CROSS-REFERENCE TO RELATED APPLICATIONS 
   This application claims the benefit of the filing date of U.S. Provisional Patent Application Ser. No. 60/447,431, filed Feb. 14, 2003, entitled “Method and Apparatus for Producing Plasma Uniformity in a Magnetic Field-Enhanced Plasma Reactor,” which is incorporated by reference herein. 


   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   This invention relates to plasma enhanced, semiconductor substrate processing systems and, more specifically, to a method and apparatus for shaping a magnetic field in a magnetically enhanced plasma reactor. 
   2. Description of the Related Art 
   Semiconductor wafer processing chambers commonly employ plasmas to enhance the performance of various processes for fabricating semiconductor devices on silicon substrates or other workpieces. Such processes include sputter etching, plasma enhanced chemical etching, plasma enhanced chemical vapor deposition, and ionized sputter deposition. The high energy level of reagents in the plasma generally increases the rate of the fabrication process, and also reduces the temperature at which the semiconductor workpiece must be maintained to perform the process. 
   Magnetically enhanced plasma chambers (also referred to as reactors) employ magnetic fields to increase the density of charged particles in the plasma to further increase the rate of the plasma enhanced fabrication process. Increasing the process rate is highly advantageous because the cost of fabricating semiconductor devices is proportional to the time required for fabrication. 
   Despite this advantage, many plasma chambers in commercial use do not employ magnetic enhancement because the magnetic enhancement has been found to increase the likelihood of damaging the semiconductor devices on the wafer. Such damage is caused by non-uniform electron density across a wafer due to the spatial contour of the magnetic field being poorly optimized. 
     FIG. 1  depicts a schematic cross section view of a magnetically enhanced plasma chamber  5  suitable for either etching or chemical vapor deposition in accordance with the prior art.  FIG. 2  depicts a top cross sectional view of the chamber  5 . The vacuum chamber  5  is enclosed by an octagonal sidewall  12 , circular bottom wall  14  and circular top wall or lid  16 . The lid  16  and bottom wall  14  may be either dielectric or metal. An electrically grounded anode electrode  18  is mounted at the bottom of the lid  16 . The anode electrode may be perforated to function as a gas inlet through which process gas enters the chamber. The side wall  12  may be either dielectric or metal. If it is metal, the metal must be nonmagnetic material such as anodized aluminum so as to not interfere with the magnetic field created by an array of electromagnetic coils  6 ,  7 ,  8 , and  9  located outside the chamber  5 . If the side wall is metal, it will function as part of the anode. 
   The semiconductor wafer or workpiece  20  is mounted on a cathode electrode  22 , which, in turn, is mounted in the lower end of the chamber  5 . A vacuum pump, not shown, exhausts gases from the chamber  5  through an exhaust manifold  23  and maintains the total gas pressure in the chamber  5  at a level low enough to facilitate creation of a plasma, typically in the range of 10 millitorr to 20 torr, with pressure at the lower and higher end of the range being typical for etching or CVD processes, respectively. 
   An RF power supply  24  is connected to the cathode pedestal  22  through a series coupling capacitor  26  or matching circuit (not shown). The RF power supply  24  provides an RF voltage between the cathode pedestal  22  and the grounded anode electrode  18  that excites the gases within the chamber into a plasma state. The plasma body has a time average positive DC potential or voltage relative to the cathode or anode electrodes that accelerates ionized process gas constituents to bombard the cathode and anode electrodes. 
   Magnetic enhancement of the plasma most commonly is implemented by a DC magnetic field in the region between the cathode and anode electrodes. The direction of the magnetic field is usually transverse to the longitudinal axis of the chamber  5 , i.e., transverse to the axis extending between the cathode and anode electrodes. Various arrangements of permanent magnets or electromagnets are conventionally used to provide such a transverse magnetic field. One such arrangement is the pair of coils  6 ,  7  shown in  FIG. 1  disposed on opposite sides of the cylindrical chamber side wall  12 .  FIG. 2  depicts a top, cross-sectional view of the chamber of  FIG. 1  that shows the orientation of opposing coil pairs  6 ,  7 ,  8  and  9 . Generally, the diameter of each coil approximately equals the spacing between the two coils. Each pair of opposing coils  6 ,  7 ,  8  and  9  are connected in series and in phase to a DC power supply, not shown, so that they produce transverse magnetic fields which are additive in the region between the coil pairs. This transverse magnetic field is represented in  FIGS. 1 and 2  by the vector B oriented along the negative X axis. An example of such a magnetically enhanced plasma chamber is described in commonly assigned U.S. Pat. No. 5,215,619, issued Jun. 1, 1993, which is hereby incorporated by reference in its entirety. 
   Because the plasma has a positive time average potential or voltage relative to the cathode electrode  22 , the time average electric field E in the plasma pre-sheath adjacent the cathode is directed downward from the plasma toward the cathode, thereby giving the free electrons in the pre-sheath a drift velocity vector whose time average values oriented upward towards the plasma body, as represented by vector Ve in  FIG. 1 . In response to the DC magnetic field vector B, these free electrons will primarily experience a qvxB force, causing the electrons and ions to move in a helical shaped path that generally follows the magnetic field vector. In additional, the electrons and ions will experience another time-averaged force due to the combination of the helical motion and the electric field. This is commonly called the ExB drift, where the direction of the drift is approximately coplanar with the semiconductor wafer  20  and orthogonal to the magnetic field vector B as illustrated in  FIG. 2  by the ExB vector oriented along the Y axis. 
   In this discussion, the term “time average” means averaged over one period of the RF frequency or frequencies at which the plasma is excited, this period typically being less than 10 −7  seconds. This time average over one RF period is unrelated to the time averaging due to the optional rotation of the magnetic field relative to the workpiece that typically has a rotation period on the order of 0.2 to 4 seconds. The frequency of the electron moving helically about the magnetic field vector is f=(qB)/2πm, where q is the electron charge, B is the magnetic field strength (Gauss), and f is the frequency (Hertz). For example, a magnetic field of 35 G will result in one turn around the helix lasting about 10e  −4  seconds. This is longer than the RF frequency, but is much shorter than the magnetic field rotation of 0.2 to 4 seconds. 
   It is believed that the ExB drift of free electrons is a major source of semiconductor device damage in conventional magnetically enhanced plasma chambers. Specifically, it is believed that ExB drift can unevenly distribute the free electrons in the plasma pre-sheath and cause non-uniformity in the ion flux. It is believed that this spatial non-uniformity of the ion flux that bombards the wafer produces electrical currents in the wafer which often damages the semiconductor devices on the wafer. 
   Conventional magnetically enhanced plasma chambers attempt to ameliorate this non-uniformity by slowly rotating the magnetic field relative to the wafer, typically at a rotation frequency in the range of one quarter to five rotations per second. In some designs, the wafer  20  or the magnets  6 ,  7 ,  8  and  9  are physically rotated. In other designs, as illustrated in  FIG. 2 , the rotation is performed electronically by providing two pairs of coils  6 ,  7  and  8 ,  9  that are arranged orthogonally to one another. The magnetic field can be rotated in 90° increments by successively and periodically connecting the DC power supply to the first coil pair  6 ,  7  with positive polarity (2) to the second coil pair  8 ,  9  with positive polarity; (3) to the first coil pair  6 ,  7  with negative polarity; and (4) to the second coil pair  8 ,  9  with negative polarity. Alternatively, the magnetic field can be rotated continuously by replacing the DC power supply with a very low frequency (in the range of 0.1-10 Hz) power supply having quadrature outputs connected to provide current to the first coil pair  6 ,  7  offset in phase by 90° from the current provided in the second coil pair  8 ,  9 . 
   Rotating the magnetic field relative to the wafer greatly reduces the time average spatial non-uniformity in the ion flux bombarding the wafer, and therefore can provide acceptable spatial uniformity of etch rate (in an etching chamber) or deposition rate (in a CVD chamber) on the wafer surface. However, rotating the magnetic field does not in any way improve the instantaneous spatial uniformity of ion flux on the wafer surface, and therefore does not completely solve the problem of semiconductor device damage in magnetically enhanced plasma chambers. 
   U.S. Pat. No. 6,113,731, issued Sep. 5, 2000, discloses a method and apparatus that further combats the ExB drift problem by driving current through the adjacent coil pairs  6 ,  9  and  7 ,  8  such that a magnetic field gradient is generated laterally across the surface of the wafer. 
   In  FIG. 2 , the magnetic field produced by driving a first current through coils  7 ,  8  is represented by arrow  10  and the magnetic field produced by driving a second current through coils  6 ,  9  is represented by the arrows  11 . The first current is less than the second current such that the magnetic field  10  is smaller than magnetic field  11  such that a magnetic field gradient is produced, i.e., the magnetic field is shaped. The ratio of the currents produces the specific shape of the gradient. This ratio is optimized for each process regime to create a nearly uniform plasma. For most process regimens, the current ratio is in the range 0.1 to 0.7. This non-uniform magnetic field produces a more uniform ion flux within the chamber by increasing the magnetic field magnitude in the region of the wafer formerly with low etch rate, and by decreasing the magnetic field magnitude in the region of the wafer formerly with high etch rate. This magnetic field gradient is then adjusted to the shape that optimizes ion flux uniformity for each process condition. The optimum magnetic field gradient is dependent upon the hardware configuration used to produce the magnetic fields. As smaller and smaller feature sizes are used on wafers, the requirements for producing a nearly uniform ion flux continue to become more stringent, especially in certain process regimes, in order to prevent damage to the electrical circuitry formed on the wafer. The optimal gradient may be produced in a static position; however when the current is switched to the next coil pair to cause rotation of the plasma, the plasma “jumps” by 90°. Such a “jump” forms a discontinuity in the plasma process that can damage the substrate or cause non-uniform processing. 
   Therefore, there is a need in the art for a method and apparatus for controlling the magnetic field gradient within a magnetically enhanced plasma chamber. 
   SUMMARY OF THE INVENTION 
   The disadvantages associated with the prior art are overcome by a method and apparatus of providing improved shaping of the magnetic field gradient within a magnetically enhanced plasma reactor to produce a uniform plasma. Generally, the invention uses a plurality of overlapping main magnetic coil sections for forming a magnetic field generally parallel to a top surface of a substrate supporting member. The overlapping magnetic coils produce a magnetic field having a shape that is improved over the prior art. In other embodiments of the invention, sub-magnetic coils are used in conjunction with the main magnetic coils (whether overlapping or not) to provide greater control over the shape of the magnetic field. Such field control can be used to provide an optimal shape to the instantaneous magnetic field as well as a nearly continuous field shape during the transitions as the magnetic field is rotated. 


   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     So that the manner in which the above recited features of the present invention are attained and can be understood in detail, a more particular description of the invention, briefly summarized above, may be had by reference to the embodiments thereof which are illustrated in the appended drawings. 
     It is to be noted, however, that the appended drawings illustrate only typical embodiments of this invention and are therefore not to be considered limiting of its scope, for the invention may admit to other equally effective embodiments. 
       FIG. 1  is a side cross-sectional view of a conventional dry etching chamber; 
       FIG. 2  is a top cross-sectional view of a magnetic field generator of the dry etching chamber shown in  FIG. 1 ; 
       FIG. 3  is a top schematic view of a process chamber having magnetic coils with extended width in accordance with one embodiment of the invention; 
       FIGS. 4A-C  depict a top schematic view of the magnetic fields respectively produced by main coils, sub-magnetic coils and both main and sub-magnetic coils; 
       FIG. 5  is a top schematic view of a process chamber having both extended width main magnetic coils and sub-magnetic coils in accordance with one embodiment of the invention; 
       FIG. 6  is a top view of two main magnetic coils and a sub-magnetic coil section shown in  FIG. 5 ; 
       FIG. 7  is a side view of main magnetic coil sections and the sub-magnetic coil shown in  FIG. 6 ; 
       FIG. 7A  depicts a schematic circuit of a double wound version of the coil configuration of  FIG. 7 ; 
       FIGS. 8A-8C  are transitional diagrams depicting the generation of the magnetic field in accordance with the prior art and an embodiment of the invention; 
       FIGS. 9-17  are top views of various embodiments of magnetic coil configurations in accordance with the invention; 
       FIGS. 18A-18B  depict perspective views of coil configurations having horizontal sub-magnetic coils in accordance with embodiments of the present invention; 
       FIGS. 19A-19C  depict perspective views of coil configurations having vertical and horizontal sub-magnetic coils in accordance with embodiments of the present invention; 
       FIGS. 20A and 20B  depict current flow through the coil configurations at  FIGS. 19A and 19B ; 
       FIG. 21  depicts a perspective view of yet another magnetic coil configuration in accordance with the invention; and 
       FIGS. 22A-22K  depict magnetic field simulation results for various embodiments of the invention. 
   


   DETAILED DESCRIPTION 
     FIG. 3  is a top view of an embodiment of a magnetic coil configuration  300  circumscribing sidewall  12  of a plasma enhanced chamber  5  in accordance with the present invention. Specifically,  FIG. 3  depicts main magnetic coils  302   1 ,  302   2 ,  302   3 , and  302   4  (collectively main magnetic coils  302 ) and main current sources  306 A,  306 B,  306 C and  306 D. As such, in this embodiment of the invention, four coils are driven by four individual currents. Illustratively, the embodiment of the coil configuration  300  is depicted as having a substantially octagonal plan form. However, that depiction is not intended to limit the scope of the invention. For example, a coil configuration in accordance with the invention can be any configuration around the periphery of a chamber  5  with each coil overlapping (or being overlapped by) at least a portion of an adjacent coil. 
   Illustratively, each of the main magnetic coils  302  has an extended width such that a portion of each coil overlaps (or is overlapped by) an adjacent main magnetic coil  302 . Although the main magnetic coils  302  are depicted as having the corners overlapping, that depiction is for illustrative purposes only. The main magnetic coils  302  can overlap more or less than the depiction in  FIG. 3 . Other embodiments of the invention that utilize overlapping coils are described below in with respect to  FIGS. 9-13  and  21 . 
   In the chamber, the magnetic field is generally contoured (or shaped) to combat ExB drift such that, at any given moment, there is a high magnetic field corner and a low magnetic field corner. It is relatively easy to control the magnetic field located in a low magnetic field corner (point C). However, difficulty arises when controlling the field in a high magnetic field corner (point A).  FIG. 3  depicts an instantaneous view of a magnetic field produced by driving coils  302   2  and  302   3  using relatively high current (arrows  304 ) and driving coils  302   1  and  302   4  using relatively low current (arrow  308 ). Larger magnetic coils (coils having extended width) allow greater control over the magnitude of the high magnetic field (point A) without affecting the magnetic field strength at points B and C. A larger area encompassed by the magnetic coils  302  provides an improved magnetic field gradient. However, the size of the main magnetic coils  302  is limited by the size of the reaction chamber. For example, due to the size of the reaction chamber and placement of its supporting hardware, generally the magnets can&#39;t generally be made taller. However, the magnets can be made wider to increase the coil area. As such, making the magnets wider produces larger coil areas to facilitate improved magnetic field shape e.g., the coils  302  of  FIG. 3  extend more than 90° about the circumference of the chamber  5 .  FIGS. 9-21D  (described in greater detail below) depict illustrative embodiments that allow greater control over the shape of the magnetic field. 
   The main current sources  306 A-D drives current through each of the main magnetic coils  302 . To generate the magnetic field, the main current sources  306 A and  306 B apply current to adjacent main magnetic coils  302   1  and  302   2  in the same direction. To produce an effective magnetic field gradient in the chamber, the current sources  306 C and  306 D apply current to flow in main magnetic coils  302   3  and  302   4 . Further, the opposing magnetic field  308  generated by main magnetic coils  302   3  and  302   4  is of a lesser magnitude than the magnetic field generated by main magnetic coils  302   1  and  302   2 . Illustratively, four current sources are depicted as causing current to flow through each of the main magnetic coils  302 . As coil pairs are driven to produce a magnetic field in a reactor having a configurable magnetic field (“CMF”), the B-field is high nearest the adjacent coils, i.e., the field strength is highest in the corner at point A, and decreases across the wafer to point C. The currents are then switched from coil pair to coil pair to rotate the magnetic field. Such a reactor that uses a CMF technique is the eMxP +  Dielectric Etch reactor manufactured by Applied Material, Inc. of Santa Clara, Calif. This reactor is the subject of U.S. Pat. No. 6,113,731, issued Sep. 5, 2000, which is incorporated herein by reference. 
   In some processes, opposite coils (e.g.,  302   1  and  302   3 ) are driven with current in pairs to produce magnetic fields that extend across the substrate. For best process results, it is desired that the magnetic field uniformly extend across the chamber with parallel lines of force. However, as depicted in  FIG. 4A , when coils  302   1  and  302   3  are driven, the magnetic field  400  has a convex shape, i.e., the outer lines of force  402  curve outward. To mitigate this convex field shape, a corrective magnetic field can be provided that has a concave shape.  FIG. 4B  depicts such a concave-shaped corrective field  404  being produced by sub-magnetic coils  504   1 ,  504   2 ,  504   3  and  504   4  that are positioned proximate the main magnetic coils  302   1 ,  302   2 ,  302   3  and  302   4 . As is discussed in detail below, the sub-magnetic coils are positioned proximate the ends of the main magnetic coils. As depicted in  FIG. 4C , the vector addition of the main and corrective fields forms a uniform field  406  extending across the chamber. As is discussed below, the addition of such sub-magnetic coils  504   1 ,  504   2 ,  504   3  and  504   4  provide a large number of other benefits including additional magnetic field shape control for both instantaneous fields and for controlling the field shape as the fields are switched to facilitate field rotation. 
   The use of corrective fields can be extended to be produced by a wide variety of coil configurations. These configurations include placing coils that generate corrective fields in a horizontal plane about the chamber, a vertical plane about the chamber, or both. A limited sample of the possible embodiments of the invention that utilize such corrective fields are discussed below. The invention is intended to encompass any combination of coils that provide corrective magnetic fields for shaping the magnetic field produced by the main coils. 
   As depicted in  FIG. 5 , for greater control over the shape of the magnetic field in the chamber, sub-magnetic coils  504   1 ,  504   2 ,  504   3 ,  504   4  (collectively referred to as sub-magnetic coils  504 ) are strategically placed proximate the main magnetic coils  302 . Illustratively, the sub-magnetic coils  504  are placed proximate the overlapping portions of the main magnetic coils  302 . The sub-magnetic coils  504  generate a magnetic field and allow “tuning” of the fields produced in the corners (i.e., the overlapping portions). The sub-magnetic coils  504  are used to control the shape of the magnetic field. The overall field contour can be established by varying the turns, angle, width, and separate current drives. The angle and width of the coils allow the placement of more coils (i.e., a stronger magnetic influence) in the reactor. More turns in a coil also provide a stronger magnet. A stronger magnet produces a stronger magnetic field and provides greater control over the magnetic field gradient. Although it is convenient to place the sub-coil in the overlapping portions—it is not mandatory. In other embodiments of the invention, the sub-magnetic coils can be placed adjacent (i.e., end to end) to the main magnetic coils (See  FIGS. 16 and 17  below). As shall be discussed in detail below, when sub-magnetic coils are used, the main coils establish an initial shape of the magnetic field and the sub-magnetic coils can then be used to adjust (or correct) the field contour to achieve an optimal magnetic field shape. 
   To achieve a desired magnetic field contour, current is driven through each of the sub-magnetic coils  504 . Specifically, current sources  308 A and  308 B drives current through sub-magnetic coils  504   1  and  504   2 , and current sources  308 C and  308 D drives current through sub-magnetic coils  504   3  and  504   4 . In one embodiment, each of the sub-magnetic coils  504  can be driven by separate current sources such that up to eight current sources can be used to drive the main and sub-magnetic coils. Such independent current facilitate wide control over the magnetic field shape. In one embodiment of the invention, four current sources can be used to provide current to the main magnetic coils  302  and sub-magnetic coils  504 . In the instance when four current sources are used, the sub-magnetic coils are “double wound” with each of the two windings series connected to a different adjacent main magnetic coil. This configuration uses the same number of currents as are used in an existing eMxP +  chamber identified above. 
     FIG. 6  is a top view of two main magnetic coils  302  (i.e., main magnetic coils  302   1  and  302   2 ,) and sub-magnetic coil  504   1 . Main magnetic coil  302 , has a central portion  410  and overlapping portions  402  and  404 . Main magnetic coil  302   2  has a central portion  412  and overlapping portions  406  and  408 . Although the sub-magnetic coil  504   1  is depicted as being positioned outside the periphery of the main magnetic coils  302  that depiction is for illustrative purposes only. In the embodiment depicted in  FIGS. 6 and 7  the sub-magnetic coils  504  are located between the overlapping portions and within the plane of the overlapping portions. 
     FIG. 7  is a side view of main magnetic coils  302  (i.e., main magnetic coils  302   1  and  302   2 ,) and sub-magnetic coil  504   1 .  FIG. 7A  depicts a schematic circuit of a double wound version of the coil configuration of  FIG. 7 . The sub-magnetic coil  504   1  is wound as two coils  504   1A  and  504   1B  onto a single “bobbin” and each coil  504   1A  and  504   1B  is respectively series connected to a main coil  302   1  and  302   2 . Additionally, the sub-magnetic coil  504   4A  is wired in series with the main coil  302   1  and sub-magnetic coil  504   1A . Thus, four current sources  306 A,  306 B,  306 C and  306 D drive current through each of the four sets of three coils. As such, each current is driven through three series connected coils, i.e., two sub-magnetic coils and a main coil. Each main and sub-magnetic coil is wound and wired in this manner to enable four current sources to shape and control the magnetic field within the chamber. During the etching process, adjacent magnetic coils generate a relatively strong magnetic field at predetermined intervals. The current through adjacent magnetic coils can flow in the same direction as shown by the arrows. Specifically,  FIGS. 7 and 7A  depict the direction of the flow of current through main magnetic coils  302   1  and  302   2 , and sub-magnetic coils  504   1 . Note that the current through main magnetic coils  302   1  and  302   2 , and sub-magnetic coils  504   1  flows in a clockwise direction. As such, the current is additive and creates a larger magnetic field than if the currents flow in opposite directions. 
     FIGS. 8A-8C  together depict transition sequences used to rotate the magnetic field in an etching chamber.  FIG. 8A  depicts the prior art application of different magnetic field intensities for magnetic coils at intervals (or degrees with respect to an initial starting point)  602 ,  604 , and  606 . For example,  FIG. 8A  comprises magnetic coils  6 ,  7 ,  8 , and  9  of the prior art; a high magnetic field  620 ; and a low magnetic field  622 . At interval  602  (zero degrees), adjacent magnetic coils  8  and  9  generate a curved high magnetic field  620 . During this same interval, magnetic coils  6  and  7  generate a curved low magnetic field  622 . When combined, the two curved magnetic fields  620  and  622  form a concave shaped field above the substrate in the chamber. During transition from one pair of adjacent coils to another pair of adjacent coils that facilitates field rotation, the plasma in the etching chamber momentarily jumps as the field is rotated. To provide a smoother field, at interval  604  (forty-five degrees), a high magnetic field  624  is generated between coils  6  and  8  by applying current to coils  6  and  8  only. This generation of the high convex magnetic field  624  at forty-five degrees helps lessen the jump in the plasma. At interval  606  (ninety degrees), the curved high magnetic field  626  is generated by magnetic coils  6  and  9 , while the low magnetic field  628  is generated by magnetic coils  7  and  8 . At this point, rotation is complete. However, the magnetic field gradient at interval  604  is substantially different from the gradient in intervals  602  and  606 . 
     FIG. 8B  depicts the transition of the high magnetic field at intervals  614 ,  616 , and  618  (zero, forty-five, and ninety degrees respectively) while maintaining the current magnetic field gradient in accordance with the present invention. For example,  FIG. 8B  comprises main magnetic coils  302   1 ,  302   2 ,  302   3  and  302   4 ; sub-magnetic coils  504 ,  504   2 ,  504   3 , and  504   4 ; a high magnetic field  630 ; and a low magnetic field  632 . At interval  614 , the curved high magnetic field  630  is generated at main magnetic coils  302   1  and  302   2  while the curved low magnetic field  632  is generated by main magnetic coils  302   3  and  302   4 . Interval  616  provides a smoother transition from zero to ninety degrees because the magnetic field gradient is maintained at the 45° position. Specifically, current is applied to sub-magnetic coils  504   4  and  504   1  which generates a high magnetic field  634 . In addition, a low magnetic field  636  is generated by sub-magnetic coils  504   2  and  504   3 . Note that at interval  616  (forty five degrees) that the magnetic fields generated are curved such that they have the same shape and gradient as the fields at zero degrees. A consistent, individual curved magnetic field within the etching chamber provides a consistent magnetic field gradient within the chamber. At interval  618  (90°), current is applied to main magnetic coils  302   1  and  302   4  which generates a high magnetic field  638 . In addition, a low magnetic field  640  is generated by the application of current to main magnetic coils  302   2  and  302   3 . 
     FIG. 8C  depicts using various combinations of coils to achieve a substantially smooth rotation of the magnetic field during a 90° rotation in accordance with another embodiment of the invention. The currents are indicated as normalized values relative to the high magnetic field coil current and the direction of the current is indicated by a plus or minus. For example, at time t 0 , a magnetic field “BCD” is generated by adjacent magnetic coils  302   2  and  302   3  (i.e., the polarity of magnetic coil  302   3  is opposite to the polarity of magnetic coil  302   2 ). Current also passes through sub-magnetic coils  504   1  and  504   3  to provide a magnetic field “A” that helps shape the magnetic field at the ends of the adjacent magnetic coils  302   2  and  302   3 . Note that the polarity of the current in sub-magnetic coil  504   1  is opposite to the polarity of the current in sub-magnetic coil  504   3 . 
   At t1, current is applied to the respective coils  302  and  504  such that a diminished magnetic field “CD” is generated by adjacent magnetic coils  302   2  and  302   3 . The numbers and respective polarities depicted represent relative (normalized) magnitude and polarity of the applied currents. For example, the current that passes through magnetic coil  302   1  has a polarity opposite to sub-magnetic coil  504   3 . As such, the portion of the magnetic field represented by “A” is transitioned between  504   3  and  302   1 . The sub-magnetic coil  504   1  causes the portion of the magnetic field represented by “B” to be generated at sub-magnetic coil  504   1  and main magnetic coil  302   3 . The transitioning process is performed by increasing and decreasing the current between main magnetic coils  302  and sub-magnetic coils  504 . 
   At t2, current is applied to the sub-magnetic coils  504   1  and  504   2  and the current is increased at main magnetic coil  302   1 . As a result, the magnetic field represented by “B” moves vertically between main magnetic coils  302   1  and  302   3 . The portion of the magnetic field represented by “C” transitions towards sub-magnetic coil  504   1 . 
   At t3, no current is applied to main magnetic coil  302   2 , and there is an increase in the current applied to main magnetic coil  302   1 . As a result, the portion of the magnetic field represented by “C” flows vertically between main magnetic coils  302   1  and  302   3 . 
   At t4, the current at main magnetic coil  302   2  is turned on and the current at  302   3  is decreased. As a result, the portion of the magnetic field represented by “D” flows between main magnetic coil  302   2  and sub-magnetic coil  504   1 . 
   At t5, the current at sub-magnetic coil  504   3  is turned off, the current at main magnetic coil  302   3  is decreased, and the current at main magnetic coil  302   2  is increased. As a result, the portions of the magnetic fields represented by “A,”“B,”“C,”and “D” flow between the coils as shown. 
   Lastly, at t6, the current is increased at main magnetic coil  302   2  and turned off at main magnetic coil  302   3 . As a result, the magnetic field gradient represented by “A” flows between sub-magnetic coils  504   2  and  504   4  and the magnetic field represented by “BCD” flows between main magnetic coils  302   1  and  302   2 , i.e., the magnetic field has been rotated by 90° while maintaining a gradient during the transition. 
     FIG. 8C  should be considered one example of using the invention to rotate the magnetic field. Other current combinations may produce useful magnetic field rotation. 
     FIG. 9  depicts a top view of an alternative embodiment of a magnetic coil configuration  700  circumscribing a cylindrical process chamber  701 . This configuration is similar to that shown in  FIGS. 3 and 5  above, except the main coils are interleaved, i.e., for each coil, one end is overlapped and one end is overlapping. The magnetic coil configuration  700  comprises overlapping main magnetic coils  702   1 ,  702   2 ,  702   3 , and  702   4  (collectively main magnetic coil  702 ) and optional sub-magnetic coil  704   1 ,  704   2 ,  704   3 , and  704   4  (collectively main magnetic coil  704 ). Each of the main magnetic coils  702  has one end  702   XB  that overlaps an end (where X is the coil number) of an adjacent magnetic coil and the other end  702   XA  of the main magnetic coil  702   X  is overlapped by an end of another adjacent main magnetic coil  702 . For example, the end  702   1B  overlaps the end  702   4A  and the end  702   1A  is overlapped by the end  702   2B . Note that each of the main magnetic coils  702  is positioned such that the ends of any of the main magnetic coils  702  is not equidistant from a center of the process chamber  701 . Because the coils are positioned on a slight angle, the magnetic coils can be made larger (wider) than if they were arranged on a common cylinder. In addition, sub-magnetic coil  704  can be placed proximate the overlapping portions of the main magnetic coils  702  to provide greater magnetic field control as described above with respect to  FIGS. 8B and 8C . The sub-magnetic coils  704  can be positioned in the plane of the main coils (as discussed with respect to  FIG. 7 ) or outside the main coils. It is appreciated that other embodiments may be used in accordance with the invention that utilizes main magnetic coils having a larger or smaller angle than the angle of the main magnetic coils  702  depicted in coil configuration  700 . 
     FIG. 9A  depicts a perspective view of one main magnetic coil (coil  702   4 ) in  FIG. 9 . The main magnetic coil  702   4  contains ends  702   4A  and  702   4B , a top portion  708   1 , a bottom portion  708   2 , and an interior area  710 . The top portion  708   1  and bottom portion  708   2  are curved and substantially parallel to each other. The top portion  708   1  and bottom portion  708   2  are connected via ends  702   4A  and  702   4B . The ends  702   4A  and  702   4B  are substantially parallel to each other. The main magnetic coil  702   4  contains an interior area  710  formed by the interconnection of the ends  702   4A  and  702   4B , the top portion  708   1 , and bottom portion  708   2 . 
     FIG. 10  depicts a top view of another embodiment of a magnetic coil configuration  800  circumscribing a cylindrical process chamber  701 . This configuration is the same as  FIGS. 3 and 5  except the chamber  701  is now cylindrical rather than octagonal. The magnetic coil configuration  800  contains main magnetic coils  802   1 , and  802   2 , (collectively main magnetic coil  802 ), main magnetic coil  804   1  and  804   2  (collectively main magnetic coils  804 ), and optional sub-magnetic coils  806   1 ,  806   2 ,  806   3  and  806   4  (collectively sub-magnetic magnetic coils  806 ). Main magnetic coils  802  are positioned opposite each other and slightly curved towards one another to partially circumscribe the process chamber  701 . Each main magnetic coil  802  covers about 90° of the circumference of the chamber  701 . Main Magnetic coils  804  are positioned outside of main magnetic coils  802  and are offset by about 90° from the main magnetic coils  802 . Each of the main magnetic coils  802 ,  804  has two ends. Specifically, main magnetic coils  802   X  (where X is the coil number) have ends  802   XA  and  802   XB , and main magnetic coils  804   X  have  804   XA  and  804   XB . The main magnetic coils  804  are positioned opposite of each other and slightly curved towards one another to partially circumscribe the process chamber  701 . In addition, main magnetic coil  804  overlap ends of main magnetic coils  802 . For example, main magnetic ends  802   1A  and  802   2B  are overlapped by ends  804   1B  and  804   1A  respectively. Further, sub-magnetic coils  806  can be positioned in or near the overlapping portions of the main magnetic coils  802  and  804  or outside the main magnetic coils  802  and  804 . 
     FIG. 11  depicts another embodiment of magnetic coil configuration  900  circumscribing a cylindrical process chamber  701 . This configuration is similar to  FIG. 10  except each of the main coils cover about 180° of the chamber circumference and the sub-magnetic coils are centrically aligned with the main coils. The magnetic coil configuration  900  contains main magnetic coils  902   1  and  902   2 , (collectively main magnetic coils  902 ), main magnetic coils  904   1  and  904   2  (collectively main magnetic coils  904 ), and optional sub-magnetic coils  906   1 ,  906   2 ,  906   3 , and  906   4  (collectively sub-magnetic magnetic coils  906 ). Main magnetic coils  902   1  and  902   2 , are positioned opposite each other and curved towards each other to circumscribe the process chamber  701 . Spaces  908  are formed between adjacent ends of the main magnetic coils  902 . Further each main magnetic coil  902  covers about 180° of the circumference of the process chamber  701 . Main magnetic coils  904   1 , and  904   2 , are positioned outside of main magnetic coils  902 , are curved inwards, and are positioned opposite of each other. Spaces  910  are formed between adjacent ends of the main magnetic coils  904 . Further the main magnetic coils  904  are offset from the main magnetic coils  902  by about 90°. Each of the main magnetic coils  904  covers about 180° of the circumference of the process chamber  701 . The coil configuration  900  is similar to the coil configuration  800  except that in the coil configuration  900  the main magnetic coils overlap more than in the coil configuration  800 . Further, the optional sub-magnetic coils  906  are juxtaposed to the spaces  908  and  910  of the main magnetic coils  902  and  904 , respectively. In this configuration, the centers of the sub-magnetic coils  906  are aligned with the centers of the respective main magnetic coils  902  and  904 . Generally, the 180 degree main magnetic coils  902  and  904  are not very effective in producing magnetic field gradients. The addition of the sub-magnetic coils  906  improves the ability of the coil configuration to produce magnetic field gradients. If the coils are driven by eight independent currents, the configuration provides substantial control of the magnetic field shape. Alternatively, the configuration may also be operated using four currents by wiring in series the following coil pairs:  904   1  and  906   1 ;  902   1  and  906   2 ;  904   2  and  906   3  and  902   2  and  906   4 . 
     FIG. 12  depicts another embodiment of a top view of a magnetic coil configuration  1000  to circumscribe a process chamber  701 . Magnetic coil configuration  1000  contains main magnetic coils  1002   1 - 1002   8 , (collectively main magnetic coils  1002 ). Each of the main magnetic coils  1002  is curved. Each of the main magnetic coils  1002  has one end  1002   XA  that overlaps an adjacent magnetic coil  1002   X  (where X is the coil number) and one end  1002   XB  that is overlapped by another adjacent magnetic coil  1002   X . In addition, each of the main magnetic coils  1002  covers about 45° to circumscribe the process chamber  701 . Although  FIG. 12  depicts the magnetic coil configuration  1000  as having eight coils other embodiments can be used (e.g., sixteen magnetic coils). In an embodiment that uses sixteen coils, each of the coils covers about 22.5° to circumscribe the process chamber  701 . In general, any number of overlapping coils may be used. Note that the use of N coils (where N is an integer greater than 1, where each coil has a width that covers greater than 360/N degrees, then the shape of the magnetic field in the chamber is improved over a coil configuration having N coils that do not overlap, i.e., wider coils improve the magnetic field shape. 
     FIG. 13  depicts a top view of another embodiment of a magnetic coil configuration  1100  to circumscribe a process chamber  701 . The coil configuration  1100  contains main magnetic coils  1102   1 ,  1102   2 ,  1102   3 , and  1102   4  (collectively main magnetic coils  1102 ), and main magnetic coils  1104   1 ,  1104   2 ,  1104   3 , and  1104   4  (collectively main magnetic coils  1104 ). Each of the main magnetic coils  1102  covers about 90° to circumscribe a process chamber  701  and has an adjacent main magnetic coil  1102 . There is a space  1108  formed between each adjacent main magnetic coil  1102 . Main magnetic coils  1104   X  are curved and placed outside of main magnetic coils  1102   X  such that each end of the main magnetic coil  1104  overlaps an end of two adjacent main magnetic coils  1102  (where X is the coil number). For example, main magnetic coil ends  1104   2A  and  1104   2B  overlap main magnetic coil ends  1102   2A  and  1102   1B , respectively. Each main magnetic coil  1104  covers about 90° to circumscribe a process chamber  701 . There is a space  1110  formed between adjacent main magnetic coils  1104 . In addition, main magnetic coils  1104  are offset from main magnetic coils  1102  by about 90°. 
     FIG. 14  depicts a top view of another embodiment of a magnetic coil configuration  1200  to circumscribe a process chamber  701 . This configuration is similar to the configuration of  FIGS. 3 and 5  except the main coils do not overlap. The magnetic coil configuration  1200  contains main magnetic coils  1202   1 ,  1202   2 ,  1202   3 , and  1202   4  (collectively main magnetic coils  1202 ) and sub-magnetic coils  1204   1 ,  1204   2 ,  1204   3 , and  1204   4  (collectively sub-magnetic coils  1204 ). Each main magnetic coil  1202  is curved inwards to circumscribe the process chamber  701  and covers about 90° of the circumference of the process chamber  701 . Each main magnetic coil  1202  is adjacent to two other main magnetic coils  1202 . The adjacent main magnetic coils  1202  are positioned end to end such that there is a space  1206  between adjacent ends of each of the main magnetic coils  1202 . 
   Sub-magnetic coils  1204  are positioned adjacent to the spaces  1206  formed between adjacent main magnetic coils  1202 . The sub-magnetic coils have centers that are positioned 45 degrees offset from the centers of the main magnetic coils. The sub-magnetic coils  1204  improve the shape of the magnetic fields generated within the chamber. If the coils are driven with eight independent currents, the configuration provides substantially improved control over the shape of the magnetic field produced in the chamber. Illustratively, the sub-magnetic coils  1204  are depicted as being located on the outer periphery of the main magnetic coils  1204 . 
   In operation, a magnetic field gradient can be produced in the chamber by energizing three coil pairs, e.g., high current to coils  1202   2  and  1202   3 , medium current to coils  1204   2  and  1204   4 , and low current to coils  1202   1  and  1202   4 . The pairs of main magnetic coils form a concave magnetic field and the pair of sub-magnetic coils forms a convex magnetic field. The vector addition of these fields produces a field with improved parallel lines of force across the substrate. 
     FIG. 15  depicts a top view of another embodiment of a magnetic coil configuration  1300  to circumscribe a process chamber  701 . The magnetic coil configuration  1300  contains main magnetic coils  1202   1 ,  1202   2 ,  1202   3 , and  1202   4  (collectively main magnetic coils  1202 ); sub-magnetic coils  1204   1 ,  1204   2 ,  1204   3 , and  1204   4  (collectively sub-magnetic coils  1204 ); and sub-magnetic coils  1304   1 ,  1304   2 ,  1304   3 , and  1304   4  (collectively sub-magnetic coils  1304 ). Each main magnetic coil  1202  is curved inwards to circumscribe the process chamber  701  and covers about 90° of the circumference of the process chamber  701 . Each main magnetic coil  1202  is adjacent to two other main magnetic coils  1202 . The adjacent main magnetic coils  1202  are positioned end to end such that there is a space  1206  between adjacent ends of each of the main magnetic coils  1202 . The sub-magnetic coils  1304  are juxtaposed to the sub-magnetic coils  1204 . The sub-magnetic coils  1304  increases the number of coil winding positioned near the spaces  1206  between main magnetic coils  1204 . The addition of sub-magnetic coils  1304  provides a magnetic field additive to the magnetic field generated by main magnetic coils  1202  and sub-magnetic coils  1204 . In this embodiment, twelve currents can be applied to achieve substantial improvement in the control of the magnetic field shape. Alternatively, the sub-magnetic coils can be wired in series with the adjacent main coils as described with respect to  FIG. 7A  such that only four current supplies are used to drive the configuration. 
     FIG. 16  depicts a top view of another embodiment of a magnetic coil configuration  1400  to circumscribe a process chamber  701 . The magnetic coil configuration  1400  contains main magnetic coils  1402   1 ,  1402   2 ,  1402   3 , and  1402   4  (collectively main magnetic coils  1402 ); and sub-magnetic coils  1404   1 ,  1404   2 ,  1404   3 , and  1404   4  (collectively sub-magnetic coils  1404 ). Each of the main magnetic coils  1402  and sub-magnetic coils  1404  is curved, in the same plane, and alternatively positioned end to end. A space  1406  is formed between each alternatively positioned main magnetic coil  1402  and sub-magnetic coil  1404 . The area covered by a main magnetic coil  1402  and a sub-magnetic coil  1404  is about 90° of the circumference of the process chamber  701 . 
     FIG. 17  depicts a top view of an embodiment of a magnetic coil configuration  1500  to circumscribe a process chamber  701 . The magnetic coil configuration  1500  contains main magnetic coils  1402   1 ,  1402   2 ,  1402   3 , and  1402   4  (collectively main magnetic coils  1402 ); sub-magnetic coils  1404   1 ,  1404   2 ,  1404   3 , and  1404   4  (collectively sub-magnetic coils  1404 ); and sub-magnetic coils  1502   1 ,  1502   2 ,  1502   3 , and  1502   4  (collectively sub-magnetic coils  1502 ). Each of the main magnetic coils  1402  and sub-magnetic coils  1404  is curved, in the same plane, and alternatively positioned end to end. A space  1406  is formed between each alternatively positioned main magnetic coil  1402  and sub-magnetic coil  1404 . The sub-magnetic coils  1502  are juxtaposed (i.e., substantially parallel) to the sub-magnetic coils  1404 . The area covered by a main magnetic coil  1402  and a sub-magnetic coil  1404  is about 90° of the circumference of the process chamber  701 . The addition of the sub-magnetic coils  1502  increases the magnetic field by providing a magnetic field additive to the magnetic field provided by sub-magnetic coils  1404 . In this embodiment, twelve currents can be applied to achieve substantial improvement in the control of the magnetic field shape. Alternatively, the sub-magnetic coils can be wired in series with the adjacent main coils as described with respect to  FIG. 7A  such that only four current supplies are used to drive the configuration. 
     FIG. 18A  depicts a perspective view of another embodiment of a magnetic coil configuration  1600 A to circumscribe a process chamber  701 . The magnetic coil configuration  1600  comprises main magnetic coils  1604   1 ,  1604   2 ,  1604   3 , and  1604   4  (collectively main magnetic coils  1604 ) and sub-magnetic coil pairs  1602   1 ,  1602   2 ,  1602   3 , and  1602   4  (collectively sub-magnetic coils  1602 ). In this embodiment, the pairs of sub-magnetic coils  1602  are aligned with an associated center of the main coil  1604 . The sub-magnetic coils  1602  are located near the top and bottom of the associated main coil. The sub-magnetic coils  1602   1 ,  1602   2 ,  1602   3 , and  1602   4  provide a corrective magnetic field to improve the shape of the magnetic field in the chamber. The main magnetic coils may overlap as shown in previous embodiments discussed herein. 
     FIG. 18B  is a perspective view of an embodiment of the invention having a coil configuration  1600 B that is similar to  FIG. 18A  except the horizontal sub-magnetic coils  1602  are positioned outside the area circumscribed by the main magnetic coil  1604 . 
     FIG. 19A  depicts perspective view of another embodiment of a magnetic coil configuration  1700 A to circumscribe a process chamber  701 . The magnetic coil configuration  1700  contains main magnetic coils  1604   1 ,  1604   2 ,  1604   3 , and  1604   4  (collectively main magnetic coils  1604 ); and vertical and horizontal sub-magnetic coil sets  1702   1 ,  1702   2 ,  1702   3 , and  1702   4  (collectively sub-magnetic coil pairs  1702 ). Each coil set, for example, contains two horizontal coils (e.g., coils  1702   1B  and  1702   1D ) and two vertical coils (e.g.,  1702   1A  and  1702   1c ). By driving each of these twenty coils with separate currents provides for substantial control over the shape of the magnetic field produced in the chamber. The twenty coils also provides flexibility in producing a magnetic field shape that optimizes processing of the substrate. Alternatively, fewer than twenty currents could be used by connecting various sub-sets of coils in series, such as those shown in  FIG. 7A . Also, alternatively, the main coils may overlap as shown in previous embodiments discussed herein. 
     FIG. 19B  depicts a perspective view of an embodiment of the invention having a coil configuration  1700 B that is similar to  FIG. 19A  except the vertical and horizontal sub-magnetic coils  1704  are positioned outside the area circumscribed by the main magnetic coil  1604 . In a further embodiment, not shown, a combination of coils within the main coils and outside the main coils is also contemplated. 
     FIG. 19C  depicts a perspective view of an embodiment of the invention having a coil configuration  1700 C that combines the features of  FIG. 5  and  FIG. 18A . Specifically, the configuration  1700 C comprises a chamber  701  surrounded by four main magnetic coils  302   1 ,  302   2 ,  302   3 ,  302   4 , four vertical sub-magnetic coils  604   1 ,  604   2 ,  604   3 , and  604   4  and eight horizontal sub-magnetic coils  1602   1 ,  1602   2 ,  1602   3 ,  1602   4 . Each of the four vertical sub-magnetic coils  504   1 ,  504   2 ,  504   3 , and  504   4  are positioned proximate the overlap of the main magnetic coils  302   1 ,  302   2 ,  302   3 ,  302   4 . The horizontal sub-magnetic coils  1602   1 ,  1602   2 ,  1602   3 ,  1602   4  are positioned as coil pairs, where one coil in the pair is positioned near the top of the main coil and one coil in the pair is positioned near the bottom of the main coil. Sixteen currents may be used to independently drive each coil. Alternatively, the configuration may be driven with as few as four currents. To accomplish a four current system, the vertical sub-magnetic coils  502   1 ,  502   2 ,  502   3 ,  502   4  are double wound and five coils are wired in series to be driven by a single coil. For example, one-half of the double wound winding of coils  504   2  and  504   3  are connected in series with coil pair  1602   1 , and main coil  302   3 . The number of turns in each sub-magnetic coil is predetermined to best shape the magnetic field produced by the main magnetic coils. 
     FIG. 20A  depicts a side view of the embodiment of  FIG. 19A  where the sub-magnetic coils  1702  are positioned inside the main coil  1604 . As such, the currents (shown as arrows) in the sub-magnetic coils  1702  are flowing in the same direction as the current in the main coil  1604 , meaning that all of the currents for the individual coils are shown moving in the clockwise direction. Thus, all of the magnetic fields generated by these five coils are pointed in the same direction, which is into the page, and are thus vectorally additive. In addition, within the portion of each sub-coil directly adjacent to the single main coil depicted, the direction of current flow is the same as for the main coil. In contrast,  FIG. 20B  depicts a side view of the embodiment depicted in  FIG. 19B , where the sub-magnetic coils  1704   1  are outside the main magnetic coil  1604   1 . As in  FIG. 20A , the currents in the sub-magnetic coils  1702  are flowing in the same direction as the current in the main coil  1604 , meaning that all of the currents for the individual coils are shown moving in the clockwise direction. Thus, all of the magnetic fields generated by these five coils are pointed in the same direction, which is into the page, and are thus vectorally additive. However since the sub-coils are located outside of the main coil, within the portion of each sub-coil directly adjacent to the single main coil depicted, the direction of current flow is the opposite as for the main coil. From a design point of view, this means that, to produce the same corrective magnetic field over the workpiece, fewer turns of wire would be necessary to create the sub-magnetic coils  1604  of embodiment of  FIG. 19A  as compared to the sub-magnetic coils  1704  of the embodiment of  FIG. 19B . 
     FIG. 21  depicts a perspective view of another embodiment of the present invention. In this embodiment, the sub-magnetic coils  2100  are divided into two coils  2100 A and  2100 B that are stacked vertically on four sides of the chamber  701 . This embodiment depicts the main magnetic coils  2102  covering 180 degrees of the chamber circumference and having the centers of the main and sub-magnetic coils aligned. The division of the sub-magnetic coils  2100  into two portions enables twelve currents to be used to establish the magnetic field shape. The configurations of other main magnetic coils discussed herein may also be used. In this embodiment, twelve currents can be applied to achieve substantial improvement in the control of the magnetic field shape. Alternatively, the sub-magnetic coils can be wired in series with the adjacent main coils such that only four current supplies are used to drive the configuration, e.g., wire together the pair of sub-coils immediately above and below each other with the one main coils that they are adjacent to and share the same coil centerpoint. 
   A number of simulations have been performed with respect to the various embodiments of the invention discussed above.  FIGS. 22A-22K  each depict a magnetic field gradient produced by the prior art as well as the foregoing embodiments of the invention.  FIG. 22A  depicts the magnetic field gradient produced by the embodiment of  FIG. 2  where two adjacent main coils are energized. Note that the field gradient slopes from  85 G to  10 G.  FIG. 22B  depicts the magnetic field gradient produced by the embodiment of  FIG. 3  when two adjacent main coils are energized. Here, the extended width coils reduce the high field strength side to  75 G, maintain the center field strength at  35 G and increases the low field strength side to  12 G. As such, the extended coils “flatten” the gradient of the magnetic field. 
     FIG. 22C  depicts the field that is produced by the embodiment of  FIG. 5  where two adjacent main coils and two opposite sub-magnetic coils are energized. Here, the gradient is further flattened and the high field side has a magnitude that is adjustable with the current magnitude to the sub-magnetic coils.  FIG. 22D  depicts the field strength produced by the embodiment of  FIG. 11  having two adjacent main coils and two adjacent sub-magnetic coils energized. This embodiment produces a substantially uniform magnetic field with the high magnetic field value being adjustable with sub-magnetic coil current.  FIG. 22E  depicts the magnetic field produced by the embodiment of  FIG. 19C  having two adjacent main magnetic field coils and the four upper and lower sub-magnetic coils and the two opposite corner coils are energized. The magnetic field has a well defined gradient and the high value side is controllable with the sub-magnetic coil currents. Thus, the progression from  FIG. 22A , to  22 B, to  22 C to  22 E shows that the overlapping of the main coils plus the addition of the corner coils plus the addition of the upper and lower coils modifies the high field end from  85 G down to  60 G, while keeping the same  35 G in the center of the workpiece and while keeping the lower field strength between  10 G and  15 G. This reduction in the field strength at the high field end has been shown to improve both the instantaneous etch rate uniformity and the time-averaged (magnetic field rotated) etch rate uniformity. Further control of the field strength at the low field end is achieved by using currents in the second pair of main coils. In addition, the magnetic field value at the high field end of the workpiece is fully controllable (e.g.,  85 G,  70 G,  60 G,  55 G, etc.) by controlling the relative currents in each of the coils to achieve the desire field shape. 
     FIG. 22F  depicts a magnetic field that is generated by the prior art of  FIG. 2  where two, opposite coils are energized. Note that that the magnetic field magnitude is not very uniform across the substrate, i.e., the field magnitude varies from  79 G to  39 G, a range of  40 G for a field strength of  50 G at the center of the substrate.  FIG. 22G  depicts the magnetic field that is produced by the embodiment of  FIG. 3  where two, opposite extended width coils are energized. The uniformity of the magnetic field is improved over the magnetic field of  FIG. 22F .  FIG. 22H  depicts the magnetic field produced by the embodiment of  FIG. 5  having two, opposite main coils and four sub-magnetic coils energized. The result is an improved uniformity of the magnetic field. When upper and lower coils are added as in the embodiment of  FIG. 19C  and these coils are energized, the result is the magnetic field of  FIG. 22I . The magnetic field is now almost completely uniform. Thus, the progression from  FIG. 22F , to  22 G, to  22 H to  22 I shows that the overlapping of the main coils plus the addition of the corner coils plus the addition of the upper and lower coils improves the uniformity of the field strength, from a range of  40 G to a range of  6 G, all for a center field strength of  50 G. Further improvement over the results could be obtained by further modification of the shapes and locations of each of the coils, the addition of more coils, and the fine tuning of the currents energizing all of the appropriate coils. 
     FIG. 22J  depicts the magnetic field produced by the embodiment of  FIG. 11  where all four of the 180 degree main coils are energized. This embodiment shows improvement over the magnetic field of the prior art ( FIG. 22F ). When the sub-magnetic coils are also energized, the magnetic field uniformity is further improved as shown in  FIG. 22K . 
   Thus, from these simulations, the use of extended width coils improves the shape of the magnetic fields produced in the chamber. To further improve the shape of the fields, additional coils that provide corrective fields can be used. 
   Furthermore, while the semiconductor wafer processing chamber is a dry etching chamber in the above embodiments, it is a matter of course that the present invention is applicable to other types of semiconductor wafer processing chambers such as a CVD chamber in which the plasma formation is accelerated by the use of electromagnets. 
   While foregoing is directed to various embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.
A magnetic field generator which provides greater control over the magnetic field is provided. The magnetic field generator has a plurality of overlapping main magnetic coil sections for forming a magnetic field generally parallel to the top surface of the supporting member. In other embodiments, sub-magnetic coil sections are placed symmetrically around the main magnetic coil sections.