DE20122681U1 - Device for growing large volume single crystals has heating element arranged on side walls of melt crucible to prevent lateral radial heat flow - Google Patents

Abstract

Device for growing large volume single crystals comprises a housing (10) in which a melt crucible (20) with side walls (22), a base (24), a top opening (26) facing the base and optionally a lid (28) are located; and at least one heating element (50, 50'). At least one heating element is arranged on the side walls of the melt crucible (20) to prevent lateral radial heat flow. An independent claim is also included for a process for growing large volume single crystals using the above device. Preferred Features: The elements arranged on the side walls prevent lateral heat flow so that a planar solid/liquid phase boundary surface is formed during crystal growth which has a bending radius of at least 1 m. The base of the crucible has a conical shape.

Description

The Invention relates to new large volume Single crystals of uniform orientation, in particular for photolithography.

Single crystals are characterized by being over their entire volume have a uniform orientation. This is a requirement for this, that one high optical homogeneity present in the entire crystal volume. That's why they are suitable Excellent for use in the optical industry or also as starting material for optical components in DUV photolithography as for steppers or excimer laser.

The Breed single crystals of the melt is known per se. In textbooks on crystal growing such as the 1088 pages comprehensive work of K.-Th. Wilke and J. Bohm, "Crystal Growth" are a variety of methods to breed of crystals, of which the most common Techniques briefly mentioned become. In principle, you can Crystals from the gas phase, the melt, from solutions or even from one solid phase can be grown by recrystallization or solid-state diffusion. These are usually only for the laboratory scale thought and not for the large-scale suitable for industrial production. The main industrial Melt grow process for the production of crystals will be briefly explained below.

At the Czochralski method is a slightly cooled crystal nucleus using a finger into a crucible with molten crystal raw material immersed and slowly pulled out, preferably with rotation. It grows when pulling out a larger crystal at.

This Method has the disadvantage that by the cooling on the crystal relatively large temperature changes are generated, which lead to a stress-induced anisotropy.

At the vertical Bridgman process is in a moving crucible a crystal raw material is melted by means of a heating mantle, in which case the crucible in an axial built by the heater Temperature gradient slowly out of the heating jacket is lowered, or it is alternatively a fixed crucible one movable heating device shifted upward, with the Melt cools and a seed added grows slowly. In a variant of this, the so-called Bridgman Stockbager method is the movable crucible in an axial gradient between two superposed heating jackets, between where a sharp temperature level is formed, forming a crystal slowly lowered.

At the so-called Vertical Gradient Freeze (VGF) method several above each other around the fixed crucible lying concentric heating circuits arranged jacket-shaped. Each of these Heating circuits can be drive separately. By slowing down the heating power Each individual heating circuit arranged around the crucible wall can be located slow down the temperature below the crystallization point, creating a radial temperature gradient along which the crystal growth takes place.

at the so-called gradient solidification method (GSM) is increased by one fixed crucible a ring surrounding this circular heating slowly down and up again.

oriented Single crystals usually show despite no homogeneous optical and mechanical properties. It is desirable Such crystals with a for to design the appropriate purpose of use suitable crystal orientation. This However, it gives rise to special problems in the production of large single crystals Problems, because they spontaneously orientate themselves during their breeding, i.e. change the position of the crystal axis, resulting in optically inhomogeneous crystals where the refraction of light not the same in all areas.

So far it was possible To produce crystals that have single of these properties, however, so far it has not been possible high volume to grow uniformly oriented crystals that are free of convergences are optically highly homogeneous, have a high transmission and also when exposed to a strong radiation source do not discolor.

In the previously known procedures, for example in the production of large calcium fluoride monocrystals, attempts were made to grow the crystal in the direction of the {111} axis, but the yield was very low, ie only about 6-8% of the growth processes to the satisfactory size. Since it is a process with about 6-week duration in such crystal growing process, and the number of such breeding plants for cost reasons be limited, only a small yield. In addition, it was not possible with the previous methods, large-volume, in particular, far in all three spatial directions extending single crystals, ie preferably produce round crystals with a diameter of> 200 mm and a height of> 100 mm, since at such dimensions within the crystal volume train blocks regularly, ie there was a reorientation of the crystal axes. Moreover, it has not yet been possible to make such large crystals in a satisfactory manner optically highly homogeneous, ie that the refraction of light is the same in all areas. Another problem for such crystals is the radiation resistance, ie that they do not discolor when exposed to a strong radiation source such as a laser, which leads to a reduction in the yield, for example, in the large-scale production of wafers.

It has already been tried to produce large single crystals by that these are bred in the form of plates. So describes For example, EP-A-0 338 411 discloses an apparatus and a method for controlled growth of large single crystals in sheet form from a melt in which a crucible with a rectangular cross-section is configured such that this relatively wide and two relatively narrow side walls and closely adjacent to the wide sides of heaters are arranged. In this case, after melting the crucible means a lift slowly lowered from the heating mantle, resulting in whose contents cool and crystallized. Although it is possible with this method large oriented However, these do not have sufficient Expansion in all three spatial directions.

The The invention therefore aims to provide such bulky crystals, in any chosen Adjustment along their {h, k, l axes} preferably in the {111} or {112} orientation are.

The Another object of the invention is to provide such large-volume crystals, which extend far in all three spatial directions.

This The aim of the invention with the in the claims reached defined crystals.

It was in fact surprising found that large-volume Crystals in hitherto unknown optical quality thereby when prepared with an axial i. parallel to Growth direction extending temperature gradient or an axial running heat flow breeds and at the same time a radial lateral heat flow avoids. This is one possible level interface between solid crystalline and molten liquid phase educated. In contrast, the prior art becomes prevalent a lateral radial heat flow generated, either as the sole Wärmezu- or heat dissipation or together with heating elements arranged above and below a crucible.

The invention therefore relates to large-volume single crystals having a diameter of at least 200 mm, preferably at least 250 mm and in particular at least 300 mm and a height of at least 100 mm, preferably 130 mm and in particular at least 140 mm. They show an extremely high optical homogeneity over the entire crystal volume, ie that the maximum change in the refractive index of the refraction across the crystal volume has a maximum difference of δn ≦ 3 × 10 ^-6, preferably ≦ 2 × 10 ^-6, in particular ≦ 1 × 10 ^{. 6} and the stress birefringence SDB <3 nm / cm, in particular <2 nm / cm, in particular <1 nm / cm. Preferred crystal materials are MgF ₂ , BaF ₂ , SrF ₂ , LiF and NaF, with CaF _{2 being} particularly preferred.

The large volume according to the invention Single crystals are grown in a device comprising a lockable housing arranged therein melting vessel and comprises at least one heating element that generates a heating power, sufficient for the present in the melting vessel crystal raw material to melt and / or already melted crystal raw mass in to keep molten state.

The Melting vessel is preferred round-shaped. In special cases but it may also be appropriate that the melting vessel is an oval or quadrangular cross-section. The melting vessel comprises an inner receiving space, or

hearth which is formed from the melting pot bottom, side walls and a floor opposite upper opening.

In a particular embodiment, the bottom opening opposite the upper opening is closed by a cover. In this case, the cover is preferably designed such that it does not rest gas-tight on the side walls, but leaves emerging during the melting evaporating impurities from the melting or crystal space. Around the crucible, at least one preferably several elements are arranged laterally, which prevent a radial lateral heat flow. Preferably, the lateral elements are heat insulators, especially those made of heat-insulating material. In a particular embodiment, the device has a laterally spaced from the crucible support heating, which should prevent lateral heat flow. Conveniently, this support heater is arranged at a distance from the melting vessel, which is sufficient so that their heat generated can exert no direct influence on the processes in the melt. The support heater is only possible, between the crucible and the compensate for its surrounding heat flow preventing elements and ambient temperature gradients. It is therefore usually spaced from the walls of the crucible by an intermediate layer of thermal insulation elements. Preferably, the support heater is designed as a jacket heater.

Of the Bottom of the melting pot can be designed arbitrarily. Usually However, it is cone-shaped lowered. He forms a pyramid or preferably one Cone out, being frustoconical Pyramids or cones are particularly preferred.

Of the Crucible bottom preferably has a downwardly exiting pocket on, the inclusion of a seed or seed crystal with a predetermined orientation serves. The germinal bag is preferably in the middle of the soil, i.e. at the cone or Pyramid tip arranged. In a preferred embodiment the germ pocket has a cooling element, in particular at its lower end on. This cooling element is preferably a water-filled cooling element, which in the Germinating pocket protects the seed crystal from melting of the crystal raw material to be prematurely on or melted. In a preferred embodiment is the cooling element heated.

In a preferred embodiment the crucible has one arranged above the melting space extended buffer space, which serves as a funnel for filling the Crystal raw material serves. In particular, he serves, however, the to equilibrate the amount of heat emitted by a lid heater, so that evenly acting on the crystal mass heat flow is generated and possibly occurring at the heating local temperature differences be compensated. Preferably, the actual melting space with a thermally conductive Cover provided the insulation space and the actual Melting room separates. It also serves the temperature equilibration and consists of a only slightly insulating or insulating material.

The Device now has at least one above the melting vessel arranged Heating element on. Due to the surrounding of the melting vessel, a lateral heat flow preventing insulation element, is created by heating this above the melting vessel arranged heating element, one in the melting vessel exclusively axial running heat flow. A lateral heat flow is prevented by the insulation elements. This upper heating element is suitably one Lid heating.

It has proved to be advantageous, in addition to the lid heating on Melting vessel bottom a floor heating to install. It can be between lid heating and floor heating an even better axial Build up heat flow or temperature gradient, which is very finely adjustable.

Conveniently, In this case, the bottom heating is arranged below the bottom of the crucible, that this does not include or at least isolate the germ pocket with respect to it is to premature unwanted melting of the crystal nucleus / seed crystal to avoid.

In a preferred embodiment are all Heating elements in an envelope surrounding the melting vessel Insulation material included to create this way to avoid unwanted and uncontrolled heat flow.

It has also proved to be useful the outer wall the melting vessel as possible without Distance closely running one or more temperature measuring elements to arrange. Preferably, the one or more measuring elements is / are as a sliding element trained, which from the outside during operation of the device along the side wall are slidably mounted around the so from the bottom of the vessel vessel cover to measure axially extending temperature gradient. Preferred measuring elements are thermocouples, thermistors and especially pyrometers.

In a particularly preferred embodiment the device has a device with which the boundary between solid crystalline and molten liquid phase can be determined. As appropriate has for this a phase switch proved, the one in a hollow guide tube extending probe rod which extends into the melting vessel and wherein the rod in the guide tube can be lowered slowly down to the solid crystalline Phase is felt. In another preferred embodiment the phase sensor consists of an ultrasonic device, which immersed in the melt from above and reflected at the phase interface Measures sound waves and determines the crystal growth in this way.

In a further embodiment, the device has a capacitor arranged above the opening of the crucible, which separates any material vapors emerging. In a further preferred embodiment, the housing of the device comprises a closable and openable cover, via which the melting vessel can be charged with crystal raw material and the finished crystal can be removed. Preferably, the housing has at least one opening to Ventilate or vent the entire interior. About this opening, the interior of the device can be placed under vacuum and / or possibly filled with a protective gas.

The inside the case arranged elements are preferably made of graphite. It will the melting vessel from a good heat conducting formed pressed graphite. The insulating material is preferably from a loosely packed graphite, in particular fiber materials Graphite wool or graphite mats. The heating elements are also expediently formed from graphite, with heat-generating, electrically conductive Graphite paths meander around the area to be heated wind and generate heat as current resistance heating. To avoid of short circuits become the live ones Elements from the adjacent graphite parts by means of insulators in Distance kept. Preferred insulators are boron nitride.

The casing usually exists made of a chemically resistant, heat-resistant material and is preferably a steel alloy, with stainless steel being particularly preferred. Indeed has in many cases Constructional steel proved sufficient.

With Such a device makes it possible the large-volume invention Produce single crystals in previously unknown optical quality. In this case, the procedure is such that you have a crystal mass in melted a vessel that a floor, side walls, an upper opening and optionally one the upper opening at least partially closes Cover has. In principle it is also possible to use the crystal raw material already in the molten state to introduce into the melting vessel.

to Production of the large-volume invention Single crystals are proceeded by starting the melt from the bottom of the crucible slowly towards the enamel surface one over the enamel surface arranged lid heating slowly cools, being at the bottom of the vessel Forming crystal nucleus, which then along the temperature gradient or along the heat flow axis grows. The procedure is such that only a heat flow or temperature gradient between the bottom of the vessel and the enamel surface or the cover or lid heating is formed. This means, that in the crucible on top of each other lying temperature surfaces which are flat, with the temperature of the bottom of the crucible to the surface the melt or lid heating increases, wherein within a temperature surface or Temperature level at all points the temperature is the same, i. that they do not exceed 2 ° C varied. Preferably, the temperature increase between the vessel bottom and the surface the melt continuously. Unless the areas in which the temperature is equal, a minimal curvature have their radius ≥ 1 m. Radii> 2 m are particularly preferred, with radii> 4 m being particularly preferred.

On This way, a phase boundary between the solid crystalline is created and the liquid molten phase, which varies along the temperature profile, i. parallel to the planes of the same temperature forms and the vertical growing to these levels.

The for the breeding the crystals of the invention necessary plane phase interface is achieved by making a lateral, i. radial heat flow avoids. This is done by means of lateral especially around the walls of the Melting vessel arranged Achieved elements. Such elements are preferably a support heater and / or an insulation material. More preferably, it is spaced along the side walls heating elements to arrange the exclusively the temperature support serve. It is the between melting vessel and spaced heating, which is preferably designed as a jacket heating, resulting Interspace filled with insulation material, which on the one hand a lateral heat dissipation and thus preventing the formation of a radial temperature gradient and which, on the other hand, prevents the support heater from overheating locally Melting vessel produced. The support heating serves essentially to eventual through the insulation jacket passing heat losses counteract and support so the radial leveling of the temperature profile.

in principle Is it possible the axial heat flow exclusively form by a cover heating arranged above the crucible. However, it is preferably also the crucible bottom by means of a floor heating to heat up, so that a temperature gradient between lid and Floor heating is formed.

To produce the crystals according to the invention, it is preferred to promote crystal growth by means of a seed crystal present at the bottom of the melting vessel. The seed crystal is preferably a monocrystal which is introduced into a seed pocket attached to the bottom of the vessel, preferably such that its orientation corresponds to the desired later orientation of the bulky single crystal. During melting, the procedure is then such that the crystal raw material present in the vessel is melted by heating the cover heating and preferably the bottom heating. Optionally, the jacket heater is used here to assist. The crucible is preferably heated to a temperature at which any water of crystallization is released first. Thereafter, the temperature is further increased, optionally dissolved gases or gaseous parts bound in the crystal bulk mass, as well as formed by heating gaseous decomposition products, are released.

Then will over a longer one Period preferably at least one day homogenized the enamel. This is achieved in particular by the heating power of the Heating elements is set such that in the melt a Convection is created, whereby this is constantly mixed, so that dissolved and unwanted Impurities reach the enamel surface, where in particular quite volatile Can evaporate substances. Here also with evaporated crystal material is in a preferably cooled Capacitor deposited. Preferably, the homogenization the melt at least two days, but in particular at least carried out five days, where at least one week is very particularly preferred.

During the Melting and during the Homogenization is the present in the germ pocket crystal nucleus preferably cooled, to prevent premature melting or melting. This usually happens by means of a water cooling. The cooling is expediently by means of a water-cooled Grafitstabes performed.

To End of melting and homogenization of the melt is the crystal germ carefully melted. This usually happens in that the cooling power is reduced and / or a germ pocket heating is turned on. there the seed crystal is carefully melted from top to bottom, so that a uniform transition between crystal nucleus and the melt arises. After that, the axial temperature gradient formed by either the Heating power of the lid heating and / or the floor heating slowly is lowered. Preferably, however, the procedure is that the Ceiling heating is set to a temperature that is the same or above, preferably slightly above the crystallization temperature of the crystal to be produced. Appropriate lid heating temperatures are 200-300 ° C above the crystallization temperature. The temperature of the floor heating is expediently at least 650 ° C preferably at least 900 ° C, However, it is lower than the melting temperature in crystal growing. Thereafter, the heating power of the floor heating is lowered slowly. By lowering the floor heating to a temperature below the crystallization temperature cools the Melt slowly along the axial temperature gradient, with the phase interface, which forms at the level of crystallization temperature, in the melting vessel slowly from top to bottom, causing the crystal to grow. in principle it is also possible Shut down the temperature of the lid heater. Here is the Shut down temperature at a speed at which the Crystal growth 0.01 to 5 mm / hour, preferably 0.1 to 1 mm / hour and in particular 0.2 to 0.5 mm / hour. These values usually become at a cooling rate from 0.001 to 5 ° C reached per hour.

It has proven to be beneficial when the temperature in the already crystallized phase, i. in the grown crystal, during the growth process not the temperature threshold falls below, in the still a plastic form takes place. Therefore, behind the phase boundary should one possible flat axial temperature gradient done.

It has proved to be useful in the lower cone-shaped Bottom part of the crucible, i. in the part that is between the Germ pocket and the crucible wall forms the bottom, at the beginning of the crystal growth form a non-planar up to the lid curved phase interface, the one radius <1 m, preferably <0.8 m, in particular <0.5 m has.

To Completion of the single crystal according to the invention the crystal thus obtained is preferably tempered. It will be possibly present crystalline inhomogeneities at elevated temperature, i.e. Crystal defects are annealed at this temperature. To the crystal growing and tempering becomes the entire large volume Single crystal slowly cooled to room temperature. Such cooling is usually over several Days to several weeks, depending on the phase and step preferably at a cooling rate of about 0.001 ° C / hour to 15 ° C / hour, in particular up to 10 ° C / hour and expediently up to 1 ° C / hour, being 0.01 ° C / hour to 8 ° C / hour, especially 3 ° C / hour is preferred. Also when cooling is preferably a substantially axial temperature gradient maintained. However, this can on the side support heating possibly be waived. By such a slow cooling high volume Get crystals that are exceptionally high Freedom from stress. The cooling rate is preferably by means of several arranged in the inventive device temperature sensor controlled. In this way can be the temperature profile of the cooling also regulate, what as well as in the crystal growth expediently performed by a computer becomes.

The for producing the inventive Crystals used crystal includes in particular raw materials, which also contain scavengers in addition to the crystal material, which react in a Homogenisierungsphase with any impurities present to volatile substances.

The crystals of the invention are preferably grown in a vacuum between 10 ^-3 to 10 ^-6 mbar (corresponding to 10 ^-1 to 10 ^-4 Pa) and preferably between 10 ^-9 and 10 ^-5 mbar (10 ^-2 to 10 ^-3 Pa) , It is particularly preferred to grow the crystals in a protective gas atmosphere, in particular a non-oxidizing atmosphere. The entire apparatus is flushed before or during the heating with an inert gas or an inert gas mixture.

at The preparation of the crystals according to the invention becomes the device preferably vibration-free stored. The melting vessel and the Heating elements are during firm and unchangeable stored to each other.

The large volume crystals of the invention are particularly suitable for the production of optical components for the DUV lithography and for the production of photoresist coated Wafers and thus for the production of electronic devices. The The invention therefore also relates to lenses, prisms, light guide rods, optical Windows and optical devices for the DUV lithography in particular stepper and excimer laser, those Contain crystals.

The Invention will be explained in more detail with reference to the following figures and the example. Show it

1 a device for cultivating the large-volume crystals according to the invention,

2 a single crystal according to the invention with a diameter of 385 mm and a height of about 160 mm produced with this device.

3 shows single crystal slices, which consist of the single crystal of 2 were manufactured.

As in 1 illustrated, the inventive device comprises a particularly double-walled housing 10 in which the crucible formed of pressed graphite 20 is arranged. The melting pot 20 has an interior 30 (Melting or crystallization space), passing through walls 22 , a cone-shaped bottom formed in the shape of a blunt cone 24 and an upper crucible opening 26 is formed, which by means of a cover 28 partially closed. In the upper part of the crucible is a funnel-shaped buffer space 40 arranged, made of the same material as the crucible 20 formed and preferably connected in one piece with the sem. The buffer space 40 itself also has side walls 42 , a cover 48 as well as a floor 44 on that with the side walls 22 of the melting vessel 20 connected is. Above the buffer space 40 is a lid heater 50 . 50 ' arranged, which a floor heating 52 opposite. The underfloor heating 52 is the side of the germ pocket 32 arranged and kept apart from this, so that the seed crystal present therein does not melt prematurely. At the bottom, the germ pocket contains a water-cooled graphite rod 70 , On the side of the germ pocket and the water-cooled graphite rod 70 are lateral heating elements 56 arranged for targeted melting of the seed crystal. In addition, side of the crucible 20 a trained as a sliding element temperature measuring element 60 arranged, with which the exact axial temperature profile can be determined.

The side walls 22 of the vessel 20 are completely covered by an insulation jacket 82 surround. The insulation jacket 82 spaced a lateral jacket-shaped support heater 54 , The heating elements 50 . 50 ' . 52 . 54 and 56 and the crucible 20 with germ pocket 32 and the overlying buffer part 40 are made of an insulating material made of graphite 80 surrounded, which prevents lateral heat flow and only one between lid heating and crucible bottom 24 or floor heating 52 trained axial temperature gradient allowed.

The device has an opening, not shown, for purging with an inert gas or for applying a vacuum. To determine the size of the growing crystal or the position of the phase interface is a passing through the outside through the housing phase sensor 90 present, which one in an outer tube 92 lying displaceable rod 94 contains, which is slowly lowered down and with which the solid phase interface can be felt. In principle, the pipe 92 also with the staff 94 be connected. For separating impurities removed during homogenization, a capacitor is above the crucible 95 arranged.

example 1

It is to produce a calcium fluoride single crystal of the interior 30 of the melting vessel 20 filled with a calcium fluoride mixture containing additional scavenger materials with a high affinity for oxygen, such as PbF ₂ , SnF ₂ or CdF ₂ , the device is filled by means of an in 1 not shown lid closed and to remove unwanted atmospheric oxygen purged with nitrogen as an inert gas. Thereafter, a vacuum of 10 ^-9 mbar (10 ^-2 Pa) is applied and while cooling the germ pocket, the lid heating 50 . 50 ' , the floor heating 52 and optionally the jacket heating 54 and slowly heated to 1450 ° C over several hours. The mixture is then homogenized for five days at this temperature, whereby convection is maintained in the melt. After homogenization, the floor heating is lowered to a temperature of 1200 ° C and by means of germ pocket heating 26 the seed crystal carefully melted. After switching off the germ pocket heating, the lid heating is activated 50 . 50 ' held constant and the floor heating slowly down several days down to a temperature below the crystallization point, starting from the crystal nucleus grows a single crystal in the direction of the surface of the melt. The resulting single crystal has the same orientation as the crystal nucleus. After the entire melt is solidified to form a single crystal, the thus obtained single crystal is annealed and cooled to room temperature over a period of three weeks. In this way, a single crystal having a diameter of 385 cm and a height of 161 mm (without a seed pocket) is obtained. The single crystal has a fluctuation of the refractive index Δn of <1 × 10 ^-6 over the entire crystal volume. Its stress birefringence SDB is <1 nm / cm. In addition, the crystal thus obtained exhibits an extremely high radiation resistance.

Claims (5)

Large volume single crystal having its entire volume having uniform orientation characterized in that the refractive index in the whole crystal volume has a maximum difference of ≤ 1 x 10 ^-6 and the birefringence SDB is <1 nm / cm. Crystal according to claim 1, characterized in that it is a MgF ₂ , BaF ₂ , SrF ₂ , LiF, NaF or CaF ₂ crystal. Crystal according to claim 1 or 2, obtainable by a crystal growth at a flat phase interface solid / liquid, the has a radius of curvature of ≥ 1 m. Crystals according to one of the preceding claims with uniform orientation obtainable from a melt of crystal raw material in a device comprising a closable housing ( 10 ) with side walls ( 22 ), a floor ( 24 ), one to the ground ( 24 ) opposite upper opening ( 26 ) and optionally a cover ( 28 ) having melting vessel ( 20 ), and at least one heating element ( 50 . 50 ' ), wherein in the melting vessel ( 20 ) present crystal raw material by means of heating elements ( 50 . 50 ' ), as long as it is heated to a temperature above the melting point until a melt having a surface, and / or already molten crystal raw material is introduced into the melting vessel, and then by lowering the temperature to at least the crystallization point at the bottom of the melting vessel a single crystal is formed with the melt, a solid / liquid phase interface at which the single crystal grows in a direction perpendicular to the phase interface to the melt surface, the phase interface is flat and has a radius of curvature of at least one meter, with between the bottom ( 24 ) of the melting vessel ( 20 ) and its upper opening ( 26 ) a vertically extending axial temperature gradient is applied and a through the side walls ( 22 ) running Wärmezu- and / or heat dissipation is avoided. Crystal according to one of the preceding claims, characterized available, that predetermined by a seed crystal, the growth direction becomes.