KR20100093398A - Method for manufacturing single crystal with uniform distribution of low density grown-in defect, apparatus for implementing the same and single crystal manufactured thereof - Google Patents

Abstract

PURPOSE: A monocrystal manufactured with a monocrystal making method with a crystal defect distribution of low density uniform, and a manufacturing device and its method are provided to have 10% of FPD(Flow Pattern Defect) density deviation in the longitudinal direction of a monocrystal, and to raise a single crystal having low FPD density distribution less than 250ea/cm^2. CONSTITUTION: A quartz crucible(20) is installed inside a chamber(10). A crucible housing(30) supports the quartz crucible to a specific form. A crucible rotation number shift(40) raises or drops the quartz crucible. A heater(50) heats the quartz crucible. A heat insulating mean(60) prevents the leakage of heat generating from the heater. A monocrystal means of pulling up(70) increases a monocrystal to the specified direction while rotating it.

Description

Method for manufacturing single crystal with uniform distribution of low density grown-in defect, Apparatus for implementing the same and Single crystal manufactured according to the present invention

The present invention relates to a single crystal manufacturing method, and more particularly, to a single crystal manufacturing method, apparatus and method for producing a low density and uniform distribution of crystal defects introduced during single crystal growth using Czochralski method. It relates to a single crystal produced by.

Semiconductor wafers used as semiconductor device substrates today are mainly manufactured from single crystals grown by the Czochralski (hereinafter referred to as CZ) method. In recent years, gate oxide integrity (GOI) is an important quality factor for highly integrated semiconductor devices and non-memory devices. In order to improve these GOI properties, it is necessary to improve the surface properties of the wafer and control the growth-in defects present in the single crystal in terms of the single crystal. In particular, it is important to control void defects such as Crystal Originated Particle (COP) and Flow Pattern Defect (FPD).

When a single crystal is grown, vacancy point defects and interstitial point defects are introduced into the single crystal due to changes in temperature gradients and pulling speeds of the liquid-liquid interface. Existing equilibrium concentrations cause aggregation to develop into three-dimensional solid defects.

According to Boronkov's theory known in the art of single crystal growth, the concentration of point defects present in single crystals depends on the V / G ratio. That is, when the V / G value exceeds a certain threshold, bacon defects tend to flow into the single crystal, and when the V / G value falls below a certain threshold, interstitial defects tend to flow into the single crystal. Where V is the growth rate of the single crystal when the single crystal is grown by the CZ method and G is the vertical temperature gradient in the crystal near the solid-liquid interface.

Void defects, such as COP and FPD, originate from bacon defects. COP is a defect in which the octahedral void defects formed by agglomeration of excess baconic defects during crystal growth are observed on the wafer surface by mirror wafer processing and observed in the form of square pits. In addition, the FPD is a defect observed in the wave flow pattern after secco etching due to the same bacon aggregate defect as the COP, except that the measurement method is different.

Previous studies have reported that the main cause of GOI deterioration is closely related to FPD defects in wafers. In order to reduce the density of the FPD, the single crystal pulling rate is lowered to decrease the concentration of bacon defects flowing into the single crystal, and the density of the single crystals is reduced to increase the size of the coagulant defects supersaturated during cooling. The so-called slow cooling method of lowering the cooling rate is mainly used.

However, the method of lowering the pulling speed of the single crystal has a problem of lowering productivity. In addition, the slow cooling method has a limitation in ensuring homogeneity of the FPD distribution in the longitudinal direction of the single crystal. The reason for this is as follows. The single crystal grown by the CZ method has a difference in thermal history in the longitudinal direction as the single crystal grows. In general, the longitudinal side of the single crystal grown early on the basis of the body of the single crystal is cooled rapidly, and the tail side of the single crystal grown in the latter half is cooled slowly. As a result, the proximal portion of the single crystal has a high density of FPD distribution by facilitating aggregation of baconic defects, and the unidentified portion of the single crystal has a low density of FPD distribution due to relatively less aggregation of baconic defects. For this reason, when the single crystal is grown by the conventional CZ method, the homogeneity of the density distribution of FPD in the longitudinal direction of the single crystal is inferior.

1 is a graph showing the measurement of the density change of FPD in the longitudinal direction of the single crystal when the silicon single crystal is grown by the CZ method while controlling the FPD density to 500ea / cm ² level, Figure 2 shows the FPD density 300ea / cm ² When the silicon single crystal is grown by the CZ method while controlling at the level, the graph shows the density change of the FPD in the longitudinal direction of the single crystal.

As shown in the figure, the FPD density was 500ea / cm ² When controlled at the level, homogeneity of the FPD density in the longitudinal direction of the single crystal could be maintained at around 10%, which did not significantly affect the yield.

However, lowering the FPD density to improve GOI characteristics results in 300ea / cm ² In the case of the level control, the homogeneity of the FPD density in the length direction of the single crystal was worsened to 50% or more, which caused a problem of lowering the yield.

Therefore, the FPD density is 300ea / cm ² Or less, more preferably 250ea / cm ² In order to manufacture a wafer having excellent GOI characteristics, it is necessary to identify process factors affecting the FPD density and readjust the process factors to improve the uniformity of the FPD density distribution throughout the single crystal.

The present invention was devised to solve the above problems of the prior art, and can improve the uniformity of the FPD density distribution in the longitudinal direction and the radial direction of the single crystal, and in particular, within 10% of the deviation in the longitudinal direction of the single crystal. It is an object of the present invention to provide a method for producing a single crystal having a uniform FPD density distribution and a low FPD density distribution of 250 ea / cm ² or less, a single crystal manufacturing apparatus for implementing the method, and a single crystal manufactured by the method. .

In order to achieve the above technical problem, the low-density single crystal manufacturing method having a uniform distribution of crystal defects according to the present invention, after dipping the seed in the melt contained in the quartz crucible, raise the top while rotating the seed to grow the Czochralski In the single crystal manufacturing method using the method, in the body process of growing a single crystal body, in the early stage of the body process, the pulling rate of the single crystal is controlled lower than the target pulling rate, and the melt gap is increased than the target melt gap, and the target is later in the body process. It is characterized by controlling the pulling speed of the single crystal higher than the pulling speed and reducing the melt gap than the target melt gap.

Preferably, the pulling speed of the single crystal is controlled to be higher or lower than the target pulling speed in the range of 5 to 15% based on the target pulling speed of the single crystal.

Preferably, the melt gap is controlled to be larger or smaller than the target melt gap in the range of 10 to 20% based on the target melt gap.

In order to achieve the above technical problem, a single crystal manufacturing apparatus having a low density crystal defect distribution according to the present invention includes a quartz crucible containing a melt, a crucible rotating means for rotating a quartz crucible, a heater installed around a quartz crucible sidewall, and a seed. In the single crystal manufacturing apparatus using the Czochralski method comprising a single crystal pulling means for pulling up the single crystal from the melt contained in the quartz crucible and a heat shield means for blocking heat emitted from the single crystal and forming a melt gap with the surface of the melt. And a single crystal growth control unit controlling the single crystal pulling unit and the crucible rotating unit, wherein in the body process of growing the single crystal body, the single crystal growth control unit controls the pulling rate of the single crystal lower than the target pulling rate at the beginning of the body process. Increase the melt gap than the target melt gap, and In the second process, the pulling speed of the single crystal is controlled higher than the target pulling speed, and the melt gap is reduced than the target melting gap.

Preferably, the single crystal growth control unit controls the single crystal pulling means to control the pulling speed of the single crystal higher or lower than the target pulling speed in the range of 5 to 15% based on the target pulling speed.

Preferably, the single crystal growth control unit controls the crucible rotating means to control the melt gap larger or smaller than the target melt gap in the range of 10 to 20% based on the target melt gap.

Alternatively, the single crystal manufacturing apparatus according to the present invention may further include heat shield driving means for moving the heat shield means up and down. In this case, the single crystal growth control unit may control the melt gap by controlling the heat shield driving means.

The above technical problem is also achieved by a single crystal grown by the single crystal manufacturing method according to the present invention. The single crystal grown according to the present invention has a density of FPD (Flow Pattern Defect) measured in the longitudinal direction based on the center of the single crystal of 250ea / cm ² Or less than 10%.

Preferably, the single crystal has an FPD density of 300ea / cm ^{2 in} the radial direction of the single crystal. It is as follows.

According to the present invention, the density distribution of the FPD can be made uniform in the longitudinal direction and the radial direction of the single crystal. In particular, it has a FPD density variation of less than 10% in the length direction of the single crystal, and 250ea / cm ² Single crystals having a low FPD density distribution below can be grown. Thereby, manufacture of the wafer excellent in GOI characteristic is attained.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. Prior to this, words used in this specification and claims are not to be construed as limiting in their usual or dictionary sense, but rather to properly define the concept of terms in order to best describe the inventor's own invention in the best way possible. It should be interpreted as meaning and concept corresponding to the technical idea of the present invention based on the principle that it can. Therefore, the embodiments described in the specification and the drawings shown in the drawings are only the most preferred embodiment of the present invention and do not represent all of the technical idea of the present invention, various modifications that can be replaced at the time of the present application It should be understood that there may be equivalents and variations.

3 is a cross-sectional view of an apparatus showing a schematic configuration of a single crystal manufacturing apparatus with low density crystal defect distribution according to an embodiment of the present invention.

Referring to FIG. 3, the single crystal manufacturing apparatus according to the present invention includes a quartz crucible in which a chamber 10, which is a space in which single crystals are grown, is installed inside the chamber 10 and a molten melt M melted at a high temperature ( 20, a crucible housing 30 surrounding the outer circumferential surface of the quartz crucible 20 and supporting the quartz crucible 20 in a predetermined shape, and installed at a lower end of the crucible housing 30, together with the quartz crucible 20 together with the housing 30. The crucible rotating means 40 for raising or lowering the quartz crucible 20 while rotating the heater, a heater 50 for heating the quartz crucible 20 at a predetermined distance from the side wall of the crucible housing 30, and the heater ( A melt (M) accommodated in the quartz crucible 20 by using a heat insulating means 60 and a seed crystal seed to prevent heat from flowing out of the heater 50 to the outside. Single crystal (C) from Single crystal pulling means 70 which is pulled while rotating and heat shield means 80 which shields the external emission of heat emitted to single crystal C and forms melt gap with melt M for temperature gradient control of the solid-liquid interface. do.

Since the above components are typical components of the single crystal manufacturing apparatus using the CZ method, which is well known in the art, detailed description of each component will be omitted.

In the exemplary embodiment of the present invention, the melt M is filled with poly silicon and a dopant and melted using heat applied from the heater 50. However, since the present invention is not limited to the type of the melt M, the type and composition of the melt M vary depending on the type of the semiconductor single crystal grown by the CZ method.

In addition to the above-described components, the single crystal manufacturing apparatus according to the present invention includes a single crystal growth control unit 200 for controlling the crucible rotating means 40 and the single crystal pulling means 70.

The single crystal growth control unit 200 controls the single crystal pulling means 70 and the crucible rotating means 40 in the body process to adjust the melt gap as well as the pulling speed of the single crystal C to lower the density of the single crystal C grown. Ensure that the FPDs are evenly distributed.

Here, the body process refers to a process of growing a single crystal (C) that is commercialized into a wafer while maintaining the diameter of the single crystal (C) at a target diameter. Before the body process, a shoulder process is performed to gradually increase the radius of the single crystal (C) to the target diameter, and after the body process, the tailing to separate the single crystal (C) from the melt (M) while gradually decreasing the radius of the single crystal (C). The process proceeds. Since the shoulder process and the tailing process are commonly used in the single crystal growth process using the CZ method, detailed descriptions thereof will be omitted.

The single crystal growth control unit 200 controls the pulling speed of the single crystal (C) in consideration of the difference in cooling history that changes in the length direction of the single crystal (C) during the body process. In other words, in the early stage of the body process in which the longitudinal side of the body is grown, the pulling rate of the single crystal (C) is decreased than the target pulling rate set as the process condition, and in the latter stage of the body process in which the tail side of the body is grown, the pulling rate of the single crystal (C) is increased. Increase the target pulling speed to the process conditions.

4 is a graph showing the results of computer simulation of the temperature gradient change at the solid-liquid interface as the length of the single crystal increases when the single crystal pulling speed is kept constant.

As shown in FIG. 4, the temperature gradient at the solid-liquid interface has a distribution that decreases from the beginning to the end of body growth. This is because as the body process proceeds, the amount of the melt M decreases so that the heat conducted from the melt M decreases toward the second half of the body process. Since the single crystal (C) grown at the solid-liquid interface is slowly cooled as it is pulled upward, if the monocrystalline pulling speed is kept constant in the body process, the longitudinal side of the single crystal (C) is cooled relatively rapidly due to the temperature gradient difference at the solid-liquid interface. The tail side of the single crystal C is cooled relatively slowly. Since the FPD results from the aggregation of caustic defects during the cooling of the single crystal (C), the density of the FPD is influenced by the cooling rate of the single crystal (C). That is, as shown in Figs. 1 and 2, the longitudinal side of the relatively fast cooling single crystal (C) has a relatively high FPD distribution, and the tail side of the relatively slow cooling single crystal (C) is relatively low FPD It will have a distribution.

However, by changing the single crystal pulling rate as in the present invention, it is possible to mitigate the formation of FPD in the single crystal (C) grown at the beginning of the body process and to strengthen the formation of FPD in the single crystal (C) grown at the later stage of the body process. have. This is because when the single crystal pulling speed is lower than the target pulling speed, the cooling rate decreases and the density of bacon defects decreases. On the contrary, when the single crystal pulling speed increases than the target pulling speed, the cooling speed increases and the density of bacon defects increases. . However, when only the single crystal pulling speed is controlled, a deviation of the FPD density distribution occurs in the radial direction of the single crystal (C), and the problem arises that the FPD density is excessively increased in the single crystal (C) grown later in the body process.

FIG. 5 is a graph showing the FPD density distribution measured in the radial direction of the single crystal sampled at the longitudinal and tail sides of the single crystal when only the pulling speed of the single crystal was changed in the embodiment of the present invention.

In the figure, <Low P / S> is the FPD density distribution for the longitudinal side of the single crystal C in which the single crystal pulling speed is set lower than the target pulling speed, and <High P / S> is the single crystal pulling speed lower than the target pulling speed. It is FPD density distribution with respect to the tail side part of the single crystal (C) set high.

Referring to FIG. 5, the longitudinal side of the single crystal (C) is grown at a lower pulling speed than the target pulling speed so that the cooling rate decreases, thereby decreasing the overall FPD density. On the contrary, the tail side of the single crystal (C) was grown at a higher pulling speed than the target pulling speed, so that the cooling rate increased and the overall FPD density excessively increased. In addition, the density of the FPD did not show uniform distribution in the direction of the single crystal in both the longitudinal side and the tail side of the single crystal (C). This resulted in a different cooling history in the radial direction as the longitudinal and tail portions of the single crystal (C) were crystallized at the solid-liquid interface and then moved upward. This is because the FPD density increase effect caused by the increase in the cooling rate due to the increase in the pulling rate is much greater than the decrease. Therefore, in order to uniformly form a low density FPD in both the longitudinal direction and the radial direction of the single crystal C, it is necessary to additionally control other process factors in addition to the single crystal pulling speed.

Therefore, the single crystal growth control unit 200 according to the present invention reduces the variation of the FPD density distribution appearing in the radial direction of the single crystal C by changing the pulling speed of the single crystal C, and reduces the FPD density distribution of the uncrystallized side of the single crystal C. The melt gap is further controlled to reduce overall and uniformly implement a low density FPD distribution in the longitudinal direction of the single crystal (C). To this end, the single crystal growth control unit 200 may apply a control signal to the mechanical mechanism for raising or lowering the crucible rotating means 40.

Specifically, the single crystal growth control unit 200 controls the crucible rotating means 40 in the body process to adjust the melt gap by moving the position of the quartz crucible 20 upward or downward. The melt gap is changed in stages in the early, mid and late stages of the body process. For example, in the early stage of the body process where the pulling speed of the single crystal C is controlled to be lower than the target pulling speed, the melt gap is controlled to be larger than the target melt gap set as the process condition, and the pulling speed of the single crystal C is approximately equal to the target pulling speed. In the middle of the matching body process, the melt gap is controlled to be substantially the same as the target melt gap set as the process condition, and in the latter part of the body process in which the pulling speed of the single crystal (C) is higher than the target pulling rate, the melt gap is used as the process condition. The control is smaller than the set target melt gap. Then, the unevenness of the FPD density distribution appearing in the radial direction of the single crystal (C) can be alleviated by the change of the single crystal pulling speed, and the FPD density distribution of the non-uniform side of the single crystal (C) is lowered as a whole, thereby decreasing the overall length and the radial direction of the single crystal (C). In all, low density FPD distributions can be made uniform. This will be described later with reference to FIGS. 6 to 9.

On the other hand, in the above-described embodiment has been described that the adjustment of the melt gap is implemented by the movement of the quartz crucible 20 adjusted by the crucible rotating means 40. However, it is apparent that the present invention is not limited by the manner of adjusting the melt gap, and may be implemented by the movement of the heat shield means 80.

In this case, the single crystal manufacturing apparatus further includes a heat shield driving means (see 210 in FIG. 1), and the single crystal growth control unit 200 controls the heat shield driving means 210 to position the heat shield means 80. Can be moved upward or downward to control the melt gap.

Although not shown in the drawing, the heat shield driving means 210 is a mechanical mechanism that enables the vertical movement of the heat shield means 80 and the guider and the heat shield means 80 for guiding the linear movement of the heat shield means 80. It includes a motor for driving).

6 and 7 are graphs showing the change profile of the single crystal pulling speed and the melt gap in the body process according to the present invention, respectively, and FIG. 8 is shown by the pulling speed and the melt gap change profile of the single crystal shown in FIGS. 6 and 7. It is a graph showing the density change of the FPD in the longitudinal direction of the single crystal when the single crystal is grown, and the single crystal is grown by the pulling rate and the melt gap change profile of the single crystal shown in FIGS. 6 and 7. It is a graph showing the density change of FPD in the radial direction of a single crystal.

6 and 7, in the beginning of the body process, the pulling speed of the single crystal is controlled to be lower than the target pulling speed, and in the latter part of the body process, the pulling speed of the single crystal is controlled to be higher than the target pulling speed. For example, in the beginning of the body process, the single crystal is pulled up at a pulling speed lower than 0.8 mm / min set as the target pulling speed, and in the latter part of the body process, the single crystal is pulled at a pulling speed higher than 0.8 mm / min set as the target pulling speed.

In the beginning of the body process, the melt gap is controlled to be larger than the target melt gap, in the middle of the body process, the melt gap is controlled to be substantially the same as the target melt gap, and in the latter part of the body process, the melt gap is controlled to be smaller than the target melt gap. For example, the melt gap is controlled larger than 45 mm set as the target melt gap at the beginning of the body process, and the melt gap is controlled equal to 45 mm set as the target melt gap at the middle of the body process, and 45 mm set as the target melt gap later in the body process. Control the melt gap small.

In the embodiment of the present invention, it has been described that the target pulling speed is set to 0.8 mm / min, and the target melt gap is set to 45 mm. However, since the present invention is not limited by the target pulling speed and the target melt gap, it is obvious that the target pulling speed and the target melt gap can be changed depending on the diameter, length, crystal quality, hot zone conditions, etc. of the single crystal.

Preferably, the single crystal pulling speed is controlled to be higher or lower than the target pulling speed in the range of 5 to 15% based on the target pulling speed, and the melt gap is higher than the target melt gap in the range of 10 to 20% based on the target melt gap. Control larger or smaller.

Here, when the single crystal pulling rate or the melt gap is less than 5% and 10%, respectively, there is no effect that can achieve homogeneity with respect to the FPD density distribution. On the other hand, if the single crystal pulling speed or the melt gap is 15% or more and 20% or more, respectively, the difference between the target pulling speed or the target melt gap is large and it is difficult to sufficiently secure the quality of the single crystal.

As shown in FIG. 8, by controlling the single crystal pulling speed and the melt gap under the above conditions, the density of the FPD in the longitudinal direction from the center of the single crystal is 250ea / cm ^2. It can be seen that it can be controlled as low as below, to improve the homogeneity of the FPD density distribution by controlling the density deviation of the FPD within 10%. In addition, as shown in FIG. 9, all of the single crystals grown in the beginning, the middle, and the second half of the body process had a density of FPD of 300ea / cm ^{2 in} the radial direction of the single crystal. It can be seen that it can be controlled to a lower or less, and can improve the homogeneity of the FPD density by reducing the FPD density deviation in the radial direction than in the prior art.

As described above, although the present invention has been described by way of limited embodiments and drawings, the present invention is not limited thereto and is intended by those skilled in the art to which the present invention pertains. Of course, various modifications and variations are possible within the scope of equivalents of the claims to be described.

The following drawings, which are attached to this specification, illustrate preferred embodiments of the present invention, and together with the detailed description of the present invention serve to further understand the technical idea of the present invention, the present invention includes the matters described in such drawings. It should not be construed as limited to.

1 shows the FPD density of 500ea / cm ² When the silicon single crystal is grown by the CZ method while controlling at the level, the graph shows the density change of the FPD in the longitudinal direction of the single crystal.

2 shows the FPD density of 300ea / cm ² When the silicon single crystal is grown by the CZ method while controlling at the level, the graph shows the density change of the FPD in the longitudinal direction of the single crystal.

3 is a cross-sectional view of an apparatus showing a schematic configuration of a single crystal manufacturing apparatus with low density crystal defect distribution according to an embodiment of the present invention.

4 is a graph showing the results of computer simulation of the temperature gradient change at the solid-liquid interface as the length of the single crystal increases when the single crystal pulling speed is kept constant.

FIG. 5 is a graph showing the FPD density distribution measured in the radial direction of the single crystal sampled at the end and the tail side of the single crystal when only the pulling speed of the single crystal is changed in the embodiment of the present invention.

6 and 7 are graphs showing the change profile of the single crystal pulling speed and the melt gap in the body process according to the present invention, respectively.

FIG. 8 is a graph showing the density change of the FPD in the longitudinal direction of the single crystal measured at the center of the single crystal when the single crystal is grown by the pulling speed and the melt gap change profile of the single crystal shown in FIGS. 6 and 7.

FIG. 9 is a graph illustrating measurement of the density change of FPD in the radial direction of the single crystal when the single crystal is grown by the pulling speed and the melt gap change profile of the single crystal shown in FIGS. 6 and 7.

Claims (9)

In the single crystal manufacturing method using the Czochralski method of growing a single crystal by dipping the seed in the melt contained in the quartz crucible and then pulling the seed upward while rotating the seed, In the body process of growing a single crystal body, At the beginning of the body process, the pulling speed of the single crystal is controlled lower than the target pulling speed, and the melt gap is increased more than the target melt gap.In the latter part of the body process, the pulling speed of the single crystal is controlled higher than the target pulling speed, and the melt gap is reduced than the target melt gap. Single crystal production method characterized by. The method of claim 1, Single crystal manufacturing method characterized in that the pulling speed of the single crystal is controlled to be higher or lower than the target pulling speed in the range of 5 to 15% based on the target pulling speed of the single crystal. The method of claim 1, Wherein the melt gap is controlled to be larger or smaller than the target melt gap in a range of 10 to 20% based on the target melt gap. A quartz crucible containing the melt, a crucible rotating means for rotating the quartz crucible, a heater installed around the sidewall of the quartz crucible, single crystal pulling means for pulling up the single crystal from the melt contained in the quartz crucible by the seed, and blocking the heat emitted from the single crystal In the single crystal production apparatus using the Czochralski method comprising a heat shield means for forming a melt gap and the surface of the melt, A single crystal growth control unit controlling the single crystal pulling means and the crucible rotating means, In the body process of growing a single crystal body, The single crystal growth control unit controls the pulling speed of the single crystal lower than the target pulling speed at the beginning of the body process, increases the melt gap than the target melt gap, and controls the pulling speed of the single crystal higher than the target pulling speed at the later stage of the body process and the target melt gap. Single crystal manufacturing apparatus characterized by further reducing the melt gap. The method of claim 4, wherein The single crystal growth control unit controls the single crystal pulling means to control the pulling speed of the single crystal higher or lower than the target pulling speed in the range of 5 to 15% based on the target pulling speed. The method of claim 4, wherein The single crystal growth control unit controls the crucible rotating means to control the melt gap larger or smaller than the target melt gap in the range of 10 to 20% based on the target melt gap. The method of claim 6, Further comprising a heat shield driving means for moving the heat shield means up and down, The single crystal growth control unit is a single crystal manufacturing apparatus, characterized in that for controlling the melt gap by controlling the heat shield driving means. The density of the FPD (Flow Pattern Defect) measured in the longitudinal direction from the center of the single crystal is 250ea / cm ² Single crystal, characterized in that less than 10% deviation. The method of claim 8, The single crystal has an FPD density of 300ea / cm ^{2 in} the radial direction of the single crystal. Single crystal characterized by the following.

Images