Patent Publication Number: US-9852847-B2

Title: High energy density and low leakage electronic devices

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a continuation of U.S. patent application Ser. No. 14/845,463, filed Sep. 4, 2015, now U.S. Pat. No. 9,607,764, which is a continuation-in-part of U.S. patent application Ser. No. 12/908,066, filed Oct. 20, 2010, now U.S. Pat. No. 9,142,354, the contents of all of which are incorporated by reference herein in their entireties. 
    
    
     INTRODUCTION 
     In order to produce a capacitor or electronic device with a Giant or very high capacitance, an insulator with a very high dielectric constant must be fabricated. In one exemplary device, a very high dielectric constant of ∈=10 7  was produced by embedding metal atoms (e.g., gold) in an insulator. The insulator was placed between two nanometer (nm) wide and micrometer (μm) long metal plates as electrodes. In another similar exemplary device, a very high dielectric constant of ∈=10 10  was produced by embedding metal strings in a porous insulator placed between two electrodes. Although these devices are capable of producing a high dielectric constant, it has not been shown for either device that the energy storage density can be increased as the dielectric thickness is reduced below 50 μm. Further, neither of these devices has yet produced a very high capacitance. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The skilled artisan will understand that the drawings, described below, are for illustration purposes only. The drawings are not intended to limit the scope of the present teachings in any way. 
         FIG. 1  is a schematic diagram showing a plot of the effective charge profile superimposed on the insulator portion of a capacitor produced by a periodic magnetic field applied perpendicular to the electrodes of the capacitor, in accordance with various embodiments. 
         FIG. 2  is a schematic diagram showing an electronic device that includes two magnetized layers between two electrode layers that apply a magnetic field to an insulator layer that is perpendicular to the electrode layers, in accordance with various embodiments. 
         FIG. 3  is a schematic diagram showing a magnetic capacitor that includes two magnetized layers that include ferro-magnetic elements within the layers that are alternately magnetized in opposite directions and apply a magnetic field to an insulator layer that is perpendicular to two electrode layers, in accordance with various embodiments. 
         FIG. 4  is a schematic diagram showing an electronic device that includes two magnetized layers outside of two electrode layers that apply a magnetic field to an insulator layer that is perpendicular to two electrode layers, in accordance with various embodiments. 
         FIG. 5  is a schematic diagram showing an electronic device that includes two magnetized layers with ferro-magnetic elements magnetized parallel to the electrode layers but in opposite directions that apply a magnetic field to an insulator layer that is perpendicular to two electrode layers, in accordance with various embodiments. 
         FIG. 6  is a schematic diagram showing a portion of a magnetic capacitor that includes a first magnetized layer and a second magnetized layer each of which includes an outer layer and an inner layer, in accordance with various embodiments. 
         FIG. 7  is a schematic diagram showing a magnetic capacitor that includes a first magnetized layer with an outer layer and an inner layer and a second magnetized layer with an outer layer and an inner layer located between a first electrode layer and a second electrode layer that apply a magnetic field to an insulator layer that is parallel to the first electrode layer and the second electrode layer, in accordance with various embodiments. 
         FIG. 8  is a schematic diagram showing a magnetic capacitor that includes a first magnetized layer with an outer layer and an inner layer and a second magnetized layer with an outer layer and an inner layer located outside of a first electrode layer and a second electrode layer that apply a magnetic field to an insulator layer that is parallel to the first electrode layer and the second electrode layer, in accordance with various embodiments. 
         FIG. 9  is a schematic diagram showing a magnetic capacitor that includes a first magnetized layer and a third magnetized layer located between a first electrode layer and a second electrode layer that apply a magnetic field to an insulator layer that is parallel to the first electrode layer and the second electrode layer and that includes a second magnetized layer and a fourth magnetized layer located between the first electrode layer and the second electrode layer that apply a magnetic field to the insulator layer that is perpendicular to the first electrode layer and the second electrode layer, in accordance with various embodiments. 
         FIG. 10  is a schematic diagram showing a magnetic capacitor that includes a first magnetized layer with an outer layer and an inner layer and a third magnetized layer with an outer layer and an inner layer located between the first electrode layer and the second electrode layer that apply a magnetic field to an insulator layer that is parallel to the first electrode layer and the second electrode layer and that includes a second magnetized layer and a fourth magnetized layer located between the first electrode layer and the second electrode layer that apply a magnetic field to the insulator layer that is perpendicular to the first electrode layer and the second electrode layer, in accordance with various embodiments. 
         FIG. 11  is a schematic diagram showing a magnetic capacitor that includes a first magnetized layer with an outer layer and an inner layer and a third magnetized layer with an outer layer and an inner layer located outside of the first electrode layer and the second electrode layer that apply a magnetic field to an insulator layer that is parallel to the first electrode layer and the second electrode layer and that includes a second magnetized layer and a fourth magnetized layer located outside of the first electrode layer and the second electrode layer that apply a magnetic field to the insulator layer that is perpendicular to the first electrode layer and the second electrode layer, in accordance with various embodiments. 
         FIG. 12  is a schematic diagram showing a magnetic capacitor that includes a first magnetized layer and a second magnetized layer located on either side of an insulator layer and between a first electrode layer and a second electrode layer, where the first magnetized layer and the second magnetized layer include ferro-magnetic elements that are magnetized at angle relative to the first electrode layer and the second electrode layer so that the magnetic fields applied by the magnetized layers to the insulator layer have components in directions both perpendicular and parallel to the electrode layers, in accordance with various embodiments. 
         FIG. 13  is a schematic diagram showing a multi-layer magnetic capacitor that includes four magnetized layers surrounding three insulator layers between two electrodes layers, where each magnetized layer of four magnetized layers includes ferro-magnetic elements that are magnetized perpendicular to the electrode layers to produce a periodic magnetic field along the length of insulator layers that is perpendicular to the electrode layers, in accordance with various embodiments. 
         FIG. 14  is a schematic diagram showing a multi-layer magnetic capacitor that includes four magnetized layers surrounding three insulator layers between two electrodes layers, where each magnetized layer of four magnetized layers includes ferro-magnetic elements that are magnetized parallel to the electrode layers to produce a periodic magnetic field along the length of insulator layers that is perpendicular to the electrode layers, in accordance with various embodiments. 
         FIG. 15  is an exemplary flowchart showing a method for fabricating a magnetic capacitor, in accordance with various embodiments. 
         FIG. 16  is an exemplary flowchart showing a method for fabricating a magnetic capacitor with one insulating layer, in accordance with various embodiments. 
     
    
    
     Before one or more embodiments of the present teachings are described in detail, one skilled in the art will appreciate that the present teachings are not limited in their application to the details of construction, the arrangements of components, and the arrangement of steps set forth in the following detailed description or illustrated in the drawings. Also, it is to be understood that the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. 
     DESCRIPTION OF VARIOUS EMBODIMENTS 
     As described above, conventional capacitors with a very high dielectric constant, ∈, between 10 7  and 10 10 , have been produced by embedding metal atoms or metal strings in an insulator placed between two electrodes. The dielectric thickness, d, of these conventional capacitors is reported to be about 50 micrometers (μm) or larger. 
     In order to determine how scalable these conventional capacitors are, a relationship between the static dielectric constant, ∈ s , and d, is developed for a constant energy storage density. The energy stored in a flat-plate capacitor is given by 
                 W   stored     =       1   2     ⁢     CV   2         ,         
where C is the capacitance and V is the voltage. The stored energy density is found by dividing W stored  by the volume Ad, where A is the area of an electrode.
 
                 W   stored     Ad     =       1   2     ⁢       CV   2     Ad             
The dielectric or insulator thickness, d, is related to the capacitance, C, by the formula
 
             C   =       ɛ   0     ⁢     ɛ   s     ⁢       A   d     .             
Substituting this formula for the capacitance into the equation for the stored energy density produces
 
                   W   stored     Ad     =       1   2     ⁢         ɛ   0     ⁢     ɛ   s     ⁢     V   2         d   2           ,         
where ∈ 0  is the electric constant.
 
     If the stored energy density and the voltage remain constant, ∈ s  is proportional to d 2 . In other words, as the dielectric thickness decreases, the energy storage density remains constant. 
     Therefore, if the dielectric thickness of a conventional capacitor is decreased below 50 μm, the dielectric constant of the capacitor will decrease proportionally even more. In other words, conventional capacitors with very high dielectric constants are not scalable to smaller dielectric thicknesses. 
     A Magnetic Capacitor 
     In various embodiments, a magnetic field is added to a capacitive device to produce a device with both a high dielectric constant and a very high capacitance. In particular, a magnetic field is applied to an electronic device to increase the dielectric constant of the device to greater than 10 10  while maintaining its dielectric or insulator thickness below 100 nm. Such electronic devices or magnetic capacitors that include a magnetic field can produce a Giant or very high capacitance that, in turn, can store a very large amount of electrical energy. 
     Perpendicular Magnetization 
     In various embodiments, an insulator is magnetized between two electrodes in the direction perpendicular to the electrodes to produce a very high capacitance and to store a very large amount of electrical energy. The insulator is magnetized according to the following periodic magnetic field formula, for example. 
               B   →     =         B   1     ⁡     (     1   +     cos   ⁡     (         2   ⁢   π     λ     ⁢   x     )         )       ⁢     z   ^             
The effective potential profile is given by the following equation.
 
               V   Beff     =         e   2       2   ⁢   m       ⁢       (       -       B   1     ⁡     (       λ     2   ⁢   π       ⁢     sin   ⁡     (         2   ⁢   π     λ     ⁢   x     )         )         +       ℏ   ⁢           ⁢     k   y       e       )     2             
According to Poisson&#39;s formula, the effective charge profile is then provided by the following equation.
 
     
       
         
           
             
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       FIG. 1  is a schematic diagram showing a plot  110  of the effective charge profile  120  superimposed on the insulator portion  130  of a capacitor  100 , in accordance with various embodiments. Effective charge profile  120  produced by a periodic magnetic field applied perpendicular to the electrodes  140  of capacitor  100 . The magnetic field (not shown) is periodic in the x-direction, which, in turn, produces periodic effective charge profile  120  in plot  110 . Under applied voltage  150 , electric dipoles  160  are formed in insulator portion  130  of capacitor  100 . 
     In various embodiments, a magnetic capacitor is fabricated as an electronic device and includes a first electrode layer, a second electrode layer, an insulator layer, a first magnetized layer and a second magnetized layer. The insulator layer is located between the first electrode layer and the second electrode layer and between the first magnetized layer and the second magnetized layer. The first magnetized layer includes a first ferro-magnetic material and the second magnetized layer includes a second ferro-magnetic material. The first magnetized layer and the second magnetized layer are located so that the first ferro-magnetic material and the second ferro-magnetic material apply a magnetic field to the insulator layer to improve an electrical property of the magnetic capacitor. 
     In various embodiments, a magnetic capacitor can also be fabricated with just one magnetized layer. For example, the first magnetized layer is located so that the first ferro-magnetic material applies a magnetic field to the insulator layer to improve an electrical property of the magnetic capacitor. 
     The first ferro-magnetic material and the second ferro-magnetic material can each include one or more ferro-magnetic elements. Ferro magnetic elements can include, but are not limited to, ferro-magnetic plates or magnetic nanodots. The first magnetized layer and the second magnetized layer can be located between the first electrode layer and the second electrode layer. 
     In order to provide a periodic magnetic field along the length of the insulator layer, the first ferro-magnetic material of the first magnetized layer and the second ferro-magnetic material of the second magnetized layer are magnetized so that the first ferro-magnetic material and the second ferro-magnetic material apply a magnetic field substantially perpendicular to the first electrode layer and the second electrode layer. Each element of the first ferro-magnetic material and each element of the second ferro-magnetic material are also magnetized in the same direction. 
       FIG. 2  is a schematic diagram showing a magnetic capacitor  200 , in accordance with various embodiments. Magnetic capacitor  200  includes a first magnetized layer  12  and a second magnetized layer  14  located between first electrode layer  6  and second electrode layer  7 . First magnetized layer  12  and second magnetized layer  14  apply a magnetic field to insulator layer  13  that is perpendicular to first electrode layer  6  and second electrode layer  7 . 
     First magnetized layer  12  and second magnetized layer  14  are located on either side of insulator layer  13 . First magnetized layer  12  includes first ferro-magnetic elements  210 , and second magnetized layer  14  includes second ferro-magnetic elements  220 . First ferro-magnetic elements  210  and second ferro-magnetic elements  220  can include the same ferro-magnetic elements or can include different ferro-magnetic elements. First ferro-magnetic elements  210  and second ferro-magnetic elements  220  are substantially aligned in the direction perpendicular to first electrode layer  6  and second electrode layer  7 . In various embodiments, first ferro-magnetic elements  210  and second ferro-magnetic elements  220  are not substantially aligned in the direction perpendicular to first electrode layer  6  and second electrode layer  7 , for example. 
     First ferro-magnetic elements  210  and second ferro-magnetic elements  220  are magnetized in the same direction to produce a periodic magnetic field along the length of insulator  13  that is perpendicular to first electrode layer  6  and second electrode layer  7 . Arrows  230  show the direction of magnetization of first ferro-magnetic elements  210  and second ferro-magnetic elements  220 . Also, all first ferro-magnetic elements  210  in first magnetized layer  12  are magnetized in the same direction. Likewise, all second ferro-magnetic elements  220  in second magnetized layer  14  are magnetized in the same direction. 
     In various embodiments, ferro-magnetic elements within each magnetized layer of a magnetic capacitor are alternately magnetized in opposite directions to produce a magnetized layer that applies a periodic magnetic field along the length of an insulator layer. Each ferro-magnetic element or each group of ferro-magnetic elements may be alternately magnetized in opposite directions, for example. 
       FIG. 3  is a schematic diagram showing a magnetic capacitor  300 , in accordance with various embodiments. Magnetic capacitor  300  includes a first magnetized layer  12  with first ferro-magnetic elements  310  and a second magnetized layer  14  with second ferro-magnetic elements  320 . Each ferro-magnetic element of ferro-magnetic elements  310  and each ferro-magnetic element of ferro-magnetic elements  320  is alternately magnetized. As a result, adjacent ferro-magnetic elements in each magnetized layer are magnetized in opposite directions. 
     In various embodiments, a first magnetized layer and a second magnetized layer of a magnetic capacitor are located on either side of an insulator layer, but outside of a first electrode layer and a second electrode layer. 
       FIG. 4  is a schematic diagram showing a magnetic capacitor  400 , in accordance with various embodiments. Magnetic capacitor  400  includes a first magnetized layer  12 ′ and a second magnetized layer  14 ′ located outside of first electrode layer  6 ′ and second electrode layer  7 ′. First magnetized layer  12 ′ and second magnetized layer  14 ′ apply a magnetic field to insulator layer  13 ′ that is perpendicular to first electrode layer  6 ′ and second electrode layer  7 ′. First electrode layer  6 ′ and second electrode layer  7 ′ are located on either side of insulator layer  13 ′. 
     In various embodiments, both a first magnetized layer and a second magnetized layer of a magnetic capacitor can include one or more additional magnetized layers to enhance the magnetic field applied to the insulator layer. The one or more additional magnetized layers can be adjacent to or separate from the first magnetized layer or the second magnetized layer. The first magnetized layer, the second magnetized layer, and each of the one or more additional magnetized layers can include the same or different insulating, ferro-magnetic materials, or ferro-magnetic elements. 
     In various embodiments, a magnetic capacitor can also include one or more additional insulating layers. An insulating layer and the one or more additional insulating layers can be layered between a first magnetized layer and one or more additional magnetized layers forming a super-lattice, for example. 
     In various embodiments, a periodic magnetic field is applied to the length of an insulator layer of a magnetic capacitor using a first magnetized layer and a second magnetized layer that each applies a magnetic field parallel to the electrode layers. The first ferro-magnetic elements of the first magnetized layer and the second ferro-magnetic elements of the second magnetized layer are magnetized in opposite directions. The parallel components of the magnetic field are, therefore, cancelled out and the resultant magnetic field applied to the insulator layer is substantially perpendicular to the electrode layers. 
       FIG. 5  is a schematic diagram showing a magnetic capacitor  500 , in accordance with various embodiments. Magnetic capacitor  500  includes a first magnetized layer  12  with first ferro-magnetic elements  510  and a second magnetized layer  14  with second ferro-magnetic elements  520 . First ferro-magnetic elements  510  and second ferro-magnetic elements  520  are magnetized in a direction parallel to first electrode layer  6  and second electrode layer  7 . However, first ferro-magnetic elements  510  and second ferro-magnetic elements  520  are magnetized in opposite directions. As a result, the parallel components of the magnetic fields of first magnetized layer  12  and second magnetized layer  14  in insulator layer  13  substantially cancel each other out. The magnetic field that remains in insulator layer  13  is then perpendicular to first electrode layer  6  and second electrode layer  7  and periodic along the length of insulator layer  13 . 
     Parallel Magnetization 
     In various embodiments, magnetizing an insulator layer between two electrode layers in the direction parallel to the electrode layers of a magnetic capacitor can also reduce the dielectric leakage current and increase the dielectric breakdown voltage. This, in turn, makes the insulator layer more insulating. As a result, the dielectric leakage current and dielectric breakdown voltage of the magnetic capacitor described above can be improved by magnetizing the insulator layer in a direction parallel to the electrodes. 
     In various embodiments, the ferro-magnetic elements of two magnetized layers of a magnetic capacitor are magnetized so that the ferro-magnetic elements apply a magnetic field to an insulator layer that is substantially parallel to the electrode layers. In order to apply a magnetic field to the insulator layer that is substantially parallel to the electrode layers, the ferro-magnetic elements of each of the two magnetized layers are magnetized in the same direction. 
     The improvement in leakage current or breakdown voltage is dependent on the concentration of the magnetic field applied to the insulating layer. The magnetic field applied to the insulating layer is produced by the two magnetized layers on either side of the insulating layer. Since magnetic field applied by the two magnetized layers is in the parallel direction, it is not directly aimed at the insulating layer and is largely concentrated in the magnetized layers. Consequently, the concentration of the magnetic field in the insulating is reduced and can be non-uniform across the length of the insulating layer. 
     In various embodiments, the magnetized layers of a magnetic capacitor include an inner layer and an adjacent outer layer that concentrate the magnetic field in the insulator layer. The inner layer is shorter in length than the outer layer. The inner layer is closer to the insulator layer than the outer layer. The shorter length of the inner layer relative to the outer layer concentrates the magnetic field in the insulator layer. 
     In various embodiments, a magnetic capacitor can also include a single magnetized layer that includes ferro-magnetic elements that apply a magnetic field to the insulator layer. The magnetic field is substantially parallel to the first electrode layer and the second electrode layer. The single magnetized layer can also include an inner and outer layer as described above. 
       FIG. 6  is a schematic diagram showing a portion of a magnetic capacitor  600  that includes a first magnetized layer  610  and a second magnetized layer  620  each of which includes an outer layer and an inner layer, in accordance with various embodiments. First magnetized layer  610  includes outer layer  611  and inner layer  612 . Second magnetized layer  620  includes outer layer  621  and inner layer  622 . Inner layer  612  is shorter in length than outer layer  611 , and inner layer  622  is shorter in length than outer layer  621 . First magnetized layer  610  applies magnetic field  631  to insulating layer  640 . Second magnetized layer  620  applies magnetic field  632  to insulating layer  640 . Inner layer  612  of first magnetized layer  610  concentrates magnetic field  631  in insulating layer  640 . Inner layer  622  of first magnetized layer  620  concentrates magnetic field  632  in insulating layer  640 . 
     In various embodiments, a magnetic capacitor can include a first magnetized layer and a second magnetized layer that each can include an inner layer and an outer layer. The first magnetized layer and the second magnetized layer can be located on either side of the insulator layer and between the first electrode layer and the second electrode layer. 
       FIG. 7  is a schematic diagram showing a magnetic capacitor  700 , in accordance with various embodiments. Magnetic capacitor  700  includes a first magnetized layer with outer layer  11  and inner layer  11 ′ and a second magnetized layer with outer layer  15  and inner layer  15 ′ located between first electrode layer  6  and second electrode layer  7 . Outer layer  11 , inner layer  11 ′, outer layer  15 , and inner layer  15 ′ apply a magnetic field to insulator layer  13 ′ that is parallel to first electrode layer  6  and second electrode layer  7 . 
     The first magnetized layer and the second magnetized layer are located on either side of insulator layer  13 ′. The first magnetized layer includes first ferro-magnetic elements  710 , and the second magnetized layer includes second ferro-magnetic elements  720 . First ferro-magnetic elements  710  and second ferro-magnetic elements  720  can include the same ferro-magnetic material or can include different ferro-magnetic materials. First ferro-magnetic elements  710  and second ferro-magnetic elements  720  are, however, magnetized in the same direction. 
     In various embodiments, a magnetic capacitor can include a first magnetized layer and a second magnetized layer that are located on either side of a insulator layer, but outside of a first electrode layer and a second electrode layer. In addition, the first magnetized layer and the second magnetized layer can each include an inner layer and an outer layer. 
       FIG. 8  is a schematic diagram showing a magnetic capacitor  800 , in accordance with various embodiments. Magnetic capacitor  800  includes a first magnetized layer with outer layer  11  and inner layer  11 ′ and a second magnetized layer with outer layer  15  and inner layer  15 ′ located outside of first electrode layer  6 ′ and second electrode layer  7 ′. Outer layer  11 , inner layer  11 ′, outer layer  15 , and inner layer  15 ′ apply a magnetic field to insulator layer  13 ′ that is parallel to first electrode layer  6 ′ and second electrode layer  7 ′. 
     The first magnetized layer and the second magnetized layer are located on either side of insulator layer  13 ′. The first magnetized layer includes first ferro-magnetic elements  810 , and the second magnetized layer includes second ferro-magnetic elements  820 . First ferro-magnetic elements  810  and second ferro-magnetic elements  820  can include the same ferro-magnetic material or can include different ferro-magnetic materials. First ferro-magnetic elements  810  and second ferro-magnetic elements  820  are, however, magnetized in the same direction. 
     Perpendicular and Parallel Magnetization 
     In various embodiments, magnetizing an insulator layer between two electrode layers in directions both substantially perpendicular and parallel to the electrode layers at the same time can increase the capacitance, increase the electrical storage, reduce the dielectric leakage current, and increase the dielectric breakdown voltage of the insulator layer. The magnetic capacitor described above can be modified to provide improvements to all of these electrical properties. 
     The magnetic capacitor is fabricated to include at least four magnetized layers. The first ferro-magnetic elements of the first magnetized layer and the third ferro-magnetic elements of the third magnetized layer are magnetized in the same direction and in a direction parallel to the first electrode layer and the second electrode layer. The second ferro-magnetic elements of the second magnetized layer and the fourth ferro-magnetic elements of the fourth magnetized layer are magnetized in the same direction and in a direction perpendicular to the first electrode layer and the second electrode layer. 
     In various embodiments, a magnetic capacitor can also include just two magnetized layers and apply magnetic field to the insulator layer that are both substantially parallel and perpendicular to the electrode layers. The first ferro-magnetic elements of the first magnetized layer are magnetized in a direction parallel to the first electrode layer and the second electrode layer. The second ferro-magnetic elements of the second magnetized layer are magnetized in the direction perpendicular to the first electrode layer and the second electrode layer. 
       FIG. 9  is a schematic diagram showing a magnetic capacitor  900 , in accordance with various embodiments. Magnetic capacitor  900  includes a first magnetized layer  11  and a third magnetized layer  15  located between first electrode layer  6  and second electrode layer  7 . First magnetized layer  11  and third magnetized layer  15  apply a magnetic field to insulator layer  13  that is parallel to first electrode layer  6  and second electrode layer  7 . Magnetic capacitor  900  also includes a second magnetized layer  12  and a fourth magnetized layer  14  located between first electrode layer  6  and second electrode layer  7 . Second magnetized layer  12  and a fourth magnetized layer  14  apply a magnetic field to insulator layer  13  that is perpendicular to first electrode layer  6  and second electrode layer  7 . 
     First magnetized layer  11  and third magnetized layer  15  are located on either side of insulator layer  13 . First magnetized layer  11  includes first ferro-magnetic elements  910 , and third magnetized layer  15  includes third ferro-magnetic elements  930 . First ferro-magnetic elements  910  and third ferro-magnetic elements  930  can include the same ferro-magnetic material or can include different ferro-magnetic materials. First ferro-magnetic elements  910  and third ferro-magnetic elements  930  are, however, magnetized in the same direction. 
     Second magnetized layer  11  and fourth magnetized layer  15  are located on either side of insulator layer  13 . Second magnetized layer  11  includes second ferro-magnetic elements  920 , and fourth magnetized layer  15  includes fourth ferro-magnetic elements  940 . Second ferro-magnetic elements  920  and fourth ferro-magnetic elements  940  can include the same ferro-magnetic material or can include different ferro-magnetic materials. Second ferro-magnetic elements  920  and fourth ferro-magnetic elements  940  are, however, magnetized in the same direction. 
     In various embodiments, the first magnetized layer and the third magnetized layer of a magnetic capacitor can each include an inner layer and an adjacent outer layer that concentrate the magnetic field in the insulator layer. The inner layer is shorter in length than the outer layer. The inner layer is closer to the insulator layer than the outer layer. The shorter length of the inner layer relative to the outer layer concentrates the magnetic field in the insulator layer. The first magnetized layer and the third magnetized layer can be located on either side of the insulator layer and between the first electrode layer and the second electrode layer. 
       FIG. 10  is a schematic diagram showing a magnetic capacitor  1000 , in accordance with various embodiments. Magnetic capacitor  1000  includes a first magnetized layer with outer layer  11  and inner layer  11 ′ and a third magnetized layer with outer layer  15  and inner layer  15 ′ located between first electrode layer  6  and second electrode layer  7 . Outer layer  11 , inner layer  11 ′, outer layer  15 , and inner layer  15 ′ apply a magnetic field to insulator layer  13 ′ that is parallel to first electrode layer  6  and second electrode layer  7 . 
     Magnetic capacitor  1000  also includes a second magnetized layer  12 ′ and a fourth magnetized layer  14 ′ located between first electrode layer  6  and second electrode layer  7 . Second magnetized layer  12 ′ and fourth magnetized layer  14 ′ apply a magnetic field to insulator layer  13 ′ that is perpendicular to first electrode layer  6  and second electrode layer  7 . 
     In various embodiments, the first magnetized layer and the third magnetized layer can be located on either side of the insulator layer, but outside of the first electrode layer and the second electrode layer. 
       FIG. 11  is a schematic diagram showing a magnetic capacitor  1100 , in accordance with various embodiments. Magnetic capacitor  1100  includes a first magnetized layer with outer layer  11  and inner layer  11 ′ and a third magnetized layer with outer layer  15  and inner layer  15 ′ located outside of first electrode layer  6 ′ and second electrode layer  7 ′. Outer layer  11 , inner layer  11 ′, outer layer  15 , and inner layer  15 ′ apply a magnetic field to insulator layer  13 ′ that is parallel to first electrode layer  6 ′ and second electrode layer  7 ′. 
     Magnetic capacitor  1100  also includes a second magnetized layer  12 ′ and a fourth magnetized layer  14 ′ located outside of first electrode layer  6 ′ and second electrode layer  7 ′. Second magnetized layer  12 ′ and fourth magnetized layer  14 ′ apply a magnetic field to insulator layer  13 ′ that is perpendicular to first electrode layer  6 ′ and second electrode layer  7 ′. 
     In various embodiments, a magnetic capacitor can include two magnetized layers where each of the magnetized layers apply a magnetic field to the insulator layer that is both substantially parallel and perpendicular to the electrode layers. The ferro-magnetic elements of each of the two magnetized layers are magnetized at angle between the parallel and perpendicular directions with respect to the electrode layers so that both parallel and perpendicular components of a magnetic field are applied to the insulator layer. 
     In various embodiments, a magnetic capacitor can include a single magnetized layer that applies magnetic field to the insulator layer that is both substantially parallel and perpendicular to the electrode layers. 
       FIG. 12  is a schematic diagram showing a magnetic capacitor  1200 , in accordance with various embodiments. Magnetic capacitor  1200  includes a first magnetized layer  12  and a second magnetized layer  14  located between first electrode layer  6  and second electrode layer  7 . First magnetized layer  12  and second magnetized layer  14  apply a magnetic field to insulator layer  13  that is both perpendicular and parallel to first electrode layer  6  and second electrode layer  7 . 
     First magnetized layer  12  and second magnetized layer  14  are located on either side of insulator layer  13 . First magnetized layer  12  includes first ferro-magnetic elements  1210 , and second magnetized layer  14  includes second ferro-magnetic elements  1220 . First ferro-magnetic elements  210  and second ferro-magnetic elements  220  are magnetized at an angle relative to first electrode layer  6  and second electrode layer  7 . Magnetizing first ferro-magnetic elements  210  and second ferro-magnetic elements  220  at an angle relative to first electrode layer  6  and second electrode layer  7  allows components of the magnetic fields of first magnetized layer  12  and second magnetized layer  14  to be applied to insulator layer  13  in directions both perpendicular and parallel to first electrode layer  6  and second electrode layer  7 . 
     Multi-Layers 
     In various embodiments, perpendicular, parallel, or both perpendicular and parallel magnetization is applied to two or more insulating layers in a multi-layer magnetic capacitor. As described above, an insulating layer and one or more additional insulating layers can be layered between a first magnetized layer and one or more additional magnetized layers forming a super-lattice, for example. Any of the various embodiments described above can be used to fabricate a multi-layer magnetic capacitor.  FIGS. 13-14  are exemplary multi-layer magnetic capacitors. 
       FIG. 13  is a schematic diagram showing a magnetic capacitor  1300 , in accordance with various embodiments. Magnetic capacitor  1300  includes four magnetized layers  12  surrounding three insulator layers  13  that are all located between first electrode layer  6  and second electrode layer  7 . Each magnetized layer of magnetized layers  12  includes ferro-magnetic elements  1310 . Ferro-magnetic elements  1310  are magnetized perpendicular to first electrode layer  6  and second electrode layer  7 . Ferro-magnetic elements  1310  are magnetized to produce a periodic magnetic field along the length of insulator layers  13  that is perpendicular to first electrode layer  6  and second electrode layer  7 . Each ferro-magnetic element of ferro-magnetic elements  1310  is alternately magnetized. As a result, adjacent ferro-magnetic elements in each magnetized layer are magnetized in opposite directions. The magnetic fields of magnetic capacitor  1300  increase the capacitance and the electrical storage of the device. 
       FIG. 14  is a schematic diagram showing a magnetic capacitor  1400 , in accordance with various embodiments. Magnetic capacitor  1400  also includes four magnetized layers  12  surrounding three insulator layers  13  that are all located between first electrode layer  6  and second electrode layer  7 . Each magnetized layer of magnetized layers  12  includes ferro-magnetic elements  1410 . Ferro-magnetic elements  1410 , however, are magnetized parallel to first electrode layer  6  and second electrode layer  7 . Ferro-magnetic elements  1410  are also magnetized to produce a periodic magnetic field along the length of insulator layers  13  that is perpendicular to first electrode layer  6  and second electrode layer  7 . Each ferro-magnetic element of ferro-magnetic elements  1410  within a magnetized layer is magnetized in the same direction, but the magnetic elements  1410  in alternating layers are magnetized in opposite directions. The magnetic fields of magnetic capacitor  1400  also increase the capacitance and the electrical storage of the device. 
     Applications 
     In various embodiments, one or more magnetic capacitors are connected to a switch, a fuse, or an inverter to protect the device and to regulate the voltage applied. In various embodiments, one or more magnetic capacitors are connected to or embedded in an electrical apparatus for storing electrical energy or providing electrical energy. For example, one or more magnetic capacitors are part of a battery system. 
     Fabricating a Magnetic Capacitor 
       FIG. 15  is an exemplary flowchart showing a method  1500  for fabricating a magnetic capacitor, in accordance with various embodiments. 
     In step  1510  of method  1500 , a first conducting material is deposited to form a first electrode layer. 
     In step  1520 , one or more first ferro-magnetic elements are deposited, a first insulating material is deposited, and the one or more first ferro-magnetic elements are magnetized to form a first magnetized layer that applies a first magnetic field. 
     In step  1530 , a second insulating material is deposited to form an insulator layer. 
     In step  1540 , one or more second ferro-magnetic elements are deposited, a third insulating material is deposited, and the one or more second ferro-magnetic elements are magnetized to form a second magnetized layer that applies a second magnetic field. 
     In step  1550 , a second conducting material is deposited to form a second electrode layer. The first conducting material, the one or more first ferro-magnetic elements, the first insulating material, the second insulating material, the one or more second ferro-magnetic elements, the third insulating material, and the second conducting material are deposited so that the insulator layer is located between the first electrode layer and the second electrode layer and between the first magnetizing layer and the second magnetizing layer. The one or more first ferro-magnetic elements and the one or more second ferro-magnetic elements are magnetized so that the first magnetic field and the second magnetic field are applied to the insulator layer to improve an electrical property of the magnetic capacitor. 
       FIG. 16  is an exemplary flowchart showing a method  1600  for fabricating a magnetic capacitor with one insulating layer, in accordance with various embodiments. 
     In step  1610  of method  1600 , a first conducting material is deposited to form a first electrode layer. 
     In step  1620 , one or more first ferro-magnetic elements are deposited to form magnetic layer and are aligned and magnetized to produce a magnetic field. 
     In step  1630 , an insulating material is deposited to form an insulating layer. 
     In step  1640 , a second conducting material is deposited to form a second electrode layer. The one or more ferro-magnetic elements are aligned and magnetized to apply the magnetic field to the insulator layer so that the magnetic field is perpendicular to the first electrode layer and the second electrode layer, and so that the magnetic field is periodic along the length of the insulator layer and results in electric dipoles being formed in the insulator layer when a voltage is applied between the first electrode layer and the second electrode layer. 
     In various embodiments, the first conducting material and the second conducting material can include, but are not limited to, Al, a doped semiconductor, W, Si, TiN, or a conducting polymer. The first conducting material and the second conducting material can also include, but are not limited to, graphene, conductive metals, or superconductors. The first conducting material and the second conducting material can be deposited using evaporation, sputtering, chemical vapor deposition (CVD), or spin coating, for example. 
     In various embodiments, the insulating material can include, but are not limited to, SiO 2 , Si 3 N 4 , SiNx, TiO 2 , BaTio 3  or Al 2 O 3 . The insulating material can also include magneto-ferroelectric materials that produce a huge dielectric constant under a magnetic field. These materials include, but are not limited to, LaSr(Mn/Fe/Co/Ni)xO3, Ba/Ti/Sr/La/Bi/Y(Fe/Co/Ni/Mn)xO3, Ho(Fe/Co/Ni/Mn)xO5, or Lu(Fe/Co/Ni/Mn)xO4, where ‘/’ implies ‘or’ and x=1, 2, or 3. The insulating material can be deposited using evaporation, sputtering, or chemical vapor deposition (CVD), for example. An insulator layer can be annealed at a suitable temperature, for example, from 200 C to 800 C to enhance the insulating quality and the endurance of the films. Then subsequently, ferro-magnetic elements can be deposited to form magnetized layers. 
     The one or more ferro-magnetic elements can include, but are not limited to, PtNi, PtFe, FeCo, CoFeO4, HfOx, or FeCoNi. 
     The one or more ferro-magnetic elements are deposited in the form of plates or magnetic nanodots between or outside of the electrodes. The one or more ferro-magnetic elements can be deposited with or without an insulating layer. Magnetic nanodots can be formed spontaneously at a certain temperature. However a ferro-magnetic plate containing many nanodots can be formed in different shapes using a lithographic process, for example. Magnetic nanodots can be formed in a number of different shapes due to the coagulation effect, for example. These shapes can include, but are not limited to, spheres, ellipsoids, rods, or cones. Magnetic nanodots can have lengths on the order of nanometers or micrometers. For example, magnetic nanodots that have a length on the order of 10 nm and are aligned perpendicular to the plane of the electrode layers can produce a periodic magnetic field with a period of about 20 nm. 
     The one or more ferro-magnetic elements are magnetized using an annealing process, for example. The elements are annealed in vacuum or in inert gas, such as Ar, or N 2  for example, or are annealed simultaneously with the deposition of an insulating material. The annealing process can be performed at an elevated temperature of 300° C. to 1000° C., for example. The ferro-magnetic plates or magnetic nanodots are annealed to a specific direction spontaneously or in a strong magnetic field, for example. 
     While the present teachings are described in conjunction with various embodiments, it is not intended that the present teachings be limited to such embodiments. On the contrary, the present teachings encompass various alternatives, modifications, and equivalents, as will be appreciated by those of skill in the art. 
     Further, in describing various embodiments, the specification may have presented a method and/or process as a particular sequence of steps. However, to the extent that the method or process does not rely on the particular order of steps set forth herein, the method or process should not be limited to the particular sequence of steps described. As one of ordinary skill in the art would appreciate, other sequences of steps may be possible. Therefore, the particular order of the steps set forth in the specification should not be construed as limitations on the claims. In addition, the claims directed to the method and/or process should not be limited to the performance of their steps in the order written, and one skilled in the art can readily appreciate that the sequences may be varied and still remain within the spirit and scope of the various embodiments.