reference will now be made in detail to the embodiments of the present invention , examples of which are illustrated in the accompanying drawings . fig3 is an elevation view of an exemplary modified czochralski process furnace of one embodiment according to the present invention . in fig3 , a furnace 10 is contained within a surrounding vacuum chamber 12 formed from an upper half shell 14 and a lower half shell 16 which are joined together by annular flanges 18 . upper half shell 14 has a viewing port 20 and a centrally located , axially extending crystal receiving chamber 22 . vacuum chamber 12 contains a centrally located , furnace 10 which includes a circular heater 24 formed of vertical graphite elements which are supplied with electrical power from electrical leads 31 which pass into the chamber through connectors 29 . heater 24 is surrounded by a protective cylindrical heat shield 28 . a centrally located shaft 30 extends axially into the lower shell 16 , and this shaft is mounted for rotational and axial movement . an upper end 32 of shaft 30 supports a graphite cup 34 in which is placed a quartz crucible 36 . crucible 36 has a flat bottom , and short side walls , thereby minimizing the quantity of the molten pool of silicon . a circular baffle 38 is centrally positioned in crucible 36 , closely surrounding cylindrical boule 35 dividing shallow molten pool 48 into a crystal growth zone 40 and an entirely surrounding annular feed zone 42 . crucible 36 is received within a graphite cup 34 which is surrounded by heater 24 and by a bottom heater 54 , wherein electrical power is supplied to bottom heater 54 by plate 56 . in one embodiment , a single seed crystal of silicon is dipped into shallow molten pool 48 in the crystal growth zone 40 and is slowly withdrawn , while being rotated in a counter - rotational direction to the rotation of the graphite cup 34 and crucible 36 . as a crystal is withdrawn , the molten silicon at the crystal solid / liquid interface crystallizes , forming a cylindrical boule 35 . a vacuum chamber is continuously swept with a flow of argon which is introduced through the crystal receiving chamber 22 and which flows along upper shell 14 , downwardly about cylindrical silicon boule 35 and across shallow molten pool 48 of the silicon . accordingly , the flow of argon sweeps silicon oxide , which is formed by reaction of the silicon melt with quartz crucible 36 , from the vacuum chamber 12 . in fig3 , a solid feed system may be housed in vessel 80 which is supported on furnace 10 , secured to nozzle 50 of upper shell 14 , and supported by an arm 52 which is attached to a support bracket 54 on the lower end plate 56 of the vessel 40 . vessel 80 is supported beside crystal receiving chamber 22 and has a nozzle 60 in its lower end plate 56 which is bolted to a flanged nozzle 50 of an upper portion of the furnace 10 . a slide gate valve 62 is placed between furnace 10 and vessel 80 , thereby permitting isolation of the vessel 80 from the furnace 10 . in addition , a static solids mixer 64 may be located along an upper portion of vessel 80 , a solids storage hopper 66 may be located along a mid - section of vessel 80 , and a solids flow controller 68 may be located along a lower portion of vessel 80 . in fig3 , a dopant alloy conveyor system may be housed in vessel 200 which is supported on the furnace 10 , secured to nozzle feedthrough 210 of upper shell 14 , and supported by a support bracket 220 which is attached to upper shell 14 . vessel 200 is supported beside crystal receiving chamber 22 and has a valve / nozzle 230 disposed above a load reading device ( i . e ., load cell ) 240 , all of which is disposed within a bottom region of vessel 200 . accordingly , nozzle feedthrough 210 is disposed immediately beneath load reading device 240 to receive dopant alloy material 250 via the valve / nozzle 230 . a measured amount of the dopant alloy material 250 is transferred to the annular feed zone 42 of the molten pool 48 of silicon via a vertical transfer tube 260 leading from the bottom region of the vessel 200 . fig4 is an elevational view , partially in cross section of one embodiment of vertical transfer tubes according to the present invention . in fig4 , both of the vertical transfer tubes 122 and 260 may have a radiation interrupt section 126 , and a flow velocity control section 128 . the velocity flow control section 128 may have a plurality of internal constrictions , which may be formed by indentations 130 in the side walls of tubes 122 and 260 , with adjacent internal constrictions ( corresponding to indentations 130 ) being located on opposite sides of tube 122 and 260 . accordingly , constrictions assist in deflecting solids passing through in the tubes 122 and 260 , interrupting their free fall into the molten pool 48 of silicon , and prevent splashing of molten silicon within annular feed zone 42 . the polycrystalline material , such as silicon in granular form , typically with an average particle diameter from 1 to about 1 . 5 millimeters , is introduced into an upper end of the vessel 14 , where it cascades downwardly . in one embodiment , the storage hopper has a capacity from 100 to about 240 kilograms of granular solids , sufficient for storage of the feed material required for one to four runs , making silicon ingots of about 50 kilograms . cylindrical boule 35 of single crystal silicon is withdrawn from crucible 36 and passes through a heated zone entirely surrounded by the cylindrical heater 24 . this heated zone serves as an annealing zone in which the crystal is annealed and conditioned to obtain maximum crystal properties . in one embodiment , the present invention is practiced and adopted to use an existing czochralski furnace and vacuum chamber with minor but significant modifications . this resulted in substantial savings in equipment and time , as the existing czochralski equipment was adaptable to practice the method . fig5 is a block diagram of an exemplary method of producing a single crystal ingot according to one embodiment of the present invention . in fig5 , a polycrystalline material , such as granular silicon , is provided to a crucible 37 ( in fig3 ) disposed within a process furnace 14 ( in fig3 ). then , the dopant material , such as granular solids , are added together to crucible 37 ( in fig3 ). next , the polycrystalline and dopant materials are heated in crucible 37 ( in fig3 ) by elevating the process furnace temperature . after the polycrystalline and dopant materials have melted and stabilized to a specific temperature , for example , of 1405 to 1415 degrees centigrade within the crucible , a single crystal seed is dipped into the melt . next , the seed and crucible are rotated along opposing directions , and the crystal is seeded . then , the seeded crystal is slowly withdrawn from the melt and an initial portion of the single crystal boule ( i . e ., neck portion ) is formed . during withdrawal of the neck portion , both a crown and shoulder are formed . next , additional amounts of polycrystalline and dopant materials are independently added to the crucible . specifically , the amounts of the polycrystalline and dopant materials are added to crucible in order to maintain about 2 . 0 inches of silicon melt in the crucible , and maintain enough of the dopant material in the silicon melt to provide an ingot having a resistivity of about 20 . 00 ohmcm . however , the amounts of the polycrystalline and dopant materials added to crucible are necessary to maintain enough of the dopant material in the silicon melt to provide an ingot having a specific resistivity . accordingly , the amounts of the polycrystalline and dopant materials added to crucible are necessary to produce an ingot having uniform resistivity ( i . e ., uniform axial resistivity ). furthermore , the amount of the dopant material may be varied depending upon the desired dopant species being used . for example , since boron and phosphorous have different segregation coefficients , then the amounts of either the boron dopant materials or the phosphorous dopant materials may be varied , but not in a same batch . accordingly , the dopant level in the melt remains constant . for example , in one embodiment , initially about a 2 . 0 inch depth of polycrystalline material is placed in the crucible along with a calculated amount of the dopant material in order to produce a p - type single crystal ingot of specific resistivity of about 20 . 00 ohmcm , which may result in a dopant concentration of about 8 . 0 × 10 14 atoms / cm 3 . of course , the amount of dopant material will be determined by the desired resistivity of the single crystal ingot . next , after the additional polycrystalline and dopant materials have been added , the seeded crystal is pulled further from the melt , thereby forming a body portion of the boule . formation of the body portion of the boule includes continued withdrawal from the melt in order to form a single crystal ingot . in addition , in one embodiment , the body portion of the boule is subjected to an annealing process to normalize crystal properties of the single crystal ingot . next , after the boule has been withdrawn from the melt by a specific amount ( usually corresponding to a final length of the boule ), the boule is pulled rapidly from the melt to form a conical tail portion . then , the finished boule ingot is annealed , removed from the process furnace . during the process , as shown in fig5 , the polycrystalline material feeding and dopant material feeding may continue during the steps of body building and tailing / annexing , but may be stopped after the step of tailing / annexing . in addition , after the step of ingot removal , the process of forming the boule is repeated in order to produce another ingot having uniform axial resistivity . this process may continue in order to repeatedly produce ingots having uniform axial resistivity . according to the present invention , a single crystal ingot may be formed having a uniform axial resistivity by independently replenishing both polycrystalline silicon and dopant materials in a process chamber . in addition , replenishment of the polycrystalline ( i . e ., the rate of the polycrystalline silicon replenishment in conjunction with the crystal growth ) and dopant materials may be varied in order to maintain a specific dopant concentration within the silicon melt . it will be apparent to those skilled in the art that various modifications and variations can be made in the method and apparatus for producing single crystal ingot of uniform axial resistivity without departing from the spirit or scope of the invention . thus , it is intended that the present invention cover the modifications and variations of this invention provided they come within the scope of the appended claims and their equivalents .