Patent Publication Number: US-2019189330-A1

Title: Two channel cosine-theta coil assembly

Description:
FIELD 
     Embodiments of the present disclosure generally relate to plasma enhanced semiconductor substrate processing, and more specifically to the physical design and use of a compact two channel cosine-theta coil assembly. 
     BACKGROUND 
     Some semiconductor wafer processing chambers are of a type in which a magnetic field is produced within the reaction chamber by providing a plurality of electromagnets around the reaction chamber to accelerate formation of the plasma. These chambers use magnetic fields to manipulate plasma density through electron cyclotron rotation. 
     However, the inventors have observed that the intensity of the magnetic field tends to be greater on the edge of a substrate placed in the reaction chamber than in the center of the wafer. Therefore, when this method of producing a magnetic field is applied to a plasma etching chamber, there is a problem that the etch rate and the selectivity are not uniform over the substrate surface. When the method is applied to a chemical vapor deposition (CVD) chamber, there is a problem of non-uniformity in the film formation upon the substrate surface. Still another problem is that the electrical components formed on the substrate may suffer charging damage due to a non-uniform plasma density. 
     The inventors have observed that control of the process plasma distribution in the etch/plasma processing chamber is important for on-wafer uniformity and device yield. Previous low-power “cosine-theta” (cos θ) coil ring designs used to control of the process plasma distribution in the etch/plasma processing chamber were not capable of sustaining the required high current densities do to over-heating of the coil wire. Thus, the inventors have provided an improved two channel cosine-theta coil assembly for controlling a magnetic field in a semiconductor wafer processing chamber capable of sustaining the high current densities. 
     SUMMARY 
     A coil assembly for controlling a magnetic field in a plasma chamber is provided herein. In some embodiments, the coil assembly may include a coil assembly mandrel, comprising an annular body having a central opening, wherein the body includes at least one upper body coolant channel and at least one lower body coolant channel fluidly coupled to the upper body coolant channel at a coolant return location in the body, a plurality of cooling fins disposed circumferentially about an outer diameter of the body and radially outward from the outer diameter, wherein at least one of the cooling fins is an active cooling fin, and wherein the active cooling fin comprises an inlet cooling fin channel formed within the active cooling fin that extends radially outward from the body to an outer edge of the active cooling fin, wherein the inlet cooling fin channel is fluidly coupled to the upper body coolant channel, and an outlet cooling fin channel formed within the active cooling fin that extends radially outward from the body to an outer edge of the active cooling fin, wherein the outlet cooling fin channel is fluidly coupled to the lower body coolant channel. 
     In some embodiments, the coil assembly may include a mandrel comprising an annular body that includes at least one upper body coolant channel and at least one lower body coolant channel fluidly coupled to the upper body coolant channel at a coolant return location in the body, and a plurality of cooling fins disposed circumferentially about an outer diameter of the body and radially outward from the outer diameter, wherein at least one of the cooling fins is an active cooling fin, an inner electromagnetic cosine-theta (cos θ) coil ring including a first plurality of inner coils wrapped around the plurality of cooling fins in the body and configured to generate a magnetic field in a first direction, and an outer electromagnetic cosine-theta (cos θ) coil ring including a second plurality of outer coils wrapped around the plurality of cooling fins and configured to generate a magnetic field in a second direction orthogonal to the first direction. 
     In some embodiments, an apparatus for processing a substrate may include a process chamber having an internal processing volume, a substrate support disposed in the process chamber to support a substrate when disposed therein, a coil assembly including an aluminum mandrel comprising an annular body that includes at least one upper body coolant channel and at least one lower body coolant channel fluidly coupled to the upper body coolant channel at a coolant return location in the body; and a plurality of cooling fins disposed circumferentially about an outer diameter of the body and radially outward from the outer diameter, wherein at least one of the cooling fins is an active cooling fin; an inner electromagnetic cosine-theta (cos θ) coil ring including a first plurality of inner coils wrapped around the plurality of cooling fins in the body and configured to generate a magnetic field in a first direction; and an outer electromagnetic cosine-theta (cos θ) coil ring including a second plurality of outer coils wrapped around the plurality of cooling fins and configured to generate a magnetic field in a second direction orthogonal to the first direction. 
     Other and further embodiments of the present disclosure are described below. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments of the present disclosure, briefly summarized above and discussed in greater detail below, can be understood by reference to the illustrative embodiments of the disclosure depicted in the appended drawings. It is to be noted, however, that the appended drawings illustrate only typical embodiments of this disclosure and are therefore not to be considered limiting of its scope, for the disclosure may admit to other equally effective embodiments. 
         FIG. 1  depicts a schematic side view of an inductively coupled plasma reactor in accordance with some embodiments of the present disclosure. 
         FIG. 2A-C  depict an isometric view, top view, and side view of the annular mandrel of the coil assembly in accordance with some embodiments of the present disclosure. 
         FIG. 3  depicts cross-sectional view of an active cooling fin and mandrel body in accordance with some embodiments of the present disclosure. 
         FIG. 4A  depicts the shape of the inner coil in accordance with some embodiments of the present disclosure. 
         FIG. 4B  depicts the shape of the outer coil in accordance with some embodiments of the present disclosure. 
         FIG. 5  depicts the further details about the coil assembly which is a cosine-theta X-Y coil in accordance with some embodiments of the present disclosure. 
         FIGS. 6A-B  depict schematic side views of electromagnet coil configurations in accordance with some embodiments of the present disclosure. 
         FIG. 7A  depicts a top view of electromagnet coil configurations in accordance with some embodiments of the present disclosure. 
         FIG. 7B  depicts an isometric view of an exemplary electromagnet coil pair having a saddle-shape in accordance with some embodiments of the present disclosure. 
     
    
    
     To facilitate understanding, identical reference numerals have been used, where possible, to designate identical elements that are common to the figures. The figures are not drawn to scale and may be simplified for clarity. It is contemplated that elements and features of one embodiment may be beneficially incorporated in other embodiments without further recitation. 
     DETAILED DESCRIPTION 
     Embodiments consistent with the present disclosure include the physical design of a two channel cosine-theta coil assembly in a compact coil form. The cosine-theta coil assembly described herein, and associated methods, could be used in any plasma etching process where a uniform magnetic field can be used to enhance center to edge etch uniformity. Embodiments of the cosine-theta coil assembly are designed to co-locate both coils formed around the same inner diameter to retain the coils at or near the substrate surface plane during plasma processing. The assembly includes internal cooling channels designed to advantageously maintain the coil temperatures below the maximum operating temperature of the coil wire material. Combining the two coils into a compact wire form advantageously allows for the inclusion of an integral cooling loop that cools both of the coils. In addition, the compact coil packaging arranges the magnetic field from both coils into a single plain uniform field directions that can be synchronized to produce a uniform planar rotating magnetic field of constant magnitude. Furthermore, embodiments consistent with the present disclosure advantageously use a cosine-theta magnetic field effect on the process plasma at high current densities without over-heating the coil wire. 
     Other advantages of the cosine-theta coil assemblies described herein include the compact packaging of the two cosine-theta coils on a single cooled winding mandrel. The ability to package the coils tightly together allow the two coils to produce a very uniform magnetic field at the wafer level and enhance the ability to “spin” the magnetic field at the wafer center in a uniform plane above the substrate. The magnitude of the magnetic field is only limited by the magnet current power supplies and the cooling effect of the coolant flowing through the mandrel. 
     Furthermore, embodiments of the present disclosure may advantageously reduce, control, or eliminate skew on a substrate that is induced by magnetic fields used in industrial plasma etch reactors. Skew generally refers to the difference in process results from one region of the substrate to another, such as left vs. right, center vs. edge, top vs. bottom of a feature, or the like (e.g., skew refers to the pattern of non-uniformity on the substrate). Skew in the substrate uniformity could also be related to, or otherwise caused by, the previous chamber used to process the substrate in the process sequence, the flow or pump or thermal asymmetries, or asymmetrical power delivery by the RF power applicator that generates plasma. Skew can be used to characterize process results such as critical dimension (CD) uniformity, etch depth uniformity, or other process results. The inventors have observed that a large volume field programmable constant transverse B-field is one way to influence plasma uniformity and direction. Thus, a method to generate and control the magnitude and direction of a constant transverse B-field in a plasma chamber is provided to manipulate plasma uniformity and direction to correct for skews. More specifically, a method to generate and control a field programmable “cosine-theta” (cos θ) coil system in an embedded liner of a substrate process chamber is provided herein to advantageously correct for skew. 
       FIG. 1  depicts a schematic side view of an inductively coupled plasma reactor  100  (ICP reactor) suitable for performing embodiments of the present disclosure. The ICP reactor  100  may be utilized alone or, as a processing module of an integrated semiconductor substrate processing system, or cluster tool, such as a CENTURA® integrated semiconductor wafer processing system, available from Applied Materials, Inc. of Santa Clara, Calif. Examples of suitable plasma reactors that may advantageously benefit from modification in accordance with embodiments of the present disclosure include the CENTRIS™ SYM3™ ETCH chambers, inductively coupled plasma etch reactors such as the DPS® line of semiconductor equipment or other inductively coupled plasma reactors, such as MESA™ or the like also available from Applied Materials, Inc. The above listing of semiconductor equipment is illustrative only, and other etch reactors, and non-etch equipment (such as CVD reactors, or other semiconductor processing equipment) may also be suitably modified in accordance with the present teachings. 
     The reactor  100  generally includes the process chamber  102  having a conductive body (wall) with chamber liner  140 , and a dielectric lid  106  (that together define a processing volume  104 ), a substrate support pedestal  160  disposed within the processing volume to support a substrate  128 , an inductive plasma source  116 , and a controller  132 . In some embodiments, the dielectric lid  106  may be substantially flat. Other modifications of the process chamber  102  may have other types of lids such as, for example, a dome-shaped lid or other shapes. The inductive plasma source  116  is typically disposed above the lid  106  and is configured to inductively couple RF power into the process chamber  102 . 
     The inductive plasma source  116  is disposed atop the process chamber  102 . The inductive plasma source includes an RF feed structure for coupling an RF power supply  110  to a plurality of RF coils, e.g., a first RF coil  118  and a second RF coil  120 . The plurality of RF coils are coaxially disposed proximate the process chamber  102  (for example, above the lid  106  of the process chamber  102 ) and are configured to inductively couple RF power into the process chamber  102  to form or control a plasma from process gases provided within the process chamber  102  (for example, via a gas source  122  coupled to a gas inlet  108 , such as a showerhead or nozzle or the like). The relative position, ratio of diameters of each coil, and/or the number of turns in each coil can each be adjusted as desired to control, for example, the profile or density of the plasma being formed via controlling the inductance on each coil. 
     The RF power supply  110  is coupled to the RF feed structure via a match network  112 . A power divider  114  may be provided to adjust the RF power respectively delivered to the first and second RF coils  118 ,  120 . The power divider  114  may be coupled between the match network  112  and the RF feed structure. Alternatively, the power divider may be a part of the match network  112 , in which case the match network will have two outputs coupled to the RF feed structure—one corresponding to each RF coil  118 ,  120 . The RF power supply  110  may illustratively be capable of producing up to about 5 kW (but not limited to 5 kW) at a tunable frequency in a range from 50 kHz to 200 MHz, although other frequencies and powers may be provided as desired for particular applications. 
     The controller  132  comprises a central processing unit (CPU), a memory, and support circuits for the CPU and facilitates control of the components of the reactor  100  and, as such, of methods of processing a substrate, such as discussed herein. The controller  132  may be one of any form of general-purpose computer processor that can be used in an industrial setting for controlling various chambers and sub-processors. The memory, or computer-readable medium, of the CPU may be one or more of readily available memory such as random access memory (RAM), read only memory (ROM), floppy disk, hard disk, or any other form of digital storage, local or remote. The support circuits are coupled to the CPU for supporting the processor in a conventional manner. These circuits include cache, power supplies, clock circuits, input/output circuitry and subsystems, and the like. The memory stores software (source or object code) that may be executed or invoked to control the operation of the reactor  100  in the manner described below. Specifically, memory stores one or more embodiments of the methods disclosed herein, such as the method  400  discussed above. The software routine may also be stored and/or executed by a second CPU (not shown) that is remotely located from the hardware being controlled by the CPU. 
     A coil assembly  124  including a plurality of electromagnets is provided to form a desired magnetic field (e.g., as represented by magnetic field lines  126 ) within the inner volume, or processing volume  104 , of the process chamber  102  at least at the substrate level  128 , or in some embodiments, within the entire processing volume  104  above the substrate. One or more magnetic field sensors  130  may be provided to measure the magnitude and direction of the magnetic field as discussed above. The coil assembly  124  may include an outer ring of electromagnetic coils  142  and an inner ring of electromagnet coils  144 . The outer and inner rings of coils  142 ,  144  may be disposed concentrically and coaxially with respect to one another. 
     In some embodiments, the plurality of coil assembly  124  may be disposed about the processing volume of the process chamber  102 . In some embodiments, the coil assembly  124  may be disposed circumferentially along the inner surface a wall of process chamber  102  or circumferentially along the inner surface of a liner  140  (also referred to as a magnet cover). In some embodiments, the liner  140  may be grounded such that the coil assembly  124  has little to no impact on the RF return currents induced by RF power supply  110 . The purpose of the liner  140  is to prevent leakages in the B-Field out into the semiconductor fabrication (fab) environment such that it doesn&#39;t affect other processes, chambers, or otherwise affect some other instrumentation in the fab (i.e., it drops the local B-Field down to very low level, and it&#39;s safe to the touch, it&#39;s safe from an instrumentation point of view, it&#39;s safe from a health endangerment point of view). Thus, the liner  140  confines/limits the magnetic field from going outside the chamber. The liner  140  may be made of a conductive metal or other conductive material. For example, in some embodiments, the liner  140  may be formed from an aluminum alloy or a painted steel. The coil assembly  124  may be electrically insulated from the conductive liner. In some embodiments, the liner may be made from a non-conductive composite material. The liner  140  may be a double walled liner having an inner wall and an outer wall. In some embodiments, one of the inner or outer walls may be formed from a non-conductive material and include the coil assembly  124  embedded within the wall, while the other wall is made from a conductive metal material that is ground. In some embodiments, the coil assembly  124  and/or the liner  140  may be temperature controlled. For example, a heat control device  146  (i.e., heater or cooling device) may be coupled to coil assembly  124  and/or the liner  140 . The heat control device  146  may be controlled by controller  132 . In some embodiments, the heat control device  146  may provide liquid or gas coolant to be flowed through the coil assembly  124  to cool the coil assembly  124  as discussed below in further detail. In some embodiments, the liner  140  may be heated by heater  146  to a desired temperature, before or after the current is provided to coils  142 ,  144  by power supplies  150 ,  152 . The liner may be heated to a temperature of about 18° C. to about 150° C. Heating the liner  140  advantageously reduces material (e.g., polymer) deposition on the liner wall during substrate processing that utilize gases that are polymerizing gas. Thus, heating the liner  140  advantageously reduces process chamber contamination and chamber cleaning time. Also, when heating the liner  140  advantageously matches the temperature of the liner  140  with other parts of chamber, such as a showerhead or ceramic lead, to reduce temperature variation inside the chamber. 
     As noted above, the coil assembly  124  includes an outer ring of electromagnetic coils  142  and an inner ring of electromagnet coils  144 . The coils  142  and  144  are wrapped around an annular mandrel  148 . In some embodiments, the mandrel  148  is formed from aluminum. In some embodiments, the aluminum is hard anodized. In other embodiments, the mandrel may be formed from other materials that have similar thermal conductivity and electrical conductivity properties as aluminum. The mandrel  148  is described in further detail with respect to  FIGS. 2A-2C  and  FIG. 3 . 
     As shown in  FIGS. 2A-2C , mandrel  148  includes a mandrel body  206  having a central opening  212 . The central opening  212  is configured to allow the coil assembly  124  to be disposed in processing chamber  100  and about processing volume  104 . The mandrel  148  further includes a plurality of cooling fins  202  uniform distributed circumferentially and uniformly about the outer diameter of the mandrel body  206 . In some embodiments, the cooling fins  202  may be integrally formed with the body  206 . In other embodiments, the cooling fins  202  may be attached to the body via welding (i.e., Electron-beam welding (EBW) or other type of welding), glues, or other types of fasteners to securely couple the cooling fins  202  to the body  206 . In some embodiments, a plurality of openings  208  are formed through the cylindrical wall of the body  206 . The openings  208  are formed between the cooling fins  202  and advantageously promote airflow and cooling of the coil assembly  124  (i.e., of the mandrel  148  and of the coils  142 ,  144 ). The body  206  includes upper and lower flanges  210  which help secure and align the coils  142 ,  144  when disposed thereon as shown in  FIG. 3 . 
     Each cooling fin  202  may be formed in the shape of an I-beam as shown in  FIGS. 2A and 2C . The I-beam structure of the cooling fin  202  advantageously promotes airflow and cooling of the coils  142 ,  144  that are wrapped around each cooling fin  202 . Different fin cross-sections may be used as well, such as rectangular, circular, and the like. Each cooling fin  202  may also include additional through-holes or openings within each fin to advantageously promote airflow and cooling of the coils  142 ,  144  and the mandrel  148 . Furthermore, in some embodiments, the minimum spacing between the cooling fins  202  is determined based on the heat dissipation requirements and coil material being used. The coil assembly  124  can include between about 16 fins to about 128 cooling fins. In some embodiments, the coil assembly  124  can include 63 or 64 cooling fins. When an active cooling fin  204  (described below) is included in the coil assembly  124 , the mandrel  148  may include 63 or an odd number of total cooling fins. 
     In some embodiments, at least one of the cooling fins  202  may be an active cooling fin  204  that facilitates active cooling of the coil assembly  124 .  FIG. 3  depicts a detailed cross section of an active cooling fin  204 . As shown in  FIG. 3 , a pair of cooling fin channels  302 ,  304  may be formed in the active cooling fin  204  that extend radially outward from the body  206  to an outer edge of the active cooling fin  204 . One of the cooling fin channels (e.g.,  302 ) may be used as an inlet that provides coolant (inlet coolant flow  220 ) to the coil assembly  124 , while the other one of the cooling channels (e.g.,  304 ) may be used as an outlet that removes coolant (outlet coolant flow  222 ) from the coil assembly  124 . In some embodiments, the cooling fin channels  302 ,  304  can optionally be plugged using plugs  306 . The inlet cooling fin channel  302  is fluidly coupled to one or more inlet body channels  308  that are formed in body  206 . Similarly, the outlet cooling fin channel  304  is fluidly coupled to at least one outlet body channels  310  that are formed in body  206 . The body channels  308  and  310  are fluidly coupled to each other within body  206  at a coolant return location  214  to reverse the flow of the coolant. When a single active cooling fin  204  is used as shown in  FIG. 2B , two coolant return locations  214  may be formed within the body  206  at the opposite end of the body  206  (i.e., about 180° from the active cooling fin  204 ) to fluidly couple two sets of body channels  308 ,  310  that each traverse 180° of the body  206 . Additional active cooling fins  204  and coolant return locations  214  may be used as desired. The body channels  308  and  310  are sealed with caps  312  and  314 , respectively. Caps  312  and  314  fluidly seal the body channels  308  and  310 . In some embodiments, the caps  312  and  314  are welded (EBW) on to fluidly seals the body channels  308  and  310 . The caps  312  and  314  may be formed from the same material as the mandrel  148  as described above. In some embodiments, coolant may be flowed into and through the mandrel  148  at a rate between about 1 gpm to about 20 gpm, or about 4 gpm. The temperature of the coolant may be from 10° C. to about 30° C. 
       FIG. 3  further shows at least one example of the coil wrapping of the inner coils  144  and the outer coils  142 . Although this example is about the active cooling fin  204 , the coil wrapping is exemplary and can be used about any cooling fin  202 . This example shows a combined inner and outer coil with 4 wraps of the inner coil  144  and 18 wraps of the outer coil  142 . In some embodiments, the number of coil wraps/layers is no more than two layers thick to improve air-flow to the ICP source. Additional wraps/layers may be used, however, additional layers may require additional cooling to keep the coil temperatures from exceeding their temperature limits. 
       FIG. 4A  depicts the shape of the inner coil  144  consistent with at least some embodiments of the present disclosure.  FIG. 4B  depicts the shape of the outer coil  142  consistent with at least some embodiments of the present disclosure. 
       FIG. 5  depicts the further details about the coil assembly  124  which is a cosine-theta X-Y coil. The inner coil is used to produce a “X” direction uniform magnetic field over the wafer and the outer coil is used to produce a “Y” direction uniform magnetic field (the X, Y field orientations are 90 degrees apart). The X coil “+” (high potential) is connected at X1+ ( 502 ). The X1 coil is wrapped around the active cooling fin  204  (i.e., the 3 o&#39;clock position in  FIG. 5 ). All X1 coils wrapped as shown with respect to the right hand rule to produce the B-field distribution shown (edge to center). The X coil “−” (low-potential) is connected at X1− ( 504 ). The jumper  510  between X1 and X2 connects X1− ( 504 ) to X2+ ( 506 ). The connection at X2+ ( 506 ) drives current through the X2 coils as shown with respect to the right hand rule to produce the b-field distribution shown (center to edge). The X coil “−” (low potential) is connected at X2− ( 508 ). In some embodiments, the expected resistance for the X1/X2 combination is 8.6 ohms (14 ga wire). The Y1/Y2 coil pair will have the same pattern offset from the X1/X2 coil pair by 90 degrees.  FIG. 5  further shows optional empty spaces  512  that separate each of the quadrants on the cosine-theta X-Y coil. 
     Each of the outer and inner rings of electromagnetic coils  142 ,  144  may be coupled to a separate DC power supplies  150 ,  152  that are independently controlled by controller  132 . In some embodiments, each of the outer and inner rings of electromagnetic coils  142 ,  144  may be coupled to the same power supply. In some embodiments, the DC power supplies  150 ,  152  are coupled to coils  142 ,  144  via stationary electric contacts since the constant transverse B-field produced may be rotated non-mechanically as described below. 
     In some embodiments, each of the outer and inner rings of electromagnetic coils  142 ,  144  are “cosine-theta” (cos θ) coils that each include a plurality of sets of coils. Each cos θ coil  142 ,  144  consists of two sets cos θ windings disposed opposite each other to generate radial fields. For example,  FIG. 6A  shows a side view of the outer cos θ coil  142  that depicts a first set of n cos θ outer coils/windings  602   1 - 602   n . A second set of cos θ outer coils/windings  602 ′ 1 - 602 ′ n  disposed opposite the first set of coils can be seen in the top down view of the outer cos θ coil  142  in  FIGS. 7A and 7B . Similarly,  FIG. 6B  shows a side view of the inner cos θ coil  144  that depicts a first set of n inner coils  604   1 - 604   n . A second set of orthogonal cos θ inner windings  604 ′ 1 - 604 ′ n  can be seen in the top down view of the outer cos θ coil  144  in  FIG. 3A . The shape formed by each coil  602   1 - 602   n ,  602 ′ 1 - 602 ′ n ,  604   1 - 604   n , and  604 ′ 1 - 604 ′ n  is a saddle shape as shown in  FIG. 7B . In some embodiments, the number of sets/pairs of coils in each cos θ coil  142 ,  144  may be from 2 sets/pairs of coils (4 coils total) to about 50 sets/pairs of coils (100 coils total). In some embodiments, the number of sets/pairs of coils in each cos θ coil  142 ,  144  may be 32 sets/pairs. 
     As shown in  FIGS. 7A and 7B , each cos θ coil  142 ,  144  includes series of saddle-shaped coils spaced uniformly with respect to cos θ on the curved cylindrical surface, where θ is the angle between the radius of the cylinder and the radial axis. Each cos θ coil  142 ,  144  consists of N cp  coil pairs spaced uniformly with respect to cos θ on the curved surface of a cylinder whose base is in the xy-plane and length is along the x-axis, such that y=r cos θ. The number of turns/windings in each coil increases as θ increases to produce the cos θ coil. For example, in some embodiments, the coils may include the following number of turns to produce a cos θ distribution: 
     coils  602   1 ,  602 ′ 1 ,  604   1 , and  604 ′ 1 =4 turns 
     coils  602   2 ,  602 ′ 2 ,  604   2 , and  604 ′ 2 =8 turns 
     coils  602   3 ,  602 ′ 3 ,  604   3 , and  604 ′ 3 =10 turns 
     coils  602   4 ,  602 ′ 4 ,  604   4 , and  604 ′ 4 =12 turns 
     coils  602   5 ,  602 ′ 5 ,  604   5 , and  604 ′ 5 =14 turns 
     coils  602   6 ,  602 ′ 6 ,  604   6 , and  604 ′ 6 =16 turns 
     coils  602   7 ,  602 ′ 7 ,  604   7 , and  604 ′ 7 =18 turns 
     coils  602   8 ,  602 ′ 8 ,  604   8 , and  604 ′ 8 =20 turns 
     coils  602   9 ,  602 ′ 9 ,  604   9 , and  604 ′ 9 =22 turns 
     coils  602   10 ,  602 ′ 10 ,  604   10 , and  604 ′ 10 =24 turns 
     coils  602   n ,  602 ′ n ,  604   n , and  604 ′ n =Z turns 
     Although the above example shows that the structure of the cos θ distribution of the outer coil  142  and the inner coil  144  are the same, in some embodiments the cos θ distribution between the outer coil  142  and the inner coil  144  may be different (i.e., the outer coil  142  and the inner coil  144  may have different spacing between coils, different number of sets of coils, and/or a different number of turns per coil.) In some embodiments, the number of turns for each coil included in the outer coil  142  and the inner coil  144  are the same, but the position of the windings may disposed such that the desired cos θ distribution is achieved. 
     Each coil in the outer cos θ coil  142  has the same current passing through each coil turn. Similarly, each coil in the inner cos θ coil  144  has the same current passing through each coil turn. At the extremities of the coil the current travels along the curved boundary of the circular base of the cylinder, in the xy-plane. In some embodiments, as shown in  FIG. 7A , the X-Plane cos θ outer coil  142  is rotated 90 degrees from the Y-Plane cos θ inner coil  144  (i.e., the outer coil  142  and the inner coil  144  are disposed orthogonally to one another). Thus, the outer coil  142  can produce a constant transverse B-field in an X-direction, for example, while the inner coil  144  can produce a constant transverse B-field in a Y-direction. The interaction of the B-fields produce a single constant transverse B-field that can be controlled (i.e., magnitude and direction can be altered). 
     By providing power/current to at least one of the cos θ coils  142 ,  144 , a constant transverse B-field  702  (i.e., magnetic field) may be produced in a plane substantially parallel to the surface of the substrate  128 . A magnetic field is the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude/strength and denoted as a vector B field measured in units of amp per meter. The B field is most commonly defined in terms of the Lorentz force it exerts on moving electric charges. 
     The inventors have observed that by controlling the magnitude and direction of the current supplied to each cos θ coil  142 ,  144 , that the magnitude and direction of a constant transverse B-field  702  may be controlled. The inventors have further observed that by adjusting/controlling the magnitude and direction of a constant transverse B-field  702  in a plasma chamber, plasma uniformity and direction can be advantageously manipulated to correct for skew and other causes of substrate non-uniformity. 
     While the foregoing is directed to embodiments of the present disclosure, other and further embodiments of the disclosure may be devised without departing from the basic scope thereof.