Abstract:
A system and method for controlling a dosage profile is disclosed. An embodiment comprises separating a wafer into components of a grid array and assigning each of the grid components a desired dosage profile based upon a test to compensate for topology differences between different regions of the wafer. The desired dosages are decomposed into directional dosage components and the directional dosage components are translated into scanning velocities of the ion beam for an ion implanter. The velocities may be fed into an ion implanter to control the wafer-to-beam velocities and, thereby, control the implantation.

Description:
TECHNICAL FIELD 
     The present embodiments relate generally to a system and method for implanting ions and, more particularly, to a system and method for controlling the dosage of ion implants during semiconductor manufacturing. 
     BACKGROUND 
     Generally, implanting dopants is a critical process step in the manufacturing of semiconductor devices that gives manufacturers a controlled method of changing the electrical characteristics of chosen regions within the semiconductor device. A typical ion implantation process uses an ion implanter to initially generate ions of the desired dopant and then accelerates these ions to an appropriate energy level. Once accelerated, the ion implanter then transports the ions along an ion beam to impact and implant into a semiconductor wafer. 
     However, because the ion beam does not typically cover the entire wafer at once, the illumination of the wafer by the ion beam is controlled by a wafer-manipulator which sweeps the wafer at constant speed across the ion beam which is anchored at a fixed position. These sweeps generally include a constant velocity implant with a number of back-and-forth motions separated by incremental advancements of the wafer occurring between each motion in one direction. Once the advancements have completed in one direction, the wafer is rotated (typically 90°) and another set of incremental passes are used with the wafer being advanced in a second direction relative to the ion beam. This causes any single point of the wafer to be included in multiple sweeps (from the first increment in which the ion beam illuminates the point and including each increment until the ion beam moves past the point), with the total ion concentration determined from the accumulation of ion implantations during each pass of the overlapping scans. 
     However, using a constant velocity implant that is controlled by a two-dimensional wafer manipulator (by performing one pass and then rotating the wafer for another pass of incremental implants) only allows for a two-dimensional control of the implantation process. This simple, two-dimensional motion control also fails to take into account the three dimensional topology of the wafer itself, which can adversely vary the doping profile of the wafer. Without such three dimensional control, the typical two-dimensional ion implanter cannot obtain a uniform functionality of the resultant semiconductor devices (e.g., drain-current vs. voltage characteristics, clock speeds, leakage currents, etc.) because it cannot take into account this third dimension. 
     What is needed is an ion implanter that can take into account variations in the topography of a wafer in order to obtain a uniform functionality across the wafer. 
     SUMMARY 
     These and other problems are generally solved or circumvented, and technical advantages are generally achieved, by embodiments which implant ions in to semiconductor wafers. 
     In accordance with embodiments, a method for manufacturing semiconductor devices comprises providing a semiconductor wafer and separating the semiconductor wafer into at least a first cell and a second cell. The first cell is assigned a first dosage and the second cell is assigned a second dosage. The first dosage is decomposed into a first dimension component and a second dimension component. The second dosage is decomposed into a third dimension component and a fourth dimension component. The first dimension component is converted into a first velocity, the second dimension component is converted into a second velocity, the third dimension component is converted into a third velocity, and the fourth dimension component is converted into a fourth velocity. Dopants are implanted into the first cell using the first velocity and the second velocity, the dopants being implanted with an ion implanter. Dopants are implanted into the second cell using the third velocity and the fourth velocity, the dopants being implanted with the ion implanter. The first dosage and the second dosage may or may not be the same value. 
     In accordance with another embodiment, a method for implanting dopants comprises providing a substrate and separating the substrate into a plurality of cells. A dosage is determined for each one of the plurality of cells. The dosage for each one of the plurality of cells is decomposed into directional components. The directional components are translated into directional velocities for each one of the plurality of cells, the translating the directional components using at least one conversion factor. The directional velocities are applied to a substrate control system, and ions are implanted into the plurality of cells as the substrate and an ion beam move relative to each other at the directional velocities for each respective cell into which the ion beam is implanting ions. 
     In accordance with another embodiment, a system for implanting dopants into a semiconductor wafer comprises an ion beam generator, a wafer holder for holding a wafer, a wafer positioning system able to adjust the position of the wafer holder along a first direction and a second direction, and a wafer positioning control system communicably coupled to the wafer positioning system, the wafer positioning control system comprising a storage element for storing a first velocity for a first cell of the wafer and a second velocity for a second cell of the wafer. 
     An advantage of an embodiment is that it allows for fine tuning of the implantation of dopants into semiconductor wafer. This allows the topology of the wafer to be accounted for and allows the dopant profile to be matched to the desired uniformity of the final electrical performances more evenly across the wafer. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of embodiments, and the advantages thereof, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which: 
         FIG. 1  illustrates an ion implanter in accordance with an embodiment; 
         FIG. 2  illustrates an ion beam as it is illuminating a wafer in accordance with an embodiment; 
         FIG. 3  illustrates a method of determining track velocity parameters for an ion implanter in accordance with an embodiment; 
         FIG. 4  illustrates a wafer that has been separated into a grid of individual regions in accordance with an embodiment; 
         FIGS. 5A-5B  illustrate resultant track velocities and their profiles using the method of the present embodiments; and 
         FIG. 6  illustrates an embodiment of a controller of an ion implanter is adapted to determine the track velocities. 
     
    
    
     Corresponding numerals and symbols in the different figures generally refer to corresponding parts unless otherwise indicated. The figures are drawn to clearly illustrate the relevant aspects of the various embodiments and are not necessarily drawn to scale. 
     DETAILED DESCRIPTION 
     The making and using of embodiments are discussed in detail below. It should be appreciated, however, that the embodiments discussed herein provide many applicable inventive concepts that can be embodied in a wide variety of specific contexts. The specific embodiments discussed are merely illustrative of specific ways to make and use the embodiments, and do not limit the scope of the embodiments. 
     The embodiments will be described with respect to embodiments in a specific context, namely an ion implantation device that modifies the velocity of the ion implantation in order to achieve a greater uniformity of the final electrical performances of devices across a wafer. These embodiments may also be applied, however, to other implantation processes. 
     With reference now to  FIG. 1 , there is shown an ion implanter  100  with which embodiments may be used. As illustrated, the ion implanter  100  may include an ion source  103 , a mass analysis magnet  105 , a linear accelerator  107 , an end station  113 , a wafer handling unit  115  and a controller  117  to control the operation of the ion implanter  100 . Each of these pieces will be discussed in the following paragraphs. 
     The ion source  103  produces an ion beam  119 . However, as the ion source  103  produces ions having a range of charge-to-mass ratio, and only a certain range of ions are suitable for implantation, the ion beam  119  is directed towards the mass analysis magnet  105  in order to electromagnetically separate those ions having a desired charge-to-mass ratio for implantation from those ions having an undesired charge-to-mass ratio. Once a coherent ion beam  121  of suitable charge-to-mass ratio is obtained, the coherent ion beam  121  is sent to the linear accelerator  107 . 
     The linear accelerator  107  is used to impart additional energy to the coherent ion beam  121  as it passes through the linear accelerator  107 . The linear accelerator  107  imparts this additional energy using a series of electrodes (not shown) that generate an electromagnetic field which, when the coherent ion beam  121  passes through the field, works to accelerate the coherent ion beam  121 . The linear accelerator  107  may vary the electromagnetic fields periodically with time or may adjust the phase of the electromagnetic fields to accommodate ions with different atomic numbers as well as ions having different initial speeds. 
     Once accelerated, the coherent ion beam  121  is directed towards the end station  113 . The end station  113  may house the wafer handling unit  115 , which handles a wafer  123  which will be implanted with ions from the coherent ion beam  121 . The wafer handling unit  115  is utilized to move the wafer  123  in relation to the coherent ion beam  121  so as to illuminate different sections of the wafer  123  with the coherent ion beam  121 . For example, the wafer handling unit  115  may comprise two motors (not shown) which may be used to control the position of the wafer  123  in at least two directions, such as an x-direction and a y-direction, relative to the coherent ion beam  121 . 
     However, as one of ordinary skill in the art will recognize, moving the wafer  123  in relation to the coherent ion beam  121  is merely one exemplary method of illuminating different sections of the wafer  123  with the coherent ion beam  121 . Other suitable methods, such as the use of deflection electrodes along the path of the coherent ion beam  121  to shift the direction of the coherent ion beam  121  in relation to the wafer  123  instead of shifting the wafer  123  in relation to the coherent ion beam  121 , using a multiple wafer rotating system to illuminate multiple wafers in order, or using angular implantation methods, may also be utilized. These methods, and any other suitable method for illuminating different portions of the wafer  123  with the coherent ion beam  121 , are fully intended to be included within the scope of the present disclosure. 
     The controller  117  is used to control the operating parameters of the ion implanter  100  during operation. The controller  117  may be implemented in either hardware or software, and the parameters may be hardcoded or fed into the controller  117  through an input port. The controller  117  may be used to store and control parameters associated with the operation of the ion implanter  100 , such as the desired ion beam current, the current to the accelerator electrodes, and the like. Additionally, the controller  117  may also be used to control the wafer handling unit  115  and, more specifically, the velocity of the motors of the wafer handling unit  115 , which, in turn, control the velocity of the wafer  123  with respect to the coherent ion beam  121 . 
       FIG. 2  illustrates the coherent ion beam  121  as it is illuminating the wafer  123  while the wafer  123  is being moved relative to the coherent ion beam  121 . As illustrated, because the coherent ion beam  121  has a height h 1  less than a height h 2  of the wafer  123 , the wafer  123  is swept beneath the coherent ion beam  121  at a first velocity v 1  to illuminate a first track  201  of the wafer  123 , where the first track  201  has the same height h 1  as the coherent ion beam  121 . When the coherent ion beam  121  has completed the first track  201 , completing an arc length l a , the position of the wafer  123  with respect to the coherent ion beam  121  is adjusted along a first direction, such as a y-direction, a distance d 1  such as between about 1 cm and about 3 cm. Once adjusted, the coherent ion beam  121  is swept back along a second track  203  to illuminate a different section of the wafer  123 . The second track  203  may overlap portions of the first track  201  so that a point P 1  within the wafer  123  may be exposed to the coherent ion beam  121  multiple times before all of the tracks are completed, or the second track  203  may be aligned with the first track  201  so as to illuminate a different section of the wafer  123  without any overlap. The movement of the wafer  123  relative to the coherent ion beam  121  as the first track  201  is being formed may be controlled by motors (not shown) located on the wafer handling system  115  (see  FIG. 1 ). The speed of these motors and, therefore, the velocity of the wafer  123  as it moves relative to the coherent ion beam  121 , may be controlled by the controller  117 . Additionally, the controller  117  may be used to dynamically adjust the velocity of the wafer  123  relative to the coherent ion beam  121  during the passage of the first track  201  and subsequent tracks. This allows for a greater control of the dosages by controlling the implantation process. The derivation of the track velocities is described below with respect to  FIG. 3 . 
     The illuminations of the wafer  123  by the incremental track adjustments may be continued until all of the desired portions of the wafer  123  (e.g., the entire wafer  123 ) have been illuminated. Once all of the tracks (e.g., the first track  201 , the second track  203 , etc.) in a certain direction have been completed, the position of the wafer  123  may be rotated 90° and implantation along a second set of tracks may be performed along a second direction (relative to the wafer  123 ), such as an x-direction. This pattern of tracking along two separate directions helps to even out fluctuations that may occur if only a single direction is utilized, and also broadens the capabilities of the ion implanter  100  by allowing for another variable in the implantation process. 
       FIG. 3  illustrates a method for adjusting the implantation parameters in order to achieve a greater uniformity of the final electrical performances of devices across the wafer  123 . This method involves, as step  301 , performing a kinematic analysis of the ion implanter  100  to determine its physical operating characteristics. A wafer  123  to be implanted is separated into a series of grid cells in step  303  and each of the cells are assigned a desired dosage. The dosage components are decomposed into directional components in step  305  and then optimized in step  307 . Conversion factors for the ion implanter  100  are calibrated in step  309  and then used to convert directional components into track velocities in step  311 . The track velocities are optimized in step  313 , and the optimized track velocities are synthesized in step  315 . Each of these method steps will be discussed separately in the following paragraphs. 
     Step  301  of the method involves performing a kinematic analysis of the scanning trajectory of the ion implanter  100  (see  FIGS. 1 and 2 ). This analysis may be performed to determine the unique, machine specific parameters for use in further calculations (described below with respect to Equations 3 and 4). This kinematic analysis may be performed using an empirical analysis of the motion of the wafer  123  with respect to the coherent ion beam  121 , and may be used to determine such parameters as the ion beam current intensity J 0 , the number of tracks along the beam height k, the arc length l a  of trajectory over the coherent ion beam  121  width, the number of tracks m along particular directions (such as the x-direction), the height h 1  of the coherent ion beam  121 , the distance d 1  of the incremental advances that may be performed by the ion implanter  100 , the critical dimension achievable line width, and the like. By way of example only, the ion implanter  100  for use in embodiments may have an ion beam intensity of less than about 15 mA, such as about 12 mA; between about 1 and about 10 tracks along the beam height (the number of tracks that would illuminate a single point P 1 ), such as about 7; an arc length of trajectory over the coherent ion beam  121  width of less than about 450 mm, such as about 300 mm; and between about 10 and about 30 tracks along the vertical lift, such as about 19. 
       FIG. 4  illustrates step  303 , in which the wafer  123  may be prepared for implantation by initially separating the wafer  123  into a grid  403 . The grid  403  is a simple way of breaking the wafer into individual cells  405 , wherein each of the individual cells  405  can be handled separately during the actual implantation (discussed further below with respect to  FIGS. 5A-5B ). As illustrated, the grid  403  may have an inner grid  407  which includes a square grid around the wafer  123  and an outer grid  409  which may be formed to extend beyond the actual wafer  123  in order to account for the movement of the coherent ion beam  121  as it enters into the wafer  123  and completely clears off of the wafer  123 . Additionally, while the grid  403  in  FIG. 4  is shown as having straight lines for the sake of simplicity, one of ordinary skill in the art will recognize that dimensions of the grid  403  may be slightly curved as illustrated by the curvature of the first track  201  in  FIG. 2 . 
     For simplicity, the grid  403  may be formed in a relatively square array, with an equal number of individual cells  405  along both an x-direction and a y-direction. Additionally, each of the individual cells  405  may also be relatively square (with the sides being slightly curved from the motion of, e.g., the first track  201  in  FIG. 2 ), with each individual side having a distance similar to the height h 1  of the coherent ion beam  121  (see  FIG. 2 ). For example, for a coherent ion beam  121  having a height h 1  of about 100 mm, each of the individual cells  405  may have a side of about 100 mm. As such, the grid  403  may have between 3 and 30 individual cells  405  per side, such as 20 individual cells  405 . 
     However, as one of ordinary skill in the art will recognize, while the grid  403  itself and each of the individual cells  405  may be relatively square, the present embodiment is not limited as such, and the grid  403  may have other shapes, such as a rectangular shape, as desired in order to separate the wafer  123  into separate individual cells  405 . Further, the individual cells  405  themselves do not all have to have identical shapes, and different individual cells  405  may have different sizes or shapes from each other. All of these modifications to the simple square example presented in  FIG. 4  may alternatively be utilized, and are fully intended to be included within the scope of the current embodiment. 
       FIG. 4  also illustrates that, once the wafer  123  has been divided into the grid  403  with individual cells  405 , each of the individual cells  405  may be matched with a number (illustrated by the arbitrary unit number values within each of the individual cells  405  in  FIG. 4 ) representing an underlying electrical characteristic, such as resistance (in units of Ohm and its multiples whereof), leakage currents (in units of amperes and its multiples whereof), dosages, or other suitable electrical characteristic. These arbitrary unit number values may represent the results of test measurements for a previously formed similar wafer (e.g., a wafer formed with a similar topology as the wafer  123  to be implanted but whose implantation has not been corrected for topography, not shown). 
     Such testing may include, e.g., a wafer acceptance test (WAT) or circuit probing (CP) test of the previously formed similar wafer for feedback control purposes. Alternatively, the test measurements may result from inline measurements prior to an implantation of critical dimensions of a wafer  123  currently being manufactured for feed-forward control of dosage adjustments as preventive measures. By determining the results of the test measurements, an uncorrected map of numbers within the grid  403  may be created as shown in  FIG. 4 . As illustrated, the uncorrected map shows the non-uniformity in underlying electrical characteristics in different sections of the wafer  123  caused by the three-dimensional topography that has yet to be corrected. 
     From this uncorrected map, desired changes to the electrical characteristics of each of the individual cells  405  may be determined in order to obtain a more uniform functionality within the previously formed similar wafer by increasing or decreasing the level of implantation. Once the underlying electrical characteristics (e.g., resistance) have been determined and mapped into the grid  403 , the underlying electrical characteristics may be transformed into a dopant adjustment using, e.g., a conversion number. Such a conversion number would take the desired changes to the underlying electrical characteristic within each individual cell  405  and translate it into a desired dopant concentration. 
     For example, a suitable WAT may include isolation tests, junction leakage tests, resistance measurements, threshold voltage measurement of complementary metal oxide semiconductor (CMOS) integrated circuits, tests for saturated drain current of individual CMOS devices, tests to determine the mobility of the electrons in individual devices, combinations of these, and the like. These tests, and specifically a test such as threshold voltage, may then be used to empirically determine an underlying electrical characteristic in different regions of the previously formed similar wafer as the previously formed similar wafer has progressed through the initial implantation process without correction for the three dimensional topography of the wafer itself. 
     By way of example only (as this method is dependent upon the individual wafers to be measured and implanted), a WAT performed on a previous formed similar wafer may determine that a first region of the previously formed similar wafer has a higher resistance than an adjacent second region because of the topography of the previously formed similar wafer, such as the first region having a resistance of 4.7585 Ohms and the adjacent second region having a resistance of about 4.75 Ohms. Because it would be beneficial to have a uniform resistance, the method may translate these resistances into dopant concentrations using a conversion number (e.g., a conversion number of 1×10 12  ions/cm 2 /mΩ), and then assign the individual cell  405  corresponding to the first region a lower dosage of between about 0.1×10 15  ions/cm 2  and about 1×10 15  ions/cm 2 , such as about 0.4×10 15  ions/cm 2 . Additionally, the method may assign the individual cell  405  corresponding to the second region a higher dosage of between about 0.1×10 15  ions/cm 2  and about 1×10 15  ions/cm 2 , such as about 0.5×10 15  ions/cm 2 . By adjusting these dopants concentrations, the variation from the topography may be reduced. 
     Optionally, if there are any of the individual cells  405  in which the WAT or other test does not provide satisfactory data for an adequate determination for a dosage concentration, the dosages of these individual cells  405  may be estimated. One type of estimation that may be used in an embodiment would be to calculate an overall mean dose value for those individual cells  405  of the wafer  123  which did provide satisfactory data and then assign the overall mean dose value to those individual cells  405  that did not provide satisfactory data. However, while the use of an overall mean dose value method has been described, it is not meant to be limiting, and any other suitable estimation technique may alternatively be used to estimate an appropriate dopant concentration. 
     In step  305 , the desired dosage concentrations of each of the individual cells  405  may be decomposed into directional components that correspond to the directions which the ion implanter  100  may utilize in the actual implantation. For example, if the ion implanter  100  utilizes two directions, such as the x-direction and y-direction described above with respect to  FIGS. 1-2 , the desired dosage concentrations may be decomposed into an x-direction component and a y-direction component. However, while the following description utilizes a two-direction system, present embodiments are not meant to be limited to a two-direction system, and any other suitable number of directions may alternatively be utilized. 
     The decomposition of the desired dosages into directional components may be performed using a matrix calculation as illustrated in Equation 1. 
     
       
         
           
             
               
                 
                   
                     
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     Where:
         n=number of square grids from the dosage map   x i =dose component for grid-i in the x-direction   y j =dose component for grid-j in y-direction   z ij =desired dose in grid (i,j)       

     Subject to the constraints that: x i ≧0, y j ≧0 ∀i,jε[1, 2, . . . , n] 
     In this calculation, each row of the first matrix utilizing ones and zeros details the position of the individual cells  405  located within the inner grid  407 . For instance, the first illustrated row indicates a one in the first position and a one in the (n+1)-th position, which corresponds to the individual cell  405  located in the first position in the x-direction the first position in the y-direction of the inner grid  407 . The next row down still indicates a one in the first position but moves the one from the (n+1)-th position into the (n+2)-th position to calculate the next individual cell  405  of the inner grid  407  in the y-direction. In this fashion, each of the individual cells  405  of the inner grid  407  can be decomposed separately using the same matrix calculation. 
     However, as one of ordinary skill in the art will recognize, solving an equation such as Equation 1 will result in a multitude of different and equally valid solutions. Accordingly, an optimization of the decompositions in step  307  may be performed on the solutions in order to determine an optimum solution. For example, the solutions may be optimized in order to minimize equations such that specified in Equation 2 (e.g., the least square error):
 
 J=Σ   i,j=1   n ( z   ij   −x   i   −y   j ) 2   Eq. 2
 
Once set up, the least square errors for each of the solutions may be calculated and the solution may be optimized to determine which solution of the dosage decompositions is optimum. However, as one of ordinary skill in the art will recognize, a least square error optimization is merely one exemplary method that may be used to optimize the multitude of solutions to the dosage decomposition calculations. Any other suitable method of optimization may alternatively be used to arrive at a desired optimum decomposition.
 
     As an example, if an individual cell  405  has a desired dosage concentration of 0.5×10 15  ions/cm 2 , the directional decomposition may, once determined and optimized, have a x-direction component of between about 0.1×10 15  ions/cm 2  and about 0.4×10 15  ions/cm 2 , such as about 0.2×10 15  ions/cm 2 . Additionally, the same desired dosage concentration may be determined to have a y-direction component of between about 0.1×10 15  ions/cm 2  and about 0.4×10 15  ions/cm 2 , such as about 0.3×10 15  ions/cm 2 . However, these solutions are merely exemplary and are not meant to be limiting. 
     In step  309 , a conversion factor ε may be determined or calibrated for converting the x-direction dosage and the y-direction dosage into track velocities. This conversion factor ε is used to translate the decomposed dosages into actual track velocities (see  FIG. 2 ) for each of the individual cells  405  in the grid  403  and may be unique to individual ion implanters  100  that may be used along with this embodiment. The conversion factor ε may be determined using empirical data from test implants and measurements of those test implants into previously formed wafers that have been implanted by the ion implanter  100 . As way of example only, the conversion factor ε may have a value of between about 1×10 −12  mA·s·cm 2 /ions and about 30×10 −12  mA·s·cm 2 /ions, such as about 15×10 −12  mA·s·cm 2 /ions. 
     After the conversion factor ε has been calibrated in step  309 , the directional decompositions, such as the x-direction decomposition and y-direction decomposition, may be converted into directional track velocities in step  311 . Looking initially at, e.g., the x-direction decompositions, the x-direction dosage may be converted into an x-direction track velocity using, e.g., Equation 3: 
     
       
         
           
             
               
                 
                   
                     
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                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   3 
                 
               
             
           
         
       
     
     Where:
         x i =dose component for grid-i in the x-direction   ε=the optimized conversion factor   J 0 =the ion beam current intensity   u i =the velocity for track-i in x-direction   k=number of tracks along the beam height   l i =arc length of trajectory over beam width   m=number of tracks along vertical lift   n=number of square grids from dosage map   Subject to the constraints that: u i &gt;0 ∀iε[1, 2, . . . , m]       

     In Equation 3, the parameters m (the number of tracks along the vertical lift), n (the number of square grids from the dosage map), k (the number of tracks along the beam height), and l a  (the arc length of trajectory over the beam width), are all dependent at least in part upon the specific kinematics of the ion-beam scanning trajectory as determined in step  301  (described above with respect to  FIG. 3 ). As such, each of these variables may be dependent at least in part on the particular ion implanter  100  being employed to implant the dopants. However, by way of example only, a typical ion implanter may comprise between 10 and 30 tracks along the vertical lift, such as 19 tracks; between 1 and 10 tracks along the beam height (the number of tracks that would illuminate a single point P 1 ), such as 7 tracks; and have an arc length less than about 450 mm, such as about 300 mm. Additionally, the ion-beam current intensity J 0  may be less than about 15 mA, such as about 12 mA. 
     Following the two-dimensional embodiment, the y-direction track velocities may be calculated from the y-direction decompositions in a similar fashion as the x-direction track velocities by using, e.g., Equation 4. 
                       [           l   1           l   2         …         l   k         0       …       …       …       …       0           0         l   1         …         l     k   -   1             l   k         0       …       …       …       0           ⋮       …       …       …       …       …       …       …       …       ⋮           0       …       …       …       …       0         l   1         …         l     k   -   1             l   k           ]     ·     [           v   1     -   1                 v   2     -   1               ⋮             v   k     -   1               ⋮             v   m     -   1             ]       =       ɛ     J   0       ·     [           y   1               y   2             ⋮             y   n           ]               Eq   .           ⁢   4               
Where:
         y i =dose component for grid-i in the y-direction   ε=the optimized conversion factor   J 0 =the ion beam current intensity   v j =the velocity for track-j in y-direction   k=number of tracks along the beam height   l i =arc length of trajectory over beam width   m=number of tracks along vertical lift   n=number of square grids from dosage map   Subject to the constraints that: v i &gt;0 ∀iε[1, 2, . . . , m]       

     Once solutions for the directional track velocities have been determined, the results may again need to be optimized in step  313 . In the two-dimensional embodiment, the optimization of each of the x-direction track velocities and the y-direction track velocities may be performed similar to the optimization performed on the dosage decompositions, such as by using a least square error minimization technique. However, any other suitable optimization technique may alternatively be utilized. The example parameters given, coupled with the example x-direction component and example y-direction component, would yield an example x-direction track velocity of less than about 0.3 mm/s, such as about 0.15 mm/s, and a y-direction track velocity of less than about 0.3 mm/s, such as about 0.2 mm/s. 
     Step  315  takes the optimized directional track velocities and synthesizes them into the ion implanter  100  by inputting the optimized track velocities into the controller  117 . In operation, the controller  117  may utilize the directional track velocities as parameters during its control of the wafer handling system  115 . This usage allows the controller  117  to dynamically adjust the track velocities as the coherent ion beam  121  moves from one of the individual cells  405  to another of the individual cells  405 . By dynamically altering the directional track velocities, the implantation of ions by the ion implanter  100  into the separate individual cells  405  may be controlled to even out variations caused by the topology of the wafer  123  itself. 
       FIGS. 5A-5B  illustrate representative directional track velocities and implantations for each track of the implanter for the grid  403  (including both the inner grid  407  and the outer grid  409 , see  FIG. 4A  above) calculated using the above described process.  FIG. 5A  illustrates the relative changes in normalized dose (or inverse velocity) of each track in relation to the normalized does (or inverse velocity) of the other tracks between the individual cells  405  of the grid  403 , as shown by the usage of arbitrary units (a.u.) for the relative inverse speeds. For example, in the horizontal x-direction, track  1  has a much smaller inverse velocity as compared to track  2 . As illustrated, by changing the scanning velocity for each track, the implantation doping concentration can be adjusted to correct for topography differences between separate ones of the individual cells  405 . 
       FIG. 5B  illustrates the resultant track velocities as determined from sample calculations of Equations (3) and (4), which are also the reciprocals of the inverse velocities illustrated in  FIG. 5A . As can be seen, as the velocities of each track increases (e.g., the relative track velocity of v in the y-direction increases from a minimum of about 2.71 in Track- 4  to a maximum of about 3.17 in Track- 1 , or the relative track velocity of u in the x-direction increases from a minimum of about 2.63 in Track- 13  to a maximum of 3.27 in Track- 17 ,  FIG. 5A ), the dopant concentration in each grid-cell decreases to different levels that even out variations due to the topography of the wafer. As such, by way of example only, in an embodiment in which the numbers within  FIG. 4  represent a dosage concentration, or a parameter related to the dosage concentration, the concentration of dopants around the wafer  123  may be implanted to have a normalized concentration between about 4.62 and 5.03 as indicated by the desired dosage map of  FIG. 4 . 
     However, as one of ordinary skill in the art will recognize, the simple two-pass process described herein (one pass in a first direction, such as the x-direction, and a second pass in a second direction, such as the y-direction) is merely meant to be an exemplary process, and present embodiments should not be limited to a two-pass process. Alternatively, a multiple pass recipe may be utilized as well, where the ion implanter  100  makes multiples passes in the x-direction and multiple passes in the y-direction, with the wafer being rotated between directions. As long as the total dosage remains the same, then making multiple passes is equivalent to reducing the time duration of exposure during each pass and may be accomplished by increasing the scanning velocity accordingly. In such an embodiment, the resultant directional track velocities determined by the method described above with respect to  FIG. 3  may be multiplied by the number of passes in each direction. For example, if the ion implanter  100  is programmed to make two passes in the x-direction, the x-direction velocities determined from the above process may be multiplied by two. Alternatively, the directional decompositions, such as the x-direction decomposition and y-direction decomposition may be divided by the number of passes in each direction. 
     Additionally, the above described method may be implemented using only a single direction, such as either the x-direction or the y-direction in isolation. In such an embodiment the dosage decomposition into an x-direction and a y-direction is foregone, and either Equation 3 or Equation 4 is utilized to calculate track velocities along a single track. However, such an embodiment is limited as such a process can only produce a single track compensation instead of the grid cell compensation that a two-dimension or greater process can achieve. 
       FIG. 6  illustrates another embodiment in which the controller  117  (see  FIG. 1 ) of the ion implanter  100  is configured and adapted to determine the track velocities from the desired dosages. In this embodiment the desired dosages for each of the individual cells  405  are input into the controller  117  at a first input port  601 . The desired dosages may be stored in memory until they are input into a decomposition module  603 . The decomposition module  603  is adapted or configured using either software or hardware to decompose the individual dosages into the directional components, such as the x-direction components and y-direction components as described above with respect to Equation 1. 
     Once decomposed, the output of the decomposition module  603  may be input (either directly or through a storage medium) into a first optimization module  605 . The first optimization module  605  is adapted or configured to optimize the x-direction components and y-direction components in order to determine an optimum solution. For example, the first optimization module  605  may use a least square error minimization process (such as the one described above with respect to Equation 2) to find an optimum x-direction component and an optimum y-direction component. 
     The output from the first optimization module  605  is routed to the input of a conversion module  607 . The conversion module  607  receives the optimized directional components and, using a conversion factor method such as the one described above with respect to Equations 3 and 4, converts the directional components into directional track velocities, such as the x-direction track velocities and the y-direction track velocities. Once converted, the directional track velocities may be output from the conversion module  607  to the second optimization module  609 . 
     The second optimization module  609  receives the directional velocities, such as the x-direction track velocities and the y-direction track velocities, from the conversion module  607  and optimizes the directional velocities to determine an optimized solution for the directional velocities in a manner similar to the one described above with respect to step  313 . The second optimization module  609  may output the optimized directional velocities to a storage unit  610 , from which a wafer control module  611  may pull in order to control the positioning and movement of the wafer  123 . Finally, the wafer control module  611  outputs signals through output port  613  to the wafer positioning control system  115 , which controls the position and velocity of the wafer  123  during the ion implantation process. 
     However, as one of ordinary skill in the art will recognize, inputting the final track velocities into the ion implanter  100  or, alternatively, inputting the desired dosages into the ion implanter  100  are not the only methods through which data may be input into the ion implanter  100 . Any combination of the above described method steps may be performed within the ion implanter  100  or outside of the ion implanter  100 . All of these combinations are fully meant to be included within the present embodiments. 
     Although the present embodiments and their advantages have been described in detail, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the embodiments as defined by the appended claims. For example, the number of tracks utilized, the particular optimization routine performed, or the number of directions chosen can all be modified without leaving the scope of the present embodiments. 
     Moreover, the scope of the present application is not intended to be limited to the particular embodiments of the process, machine, manufacture, composition of matter, means, methods and steps described in the specification. As one of ordinary skill in the art will readily appreciate from the disclosure of the present embodiments, processes, machines, manufacture, compositions of matter, means, methods, or steps, presently existing or later to be developed, that perform substantially the same function or achieve substantially the same result as the corresponding embodiments described herein may be utilized according to the present embodiments. Accordingly, the appended claims are intended to include within their scope such processes, machines, manufacture, compositions of matter, means, methods, or steps.