Abstract:
Heat shields for Czochralski pullers include a ring-shaped heat shield housing comprising inner and outer heat shield housing walls and an oblique heat shield housing floor and a heat shield housing roof that extend between the inner and outer heat shield housing walls. The heat shield housing contains insulating material therein. A support member is configured to support the heat shield housing within the crucible in a Czochralski puller. In one embodiment, the support member includes at least one support arm that extends to the ring-shaped heat shield housing. The at least one support arm may be hollow and may contain insulating material therein. In another embodiment, the support member is a ring-shaped support member. The ring-shaped support member may include inner and outer support member walls containing insulating material therebetween. The ring-shaped support member may also include at least one window therein. The ring-shaped member may be oblique. According to another aspect, the Czochralski puller also includes a heat pack in the enclosure, surrounding the heater. The heat pack includes an upper heat pack housing and a lower heat pack housing. The lower heat pack housing is filled with heat absorbing material. However, the upper heat pack housing is at least partially unfilled with the heat absorbing material. Preferably, all of the heat absorbing material is removed from the upper heat pack so that the upper heat pack housing is free of the heat absorbing material.

Description:
RELATED APPLICATIONS  
       [0001]    This application is a continuation-in-part of U.S. application Ser. No. 08/989,591 entitled “Methods of Manufacturing Monocrystalline Silicon Ingots and Wafers by Controlling Pull Rate Profiles in a Hot Zone Furnace, and Ingots and Wafers Manufactured Thereby”, filed on Dec. 12, 1997, which itself claims the benefit of U.S. Provisional Application No. 60/063,086, entitled “Methods of Forming Semiconductor Ingots and Ingots and Wafers Formed Therefrom”, filed on Oct. 24, 1997, Korean Application No. 97-4291, filed Feb. 13, 1997, and Korean Application No. 97-54899, filed On Oct. 24, 1997, the disclosures of all of which are hereby incorporated herein in their entirety be reference.  
     
    
     
       FIELD OF THE INVENTION  
         [0002]    This invention relates to microelectronic manufacturing methods and devices, and more particularly to silicon ingot manufacturing methods and silicon ingots and wafers manufactured thereby.  
         BACKGROUND OF THE INVENTION  
         [0003]    Integrated circuits are widely used in consumer and commercial applications. Integrated circuits are generally fabricated from monocrystalline silicon. As the integration density of integrated circuits continues to increase, it generally is of increasing importance to provide high-quality monocrystalline semiconductor material for integrated circuits. Integrated circuits are typically produced by fabricating a large ingot of monocrystalline silicon, slicing the ingot into wafers, performing numerous microelectronic fabrication processes on the wafers and then dicing the wafers into individual integrated circuits that are packaged. Because the purity and crystallinity of the silicon ingot can have a large impact on the performance of the ultimate integrated circuit devices that are fabricated therefrom, increased efforts have been made to fabricate ingots and wafers with reduced numbers of defects.  
           [0004]    Conventional methods of manufacturing monocrystalline silicon ingots will now be described. An overview of these methods is provided in Chapter 1 of the textbook “Silicon Processing for the VLSI Era, Volume 1, Process Technology”, by Wolf and Tauber, 1986, pp. 1-35, the disclosure of which is hereby incorporated herein by reference. In manufacturing monocrystalline silicon, electronic grade polysilicon is converted into a monocrystalline silicon ingot. Polycrystalline silicon such as quartzite is refined to produce electronic grade polycrystalline silicon. The refined electronic grade polycrystalline silicon is then grown into a single crystal ingot using the Czochralski (CZ) or Float Zone (FZ) technique. Since the present invention relates to manufacturing a silicon ingot using the CZ technique, this technique will now be described.  
           [0005]    Czochralski growth involves crystalline solidification of atoms from a liquid phase at an interface. In particular, a crucible is loaded with a charge of electronic grade polycrystalline silicon and the charge is melted. A seed crystal of silicon of precise orientation tolerances is lowered into the silicon melt. The seed crystal is then withdrawn at a controlled rate in the axial direction. Both the seed crystal and the crucible are generally rotated during the pulling process, in opposite directions.  
           [0006]    The initial pull rate is generally relatively rapid so that a thin neck of silicon is produced. Then, the melt temperature is reduced and stabilized so that the desired ingot diameter can be formed. This diameter is generally maintained by controlling the pull rate. The pulling continues until the melt is nearly exhausted, at which time a tail is formed.  
           [0007]    [0007]FIG. 1 is a schematic diagram of a Czochralski puller. As shown in FIG. 1, the Czochralski puller  100  includes a furnace, a crystal pulling mechanism, an environment controller and a computer-based control system. The Czochralski furnace is generally referred to as a hot zone furnace. The hot zone furnace includes a heater  104 , a crucible  106  which may be made of quartz, a succeptor  108  which may be made of graphite and a rotation shaft  110  that rotates about an axis in a first direction  112  as shown.  
           [0008]    A cooling jacket or port  132  is cooled by external cooling means such as water cooling. A heat shield  114  may provide additional thermal distribution. A heat pack  102  is filled with heat absorbing material  116  to provide additional thermal distribution.  
           [0009]    The crystal pulling mechanism includes a crystal pulling shaft  120  which may rotate about the axis in a direction  122  opposite the direction  112  as shown. The crystal pulling shaft  120  includes a seed holder  120   a  at the end thereof. The seed holder  120   a  holds a seed crystal  124 , which is pulled from the melt  126  in the crucible  106  to form an ingot  128 .  
           [0010]    The ambient control system may include the chamber enclosure  130 , the cooling jacket  132  and other flow controllers and vacuum exhaust systems that are not shown. A computer-based control system may be used to control the heating elements, puller and other electrical and mechanical elements.  
           [0011]    In order to grow a monocrystalline silicon ingot, the seed crystal  124  is contacted to the silicon melt  126  and is gradually pulled in the axial direction (up). Cooling and solidification of the silicon melt  126  into monocrystalline silicon occurs at the interface  130  between the ingot  128  and the melt  126 . As shown in FIG. 1, the interface  130  is concave relative to the melt  126 .  
           [0012]    Real silicon ingots differ from ideal monocrystalline ingots because they include imperfections or defects. These defects are undesirable in fabricating integrated circuit devices. These defects may be generally classified as point defects or agglomerates (three-dimensional defects). Point defects are of two general types: vacancy point defects and interstitial point defects. In a vacancy point defect, a silicon atom is missing from one of its normal positions in the silicon crystal lattice. This vacancy gives rise to a vacancy point defect. On the other hand, if an atom is found at a non-lattice site (interstitial site) in the silicon crystal, it gives rise to an interstitial point defect.  
           [0013]    Point defects are generally formed at the interface  130  between the silicon melt  126  and the solid silicon  128 . However, as the ingot  128  continues to be pulled, the portion that was at the interface begins to cool. During cooling, diffusion of vacancy point defects and interstitial point defects may cause defects to coalesce and form vacancy agglomerates or interstitial agglomerates. Agglomerates are three-dimensional (large) structures that arise due to coalescence of point defects. Interstitial agglomerates are also referred to as dislocation defects or D-defects. Agglomerates are also sometimes named by the technique that is used to detect these defects. Thus, vacancy agglomerates are sometimes referred to as Crystal-Originated Particles (COP), Laser Scattering Tomography (LST) defects or Flow Pattern Defects (FPD). Interstitial agglomerates are also known as Large Dislocation (L/D) agglomerates. A discussion of defects in monocrystalline silicon is provided in Chapter 2 of the above-mentioned textbook by Wolf and Tauber, the disclosure of which is hereby incorporated herein by reference.  
           [0014]    It is known that many parameters may need to be controlled in order to grow a high purity ingot having low numbers of defects. For example, it is known to control the pull rate of the seed crystal and the temperature gradients in the hot zone structure. Voronkov&#39;s Theory found that the ratio of V to G (referred to as V/G) can determine the point defect concentration in the ingot, where V is the pull rate of the ingot and G is the temperature gradient of the ingot-melt interface. Voronkov&#39;s Theory is described in detail in “ The Mechanism of Swirl Defects Formation in Silicon ” by Voronkov, Journal of Crystal Growth, Vol. 59, 1982, pp. 625-643.  
           [0015]    An application of Voronkov&#39;s Theory may be found in a publication by the present inventor et al. entitled “ Effect of Crystal Defects on Device Characteristics ”, Proceedings of the Second International Symposium on Advanced Science and Technology of Silicon Material, Nov. 25-29, 1996, p. 519. At FIG. 15, reproduced herein as FIG. 2, a graphical illustration of vacancy and interstitial concentrations, as a function of V/G, is shown. Voronkov&#39;s Theory shows that the generation of a vacancy/interstitial mixture in a wafer is determined by V/G. More particularly, for V/G ratios below a critical ratio, an interstitial rich ingot is formed, while for V/G ratios above the critical ratio, a vacancy rich ingot is formed.  
           [0016]    Notwithstanding many theoretical investigations by physicists, material scientists and others, and many practical investigations by Czochralski puller manufacturers, there continues to be a need to provide Czochralski pullers that can reduce the defect density in monocrystalline silicon wafers.  
         SUMMARY OF THE INVENTION  
         [0017]    The present invention provides heat shields for Czochralski pullers that include a ring-shaped heat shield housing comprising inner and outer heat shield housing walls and an oblique heat shield housing floor and a heat shield housing roof that extend between the inner and outer heat shield housing walls. The heat shield housing contains insulating material therein. A support member is configured to support the heat shield housing within the crucible in a Czochralski puller. The inner and outer heat shield walls preferably are vertical inner and outer heat shield walls, and the heat shield housing roof preferably is an oblique heat shield housing roof.  
           [0018]    In one embodiment, the support member includes at least one support arm that extends to the ring-shaped heat shield housing. The at least one support arm may be hollow and may contain insulating material therein. In another embodiment, the support member is a ring-shaped support member. The ring-shaped support member may include inner and outer support member walls containing insulating material therebetween. The ring-shaped support member may also include at least one window therein. The ring-shaped member may be oblique.  
           [0019]    Czochralski pullers according to the present invention may include an enclosure, a crucible in the enclosure that holds a silicon melt, a seed holder in the enclosure adjacent the crucible and a heater in the enclosure surrounding the crucible. A heat shield as described above may also be provided, including a ring-shaped heat shield housing within the crucible and a support member that supports the heat shield housing within the crucible. Czochralski pullers also include means for pulling the seed holder away from the crucible, to thereby pull a monocrystalline silicon ingot from the silicon melt. The monocrystalline silicon ingot has an axis and a cylindrical edge. The silicon melt and the ingot define an ingot-melt interface therebetween. The oblique heat shield floor makes a first angle with the horizontal and the oblique heat shield housing roof makes a second angle with the horizontal. At least one of the inner wall length, the first angle and the second angle preferably are selected to produce a temperature gradient at the ingot-melt interface at the axis that is at least about equal to the temperature gradient at a diffusion length from the cylindrical edge.  
           [0020]    According to another aspect of the invention, the Czochralski puller also includes a heat pack in the enclosure, surrounding the heater. The heat pack includes an upper heat pack housing and a lower heat pack housing. The lower heat pack housing is filled with heat absorbing material. However, the upper heat pack housing is at least partially unfilled with the heat absorbing material. Preferably, all of the heat absorbing material is removed from the upper heat pack so that the upper heat pack housing is free of the heat absorbing material.  
           [0021]    The heat shield support member is preferably attached to the upper heat pack housing to support the ring-shaped heat shield housing within the crucible. Accordingly, improved heat shields and Czochralski pullers may be provided.  
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0022]    [0022]FIG. 1 is a schematic representation of a Czochralski puller for growing monocrystalline silicon ingots.  
         [0023]    [0023]FIG. 2 graphically illustrates Vronokov&#39;s Theory.  
         [0024]    FIGS.  3 A- 3 E illustrate an overview of the fabrication of wafers having a vacancy rich region at the center thereof and a pure region between the vacancy rich region and the wafer edge.  
         [0025]    FIGS.  4 A- 4 E illustrate an overview of the fabrication of wafers that are free of agglomerates.  
         [0026]    [0026]FIG. 5 illustrates modified Czochralski pullers and modification methods according to the present invention.  
         [0027]    [0027]FIG. 6 is an enlarged view of a heat shield of FIG. 5.  
         [0028]    FIGS.  7 A- 7 D are cutaway perspective views of embodiments of heat shields according to the present invention.  
     
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS  
       [0029]    The present invention now will be described more fully hereinafter with reference to the accompanying drawings, in which preferred embodiments of the invention are shown. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. Like numbers refer to like elements throughout.  
         [0030]    Overview: Vacancy Rich and Perfect Wafers  
         [0031]    Referring now to FIGS.  3 A- 3 E, an overview of the fabrication of semi-pure wafers having (1) a vacancy rich region at the center thereof that may include vacancy agglomerates and (2) a pure region between the vacancy rich region and the wafer edge that is free of vacancy agglomerates and interstitial agglomerates, according to application Ser. No. 08/989,591, will now be described. As shown in FIG. 3A, the fabrication of these vacancy rich wafers can begin with an overview of Voronkov&#39;s Theory. Voronkov&#39;s Theory is graphically illustrated in FIG. 3A. As shown by the line beginning from the edge (E) and ending at the center (C), it has been found according to the invention of application Ser. No. 08/989,591 that if the ratio of pull rate to temperature gradient at the ingot melt surface, referred to as V/G, is maintained greater than (V/G) 1  at a diffusion length from the edge E, identified by point a, and less than (V/G) 2  at the center C, then semi-pure wafers having a vacancy rich region at the center thereof and a pure region between the vacancy rich region and the wafer edge may be fabricated. In particular, V/G will vary radially across a wafer in an ingot, and generally will decrease from the wafer center to the wafer edge due to the differing thermal characteristics at the center and edge of the wafer. Thus, a given wafer experiences a radial V/G range as shown in FIG. 3A from the center (C) to the edge (E) thereof.  
         [0032]    A critical concern in the fabrication of silicon ingots and wafers is the formation of agglomerates, either vacancy or interstitial, in the wafer. It is known that agglomerates are formed due to coalescence of point defects that are formed during the initial fabrication of the ingot from the melt. The point defect concentration is generally determined by conditions at the interface between the silicon ingot and the silicon melt. Then, as the ingot is pulled further, diffusion and cooling determines the coalescence of point defects to form agglomerates.  
         [0033]    As shown in FIG. 3B, it has been found, according to the invention of application Ser. No. 08/989,591, that a critical vacancy point defect concentration [V]* and a critical interstitial point defect concentration [I]* exist, below which point defects will not coalesce into agglomerates. It has been found according to the present invention that if the concentration of point defects is maintained below these critical concentrations in the peripheral area of the wafer, then a vacancy rich region is formed at the center of the wafer, but a pure region is formed between the vacancy rich region and the wafer edge.  
         [0034]    Thus, as shown in FIG. 3B, the vacancy concentration is maintained below the critical vacancy concentration [V]* across the wafer except near the center C thereof. As shown in FIG. 3C, a vacancy rich region [V] is formed at the center thereof, but the area outside the vacancy rich region [V] to the wafer edge, is free of vacancy agglomerates and is therefore designated [P] (pure or perfect).  
         [0035]    Referring again to FIG. 3B, for interstitials, the interstitial concentration is maintained below the critical interstitial concentration [I]* from the center C of the wafer until a diffusion length L I  from the edge E of the wafer corresponding to point a. Between the diffusion length L I  of the wafer and the edge E, even if the interstitial concentration is initially above the critical concentration [I]* at the ingot-melt interface, diffusion will allow the interstitial vacancies to diffuse out of the ingot and not form agglomerates during the crystal growth. The diffusion length L I  is generally between about 2.5 and 3 cm for 8 inch wafers. Accordingly, as shown in FIG. 3C, a semi-pure wafer having a vacancy rich region [V] at the center thereof and a perfect region [P] between the vacancy rich region and the edge, is formed. Preferably, the pure region [P] is at least 36% of the wafer area and more preferably is at least 60% of the wafer area.  
         [0036]    In order to form wafers of FIG. 3C, V/G must be maintained greater than (V/G) 1  at point a and less than or equal to (V/G) 2  at the center C. In order to maintain the ratio of V/G between these two critical values, two thermal considerations are taken into account. First, the radial temperature gradient G experienced from the center C of the wafer to the diffusion length a of the wafer must be maintained within these values. Thus, V/G at the center should be close to (V/G) 2  in order to confine vacancy agglomerates to the vacancy rich region. Moreover, V/G at the diffusion length L I  from the edge must be maintained greater than (V/G) 1  in order to prevent interstitial agglomerates. Accordingly, the hot zone of the furnace should preferably be designed to maintain a variation in G from the center of the wafer to the diffusion length of the wafer, such that V/G is maintained between (V/G) 2  and (V/G) 1 .  
         [0037]    A second consideration is that G will vary axially as the wafer is pulled from the melt beginning at the seed and ending at the tail. In particular, the increasing thermal mass of the ingot, the decreasing thermal mass of the melt and other thermal considerations will generally cause G to decrease as the ingot is pulled from the melt. Thus, in order to maintain V/G within the first and second critical ratios, the pull rate profile is adjusted as the ingot is pulled from the silicon melt in the hot zone furnace.  
         [0038]    By controlling V/G as the ingot is pulled, vacancy agglomerates can be confined to a vacancy rich region [V] near the axis A of the ingot shown in FIG. 3D. Interstitial agglomerates are not formed, so that the area of the ingot outside the vacancy rich region [V] is labeled [P] for pure or perfect. As also shown in FIG. 3D, this yields a plurality of semi-pure wafers having vacancy rich regions [V] at the center thereof that include vacancy agglomerates, and pure regions between the vacancy rich region and a wafer edge that is free of vacancy agglomerates and interstitial agglomerates. The diameter of the vacancy rich region [V] is the same in each wafer. The identification of the plurality of wafers that are formed from a single ingot may be found by the ID number, labeled ID in FIG. 3D, which is generally an alphanumeric code that is marked on every wafer. This eighteen character field can identify the wafers as all coming from a single ingot.  
         [0039]    [0039]FIG. 3E illustrates a pull rate profile that is used to maintain V/G between the two critical ratios, as the ingot is pulled from the melt. Since G generally decreases as the ingot is pulled from the melt, the pull rate V is also generally decreased to maintain V/G between the two critical ratios. In order to allow for expected process variations, V/G is preferably maintained midway between the first and second critical ratios. Thus, a guard band is preferably maintained to allow for process variations.  
         [0040]    FIGS.  4 A- 4 E correspond to FIGS.  3 A- 3 E and illustrate the control of a pull rate profile to form pure silicon ingots and wafers according to application Ser. No. 08/989,591. As shown in FIG. 4A, if V/G is maintained within a tighter tolerance between the wafer center C and a diffusion length a from the wafer edge E, the formation of vacancy agglomerates as well as interstitial agglomerates may be prevented throughout the wafer. Thus, as shown in FIG. 4B, in the center of the wafer (the axis A of the ingot), the ratio of V/G is maintained lower than the critical ratio (V/G) 2  which would form vacancy agglomerates. Similarly, V/G is maintained above the critical ratio (V/G) 1  that would form interstitial agglomerates. Accordingly, pure silicon [P] of FIG. 4C is formed that is free of interstitial agglomerates and vacancy agglomerates. The pure ingot is shown in FIG. 4D, along with a set of pure wafers. A pull rate profile for pure silicon is shown in FIG. 4E.  
         [0041]    Overview: Modified Czochralski Pullers and Heat Shields  
         [0042]    Referring now to FIG. 5, modified Czochralski pullers according to the present invention will now be described. As shown in FIG. 5, a modified Czochralski puller  200  includes a furnace, a crystal pulling mechanism, an environment controller and a computer-based control system. The Czochralski furnace is generally referred to as a hot zone furnace. A hot zone furnace includes a heater  204 , a crucible  206  which may be made of quartz, a susceptor  208  which may be made of graphite and a rotation shaft  210  that rotates about an axis in a first direction  212  as shown.  
         [0043]    A cooling jacket or port  232  is cooled by external cooling means such as water cooling. A heat shield  214  may provide additional thermal distribution. A heat pack  202  includes heat absorbing material  216  therein to provide additional thermal distribution.  
         [0044]    The crystal pulling mechanism includes a crystal pulling shaft  220  which may rotate about the axis in a direction  222  opposite the direction  212  as shown. The crystal pulling shaft  220  includes a seed holder  220   a  at the end thereof. The seed holder  220   a  holds a seed crystal  224  which is pulled from the melt  226  in the crucible  206  to form an ingot  228 .  
         [0045]    The ambient control system may include the chamber enclosure  230 , the cooling jacket  232  and other flow controllers and vacuum exhaust systems that are not shown. A computer-based control system may be used to control the heating element, the puller and other electrical and mechanical elements.  
         [0046]    In order to grow a monocrystalline silicon ingot, the seed crystal  224  is contacted to the silicon melt  226  and is gradually pulled in the axial direction (up) by crystal pulling shaft  220  or other conventional means for pulling the seed holder away from the crucible. Cooling and solidification of the melt  226  into monocrystalline silicon occurs at the interface  220  between the ingot  220   a  and the melt  226 .  
         [0047]    As also shown in FIG. 5, a conventional heat shield is modified by adding a heat shield cover  234  at the heat shield bottom. The heat shield cover  234  is preferably filled with a heat conservation material such as carbon ferrite. The physical dimensions of the heat shield cover  234  may also be varied as will be described in detail below.  
         [0048]    Modification of the heat pack material  216  may also be provided according to the present invention. More specifically, as shown in FIG. 5, the heat pack housing  202  includes an upper heat pack housing  202   a  and a lower heat pack housing  202   b.  Heat absorbing material  216 , generally carbon ferrite, may be removed from the upper heat pack housing  202   a.  In one embodiment, heat absorbing material is removed from the entire upper heat pack housing  202   a.    
         [0049]    Detailed Design of Heat Shield  
         [0050]    It has been found that the design of the heat shield  214  of FIG. 5 can have a profound influence on the performance of the Czochralski puller. The detailed design of the heat shield  214  will now be described.  
         [0051]    [0051]FIG. 6 is an enlarged view of the heat shield  214  of FIG. 5 and the elements that surround the heat shield  214 . As shown in FIG. 6, the heat shield  214  preferably includes a ringed-shaped heat shield cover or housing  234  within the crucible  206 . The ring-shaped heat shield housing  234  may comprise carbon coated silicon carbide and preferably comprises an inner heat shield housing wall  610 , an outer heat shield housing wall  620 , an oblique heat shield housing floor  630  and a heat shield housing roof  640  that is also preferably oblique. The heat shield housing contains insulating material  660  such as carbon ferrite therein. A support member  650  supports the ring-shaped heat shield housing  234  within the crucible  206 . The support member  650  also may comprise carbon coated silicon carbide.  
         [0052]    As shown in FIG. 6, the inner and outer heat shield walls  610  and  620  respectively, are preferably vertical inner and outer heat shield walls. The heat shield housing floor  630  and the heat shield housing roof  640  are preferably oblique, making angles α and β respectively with the horizontal.  
         [0053]    It has been found according to the invention that many of the physical parameters of the ring-shaped heat shield housing  234  may be varied to change the temperature gradient at the center of the ingot  228  compared to at the edge of the ingot  228 . Among the variables that can be changed are the angle α of the floor  630 , angle β of the roof  640 , the length a of the inner wall  610 , the distance b between the inner wall  610  and the outer wall  620 , the length c of the outer wall  620 , the distance d between the crucible  206  and the inner wall  620 , and the distance e between the crucible top and the oblique floor  630 .  
         [0054]    In general, the ring-shaped heat shield housing  234  includes insulating material  660  therein. The insulating material  660  insulates heat from the heater  204  relative to the ingot  228 . The insulating material  660  also conserves heat that is radiated from the ingot  228 .  
         [0055]    In particular, when increasing a and maintaining all other variables equal, the temperature at point x, at the intersection of the ring-shaped heat shield housing inner wall  610  and floor  630 , may increase. The temperature at point y adjacent the ingot  228  also may increase due to increased heat conservation from the ingot  228 . Moreover, if length a is increased relative to length c, more heat conservation from the ingot may take place so that the temperature at point x may increase and the temperature at point b may increase, but the temperature gradient at the center of the ingot  228  may decrease. In contrast, if β is increased, then the temperature gradient at the center of the ingot may increase.  
         [0056]    The position of the heat shield housing  234  relative to the crucible  206 , denoted by d in FIG. 6 also may impact the performance of the Czochralski puller. In particular, as d increases there may be more heat conservation caused by heat radiation from the ingot so that the temperature at point x and point y may increase. Moreover, the difference in temperature gradient between the center and edge of the ingot  228  may decrease and the temperature at the center of the ingot also may decrease. Finally, the axial distance between the heat shield housing  234  and the crucible  206 , shown as e in FIG. 6, also may be varied. Specifically, as the heat shield housing  234  is moved upwardly relative to the crucible  206 , thereby decreasing distance e, the temperature gradient at the center of the ingot may increase and the difference between the temperature gradient between the center of the ingot and the edge of the ingot also may increase.  
         [0057]    Preferably, all of these parameters may be varied in order to produce a temperature gradient at the ingot-melt interface at the axis (shown as point A in FIG. 5) that is at least about equal to the temperature gradient at a diffusion length from the cylindrical edge of the ingot (shown as point B in FIG. 5).  
         [0058]    FIGS.  7 A- 7 D also illustrate various configurations of the support member  650  that can also impact the thermal characteristics of the Czochralski puller. FIGS.  7 A- 7 D are partial perspective views of a heat shield  214 . As shown in FIG. 7A, the support member  650  may include one or more supporting arms  710 . Alternatively, as shown in FIG. 7B, the support member  650  may be a ring-shaped support member  720 . The ring-shaped support member  720  may include one or more windows  730  therein. The windows  730  may be openings or may be quartz windows. The ring-shaped support member may be oblique as shown.  
         [0059]    As shown in FIG. 7C, the support arms  710  may be hollow support arms  710 ′ that contain insulating material  740  therein. Similarly, as shown in FIG. 7D, the ring-shaped support member  720  may be a hollow ring-shaped support member  720 ′ containing insulating material  750  therein. It will also be understood that the support member need not be attached to the ring-shaped heat shield housing  234  at the outer wall thereof as illustrated. Rather, the attachment position may be varied between the outer and inner walls thereof.  
         [0060]    It has been found that the addition of insulating material in the supporting member  710  or  720  to produce hollow supporting members  710 ′ and  720 ′ respectively may insulate the heater  204  from the ingot  228  and may also provide faster heat transfer from the ingot surface. Thus, temperature gradients at the center of the ingot may increase and the difference between temperature gradients at the ingot center compared to the ingot edge also may decrease.  
         [0061]    When modifying the Czochralski puller to provide a temperature gradient at the ingot-melt interface at the axis that is at least about equal to the temperature gradient at a diffusion length from the cylindrical edge, it has been found that adjusting α, a and c may dominate to produce a temperature gradient at the ingot-melt interface that is greater at the axis than at a diffusion length from the cylindrical edge. Moreover, adjusting β and providing insulating material in the support arm may dominate the temperature gradient at the axis. Accordingly, in designing the heat shield  214 , α, a and c may be increased to reduce ΔG′. Then, β may be increased and insulation material may be added to obtain sufficiently high G center . One design of the ring-shaped heat shield housing includes an outer wall  620  of length c 125 mm, an inner wall  610  of length a 55 mm, a distance d of 7.4 mm and an angle α of 5 degrees.  
         [0062]    In the drawings and specification, there have been disclosed typical preferred embodiments of the invention and, although specific terms are employed, they are used in a generic and descriptive sense only and not for purposes of limitation, the scope of the invention being set forth in the following claims.