] Cao Weilou, Deng Ximing et al,, Acta Opt. Siica 9 (1986) 769. [5] Cao Weilou and Zhang Meizhen, Opt. News 12 (9) (1986) 208. [6] Specification of Leitz Corporation, Application of Microscopy (Leaflet). [7] 5. Amelinckx, Solid State Physics, Suppl. 6 (Academic Press, New York, 1964) p. 105.
[8] [9] [10]
H. Komatsu, Japan. Cryst. Soc. 16 (1974) 28. Liang Quenting, Physical Optics (Mechanical Industry Press, Beijing, 1981). K. Moriya and T. Ogawa, J. Crystal Growth 44 (1978) 53.
[11] Deng Peizhen and Qiao Jinwen, J. Crystal Growth 82 (1987) 579. [12] J.W. Matthews, E. Kloktlolm, T.S. Plaskeh and V. Sadegopan, Phys. Status Solidi (a) 19 (1973) 671. [13] H.S. Bagdasarov and L.M. Doduk, Kristallografia 15 (1970) 334 [14] Deng Peizhen, Zhang Shoudu, Wang Haobmg and Qian Zhemn, J. Chinese Silicate Soc. 7 (1979) 168. [151J. Friedel, Dislocations (Pergamon, Oxford, 1964) pp. 123—133. [16] J.P. Hirth, Theory of Dislocations, 2nd ed. (1982) p. 589. [17] J. Friedel, Dislocations (Pergamon, Oxford, 1964) p. 124. [18] J. Friedel, Dislocations (Pergamon, Oxford, 1964) p. 326. [19] Qiao Jinwen, Den Peizhen and Qian Zhenin, Artifacial Crystals 1 (1986) 69. [20] WA. Tiller and K.A. Jackson, Acta Met, 1 (1953) 428. [21] R.A. Laudise, The Growth of Single Crystals (Prentice Hall, Englewood Cliffs, NJ, 1970). [22] NB. Urli and J.W. Corbett, in: Radiation Effects in Semiconductors 1976, Inst. Phys. Conf, Ser. 31, Eds. N.B. Urli and J.W. Corbett (Inst. Phys., London—Bristol, 1977) p. 12. [23] J.L. Caslavsky and D. Viechinicki, J. Mater. Sci., 15 (1980) 1709. [24] Deng Peizhen, Zhang Shoudu, Qiao Jinwen and Qian Zhemn, Ada Phys. Sinica 4 (1976) 284.
Journal of Crystal Growth 92 (1988) 276—286 North-Holland, Amsterdam
PERFECTION AND LASER PERFORMANCES OF Nd:YAG CRYSTALS GROWN BY TEMPERATURE GRADIENT TECHNIQUE (TGT) DENG Peizhen, QIAO Jingwen, HU Bing, ZHOU Yongzong and ZHANG Meithen Shanghai Institute of Optics and Fine Mechanics, Academia Sinica, P.O. Box 8211, Shanghai, People’s Rep. of China Received 27 September 1987; manuscript received in final form 15 June 1988
The formation and development of defects in the Nd: YAG crystal grown by the temperature gradient technique (TGY) have been systematically studied. The morphology of the submicron-defects in the crystal samples are clearly shown by high resolution dark-field and phase contrast microscopy. The distribution of the different defects in some crystals revealed that the growth process can be considered as consisting of three parts, of which, the intermediate one yields very high quality crystals. An analysis of the defect forming mechanism enabled the enlargement of high quality part via the modification of the growth parameters. The TEM~ and single-axial-mode laser operations have been obtained from transversally-cut high Nd 203 doping (Nd203 >1 wt%) and with high optical homogeneity (4N = ix 10—6) rod. Nonuniform intensity of growth striations that always occur during crystal growth, cause an inhomogeneity along the growth direction. Sometimes, the refractive index inhomogeneity ~n is up to lx iO~, as measured by a Zygo interferometer. The effects of such an inhomogeneity on laser beam quality and on the threshold of a disk laser are also reported.
1. Introduction The temperature gradient technique (TGT) has been used to grow perfect Nd : YAG single crystals with high Nd-doping concentrations, with 75 X 130 mm diameter and weight of 2 kg [1,2]. Good TEM~ and single-axial-mode laser operations have been carried out with laser rods transverally cut from such crystals [3,4]. A pulse laser output with 0.6% efficiency from the Nd: YAG disk, laser was also obtained [5]. In this paper, we pay most of our attention to the morphology, properties and ditribution of defects in the crystals grown by TGT. While preparing the crystals, we have systematically examined the defect type and distribution in each crystal, and found that the formation and distribution of defects are generally dependent upon both material structural properties and growth parameters. The types of defects found in the TGT grown Nd: YAG crystals were metal particles, three-dimensional’ point defect clusters, dislocation loops, helical and zigzag dislocations, straight edge dislocations, cracks, foreign phase inclusions due to constitutional supercooling and non-uniform growth
striations. According to the distribution of the defects, it is possible to devide the crystal into three parts with different crystal quality. An analysis of mechanisms of defect formation in the crystal enabled us to effectively decrease the area with defects and to increase the perfect area via the modification of the growth parameters. We have also quantitatively measured the optical path difference (PV) at the defect area in the crystal with Zygo Mark III interferometer, and the refractive index inhomogeneity (L~n) was calculated. The effects of defects on the quality of the laser beam and on the laser threshold could be deduced from the laser near field pattern of a disk laser. These studies are highly useful for the optimization of the quality of Nd : YAG laser material prepared from the TGT crystals. 2. Experimental 2.1. Sample preparation In order to examine the general optical inhomogeneity and the stresses caused by crystal de-
0022-0248/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Deng Peizhen et at
/ Perfection and
fects, we first cut off the seed and the bottom part of boules perpendicularly to the growth direction, and then grind and polish the cut surfaces of both end. The obtained crystal boule is further cut into several slabs in parallel to the growth direction, for revealing the morphology and the general distribution of crystal defects.
laser performances of Nd: YA G crystals
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_____
G __.__~-=-_==~~~
2.2. Evaluation procedures (1) To observe the submicron-defects in crystals, a Leitz wide field microscope was used. Its resolution is 0.2 ,.Lm for conventional transmission or reflection [6], several microns for optical birefringence topography with polarized microscopy [7] and as high as 40 A (diffraction effect) for dark field [8] and high contrast effect for phase contrast microscopy [9]. (2) Laser light scattering topography with 100—400 A resolution (scattering effect) [10,11] is carried out to observe and distinguish the decorated and undecorated dislocations. (3) EDS and EPMA were used to analyze the composition of the inclusions in crystals. (4) X-ray transmission topography is employed to show the space distribution of defects and identify the characteristics of dislocations in crystals. (5) A Mark II Zygo interferometer was used to quantitatively determine the optical homogeneity of the crystals. (6) A Nd : YAG disk pulse laser was fabricated in order to study the effect of the defects in the crystals on laser performances. (7) Laser rods were evaluated for their lasing performance and the results were published elsewhere [3,4].
3. Results and aflalYsiS The perfection of the TGT Nd YAG crystal was studied from two viewroints: defect distribution/ characteristics and optical homogeneity. 3.1. Defect distribution and characteristics The examination of typical longitudinal segements from crystal reveals the distribution of
Fig. i. Schematic distribution of defects in TGT Nd:YAG crystal boules: (1) the first part contains point-defect clusters, small size dislocation loops, helices and zigzag dislocations; (2) the second part with less scattering centers and dislocations, and with high quality; (3) the third part (last to freeze section), with macroscopic defects and dislocations both produced by constitutional supercooling. G = growth direction.
crystal defects through the whole crystals. This, and a closer inspection of the defects enable conclusions on the factors affecting the formation and evolution of these defects. Fig. 1 schematically shows the distribution of different defects along a longitudinal section of a crystal boule (sample No. 1) as revealed by different methods. In general, the crystals can be divided into three parts according to the defect’s nature and distribution. The first part consists of the area from the seed to the shouldering zone. There is a variety of defects in this part, e.g. scattering partides, point-defect clusters, dislocation loops, different kinds of dislocations and cracks. The second part is the best quality part, where less dislocations or scattering centers can be found. It extends from zone to somewhere below the topthe of shouldering the crystal sometimes at about 87% of the crystal height. The third part consists of the last portion of the growth, and hence contains macro-defects and dislocation lines due to constitutional supercooling. In the following, the details of the observations performed on the defects in the different parts will be described.
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Fig. 2. (a) Optical hirefringence image of ~strings~’ and of scattering centers (under crossed poladzers(. (b) The strong stress field caused by a “string”, ~ n = (6—8) x 10
3.1.1. The first part of the crystal Many scattering centers and “strings” are revealed in the first part of sample No. 1 when it is illuminated by a He—Ne laser beam. The optical birefringence topography is a good technique to show the photoelastical pattern induced by defects in isotropic crystals with larger lattice parameter such as GGG and Nd : YAG [12,13]. The birefrmgence pattern of “strings” and of some scattering centers are obtained with crossed polarizers (fig. 2a). Some of the “strings” are zigzag-shaped. The optical birefringence image of scattering centers looks like a petal with four- or two-fold symmetry. Due to the resolution limit of optical birefringence topography (about several microns), the details of these scattering centers and some of the “strings” cannot be resolved. It is possible, however, to reveal large strains correlated with some “strings”, as shown in fig. 2b. The refractive index inhomogeneity within this area was measured with a tilting compensator and was found to be (6—8) x 10 This amount of inhomogeneity is surely harmful to the optical quality of the crystals. All the defects were decorated by impurities or point defects which deposited from the melt during crystal growth [14]. The size of the decorated defec’ts is too small to reveal them by scanning electron microscopy (resolution of 100 A). However, their details can successfully be revealed by dark field and phase contrast microscopy due to ~.
diffraction effects. These indicate that the scattering centers are three-dimensional point-defect clusters (fig. 3a) and small dislocation loops and also that the “strings” are zigzag or helical dislocations caused by jogging, kinking, glinding or climbing motions. The helical dislocations are shown in fig. 4. Fig. 4a shows two helical dislocations which look like “springs” and there are no precipitated particles at the centers of the helical loops. This kind of helix probably originates from dislocation climbing which is forced by the supersaturation of point defects in the crystal melt. Fig. 4b shows the helix originating from an edge dislocation line and the entrapment of inclusions by the climbing motion. Another kind of dislocations is the zigzag ones, formed by jogging, gliding or kinking of formerly straight dislocation lines. Fig. 5 shows the zigzag dislocations, and the theoretical explanation of their formation is illustrated in fig. 6 [16]. It seems that when there is a supersaturation of point defects in the melt, straight dislocation lines can jog, then glide into zigzag lines. At the same time, vacancies of interstial atoms can be emitted or absorbed. In conclusion, the appearances of point defect clusters, dislocation loops and various dislocation lines reveal that all the occur due to the existence of supersaturated point defects in a primary growth step. Since no second phase precipitates are found in this part of the crystal sample, it is proposed that the su-
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Perfection and laser performances of Nd: YA G crystals
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* 2 jim
Fig. 3. Details of the scattering centers revealing point-defect clusters and small size dislocation loops (phase contrast microscopy): (a) point-defect clusters with different shapes; (b) small dislocation loops with different shapes.
persaturation of point defects resulted from a slight deviation from stoichiometry that can thermodynamically resolve itself by formation of crystal defects rather than by precipitation of a second phase [17]. The metal particles found in the crystal appear to be with cubic or hexagonal symmetry, and they are identified by EDS and EPMA to be molybdenum which is introduced via reactions/ volatilization of the charge and of the crucible material. When the vaccum degree in the melting
b
200pnt~
a
Fig. 4. The two kinds of helical disloctions in TGT Nd: YAG crystals (phase contrast microscopy): (a) spring-shaped helices; (b) helix, containing large inclusions in the center of each loop,
container increased, the content of the metal partides clearly decreases. In this part of the crystal sample, cracks are also observed. Some of them appear when the dislocation lines start or stop forming (fig. 7). It is necessary for the formation of the cracks that
200iim Fig. 5. A mixed zigzag dislocation formed by jogging and gliding motions from straight dislocation lines (dark field microscopy).
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larger than the theoretical elastic limit
00
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(ag =
7
difficult 1/10 aseeds, brittle gm) and for material, slip. Intherefore occur. addition, The origin plastic Nd :of YAG relaxation the stresses crystal to is assigned as tocracks well the supercooling as the local in stress the area caused linked byis climbing motion of dislocations.
~
3.1.2. The second part of the crystal In this part of the crystal, there are fewer dislocations, and fewer scattering centers. It can be assumed that at the beginning of the growth,
0 0 0
•i o ~ b\ Fig. 6. The theoretical model of the formation mechanism of the mixed dislocation in fig. 5. A jogged left-handed screw dislocation which produces vacancies when it moves to the right; b = Burgers vector, I = ghding length, h = jogging height.
there is a central area of higher local stress which might be caused by local supercooling, precipitates, pile-up of dislocations or by grain boundaries. When the tensile stress causing cracks meets the following equation [18]: a’t2r/btl/Sjs, (1) where r is the surface energy, ~t is the shear modulus, b is the Burgers vector, and a’ is the tensile stress. It is indicated that a’ has been
Urn
thermal fluctuations (due to fluctuations in the cooling water and thermal field) cause non-equilibrium growth defects and thatare with progress of the growth, these fluctuations being damped out because of insulating effect of already-grown crystal part. In this part, the above mentioned defects such as point defect clusters, dislocation loops, helical and zigzag dislocations reduced gradually because the melt has got into an equilibrium of stoichiometry. This part is of the highest quality of all the three parts, and it is the part which is often used to produce good laser rods or slabs. In this part, nd3 + doping concentration is 1.0—1.7 wt% and fluorescence lifetime is 190—200 ~ts from the bottom to the top of this part. 3.1.3. The third part of the crystal The third part is crystallized in the latter or close-to-end period of growth. In this part, a large number of bubbles, trail tracks of solute, second-phase precipitates, as well as straight and zigzag dislocation lines appear (fig. 1). The tomography and distribution of straight dislocation lines are observed with laser light scattering tomography (fig. 8), and taking the advantage of X-ray transmission topography, we confirm these dislocations to be undecorated edge dislocations [19].
As iswhen well known constitutional occurs G/V< mCL( the Kfollowing equationsupercooling is satisfied [20]: where G is the0temperature 1)/DK0, gradient at the interface in the melt, V is the growth rate, D is the diffusion coefficient of the solute, m is the slope of liquidus, K0 is equilibrium dopant distribution —
Fig. 7. Cracks formed on helices (dark field microscopy): (a) crack formed on the initial part and (b) crack formed on the final part of a helix,
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Perfection and laser performances of Nd: YA G crystals
coefficient, and CL is the dopant equilibrium concentration in the melt. Due to the small distribution coefficient of Nd3~in YAG, the Nd3~concentration in the melt remarkably increases as the crystallization is near to completion, and it is therefore easy to meet the condition of constitutional supercooling at this stage. However, this process can be delayed if the temperature gradient at the growth interface is modified according to the relationship between composition and melting point temperature [21]: RT2 m
(~H *
(1 _K*)X.~~,
)F A
.
I
.
(3)
I
.
L
.
where K. is effective distnbution coefficient, X, the concentration of i (solute) in the melt, RT,~/ (i~Hm ~ a constant for the decrease in the solidification point A, and i.~T the temperature gradient at the interface in the melt. From eq. (3), we can see that when L~Tis increased along with the increment in X,’, the constitutional supercooling area can be ~n~-
I
_______
~
r
-
-
.
Fig. 9. Optical homogeneity of a cross section of a crystal boule (sample No. 2, cross-section 50 x 25 mm); PV = 0.312X, RMS=0.073X ~n=0.7X105.
mized. Experimentally it was found possible to reduce the area with constitutional supercooling effects to as low as 20 mm at the end of the growth. 3.2. Optical homogeneity of Nd. YAG crystals grown by TGT the crystal samples were taken from part 2 of All the crystal boules. 3.2.1. Cross sections of the crystal boules Fig. 9 gives the interference fringe pattern with the calculated values of PV for a 25 mm thick cross section of crystal sample No. 2. Three facets which are located at the peripheral edge of crystal are observed. Most of the section if of high optical homogeneity and the ~ n within it is calculated to be 0.7 x iO~. A laser rod, sample No. 3, which was transversally cut from such a region of this crystal, reveals a PV of 0.097X and z~nof 1 X 106 (fig. 10). This is probably due to the high homogeneity and also because there are few dislocations and scattering centers inside. The optical quality
_______ _____
________ _____
________ ________
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_____
rod is competible with that of Nd-doped
_______
10 Ohm Fig. 8. A number of undecorated edge and zigzag lines produced at the end ofcrystal boules (taken by laser light scattering tomography); G = growth direction, S = incident direction.
3.2.2. Optical homogeneity in longitudinal direction of the crystal boules .
.
.
There is often some nonumform intensity distribution of growth striations (under crossed
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hg. 10. High-quality laser rod (sample No. 3. Nd- concentration =1—2 wt%), PV= 0.097X. RMS = 0.024X, L~n=1 X106.
polarizers) in the longitudinal segment parallel to the growth direction. Fig. 11 illustrates the optical birefringence pattern of the longitudinal segment of sample No. 4. Fig. 12 shows the interference fringe pattern and the measured PV value of sample No. 4, which indicates that the inhomogeneity caused by growth striations has considerably distorted the interference fringe pattern and deteriorated the optical quality of the crystal. The /.~nof sample No. 4 is 1
x iO~.
3.3. Laser performances experiments There are two remarkable virtues for the Nd : YAG crystals grown by TGT: one is that there is a large area of high optical quality in the
-
~
laser performances of Nd: YAG crystals
Fig. 12. The optical homogeneity of a longitudinall~cut slab 4. (sampleNo. 4); PV= 0.95X, RMS=0.136X ~n =1X10
cross section of the crystal, so it is easy to cut high optically homogeneous laser rods transversally. The second virtue is the relatively high doping concentration of Nd3 + about 0.7 2.3 wt% from the lowest part to the end of the crystal boules. This ensures a lower laser threshold and higher efficiency, so as to meet the requirement for TEM~ and single-axial-mode lasers. —
3.3.1. The TEM 00 and single-axial-mode laser operations Laser operations have been successfully carried out with such laser rod, sample No. 2 (cross section 5 x 50 mm) transversally cut from part 2 of the crystal boules. Fig. 13a shows the arrangement of TEM0Ø laser device. The laser is Q-switched by a LiF crystal and mode-selected by a hole of 0.81 mm diameter. No optical elastical distortion can be observed from the crystal rod because there are fewer micron-defects such as inclusions or dislocations, hence a fairly homogeneous far field laser pattern is exhibited. Fig. 13b exhibits the very uniform field pattern taken 8 m after from the cavity. This figure clearly indicates that the crystal is of high optical quality. Fig. 13c shows the field distribution of the TEM~ laser output and in comparison with theoretical Gaussian curve I = I~exp( r/r0), the two curves are in good agreement. lasers demand higher quality Single-axial-mode rods than TEM~lasers do. This is because (1) the rods should have higher optical homogeneity, otherwise, the single-axial-mode can not be —
200jm -
-
-
Fig. 11. The strong stress-field caused h~ growth striations (under crossed polarizers),
—
a
g
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I
283
oscillators with quasi-cw prelase or pulsed prelase have been developed successfully and have been used in a big laser fusion system with high quality Nd : YAG laser rods grown by TGT by Cao Weilou [4].
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laser performances of Nd: YA G crystals
3.3.2. The disk laser operation During the past years, much efforts have been made on developing high average powder solid state lasers. Due to the limitation of the cross area of rod and slab lasers, the output power was limited. Using the large size Nd : YAG crystals grown by TGT, a 40 mm clear aperture Nd : YAG disk laser has been successfully built. The schematic diagram of the Nd : YAG disk laser oscillator is shown in fig. 14a. Two Nd—YAG disks with dimensions of 6 x 40 X 80 mm3 were mounted at a Brewster angle to the laser beam and surrounded by four flash lamps. Surface pumping and surface cooling made a temperature gradient along the propagation direction of the laser beam. The heat deposited in the disks could be easily removed by the coolant due to its high thermal conductivity and small thickness. The laser output energy versus pumping power density is shown in fig. 14b. When the reflectivity R 91%, the laser pulse efficiency can be achieved to ~ 0.6%. The laser output energy is about 6J for each shot and the repetition rate could be up to 100 Hz. From the above mentioned results and calculations, four pieces of disks could provide 1000 W average laser power which is very useful for laser ranging, laser processing lithography, laser fusion, laser plasma, X-ray (LPX) and military systems. In order to evaluate the effects of nonuniform =
=
0
1
Fig. 13. The TEM~ laser experimental results of a transversally cut laser rod (sample No. 3). (a) Arrangement diagram of the TEM~laser: (1) LiF Q switch; (2) Nd: YAG crystal rod; (3) 0.81 mm hole. (b) The uniform laser far field pattern (8 m) of the laser rod. (c) The field distribution of the TEM~laser output: ( ) experimental values; (— — —) theoretical values,
selected due to existence of many other modes; (2) the doping concentration of Nd3 + in the same cross section of the rods should be homogeneous in order to get the same laser gain through the whole rod; (3) there should be no single-axial-mode laser disturbance caused by the interference of the original laser wavefronts with scattered laser wavefronts arising from the scattering centers within the rods. The long duration 100% singleaxial-mode Q-switched Nd : YAG and Nd : YLF
growth striations on laser performance, the pulse performance such as the quality of near field laser pattern of a disk laser with slabs No. 4 and No. 5 was checked. The inhomogeneity of the growth striations obviously affects the quality of the laser beam and the laser threshold. Fig. 14b shows a different near field pattern with variable input power from which we can conclude that the inhomogeneity of the growth striation in the samples, No. 4 and No. 5 is corresponding to that of nonuniform intensity distribution of near field patterns. From the above-mentioned experimental results, it is shown that although a good laser
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~~Ø2222Z’22/’i
__
-
__
1cm
E
(0,0)
R=91.67%
(j)
0.5
i.0
E
(kj)
Fig. 14. Laser experiment of disk laser, (a) Diagram of the Nd: YAG disk laser: (1) xenon flash lamp; (2) Nd: YAG slabs (samples No. 4 and No. 5); (3) glass window; (4) filters, (5) laser output beam. (b) Laser output energy versus pumping power; R = reflectivity of coupling mirror.
operation was achieved with laser rods that were transversally cut from TGT crystals, it was difficult to achieve a very good slab and disk laser longitudinally cut from the crystal. This is because of the existence of nonuniform growth striations in such slabs. It is therefore essential to improve the growth process in order to reduce the nonumform growth striations or to enlarge the dimension
of crystal boules to get slabs transversally cut from the crystal boules.
4. Conclusion Due to the complicated effects of various factors, it is almost impossible to grow a large piece
DengPeizhen et a!. / Perfection and laser performances of Nd: YA G crystals
605j
585j
626j
564j
648j
692j
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552j
544j
532j
285
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Fig. 15. The laser near field pattern obtained with different input energies and with a disk laser operation.
of Nd : YAG crystal without any defect. That is just the same as the occurrence of Swirl defects in free-dislocation silicon single crystal [22]. Our goal is, of course, to decrease the area with defects and to increase the area of qualified material achieved by TGT. As we have shown, the existence of the defects mentioned above, heavily depends on Nd : YAG crystal-structure properties and on the growth parameters of TGT. There are three main mechanisms for the formation of crystal defects: (a) Due to constitutional supercooling, a large number of defects such as bubbles, tunnels, second-phase compounds and dislocations are formed. Constitutional supercooling and the resulting defects also occurred in Nd : YAG crystals that were grown by the heat exchange method [23]. This must be avoided for the primary step growth, and we have successfully done that by designing a suitable thermal field and keeping a very slow growth rate. (b) The dislocation lines which are caused by thermal stresses can extent through the whole length of the crystal if the solid—liquid interface is nearly flat. In our experi-
ments the solid—liquid interface is slightly convex and some of the dislocations grow out of the crystals [24]. (c) Small point defect clusters and dislocation loops, helical and zigzag dislocations, cracks and so are caused by the supersaturation of the point defects and originated from slight deviations from stoichiometry and from local supercooling. These defects can be gradually reduced when the melt gets into a better equilibrium of stoichiometry and the local supercooling region is eliminated by modifying the thermal field at the lowest part of the crucible. This is done by carefully controlling the flow or cooling water and controlling the gradients and growth rates. Besides, the point defect clusters and dislocation loops are closed-type defects and therefore cannot propagate into subsequent growing crystal portions. Also, the helical and zigzag dislocations can be reduced by stoping the climbing and jogging motion when the supersaturation degree of point defects in the melts is decreased. Thus, by studying the mechanisms of defect formation and modifying the growth parameters
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at different stages, we effectively reduced the formation of crystal defects and enlarged the high quality crystal fraction.
Acknowledgement We wish to thank Professor Cao Weilo for his sincere help in the lasing experiments. We are also grateful to Professor Deng Ximing for valuable suggestions.
References [1] Zhou Yongzong, Deng Peizhen and Qiao Jinwen, J. Chinese Silicate Soc. 11(1983) 357. [2] Zhou Yongzong, J. Crystal Growth, 78 (1986) 31. [3] Zhang Meizhen and Li Chengfu, Chinese J. Lasers 11 (1984) 665. [4] Cao Weilou, Deng Ximing et al,, Acta Opt. Siica 9 (1986) 769. [5] Cao Weilou and Zhang Meizhen, Opt. News 12 (9) (1986) 208. [6] Specification of Leitz Corporation, Application of Microscopy (Leaflet). [7] 5. Amelinckx, Solid State Physics, Suppl. 6 (Academic Press, New York, 1964) p. 105.
[8] [9] [10]
H. Komatsu, Japan. Cryst. Soc. 16 (1974) 28. Liang Quenting, Physical Optics (Mechanical Industry Press, Beijing, 1981). K. Moriya and T. Ogawa, J. Crystal Growth 44 (1978) 53.
[11] Deng Peizhen and Qiao Jinwen, J. Crystal Growth 82 (1987) 579. [12] J.W. Matthews, E. Kloktlolm, T.S. Plaskeh and V. Sadegopan, Phys. Status Solidi (a) 19 (1973) 671. [13] H.S. Bagdasarov and L.M. Doduk, Kristallografia 15 (1970) 334 [14] Deng Peizhen, Zhang Shoudu, Wang Haobmg and Qian Zhemn, J. Chinese Silicate Soc. 7 (1979) 168. [151J. Friedel, Dislocations (Pergamon, Oxford, 1964) pp. 123—133. [16] J.P. Hirth, Theory of Dislocations, 2nd ed. (1982) p. 589. [17] J. Friedel, Dislocations (Pergamon, Oxford, 1964) p. 124. [18] J. Friedel, Dislocations (Pergamon, Oxford, 1964) p. 326. [19] Qiao Jinwen, Den Peizhen and Qian Zhenin, Artifacial Crystals 1 (1986) 69. [20] WA. Tiller and K.A. Jackson, Acta Met, 1 (1953) 428. [21] R.A. Laudise, The Growth of Single Crystals (Prentice Hall, Englewood Cliffs, NJ, 1970). [22] NB. Urli and J.W. Corbett, in: Radiation Effects in Semiconductors 1976, Inst. Phys. Conf, Ser. 31, Eds. N.B. Urli and J.W. Corbett (Inst. Phys., London—Bristol, 1977) p. 12. [23] J.L. Caslavsky and D. Viechinicki, J. Mater. Sci., 15 (1980) 1709. [24] Deng Peizhen, Zhang Shoudu, Qiao Jinwen and Qian Zhemn, Ada Phys. Sinica 4 (1976) 284.