Abstract:
A doped silicon single crystal having a resistivity variation along a longitudinal and/or radial axis of less than 10% and a method of preparing one or a sequential series of doped silicon crystals is disclosed. The method includes providing a melt material comprising silicon into a continuous Czochralski crystal growth apparatus, delivering a dopant, such as gallium, indium, or aluminum, to the melt material, providing a seed crystal into the melt material when the melt material is in molten form, and growing a doped silicon single crystal by withdrawing the seed crystal from the melt material. Additional melt material is provided to the apparatus during the growing step. A doping model for calculating the amount of dopant to be delivered into the melt material during one or more doping events, methods for delivering the dopant, and vessels and containers used to deliver the dopant are also disclosed.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is based on and claims priority to U.S. Provisional Patent Application Ser. No. 61/402,776 filed on Sep. 3, 2010. 
     
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
       [0002]    Not applicable. 
       FIELD OF THE INVENTION 
       [0003]    This invention generally relates to single crystal ingots grown using the batch and continuous Czochralski methods and is more specifically directed to silicon single crystal ingots doped with gallium, indium and/or aluminum and methods of making and using the same. 
       BACKGROUND OF THE INVENTION 
       [0004]    Several processes are known in the art for growing crystal ingots of semi-conductor materials for use in fabricating integrated circuits and photovoltaic devices such as solar cells. Batch and continuous Czochralski (“CZ”) processes are widely used for semiconductor materials such as silicon, germanium, or gallium arsenide doped with an elemental additive such as phosphorus (n-type dopant) or boron (p-type dopant) to control the resistivity of the crystal. These processes are generally summarized as follows. A heated crucible holds a melted form of a charge material from which the crystal is to be grown. A seed is placed at the end of a cable or rod that will enable the seed to be lowered into the melt material and then raised back out of the melt material. When the seed is lowered into the melt material, it causes a local decrease in melt temperature, which results in a portion of the melt material crystallizing around and below the seed. Thereafter, the seed is slowly withdrawn from the melt material. As the seed is withdrawn or pulled from the melt material, the portion of the newly formed crystal that remains within the melt material essentially acts as an extension of the seed and causes melt material to crystallize around and below it. This process continues as the crystal is withdrawn or pulled from the melt material, resulting in crystal ingot growth as the seed is continually raised. 
         [0005]    In batch CZ, the entire amount of charge material (semi-conductor and dopant) required for growing a single crystal ingot is melted at the beginning of the process. In continuous CZ (“CCZ”), the charge material is continually or periodically replenished during the growth process. In CCZ, the growth process may be stopped at intervals between crystal growth to harvest the crystal or may continue without stopping between crystal growth. 
         [0006]    The batch CZ process is typically carried out using a pulling apparatus comprising a gas chamber, a quartz crucible positioned inside the chamber, semiconductor charge material and dopant loaded into the crucible, a heater for melting the charge material, and a pulling mechanism for pulling or drawing up a single crystal ingot of the doped semiconductor material. To carry out the CCZ process, it is necessary to modify the traditional apparatus to include a means for feeding additional charge material to the melt in a continuous or semi-continuous fashion. In an effort to reduce the adverse effects of this replenishing activity on simultaneous crystal growth, the traditional quartz crucible is modified to provide an outer or annular melt zone (into which the semi-conductor is added and melted) and an inner growth zone (from which the crystal is pulled). These zones are in fluid flow communication with one another. 
         [0007]    In general, it is desirable for the dopant concentration in the crystal ingot to be uniform both axially (longitudinally) and radially. This is difficult to achieve due, in part, to segregation. Segregation is the tendency of the impurity or dopant to remain in the melt material instead of being drawn-up into the crystal ingot. Each dopant has a characteristic segregation coefficient that relates to the comparative ease with which the dopant atom can be accommodated into the ingot&#39;s crystal lattice. For example, because most dopant atoms do not fit into the silicon crystal lattice as well as a silicon atom, dopant atoms typically are incorporated into the crystal at less than their proportional concentration in the melt, i.e., dopants in a silicon melt generally have a segregation coefficient of less than 1. After the doped silicon is melted and crystal growth has begun, the dopant concentration increases in the melt due to rejection of the dopant at the crystal growth interface. 
         [0008]    In general, the dopant concentration of the pulled single crystal is given as kC where the dopant concentration in the molten polycrystalline or raw material is C and where k is a segregation coefficient that is typically less than 1. During a doped batch CZ process, the amount of melt material in the crucible decreases as the crystal ingot grows, and as a result of segregation, the dopant concentration gradually increases in the remaining melt material. Due to the higher dopant concentration in the melt material, the dopant concentration in the crystal ingot also becomes higher, resulting in varying resistivity along the radial and longitudinal axis of the crystal. A doped batch CZ process potentially results in an ingot having the desired resistivity in only a small portion of the ingot. 
         [0009]    It has been suggested that more uniform resistivity may be obtained using a CCZ process where the dopant concentration in the raw material fed successively into the annular melt zone is made equal to the dopant concentration in the pulled single crystal and the amount of single crystal pulled per unit time is made equal to the amount of charge material supplied. In so doing, it is intended that the amount of dopant supplied and pulled are balanced with each other so that the dopant concentration in the inner crucible equals C/k and the concentration in the outer crucible equals C in a steady state. A variety of different processes and configurations of crucibles have been suggested in an effort to maintain the relative concentrations of the dopant within the inner and outer zones of the crucible and to otherwise achieve uniform resistivity. One problem that continues to persist during a CCZ run is the tendency for dopant to migrate or diffuse to the outer melt zone of the crucible (due to the concentration gradient), which results in lower dopant concentration and higher resistivity at the seed end of the next crystal ingot until the steady state can be achieved again. 
         [0010]    In the past, boron has traditionally been used as the dopant for silicon single crystals used in photovoltaic solar cell applications. It has been recognized, however, that boron forms recombination active defects with oxygen under illumination thereby lowering the minority carrier lifetime. This effect known as “light induced degradation” or “LID” causes a significant voltage and current drop of the solar cells when in operation. See, J. Schmidt, A. G. Aberle and R. Hezel, “ Investigation of carrier lifetime instabilities in Cz - grown silicon ,” Proc. 26th IEEE PVSC, p. 13 (1997); S. Glunz, S. Rein, J. Lee and W. Warta, “ minority carrier lifetime degradation in boron - doped Czochralski silicon ,” J. Appl. Phys., 90, pp. 2397 (2001). This problem can be circumvented by using low-oxygen material or high-resistivity material to minimize boron content; however, it is also known that higher efficiencies can be obtained using relatively low-resistivity material (around 1.0 Ω-cm or below). Low-resistivity material requires a higher dopant concentration. 
         [0011]    It has been suggested that boron can be replaced by gallium, which shows similar electronic behavior in the silicon band structure but does not form recombination active defects under illumination. While it has been suggested that a gallium doped silicon single crystal can be produced via a batch CZ process, gallium has a much smaller segregation coefficient than boron, which means the batch CZ process results in a gallium doped crystal that exhibits a large axial resistivity variation. This lack of uniformity increases the cost of production due to the limited amount of acceptable material in each ingot and/or the cost of development of cell manufacturing processes that can accommodate material exhibiting a wide resistivity range. For this reason, the use of gallium doped crystals for solar cell applications has not been widely adopted in an industrial setting although the advantages of gallium doped silicon wafers in terms of LID reduction has been known for decades. 
         [0012]    The use of CCZ has not been suggested for making ingots doped with gallium, aluminum, or indium, all of which have a small silicon segregation coefficient. This is likely due to the fact that elemental gallium (the most preferred of the three dopants) would be difficult to add in a sufficiently high concentration using a continuous or semi-continuous feeding apparatus because it melts near room temperature and would stick to the apparatus. This not only has the potential of damaging the apparatus, but also creates operational problems such as a lack of control of the actual amount of gallium being added to the melt. In addition, gallium forms a highly volatile suboxide (Ga 2 O) that results in significant loss of gallium from the melt due to evaporation. This evaporation effect would be exacerbated in a CCZ system due to the longer run times and greater melt surface area associated with CCZ. 
       BRIEF SUMMARY OF THE INVENTION 
       [0013]    The present invention relates to a gallium, indium, or aluminum doped silicon single crystal ingot and a method of making the same. The ingot is characterized by uniform radial resistivity and uniform resistivity in the direction of growth (axial or longitudinal resistivity). Preferably, the radial and/or axial resistivity along the length of the ingot varies by less than 10%, more preferably by less than 5%, and most preferably less than 2%. 
         [0014]    In one embodiment of the invention, a silicon single crystal ingot having relatively uniform radial and axial resistivity is grown using a CCZ process wherein a dopant selected from the group consisting of gallium, aluminum and indium or a combination thereof, and most preferably comprising gallium, is included within an initial charge of silicon and then subsequently added to the silicon melt within the inner growth chamber of the crucible between the growth of each crystal ingot. The dopant is preferably added to the inner growth chamber between ingot growth using a “sacrificial vessel” made from the melt material. The dopant is placed in the vessel in solid or liquid form and delivered to the melt in the inner growth chamber via lowering of the seed chuck. Adding dopant to the growth zone allows the system to reach its steady state more quickly, which reduces downtime and results in crystals having more uniform resistivity at the seed end. In addition and/or alternatively, dopant may be fed to the outer chamber in a continuous or semi-continuous manner during crystal growth and/or between crystal ingot growth utilizing a silicon/dopant alloy cube or a container made from silicon that encloses and retains solid or liquid elemental dopant. Given that the containers are made of silicon, the containers can be added via the feeding apparatus, along with the silicon charge material, without the dopant melting and sticking to portions of the feed apparatus during delivery. 
         [0015]    In a related embodiment of the invention, the amount of dopant added in the initial charge, in the inner growth chamber at inter-ingot intervals and/or continuously or semi-continuously in the outer chamber is determined in accordance with a doping model that calculates the anticipated dopant concentration of the melt within the inner growth chamber by taking into consideration not only the amount of dopant removed from the melt via crystal growth but also the amount of dopant removed via evaporation. The amount of dopant determined to be added at each interval using the doping model is precisely controlled using containers or vessels filled with the correct amount of dopant. To achieve uniform resistivity in the ingot throughout crystal growth, additional dopant may be added in a controlled fashion to the outer chamber via the sealed containers (for higher concentrations of dopant) or alternatively silicon/dopant alloy (for lower concentrations of dopant). It is also anticipated that the doping model can be used to determine the appropriate amount of dopant to be incorporated within the initial charge for a batch CZ process and/or adjustments that could be made in relation to other parameters impacting the rate or amount of evaporation. 
         [0016]    In a preferred embodiment, a gallium doped silicon single crystal is made having a resistivity ranging from 15 to 0.1 Ωcm and more preferably 10 to 0.1 Ωcm and most preferably 3 to 0.5 Ωcm. The resistivity is relatively uniform in the axial or longitudinal direction, preferably with a variation less than 10%, more preferably less than 5% and most preferably less than 2%. In addition, the radial resistivity is relatively uniform, preferably with a variation less than 10%, more preferably less than 5% and most preferably less than 2%. For the preferred resistivity ranges, the approximate concentration of gallium in the crystal ranges from about 8.9×10 14  atoms/cm 3  to 2.77×10 17  atoms/cm 3 , more preferably 1.34×10 15  atoms/cm 3  to 2.77×10 17  atoms/cm 3 , and most preferably 4.56×10 15  atoms/cm 3  to 3.21×10 16  atoms/cm 3 . The interstitial oxygen level is preferably less than 25 parts per million atoms, more preferably less than 18 parts per million atoms and most preferably less than 15 parts per million atoms. 
         [0017]    The present invention also encompasses the use of a control system that utilizes the doping model to calculate and control the amount of dopant added during one or more doping events. A single ingot or a sequential series of ingots may be grown in accordance with the present invention. The silicon single crystal ingot grown in accordance with the present invention may be utilized as a substrate for the manufacture of photovoltaic devices such as solar cells. 
         [0018]    Additional aspects of the invention, together with the advantages and novel features appurtenant thereto, will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following, or may be learned from the practice of the invention. The objects and advantages of the invention may be realized and attained by means of the instrumentalities and combinations particularly pointed out in the appended claims. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0019]      FIG. 1  is a cross-sectional view of an exemplar apparatus for pulling single crystals by CCZ method used in the present invention. 
           [0020]      FIG. 2  is a summary diagram of the dopant model, including Formula I. 
           [0021]      FIG. 3  is a summary of the dopant model as used to calculate dopant additions in batch CZ without evaporation in accordance with the present invention. 
           [0022]      FIG. 4  is a summary of the dopant model as used to calculate dopant additions in CCZ without evaporation in accordance with the present invention. 
           [0023]      FIG. 5  is a summary of the dopant model as used to calculate dopant additions in CCZ with evaporation in accordance with the present invention. 
           [0024]      FIG. 6  is a perspective view of a vessel formed on the end of a seed crystal in accordance with one embodiment of the invention. 
           [0025]      FIG. 7  is a perspective view of a seed crystal inserted into a dopant vessel in accordance with one embodiment of the present invention. 
           [0026]      FIG. 8  is a perspective view of the dopant vessel of  FIG. 7  mounted on the seed crystal via friction. 
           [0027]      FIG. 9  is a perspective view of a dopant vessel in accordance with another embodiment of the present invention. 
           [0028]      FIG. 10  is a perspective view of the dopant vessel of  FIG. 9  mounted on the seed crystal via friction a wedge portion. 
           [0029]      FIG. 11  is a summary chart of dopant properties relevant to the present invention. 
           [0030]      FIG. 12  is a perspective view of a sealed dopant container used in accordance with the present invention. 
           [0031]      FIG. 13  is a perspective view of an unsealed dopant container used in accordance with the present invention. 
           [0032]      FIG. 14  is a perspective view of an alloy cube in accordance with one embodiment of the present invention. 
           [0033]      FIG. 15  is a graph of radial resistivity of a single crystal ingot made in accordance with the present invention. 
           [0034]      FIG. 16  is a graph of longitudinal resistivity of a single crystal ingot made in accordance with the present invention. 
           [0035]      FIG. 17  is a chart of dopant additions relating to three single crystal ingots made in accordance with the present invention. 
           [0036]      FIG. 18  is a graph of longitudinal resistivity of three single crystals made in accordance with the present invention. 
           [0037]      FIG. 19  is a graph of longitudinal resistivity of three single crystals made in accordance with the present inventions. 
           [0038]      FIG. 20  is a flow diagram of the selective emitter approach used in Example 3. 
           [0039]      FIG. 21  is a graph of normalized open circuit voltage of one boron doped solar cell over a 48 hour irradiation period. 
           [0040]      FIG. 22  is a graph of normalized open circuit voltage of one gallium doped solar cell over a 48 hour irradiation period. 
           [0041]      FIG. 23  is a graph of the average VOC of boron and gallium cells over a 4 week daylight exposure period. 
       
    
    
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     CCZ Silicon Crystal Apparatus 
       [0042]    With reference to  FIG. 1 , the present invention may be practiced and made using a CCZ crystal ingot growing apparatus, which is shown in cross-section and generally designated by the numeral  10 . The process begins with loading an outer or annular chamber  12  and inner chamber  14  of a crucible  15  with a predetermined amount of charge material  22 . Crucible  15  is preferably made of quartz and coated with a devitrification promoter. The amount of dopant or dopant/silicon alloy added to inner chamber  14  and outer chamber  12  ultimately depends on the desired resistivity of the resulting ingot. Ingot resistivity and dopant concentration are substantially inversely related according to a function well known in the art. However, several factors affect the dopant concentration in the melt at the time the system reaches a steady state during crystal ingot pulling. The amount of dopant necessary to achieve the desired steady state dopant concentration, and thus produce an ingot having the desired resistivity, is determined in accordance with the doping model described below. 
         [0043]    Crucible  15  is preferably configured to have a low aspect ratio (i.e., shallow) configuration so as require a relatively small charge mass within the crucible at any given time. The minimum melt mass within the crucible is preferably greater than 10 kg. Crucible  15  preferably has a relatively large diameter so as to enable growth of large diameter crystals ranging in diameter from 4 to 12 inches, preferably ranging from 6 to 9 inches, and a crystal ingot length ranging from 10 to 160 inches, preferably 40 to 120 inches. Outer chamber  12  has a diameter of about 18 inches to about 36 inches, preferably about 18 inches to about 28 inches. Inner growth chamber  14  has a diameter of about 10 inches to about 30 inches. Crucible  15  is supported by susceptor  30  and enclosed within furnace tank  16 . After chambers  12  and  14  are loaded with charge material  22 , furnace tank  16  is closed and backfilled with a continuous flow of inert gas, preferably dry argon gas. The flow of gas through the system is directed in part by purge cone  32 . 
         [0044]    Next, melting is initiated by powering at least one periphery heater  18  and at least one bottom heater  19 . Heat shields  20  and  21  may be generally positioned within furnace tank  16  to control radiation and create the appropriate thermal gradients. As melting occurs, additional charge material  22  is fed into outer chamber  12  using feeding device  24  until the desired mass of melt material  42  is present in crucible  15 . Feeding device  24  generally comprises hopper  26  and vibratory chute  28 . As charge material  22  in outer chamber  12  melts, it flows into inner growth chamber  14  via a passageway (not shown). The passageway may comprise an aperture, a notch, or a pipe, all as known in the art. The area between the wall of outer chamber  12  and the wall of inner growth chamber  14  is referred to as melt zone  34 . The area within the wall of inner growth chamber  14  is referred to as growth zone  36 . A baffle, weir, partition wall, or other dividing structure may optionally be provided within melt zone  34 . 
         [0045]    After the desired amount of charge material  22  is substantially melted in zones  34  and  36 , crystal ingot growth is initiated with seed crystal  38  mounted in seed chuck  40 . Seed crystal  38  may be a sample of the desired crystal material or any other material that has the same crystalline structure and a higher melting temperature than melt material  42 . To begin growth, seed crystal  38  is lowered into molten melt material  42  in growth zone  36  using seed cable  44  and pull head assembly  46 . As the portion of melt material  42  in contact with seed crystal  38  cools and crystallizes, seed crystal  38  is raised. During crystal ingot growth, pull head assembly  46  and seed cable  44  rotate seed crystal  38  in one direction and susceptor  30  rotates crucible  15  in the opposite direction. The rate of raising and rotation for seed crystal  38  and the rotation of susceptor  30  can be manipulated to change the mixing phenomenon the counter rotation creates in melt material  42 , the amount of dopant taken up into crystal  52 , and the size and shape of crystal  52 . A typical crystal ingot  52  comprises a neck  47 , shoulder  48 , body  50 , and tail (not shown). These various parts of crystal ingot  52  are grown by altering the rates of rotation, heating and lift. During growth, additional charge material  22  may be added to melt zone  34  using feeding device  24 . 
         [0046]    After crystal ingot growth is terminated, crystal ingot  52  is separated from melt material  42  and lifted into pull chamber  54  where it is isolated from the environment in furnace tank  16  and allowed to cool. After cooling, crystal ingot  52  is harvested in a standard manner known to those skilled in the art. The growth process may then be repeated to form a second crystal ingot in a sequential series of ingots. 
       Doping Model and Control System 
       [0047]    One embodiment of the invention is directed to the use of a doping model that factors in the evaporation of the dopant when determining the concentration of the melt at any given time. The doping model is used to calculate the amount of additional dopant needed to achieve uniform resistivity. This model can be employed utilizing a controller to calculate the amounts and direct the addition of the precise amount of dopant needed at any given time. The controller may be a CPU or other computerized controller adapted to monitor the melt level, crystal ingot weight, charge material weight, crystal ingot rotation rate, susceptor rotation rate, crystal ingot diameter, melt material temperature, and other variables relating to the CCZ process. 
         [0048]    The controller is also programmed to monitor the run time of the system beginning with the initial charge and ending with conclusion of growth of the last crystal ingot within the run. Typically a run will last for about 25 to 400 hours with the growth of about 2 to 20 ingots. The controller is also programmed to control the amount of dopant and silicon charge material fed to the system during the initial charge, inter-ingot doping to inner growth chamber  14  and continuous or semi-continuous feeding and doping to outer chamber  12 . The amount of dopant added is determined by the controller in accordance with Formula I, as identified below and shown in  FIG. 2 , which predicts the dopant concentration of the melt in inner growth chamber  14  at any given time, and then calculating the amount of additional dopant needed based on the desired resistivity for the ingot. Formula I: 
         [0000]    
       
         
           
             
               
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         [0049]    Where t=time, N d =number of atoms of dopant in the melt, M L =melt mass, C L =dopant concentration in melt=N d /M L , M x =crystal mass, M F =fed mass, N F =fed dopant, k=segregation coefficient, g=evaporation rate coefficient and A s =melt free surface area. The evaporation rate coefficient g will be a function of a number of factors, including the dopant type and concentration in the melt, the hot zone configuration (i.e. melt volume, melt temperature, seed and crucible rotations), the pressure and gas flow rates and path, the oxygen concentration in the melt, the dopant atoms in the feed entering the inner growth zone from the annular or melt zone (N F ), and the path through the melt zone to the inner growth zone. The melt free surface area (A s ) will be different during crystal growth (where there is less free surface area) and in the intervals between crystal growth (where there is greater free surface area).  FIG. 2  depicts a model system and shows the derivation of Formula I. Most parameters of the model will have dependence on various environmental factors. These dependencies may be neglected for engineering purposes to the extent their impact on precision is small or may be incorporated into the model to further refine it.  FIG. 3  shows an example of how Formula I is applied to batch Cz when evaporation is not a factor. In FIG.  FIG. 4  shows an example of how Formula I is applied to CCZ when evaporation is not a factor. In  FIG. 5  shows an example of how Formula I is applied to CCZ when evaporation is a factor. 
       Addition of Dopant to Inner Growth Chamber 
       [0050]    In a second embodiment of the present invention, a predetermined amount of dopant is added to inner growth chamber  14  at intervals between growth of crystal ingot  52 . After a first crystal ingot is harvested, dopant is added to inner growth chamber  14  to replace dopant lost from melt material  42  through evaporation and taken up in the prior crystal. To avoid contamination of melt material  42 , the present inventors have developed a system for inter-ingot doping comprising the use of an open “sacrificial vessel” lowered into growth zone  36  via seed chuck  40 . 
         [0051]    In a one embodiment shown in  FIG. 6 , a sacrificial vessel  102  is grown on seed crystal  38  (or the neck of the prior crystal). A preferred shape for the vessel is a cup. The cup shaped vessel  102  may be grown by using seed crystal  38  to grow neck  47 . Then the seed lift is reversed slightly such that a small portion of neck  47  is positioned just below the surface level of the melt material. Surface tension creates cup shaped vessel  102  around the portion of neck  47  positioned just below the melt surface level, which permits upward growth around the perimeter of the meniscus. When the cup shaped vessel  102  is grown to a desired size, preferably having about a 6 cm diameter, the cup is rapidly withdrawn. It may then be filled with elemental dopant such as solid gallium pellet(s) and then submerged into growth zone  36  where it will melt and release the dopant. 
         [0052]    In another embodiment, a pre-formed sacrificial silicon vessel is mounted on seed crystal  38  (or the neck of the prior crystal) at intervals between growth of crystal ingot. To prevent contamination of the melt, the pre-formed vessel may be cleaned by acid etching using a mixture of hydrofluoric acid, nitric acid, and acetic acid as is well known in the art. In one embodiment shown in  FIGS. 7 and 8 , pre-formed vessel  68  is a machined rectangular silicon plate having an off-set aperture  74  through which the end of seed crystal  38  may be inserted for mounting the plate on the seed crystal. Top surface  70  of vessel  68  also has a pit or well  72  configured to hold an amount of dopant such as elemental gallium. Once the dopant is loaded into the well  72 , the lower end of seed crystal  38  is inserted through aperture  74  and the vessel  68  is moved upward such that it is positioned around the crystal at a location remote from the lower end of seed crystal  38 . As shown in  FIG. 8 , when support for vessel  68  is removed, vessel  68  tilts due to the off-set nature of aperture  74  and the weight of the vessel. Vessel  68  is thereby mounted to the seed crystal via friction without the need for other attachment means. Vessel  68 , holding the dopant in well  72 , is then lowered into growth zone  36  via lowering of seed crystal  38  where it will melt and release the dopant. Using a machined vessel such as vessel  68 , as opposed to growing a sacrificial vessel, saves time in the crystal pulling process. 
         [0053]    In an alternative embodiment, shown in  FIGS. 9 and 10 , pre-formed vessel  78  is a machined rectangular silicon plate having an off-set aperture  80  through which the end of seed crystal  38  may be inserted for mounting the plate on the seed crystal. Aperture  80  is generally diamond shaped and is positioned adjacent one edge of vessel  78 . A slot  82  extends from the outer edge of vessel to aperture  80  to accommodate expansion of the aperture. Top surface  84  of vessel  78  also has a well  98  configured to hold an amount of dopant such as elemental gallium. An elongated triangular shaped wedge  86  formed in vessel  78  has inner and outer serrated edges  88   a  and  88   b , a top edge  90  and a lower edge  92 . A central slot  94  extending a distance from lower edge  92  toward top edge  90  of the wedge accommodates compression of the wedge. An opening is formed adjacent top edge  90 , inner side edge  88   b  and a major portion of lower edge  92  so that these portions are not connected to the remainder of vessel  78 . The only connection between wedge  86  and the remainder of vessel  78  is a break-off bridge  96  extending from a portion of lower edge  92  along outer side edge  88   a . Before using vessel  78 , wedge  86  will be broken off from the remainder of vessel  78  along break-off bridge  96 . Dopant is loaded into well  72 , the lower end of seed crystal  38  is inserted through aperture  80  and vessel  78  is moved upward such that it is positioned around the crystal at a location remote from the lower end of seed crystal  38 . As shown in  FIG. 10 , wedge  86  is then inserted upward through aperture  80  adjacent seed crystal and pushed until it is securely positioned in abutting engagement with portions of the inner edge of aperture  80  and seed crystal  38 . In this manner, vessel  78  is mounted to the seed crystal via friction without the need for other attachment means. The shape of wedge  86  accommodates various sizes of seed crystals within aperture  80  by permitting wedge  86  to be inserted further upward through aperture for smaller seed crystals to obtain a secure fit. Vessel  78 , holding the dopant in well  98 , is then lowered into growth zone  36  via lowering of seed crystal  38  where it will melt and release the dopant. 
         [0054]    Because varying amounts of dopant may be selectively added to the vessel, the controller may control the precise amount of dopant to be added to growth zone  36  to achieve the desired concentration. For example, uniformly sized elemental gallium pellets having a fixed mass can be added to the vessel at the direction of the controller in the precise amount calculated in accordance with Formula I above to achieve the desired concentration for any given ingot. It should be understood, that while various configurations of the vessel have been described, other configurations of crystalline material grown from the melt material or pre-manufactured from crystalline material capable of receiving, retaining and delivering varying amounts of dopant to the melt in inner growth chamber  14  via lowering of the seed chuck  40  are within the scope of this invention. 
       Addition of Dopant to Outer Chamber 
       [0055]    In another embodiment of the present invention, predetermined amounts of dopant are added to melt zone  34  at least once during growth of crystal ingot  52 . Several methods of adding dopant during the CCZ process are known in the art. These methods include adding dopant in the form of thin rods, which are fed continuously into the melt, or feeding dopant pellets into the melt. Although these methods may be sufficient for adding dopants with relatively high melting points, they are not sufficient for a dopant with a relatively low melting point, like gallium (see  FIG. 11 ). The present inventors have devised a novel system for adding dopants, like gallium, at least once during growth of crystal ingot  52  using dopant container  64  that fully encapsulates the dopant. As shown in  FIG. 12 , dopant container  64  comprises container body  58 , threaded plug  62 , and dopant. 
         [0056]    With reference to  FIG. 13 , container body  58  is preferably a hollow cube constructed out of charge material  22 , such as silicon. For purposes of doping with gallium, container body  58  preferably has a dimension ranging from about 4-24 mm 2 , most preferably about 12 mm 2 . Container body  58  includes threaded cavity  60 . A predetermined amount of elemental dopant is added to cavity  60  in solid form (such as a pellet) or liquid form. In the case of gallium, for example, elemental gallium in the form of a pellet having a diameter ranging from 0.5-5 mm, preferably 1 mm, and weighing approximately 0.015-0.15 g, preferably 0.03 g may be used. After the dopant has been loaded, threaded plug  62  is screwed into cavity  60 . Threaded plug  62  may be screwed in short of flush, flush (as shown in  FIG. 12 ), or past flush with the top of container body  58 . Slot  66  is provided in the top of threaded plug  62  such that a screwdriver or other tool may be used to screw threaded plug  62  into cavity  60  of container body  58  to the desired depth. Container body  58  and plug  62  are machined using diamond-tipped tools, then etched with a formulation of acids and other materials known in the art, and finally bagged, preferably in polyethylene or other non-contaminating bags. Of course, dopant containers  64  may be any shape that can enclose a desired amount of dopant. The process for making, cleaning, and storing dopant containers  64  must be carefully controlled so as to avoid contamination, including iron contamination. Although doping using dopant containers  64  is particularly advantageous for volatile dopants or dopants with low melting points, any desired dopant or additive may be added to melt material  42  in this way. Potential dopants include phosphorous, boron, gallium, aluminum, indium, antimony, germanium, arsenic or silicon alloys thereof. Dopant containers  64  may also be used to dope between ingots (as described below) or in batch CZ as well. 
         [0057]    Alternatively, solid dopant alloy cubes  100  as shown in  FIG. 14 , may also be used to replenish the dopant in melt material  42 . Dopant alloy cubes can be made using the CCZ process (or any other silicon crystal growth process) to grow a silicon ingot that has a desired concentration of dopant (dopant containers  64 , described above, may be used to deliver dopant into the CCZ process used to grow the desired doped ingot) and then machining the ingot into the desired size cubes so as to have a precise amount or concentration of dopant. Of course other shapes may be used, such as a pyramid or sphere shape, and preferably each type of dopant alloy would have its own shape so as to avoid doping with the wrong dopant. When the dopant alloy is cube-shaped, the dimensions are preferably 8 mm 3 . 
         [0058]    The dopant concentration in each dopant alloy cube is obtained by measuring the resistivity and using well-known relationships between geometry and concentration. The device used to measure resistivity is typically a four-point probe which measures resistivity through current and voltage characteristics of the material. This technique is well known to one of ordinary skill in the art and incorporates the international standards and procedures of organizations such as SEMI. The use of dopant alloy cubes is limited by the liquid solubility of the dopant in silicon (solid solubility values, which are useful for a relative comparison of solubility among the listed dopants, are provided for the dopants in  FIG. 11 ). For example, when a dopant, such as gallium has a relatively low solubility in silicon, the required concentration of gallium in the liquid to make an 8 mm 3  dopant alloy cube is very large. 
         [0059]    Dopant alloy cubes  100  or dopant containers  64  may be added to outer chamber  12  during crystal ingot growth using a doper mechanism configured to deliver a very well controlled amount of dopant. For example, dopant alloy cubes of phosphorous or boron may contain about 1e-4 g and up to about 1e-5 g of dopant per alloy cube. Dopant containers  64  may be designed to each contain similar amounts of boron or phosphorous or about 0.001 g to about 0.03 g of gallium depending on the resistivity level desired in the finished ingot. Because dopant containers  64  are formed of silicon, the dopant contained within the containers will likely melt during the feeding process, but the containers will not melt until they are incorporated into the melt. Thus, dopants having low melting points can be conveniently fed into melt zone  34  or growth zone  36  in precise quantities and without damaging the apparatus. The amount of dopant included within the containers may be a fixed amount or there may be a series of different containers with different fixed amounts of dopant available for selection by the controller depending upon the amount of dopant required in accordance with the doping model. For instance, where a larger concentration of dopant is required, dopant containers  64  are preferred since they hold elemental dopant. Where lower amounts of dopant are required, the silicon/dopant alloy cubes may be utilized in accordance with the doping model. 
         [0060]    In one embodiment, the doper is located inside furnace tank  16  and is in flow communication with feeding device  24 . The doper comprises a loadable magazine and a dispensing actuator. One or more dopant containers  64  or dopant alloy cubes are loaded into the magazine. At one or more predetermined times during crystal growth, the dispensing actuator dispenses a dopant container or dopant alloy cube from the magazine into feeding device  24 , which deposits it in outer chamber  12 . In outer chamber  12 , dopant container  64  or dopant alloy cube melts and releases the dopant contained therein. A series of valves and isolation chambers may also be provided to allow reloading of the magazine during a run without losing pressure in or contaminating furnace tank  16 . Alternatively, the magazine may be positioned outside furnace tank  16 . In this embodiment, dopant containers  64  or dopant alloy cubes cross a pressure boundary just prior to being dispensed into a component of feeding device  24  within furnace tank  16 . 
       Example 1 
       [0061]    In  FIG. 15 , the radial resistivity of a crystal ingot (sample  1 ) made in accordance with the preferred embodiment of this invention is shown. The crystal was the third ingot grown in a CCZ run wherein elemental gallium was added in the initial charge and within the growth zone  36  via a cup-like vessel formed on seed crystal  38  between ingots in an amount determined in accordance with the doping model. No additional dopant was added into the melt zone  34  during crystal growth or between ingot growth. As can be seen, the radial resistivity is relatively uniform throughout the length of the crystal. It is noted that the resistivity measurements for all examples were taken post thermal donor kill or TDK, a heat treatment that is applied to silicon wafers so that their measured resistivity better reflects actual working resistivities for use in solar cells.  FIG. 16  shows the resistivity of the crystal sample  1  along the axial length of sample  1 . 
       Example 2 
       [0062]      FIG. 17  shows the actual amount of gallium dopant added to three crystal ingots produced using the CCZ process and in accordance with the doping model of the present invention. The amount of dopant added inter-ingot was determined in accordance with the doping model and based upon the desired resistivity of the ingot. No additional dopant was added in the outer chamber during or between ingot growth.  FIG. 17  shows the anticipated resistivity in accordance with the model and the actual measured resistivity. 
         [0063]      FIG. 18  shows the actual resistivity of the three crystals grown and shown in preceding  FIG. 17  along the length of each crystal.  FIG. 19  shows the axial resistivity of crystals grown with both gallium doping in the inner growth chamber between ingot growth and additional dopant added during growth to the outer chamber by means of dopant containers, in comparison to a crystal with doping only to the inner growth chamber between ingot growth. It is noted that the resistivity is further flattened when additional dopant is added during growth. 
       Example 3 
       [0064]    For this experiment, 40 solar cells were made from 125 mm×125 mm pseudo-square wafers. Next to a control group of 10 wafers for the optimization, 15 cells were made of boron doped substrates using a CCZ process with addition of dopant to the inner growth chamber between ingot growth and addition to the outer growth chamber during growth, and 15 cells were made of gallium doped substrates with addition of dopant to the inner growth chamber between ingot growth. The resistivities of the wafers are given in Table I. Note that Group 2 has approximately double the dopant concentration compared to Group 1. 
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
               
             
           
               
                 TABLE I 
               
             
             
               
                   
               
               
                 Resistivities of the used substrates. 
               
             
          
           
               
                   
                 Base doping 
                 Resistivity 
               
               
                   
                   
               
             
          
           
               
                   
                 Group 1 
                 p-type, Boron 
                 2.1 Ω cm 
               
               
                   
                 Group 2 
                 p-type, Gallium 
                 1.0 Ω cm 
               
               
                   
                   
               
             
          
         
       
     
         [0065]    With reference to  FIG. 20 , the solar cell process used in this experiment was a selective emitter approach adhering closely to standards used in the industry. The cells underwent an alkaline texturing before POCl3 emitter diffusion to about 30 Ω/sq and plasma edge isolation. Subsequently, an etch resist grid was applied by inkjet printing, followed by selective emitter formation via acidic etch-back to around 70 Ω/sq. Afterwards, a SiNx anti-reflection coating was deposited by plasma-enhanced chemical vapor deposition (PECVD) and the cells were metalized by screen printing Ag-paste on the front and Al-paste on the rear side before being cofired in a belt furnace. 
         [0066]    Usually, the emitter is a major contributor to overall recombination due to its heavily doped “dead layer.” Application of a selective emitter helped to make the solar cells more sensitive to slight changes in the bulk lifetime since the recombination in the emitter region is suppressed. Immediately after firing, the solar cells were I-V measured to determine their undegraded initial state. The results are displayed in Table II. 
         [0000]                                                                    TABLE II                   Solar Cell Results                    J SC     V OC                 FF   [mA/cm 2 ]   [mV]   Efficiency                            B, avg.   78.7%   35.9   633   17.9%           B, best   79.0%   36.1   634   18.1%           Ga, avg.   79.2%   35.7   634   17.9%           Ga, best   79.6%   35.9   637   18.2%                        
Both groups are nearly identical in terms of efficiency. The gallium doped group shows a slight advantage in fill factor and VOC while the boron doped cells have a higher JSC. This could be an effect of the different net doping (see Table I).
 
       Continuous Irradiation 
       [0067]    After the initial IV measurements, the cells were subjected to continuous irradiation under 1 sun at 25° C. while their VOC was recorded along with cell temperature and illumination intensity for normalization purposes. Two exemplary graphs of these measurements are shown in  FIGS. 21 and 22  for the boron doped cells and for the gallium doped cells respectively. The well-known kinetics of light-induced degradation can be observed: as shown in  FIG. 21 , the cells lose around 5-6 mV due to the formation of recombination-active boron-oxygen pairs in an exponential decay over about 48 hours to a new plateau level. Its time constants are in accordance to those published for the boron-oxygen complex and saturation at the new VOC level is generally reached between 48 and 72 hours. 
         [0068]    As shown in  FIG. 22 , quite a different picture can be seen with the gallium doped cells. Their VOC development under illumination is displayed above and no degradation within the measurement errors can be detected. It is noteworthy that no gallium doped cell showed more than 0.5 mV VOC difference after 72 hours of continuous illumination. 
         [0069]    After this procedure, the degraded cells were measured once again. A comparison of the cell parameter developments is given in Tables III and IV for the aforementioned exemplary solar cells. 
         [0000]    
       
         
               
             
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE III 
               
             
             
               
                   
               
               
                 Boron cell before and after 48 hours of continuous irradiation at 25° C.: 
               
             
          
           
               
                   
                 Before 
                 Diff. 
                 After 
               
               
                   
                   
               
             
          
           
               
                   
                 FF 
                 77.9% 
                 −0.8 
                 77.1% 
               
               
                   
                 J SC  [mA/cm 2 ] 
                 36.1 
                 −0.1 
                 36.0 
               
               
                   
                 V OC  [mV] 
                 637 
                 −6 
                 631 
               
               
                   
                 Efficiency 
                 17.9% 
                 −0.3 
                 17.6% 
               
               
                   
                   
               
             
          
         
       
     
         [0000]                                                            TABLE IV                   Gallium cell before and after 48 hours of continuous irradiation at 25° C.:                Before   Diff.   After                            FF   79.6%   0.0   79.6%           J SC  [mA/cm 2 ]   35.9   0.0   35.9           V OC  [mV]   637   0   637           Efficiency   18.2%   0.0   18.2%                        
Here, the boron doped cells show a deterioration in all solar cell parameters, leading to a decrease of 0.3% absolute in cell performance while the gallium doped cells&#39; parameters remain largely unchanged within measurement error by the procedure.
 
         [0070]    Some of the cells were exposed to daylight for 4 weeks. They were held under open circuit conditions. While the degradation experiments involving days of constant  1  sun illumination do not resemble realistic operation conditions, they match the voltage drop results found in these practical tests. The results of the 4 week test are shown in  FIG. 23 . The boron doped cells show the same drop in VOC as seen in the continuous irradiation experiment after the saturation time, around 6 mV. The gallium doped samples&#39; performance loss was on average 0.4 mV. 
         [0071]    From the foregoing it will be seen that this invention is one well adapted to attain all ends and objectives herein-above set forth, together with the other advantages which are obvious and which are inherent to the invention. Since many possible embodiments may be made of the invention without departing from the scope thereof, it is to be understood that all matters herein set forth or shown in the accompanying drawings are to be interpreted as illustrative, and not in a limiting sense. 
         [0072]    While specific embodiments have been shown and discussed, various modifications may of course be made, and the invention is not limited to the specific forms or arrangement of parts and steps described herein, except insofar as such limitations are included in the following claims. Further, it will be understood that certain features and sub combinations are of utility and may be employed without reference to other features and sub combinations. This is contemplated by and is within the scope of the claims.