Abstract:
Techniques for producing and manipulating magnetic fields. The techniques employ the mutual repulsion of magnetic fields to create uniform magnetic fields and to manipulate the uniform magnetic fields. The uniform magnetic field is created between two planar magnets. The planar magnets have cores which describe a closed curve. Like poles of the electromagnets are connected by the cores. When the electromagnets are activated, repulsion between the magnetic fields generated by the electromagnets creates a magnetic field which extends above and below the planes of the planar magnets. If the planar magnets are positioned parallel to each other and aligned so that the magnetic fields generated by the planar magnets repel each other in the space between the planar magnets, the repulsion between the fields generates a resultant field. When the distance between the planar magnets is approximately ½ the diameter of the closed curve, the resultant field is uniform over a considerable volume of the space between the planar magnets. The uniform field may be manipulated by varying the magnitude and direction of the current provided to the electromagnets. Depending on the number and positions of the electromagnets and how power is supplied to them, the uniform field may be rotated, tilted in the horizontal and/or vertical planes, warped in the horizontal and/or vertical planes, and given gradients in the horizontal and/or vertical planes. The planar magnets may be fitted around the chambers of reactors such as those used for MERIE and the uniform field may be used to manipulate the plasma in the reactor chamber.

Description:
CROSS REFERENCES TO RELATED APPLICATIONS  
       [0001]    The present patent application claims priority from U.S. provisional patent application 60/409,323, Eugene L. Oster, “Any Angle” uniform field etch plasma magnet array, filed Sep. 9, 2002 and from U.S. provisional patent application 60/486,676, Eugene L. Oster, Improved “any angle” uniform field etch plasma magnet array, filed Jul. 11, 2003, and incorporates U.S. Pat. No. 6,015,476, Schlueter, et al., Plasma reactor magnet with independently-controllable parallel axial current-carrying elements, issued Jan. 18, 2000, by reference for all purposes. 
     
    
     
       BACKGROUND OF THE INVENTION  
         [0002]    1. Field of the Invention  
           [0003]    The invention relates to electromagnets generally and more specifically to electromagnets used to manipulate magnetic fields in enclosed vessels.  
           [0004]    2. Description of Related Art  
           [0005]    Magnetic fields have long been used to manipulate particles that respond to them such as charged particles or polar particles. In one large class of such uses, electromagnets located outside a vacuum vessel or reactor vessel are used to affect the behavior of particles that respond to the magnetic fields within the vessel. Examples of such uses are focusing electromagnets in cathode ray tubes or particle accelerators and electromagnets used to manipulate plasmas in plasma reactors or to control crystal growing processes.  
           [0006]    An exemplary use of electromagnets to manipulate plasmas is magnetic enhanced reactive ion etching, or MERIE. Part of the process of producing an integrated circuit is etching the substrate for the circuit. A common way of doing this is by reactive ion etching, in which reactive ions do the etching. The parts of the substrate which are not to be etched are covered by a mask which is resistant to the reactive ions and the masked substrate is placed in a vessel in which a plasma of reactive ions is formed from a reactive gas. The reactive ions react with the unmasked areas of the substrate and the reaction etches the substrate. In MERIE, a magnetic field is used to manipulate the plasma to keep the plasma within the area over the substrate and increase the plasma&#39;s density, which increases the rate of etching. For details on MERIE and the reactors generally used in MERIE, see the Schlueter patent cited above.  
           [0007]    One approach to manipulating the plasma in a MERIE reactor is simply to generate a constant uniform magnetic field in the vessel that keeps the plasma where it is wanted. One way of doing this employs the principles of the Helmholtz coil. A Helmholtz coil consists of two plane circular coils of radius r whose planes are parallel to each other. The centers of the coils are on a line perpendicular to the planes and the planes are r apart. In the area between the coils, the combined fields of the coils produce a generally constant magnetic field. An example of the use of the principles of the Helmholtz coil in a chemical vapor deposition reactor may be found in U.S. Pat. No. 4,668,365, Foster et al., Apparatus and method for magnetron-enhanced plasma-assisted chemical vapor deposition, issued May 26, 1987, in which a pair of electromagnetic coils having the geometry of the Helmholtz coil are used to provide a uniform magnetic field in which material is deposited on a substrate that is perpendicular to the planes of the Helmholtz coil. An example of the use of pairs of electromagnetic coils having the geometry of the Helmholtz coil to confine the plasma in a reactor vessel to the area between the electrodes of the vessel may be found in U.S. Pat. No. 5,527,394, Heinrich, et al., Apparatus for plasma enhanced processing of substrates, issued Jun. 18, 1996.  
           [0008]    Another way of producing a more uniform magnetic field is described in U.S. Pat. No. 5,718,795, Plavidal, et al., Radial magnetic field enhancement for plasma processing, issued Feb. 17, 1998. Here, the magnet which produces the field is located above the ceiling of the vessel. The magnet has a ferrous yoke which has a hub connected by spokes to an outer ring. The hub, spokes, and ring form a shallow cone. The spokes have windings which are connected to an AC, DC, or RF power supply. The angle of the spokes is chosen to produce a relatively uniform radially symmetrical magnetic field at the level of the substrate.  
           [0009]    A way of dealing with non-uniform plasmas is to use the electromagnets not only to keep the plasma where it is wanted, but to move the plasma. The most common arrangement for doing this is described in the Background Art portion of the Schlueter patent. Four electromagnetic coils are mounted 90° from each other on the sides of the vessel. The coils have vertical legs and horizontal legs, with the horizontal legs sometimes being bent to conform to the curve of the sides of the vessel. While the magnetic field produced by an opposed pair of the electromagnetic coils is not particularly uniform, the field can be rotated by varying the amount and direction of current in pairs of opposite coils. Rotation may be achieved by switching the current in the coils or more smoothly by applying AC currents to the coils in the amounts, phases and frequencies required to rotate the magnetic field. Slowly rotating the plasma in this fashion reduces the exposure of the circuitry in the substrate to irregularities in the plasma which can damage the circuitry.  
           [0010]    Though the electromagnetic coils on the sides of the vessel permit rotation of the magnetic field, the lack of uniformity of the magnetic field both causes irregularities in the plasma and these in turn may lead to damage in the substrate. One way of producing a more uniform rotating magnetic field is described in the Schlueter patent; there, the magnetic field is generated by a number of coils wound on a ferrous cylinder that surrounds the outside of the vessel that contains the substrate at the position of the substrate. On the inside of the ferrous cylinder, the windings are parallel to the vertical axis of the vessel. The main function of the ferrous cylinder is to shield the windings on the inside of the ferrous cylinder from the windings on the outside of the cylinder. The windings on the inside of the ferrous cylinder generate a magnetic field in the area of the substrate. The field can be varied by varying the amounts of current provided to the different coils and the field can be rotated by varying the amounts and directions of the current in the coils according to a periodic pattern.  
           [0011]    None of the foregoing techniques for producing magnetic fields inside a reactor vessel provides a perfect solution for MERIE. Ideally, it should be possible not only to produce a uniform magnetic field but also to produce a magnetic field with controlled gradations across the plane of the substrate and/or along the vertical axis of the vessel, and it should be possible to rotate or otherwise move whatever field is produced. It is further desirable to be able to retrofit current reactors employing coils on the sides of the vessels to produce rotating magnetic fields with electromagnets that are capable of producing highly-uniform rotating magnetic fields without affecting the retrofitted reactor&#39;s power supplies or arrangements for inserting and removing substrates or providing gaseous inputs.  
           [0012]    It is thus an object of the invention disclosed herein to provide electromagnets which are capable of producing uniform magnetic fields, magnetic fields with controlled gradations in either the horizontal or vertical directions, and magnetic fields which can be rotated and moved and which can further be retrofitted to existing reactor vessels that employ coils on the sides of the vessels.  
         SUMMARY OF THE INVENTION  
         [0013]    The object of the invention is achieved by apparatus for producing a magnetic field that includes two sets of magnetic elements. Each set defines a separate surface and produces a separate magnetic field by repulsion between the magnetic elements in the set. The set&#39;s magnetic field extends above and/or below the surface. The sets of magnetic elements are positioned relative to each other such that the surfaces are approximately parallel and the magnetic field produced by the apparatus is formed between the surfaces by repulsive interaction of the sets&#39; magnetic fields. One or more of the magnetic elements may be an electromagnetic element and the magnetic field produced by the apparatus may be manipulated by changing the direction and/or magnitude of the current in selected ones of the electromagnetic elements. If each set includes two pairs of electromagnetic elements, the magnetic field may be manipulated to impart a rotary motion to the magnetic field.  
           [0014]    In a particularly useful version of the apparatus, the magnetic elements comprise a pair of magnetic elements, the like poles of the elements in the pair being connected by a core and the first and second sets of magnetic elements being positioned relative to each other such that a portion of the magnetic field produced by the apparatus is uniform. More particularly, the magnetic elements in the pair are separated in the surface by a distance D and the surfaces are separated by a distance D/2. If each set contains two pairs of electromagnetic elements whose like poles are connected by the core, a rotary motion may be imparted to the uniform field by changing the direction and/or magnitude of the current in the pairs of electromagnetic elements. The uniform field may also be manipulated in other ways by changing the direction and/or magnitude of the current in the electromagnetic elements. An important use of the uniform field is manipulating particles in a vessel.  
           [0015]    In another aspect, the invention is an electromagnet that may be used as one of the electromagnets in the apparatus for producing a magnetic field. In still another aspect, the invention is a kit for retrofitting a reactor vessel that employs magnetic enhancement with the apparatus for producing a magnetic field.  
           [0016]    Other objects and advantages will be apparent to those skilled in the arts to which the invention pertains upon perusal of the following Detailed Description and drawing, wherein: 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWING  
       [0017]    [0017]FIG. 1 shows the magnetic field generated by an electromagnet consisting of two coils on opposite sides of a circular core which are powered such that the poles of coils oppose each other;  
         [0018]    [0018]FIG. 2 shows a preferred embodiment  201  of an electromagnet  101 ;  
         [0019]    [0019]FIGS. 3-8 show magnetic fields produced by a Helmholtz core arrangement which employs a pair of magnets  201 ;  
         [0020]    [0020]FIG. 9 shows a system of MERIE vessels which may be retrofitted with electromagnets  201 ;  
         [0021]    [0021]FIG. 10 shows details of the arrangements for retrofitting a vessel with an electromagnet  201 ;  
         [0022]    [0022]FIG. 11 shows an overview of a Helmholtz core arrangement that uses the magnets  105 ;  
         [0023]    [0023]FIG. 12 shows magnetic fields produced by the Helmholtz core arrangement of FIG. 11;  
         [0024]    [0024]FIG. 13 shows different cross sections for a core of an electromagnet  201 ;  
         [0025]    [0025]FIG. 14 shows how non-magnetic shims may be used for fine adjustments in an electromagnet  201 ; and  
         [0026]    [0026]FIG. 15 shows details of a preferred embodiment of an electromagnet  201 . 
     
    
       [0027]    Reference numbers in the drawing have three or more digits: the two right-hand digits are reference numbers in the drawing indicated by the remaining digits. Thus, an item with the reference number  203  first appears as item  203  in FIG. 2.  
       DETAILED DESCRIPTION  
       [0028]    The following Detailed Description will first present an overview of the invention, will then disclose a preferred embodiment of an electromagnet that may be used in the invention, and will finally disclose how existing reactor vessels may be retrofitted with the invention.  
         [0029]    Overview of the invention  
         [0030]    The following overview will first describe a type of magnet used in the invention in which the magnetic field is produced using opposed magnetic elements, will then describe how magnetic fields may be made by arranging such magnets above each other, and will finally describe a particularly useful arrangement of such magnets which is termed herein a Helmholtz core arrangement.  
         [0031]    A Magnet in Which the Magnetic Field is Produced by Opposing Magnetic Elements: FIG. 1  
         [0032]    [0032]FIG. 1 shows a magnet  101  in which two active magnetic elements  105 ( i ) and ( j ) of equal strength are connected by a circular core  103  of a magnetically permeable material. The magnetic elements may be either electromagnets or permanent magnets. A top view of the magnet is shown at  102  and a side view at  109 . The magnetic elements  105 ( i ) and ( j ) are arranged as shown in FIG. 1: namely, one side of core  103  connects the north poles of the elements  105  and the other side connects the south poles of the elements.  
         [0033]    The part of the magnetic field that results from this arrangement which is inside core  103  is shown as viewed from the top at  107  and as viewed from the side at  111 . The magnetic field is represented by field lines. Top view  107  shows the field lines as viewed from above and side view  111  shows the field lines as viewed from the side. Because the poles of magnets  105 ( i ) and ( j ) connected by the cores are opposed, the magnetic field is forced out of the cores and north pole  104  for the entire magnet  101  is equidistant between magnetic elements  105 ( i ) and ( j ) on core portion  103 ( b ), while south pole  106  for the entire magnet  101  is equidistant between magnetic elements  105 ( i ) and ( j ) on core portion  103 ( b ). Seen from the top, the field lines within the circle defined by magnet  101 &#39;s core run as shown at  107 . Only ½ of field  107  is shown here; the other half is symmetrical to what is shown here. As seen from the top, field lines appear as curves that approach straight lines as the parts of the opposite sides of the core connected by the lines of force approach north pole  104  and south pole  106 . Because magnetic fields running in the same direction repel each other, the magnetic field lines as seen from above are distributed uniformly across the circle defined by core  103 . In the area in the neighborhood of north pole  104  and south pole  106 , the mutual repulsion of the magnetic field produced by element  1050 ) and those (not shown) in the magnetic field produced by element  105 ( i ) results in field lines in the area around the center of the circle defined by magnet  101  that when seen from above are parallel and spaced uniform distances apart.  
         [0034]    Of course, the magnetic field produced by magnet  101  actually also runs through the space above and below the surface defined by magnet  101 , as shown in side view  109 . The field lines representing the magnetic field produced by magnet  101  have the curves shown at  111  when viewed from the side. Again, only ½ of the side view is shown; the portion of the field above the surface is symmetrical to the portion below.  
         [0035]    Using Sets of Magnets  101  to Generate Magnetic Fields: FIGS. 11 and 12  
         [0036]    [0036]FIG. 11 shows an arrangement  1101  of two magnets  101  in which the magnets  101  define parallel planes and the circles defined by the cores are centered on a line which is perpendicular to the parallel planes. When the magnetic field produced by a single magnet  101  is looked at in the context of arrangement  1101 , it will be immediately seen that the magnetic field in the volume between the two magnets must be the resultant of the magnetic field produced in the volume by each of the magnets  101 . As shown, corresponding magnetic elements  105  of each of the magnets  101  are on lines perpendicular to the planes defined by the magnets and are oriented in the same way. Thus, the corresponding poles of the magnets  101  are also on lines perpendicular to the planes. That of course means that the magnetic fields generated in the space between the magnets  101  repel each other. The effect of this repulsion is shown in FIG. 12, which is a side view of arrangement  1101 . Because magnetic field  1203  is the resultant of the magnetic fields produced between the magnets  101 , and because the two magnetic fields repel each other, the field lines in magnetic field  1207  are flattened compared with the lines shown at  111  in FIG. 1. Again, the portion of magnetic field  1203  below line  1205  is symmetrical to the portion  1207  above line  1205  and is not shown.  
         [0037]    As is immediately apparent from FIG. 12, arrangement  1101  may consist of any number of magnets  101  arranged on parallel planes in the same fashion as magnet  101 ( 1 ) and  101 ( 2 ). Such arrangements are useful for manipulating magnetic fields in long vessels such as pipes. In the following, magnets of type  101  that have identical cores and arrangements of elements  105  will be termed congruent magnets  101 ; those that have the same arrangement of elements  105  on the core but are of a different size will be termed similar magnets  101 .  
         [0038]    Many versions of arrangement  101  may be constructed. For example, core  103  may have more than two elements  105 . Particularly useful configurations in this regard employ pairs of elements  105  on opposing sides of the core. If the elements are electromagnets, changing the direction and amounts of power to the elements permits creation of fields having many different configurations, and if the changes are sequenced properly, the fields may be made to rotate. The cores may define many shapes. Closed curves are useful and polygons with parallel sides are particularly useful. While planar magnets  101  are simple and useful, the magnets  101  may define non-planar surfaces. The distances between the magnets  101  may also be varied as the application requires.  
         [0039]    Helmholtz Core Arrangements: FIGS. 11 and 12  
         [0040]    A particularly effective version of arrangement  1101  is the Helmholtz core arrangement. As shown in FIG. 11, in a Helmholtz core arrangement, congruent magnets  101  are arranged in parallel planes with corresponding elements  105  being on lines perpendicular to the parallel planes and the distance between the planes being that of the coils in a Helmholtz coil, that is, the distance between magnets  101  is approximately {fraction (1/2)} the diameter of the rings. Magnetic field  1207  shown in FIG. 12 is generated by such a Helmholtz core arrangement. The Helmholtz geometry produces a uniform field as does a standard Helmholtz coil, but the uniform field is produced by the repulsive interaction of the fields generated by the magnets  101 . The uniform field is in the center of the volume defined by the magnets  101  and is parallel to the planes of the magnets  101 . Again, more than 2 magnets  101  may be used to produce a uniform magnetic field of any length. In such an arrangement, termed a picket fence arrangement herein, each pair of adjacent magnets in the set of magnets has the Helmholtz core arrangement. To produce the uniform field, the fields produced by the magnets that are not at the ends of the picket fence arrangement should have a magnitude 25% less than those produced by the magnets at the ends of the arrangement.  
         [0041]    Even in simple Helmholtz core arrangement  1101 , the use of windings for magnetic elements  105  permits some manipulation of the uniform magnetic field. By varying the current in the coils, the strength of magnetic field  1203  may be varied, and by reversing the current direction in the coils  1107 , the polarity of the magnetic field may be reversed. However, even in this arrangement, if separate power supplies are provided to the coils which make up the corresponding magnetic elements  105 , so that elements  105 ( 1 )( 1  and  2 ) and elements  105 ( 2 )( 1  and  2 ) receive differing amounts of power, a magnetic field with a vertical gradient may be established between magnets  101 ( 1 ) and ( 2 ). As the number of opposing pairs of coils on magnet  1103  increases, the number of possible manipulations increases. For example, by adding another opposing pair of coils on each magnet  101  at 90° to the first pair, the directions and magnitudes of the power provided to the coils can be sequenced in a fashion which causes magnetic field  1203  to rotate smoothly around the line upon which the magnets  101  are centered. The number of possible manipulations can be further increased by providing separate power supplies for the coils and by increasing the number of coils.  
         [0042]    Theory of the Helmholtz Core Arrangement  
         [0043]    A useful way of thinking about the Helmholtz core arrangement is the following: the magnetic field lines of the magnetic field generated by magnet  101  within the circle defined by core  103  define field surfaces that are perpendicular to the plane of the magnet. Because of the effects of repulsion, as the poles of  104  and  106  of magnet  101  are approached, the surfaces become increasingly planar and are increasingly at uniform distances from each other, as seen at  107  in FIG. 1. Thus, there is an area on either side of a line drawn between north pole  104  and south pole  106  where the field surfaces become parallel field planes that are at equal distances from each other.  
         [0044]    When a pair of magnets  101  are arranged as shown in FIG. 11, the field surfaces of the magnetic fields generated by the magnets  101  are aligned with each other in the area between the magnets. Each aligned surface has field lines from both magnets  101 , and these field lines all repel each other. As a result, the field lines in the aligned surfaces become more and more parallel as the center of the space between the magnets  101  is approached, as shown at  1207  in FIG. 12. Since the aligned surfaces also become more and more parallel as the center of the space is approached, there is an area around the center of the space in which the field lines become parallel. These parallel field lines define not only the parallel planes of FIG. 1, but also a set of parallel planes that are parallel to magnets  101 . Each of the parallel field lines is at the intersection of a plane that is perpendicular to the magnets  101  and one that is parallel to it.  
         [0045]    As indicated above, the uniform magnetic field produced by the Helmholtz core arrangement can be manipulated by adding electromagnets to the Helmholtz core arrangement and varying the magnitude and direction of the current that is provided to these electromagnets. The entire uniform magnetic field can thus be rotated around the axis of arrangement  1101 ; if sufficient electromagnets are provided and the magnitude and direction of the current to the electromagnets is properly varied, the uniform field can be modified such that the planes defined by the field lines in the uniform magnetic field appear to have been tilted in a horizontal and/or vertical direction or warped in a horizontal and/or vertical direction.  
         [0046]    A Preferred Embodiment of an Electromagnet  101 : FIG. 2  
         [0047]    [0047]FIG. 2 shows a presently-preferred embodiment  201  of an electromagnet  101  for use in a Helmholtz core arrangement. Electromagnet  201  is designed to be retrofitted to a MERIE vessel of the type described above in which four electromagnetic coils are attached to the sides of the vessel. Electromagnet  201  fits around the circumference of the vessel. The four electromagnetic coils are removed and in their place are installed two electromagnets  201  which are connected to the power supplies for the four coils. The two electromagnets are separated by a vertical distance of approximately d/2, or ½ the interior distance d between opposed element sets  205  of electromagnet  201 . In an exemplary embodiment of electromagnet  201 , the distance d is approximately 15 inches. The portion of the volume between the magnets  201  in which the field is highly uniform is centered on the vertical axis of the Helmholtz core arrangement and the plane midway between the magnets  201 . The highly uniform area includes 50% of the horizontal distance d and 20% of the vertical distance d/2. Vertical displacements of the electromagnets  201  of 1 inch above and or below the distance d/2 of 7½ inches had no significant effect on the uniformity of the magnetic field.  
         [0048]    Continuing in more detail, electromagnet  203  includes a ferrous core  203  which is shaped to fit within the form constraints imposed by the MERIE vessel being retrofitted. In electromagnet  201 , the core consists of low-carbon steel bars connected by low-carbon steel cornerpieces  204 . Wound around each bar is an element set  205  consisting of four coil elements  207 . In the preferred embodiment, elements  207 ( 1 ) and ( 4 ) are identical and have more windings than elements  207 ( 2 ) and ( 3 ), which are also identical. The purpose of the extra windings in elements  207 ( 1 ) and ( 4 ) is to compensate for the lack of windings on corner pieces  204 . In an ideal element set  205 , the number of windings would decrease smoothly until the center of the element set was reached and then would increase smoothly in the same fashion, but the approximation used in electromagnet  201  is sufficient for most purposes. In the preferred embodiment, elements  207 ( 1 ) and ( 4 ) have N windings and elements  207 ( 2 ) and ( 3 ) have ⅔ N windings. Indeed, if space restrictions make it necessary, an element set  205  for producing a rotating uniform field may consist only of element  207 ( 1 ) and  207 ( 4 ). Of course, the smaller number of elements reduces the extent to which the magnetic field can be manipulated. The manner in which elements  207  are connected to power supplies depends on the kind of magnetic field that is desired in an apparatus  101  made using electromagnets  201 .  
         [0049]    As may be seen from FIG. 2, element sets  205  and the bars they are wound on form a polygon (in this case, a square) around the circumference of the vessel, with the corner pieces  204  providing the corners of the polygon. The polygon may have any useful number of sides. If the fields produced by a set of electromagnets like electromagnet  201  are intended to rotate, the polygons must have opposing sides that are substantially parallel. The shapes and cross section of the corner pieces and the cross section of the bars are not critical. FIG. 13 shows two possible core cross sections. Circular cross section  1301  is preferred, but space constraints or constraints resulting from the environment into which an electromagnet  201  is retrofitted may require a rectangular cross section like that shown at  1303 . In such a cross section, better contact between the windings and the core is possible when the sides of the rectangular core are convex, as shown at  1305 , and the corners are rounded, as shown at  1307 . Good contact between the windings and the core facilitates the transfer of heat from the windings to the corner pieces via the core.  
         [0050]    There is no requirement that core  203  be continuous; indeed, non-magnetic shims between portions of core  203  may be used for fine adjustment of the magnetic fields produced by electromagnet  201 , as shown in FIG. 14. There, shims  1405  are used in a version  1401  of electromagnet  201  with square corner pieces  1403 . A shim  1407  has been placed in the center of each of the magnet&#39;s bars  1405 . The effect of the shims of FIG. 14 in a rotating magnetic field when the cores are saturated is to preferentially inhibit the strength of the field generated by a Helmholtz core arrangement of the magnets  1401  in one direction with regard to the field generated at 45° when the field is rotated. Preferentially inhibiting the field&#39;s strength in this manner may be used to correct at least partially for inevitable air gap field differences caused by saturation effects at 0° and 45°. Shims can also be used for field correction in situations where saturation and/or rotation are not involved. The magnetic field may also be adjusted by altering the shapes of the core and corner pieces. Examples of problems that can be dealt with by these fine adjustments include less than ideal distances between the electromagnets  201 , less than ideal element locations, or saturation effects in the core.  
         [0051]    [0051]FIG. 15 shows a Helmholtz core arrangement  1501  made with two electromagnets  1503  which form squares with square corner pieces. The dimensions of Helmholtz core arrangement  1501  are given in terms of the length L of the bar upon which the elements  1505  and  1507  are wound.  
         [0052]    The distance between the electromagnets  1503  is thus approximately L/2 and each element  1505  or  1507  has a length of L/4. Element  1505  has n turns and element  1507  has ⅔ n turns. As shown at  1509 , the bar has a circular cross section and the relationship between the diameter d of the circular cross section and the length L is such that d/L is approximately equal to 0.1 where maximum field strength of 100 Gauss is desired.  
         [0053]    Examples of Magnetic Fields Generated Using an Apparatus  101  with Two Electromagnets  201 :  
         [0054]    [0054]FIGS. 3-9 
         [0055]    [0055]FIGS. 3-9 show how the uniform magnetic field generated by a simple Helmholtz core arrangement can be further manipulated by varying the magnitudes and directions of the currents flowing through the elements  207 . The figures show the magnetic field generated in a Helmholtz core arrangement of two electromagnets  201  at position  1205  midway between the electromagnets with various combinations of magnitude and direction of current to the elements  207 . In each of these figures, the magnetic field is shown by means of an array of freely rotating magnetic needles  303  which is mounted on a card that occupies position  1205 . Each figure also includes a schematic representation of electromagnet  201  in which element set  205 ( 1 ) is labeled N, set  205 ( 2 ) is labeled E, and so on. Elements  207  are shown as square boxes numbered  1 - 4 , with box  1  corresponding to element  207 ( 1 ), box  2  to element  207 ( 2 ), and so on. The heavy arrows  305  above the element sets  205  show the direction of the magnetic field in the elements malting up the set. Thus, the magnetic field in elements  207 ( 1 ) and ( 2 ) of element set  205 ( 1 ) has the opposite direction from that in elements  207 ( 3 ) and ( 4 ). The direction of the magnetic field produced by an element is of course determined by the direction in which the current flows through the element. What elements have current flowing through them and the relative strengths of the magnetic fields produced by the elements that have current can be seen from table  307 , which specifies the ampere turns used in each element to produce the magnetic field shown at  303 . Thus, in the case of FIG. 3, the concave magnetic field  301  shown by the needles is produced by providing 1722 ampere turns to elements  207   2  and  4  in each of the E and W element sets  205  in the direction required by the arrows  305  for those elements and 3366, 2417, 2417, and 3366 ampere turns to elements  207 ( 1 )-( 4 ) respectively of element sets  207   1  and  3  in the directions required by the arrows  305  for those elements in both of the magnets  201 ( 1 ) and ( 2 ).  
         [0056]    Continuing in more detail about individual FIGS. 3-8,  
         [0057]    [0057]FIG. 3 shows how a concave field  301  may be produced as shown at  303  with power supply connections to the elements  207  that produce the ampere turns indicated at  307 .  
         [0058]    [0058]FIG. 4 shows how a convex field  401  may be produced as shown at  403  with power supply connections to the elements  207  that produce the ampere turns indicated at  407 .  
         [0059]    [0059]FIG. 5 shows how a SW-NE oriented fan field  501  may be produced as shown at  503  with power supply connections to the elements  207  that produce the ampere turns indicated at  507 .  
         [0060]    [0060]FIG. 6 shows how a quad field  601  may be produced as shown at  603  with power supply connections to the elements  207  that produce the ampere turns indicated at  607 .  
         [0061]    [0061]FIG. 7 shows how an N-S oriented fan field  701  may be produced as shown at  703  with power supply connections to the elements  207  that produce the ampere turns indicated at  707 .  
         [0062]    [0062]FIG. 8 shows how a uniform field  801  may be produced as shown at  803  with power supply connections to the elements  207  that produce the ampere turns indicated at  807 .  
         [0063]    Of course, any of the above fields may be rotated by sequencing the amount and direction of power provided to each of the element sets  205  and vertical gradients may be introduced in any of the fields by providing differing amounts of power to corresponding elements in upper magnet  201 ( 1 ) and lower magnet  201 ( 2 ).  
         [0064]    Retrofitting an Electromagnet  201  to an Existing MERIE Apparatus: FIG. 9  
         [0065]    [0065]FIG. 9 is based on figures from U.S. Pat. No. 5,809,442, Olmer, et al., Silicon dioxide deposition method using a magnetic field and both sputter deposition and plasma-enhanced CVD, issued Feb. 18, 1992. The method described in the patent is applied in the system of FIG. 9. The system employs  5  MERIE reactors  905 ( 1  . . .  5 ) of the type shown at  905  in the configuration shown at  901 . In the center of configuration  901  is transfer chamber  903 . Each of the 5 MERIE reactors has a closable port that opens onto transfer chamber  903 . A robot arm in transfer chamber  903  can transfer wafers from one MERIE reactor  905  to another. Configuration  901  thus permits performance of multiple steps of wafer processing at a single location. MERIE reactors  905  are of the type described in the Description of related art. Reactor  905  has an interior chamber  909  with a table  907  upon which a wafer may be mounted for processing. Around chamber wall  911  are arranged four coils  913 ( 1  . . .  4 ), each of which has two horizontal and two vertical legs. Each of the coils has its own power supply. A magnetic field is generated in interior chamber  909  by activating a pair of adjacent magnets (for example,  913 ( 1 ) and ( 2 )) with current flowing in one direction one power supply and the opposite pair ( 913 ( 3 ) and ( 4 )) with another current flowing in the opposite direction form another power supply. By sequencing the manner and direction in which power is provided to the coils, the magnetic field can be made to rotate.  
         [0066]    Successful retrofitting requires that the fewest possible changes be made to the system which is being upgraded. In the context of system  901 , what this means is that the retrofitting cannot disturb the arrangements used to transfer wafers among the reactors  905  and to introduce gases into the reactors and that the retrofitted reactor should be able to use the same power supplies as the original reactor. Helmholtz core arrangements of electromagnets  201  are particularly suited to dealing with the above constraints. As shown in FIG. 8, only two power supplies are needed to produce a rotating uniform field  803 ; four are typically available in a reactor  905 . Moreover, the facts that the electromagnets  201  in the Helmholtz arrangement are a good distance apart and that the surface of table  907  that holds the wafer is approximately midway between the electromagnets  201  mean that the Helmholtz core arrangement does not interfere with the closable ports or the robot arm. Finally, the square configuration of magnets  201  means that the mounting arrangements for coils  913 ( 1  . . .  4 ) may be easily adapted for mounting magnets  201 .  
         [0067]    [0067]FIG. 10 shows details  1001  of retrofitting to a reactor  905 . A top view is shown at  1002  and a side view at  1004 . As shown at  1002 , reactor vessel  1003  has an octagonal cross section. The octagon has four long sides and four shorter sides. The coils  913  were mounted on the long sides. Side view  1004  shows one of the long sides  1005 ; all that is left of the mounting arrangements for the coil  913  are tapped holes  1007 ( 1  . . .  3 ); the other sides have similar tapped holes.  
         [0068]    Top view  1002  shows a portion of electromagnet  201 ( 1 ) and the arrangements for mounting electromagnet  201 ( 1 ) and ( 2 ) on side  1005 . As set up for retrofitting, electromagnet  201  is made with a core consisting of four bars around which the coil elements  105  are wound and four corner pieces  204 . Each element set  205  is potted to make a single rectangular structure  1013 . Electromagnet  201  is assembled during retrofitting by connecting the bars with the corner pieces.  
         [0069]    Each electromagnet  201  is supported by brackets like brackets  1009  on the long sides. The brackets are attached to the sides by screws that pass through the brackets and into tapped holes  1007 ; as shown, there are three sets of tapped holes on side  1005  and a bracket corresponding to each set of holes. Brackets  1009 ( 1 ) and ( 2 ) support electromagnet  201 ( 1 ), while bracket  1009 ( 3 ) supports electromagnet  201 ( 2 ). Similar brackets are employed to support electromagnets  201 ( 1 ) and ( 2 ) on the other sides. Electromagnet  201 ( 1 ) is assembled so that it sits on top of the top brackets and electromagnet  201 ( 2 ) is assembled so that it sits below the bottom brackets. A strap  1011  at each corner of the electromagnets  201  runs around the corresponding corner pieces of electromagnet  201 ( 1 ) and ( 2 ) and is tightened to urge the electromagnet  201 ( 1 ) against the top brackets and electromagnet  201 ( 2 ) against the bottom brackets. Depressions such as those shown at  1010  in the brackets correspond to bumps  1015  in rectangular structure  1013  and prevent slippage of the electromagnets  201  on the brackets. Once the electromagnets  201  have been mounted on reactor vessel  1003  in the manner just described; all that is required to complete the retrofitting is connecting the elements  207  to the original power supplies as required to produce the desired magnetic field.  
       CONCLUSION  
       [0070]    The foregoing Detailed Description has disclosed to those skilled in the technology of building magnets how to make and use the apparatus for manipulating magnetic fields disclosed herein.  
         [0071]    The Detailed Description has further disclosed the best modes presently known to the inventor of making and using his invention. It will be immediately apparent to magnet builders that the underlying principles of the techniques disclosed herein are very general and that many different kinds of apparatus may be constructed which will produce magnetic fields according to the principles disclosed herein. It will further be apparent that the magnetic fields produced using the techniques disclosed herein have many applications in addition to the ones described herein, and that the ways in which the disclosed techniques are applied will vary from application to application. For all of these reasons, the Detailed Description is to be regarded as being in all respects exemplary and not restrictive, and the breadth of the invention disclosed here in is to be determined not from the Detailed Description, but rather from the claims as interpreted with the full breadth permitted by the patent laws.