Abstract:
Disclosed herein are processes to manufacture sliders having extended three-dimensional air-bearing surfaces and non-transitory computer-readable storage media storing machine-executable instructions to cause at least one processor to perform the processes. A disclosed method of manufacturing a slider for use in a hard disk drive comprises removing a first portion of material from a wafer, the first portion of material comprising substrate, and, using an additive fabrication technique, forming at least a portion of a feature of the slider in a first location formerly occupied by at least some of the first portion of material. The additive fabrication technique may comprise three-dimensional printing, stereo lithography, fused deposition modeling, selective laser sintering, or multi jet modeling. Also disclosed are sliders manufactured using the disclosed methods of manufacture and disk drives comprising such sliders.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of, and hereby incorporates by reference the contents of, U.S. provisional patent application No. 62/275,857, filed Jan. 7, 2016, entitled “SLIDERS WITH EXTENDED THREE-DIMENSIONAL AIR-BEARING SURFACES, AND METHODS FOR FABRICATING SUCH SLIDERS”, having inventors Weidong Huang and Akiko Tadamasa. 
     This application is being filed on the same day as, and hereby incorporates by reference the contents of, the related U.S. application Ser. No. 15/164,811, entitled “SLIDER WITH EXTENDED THREE-DIMENSIONAL AIR-BEARING SURFACE”, having inventor Weidong Huang, and Ser. No. 15/164,822, entitled “SLIDER WITH TUNNEL FEATURE”, having inventors Weidong Huang and Akiko Tadamasa. 
    
    
     BACKGROUND 
     Magnetic storage systems, such as hard disk drives, are used to store large amounts of information. A magnetic head in a magnetic storage system typically includes a read/write transducer for retrieving and storing magnetically encoded information on a magnetic recording medium, such as a disk. A suspended slider supports the magnetic head. The slider provides mechanical support for the magnetic head and the electrical connections between the magnetic head and the rest of the magnetic storage system. 
     During operation, the slider floats a small distance above the magnetic recording medium (i.e., the hard disk), which rotates at high speeds. Components of a disk drive move the slider and, therefore, the magnetic head to a desired radial position over the surface of the rotating disk, and the magnetic head reads or writes information. The slider rides on a cushion or bearing of air created above the surface of the disk as the disk rotates at its operating speed. The slider has an air-bearing surface (ABS) that faces the disk. The ABS is designed to generate an air-bearing force that counteracts a preload bias that pushes the slider toward the disk. The ABS causes the slider to fly above and out of contact with the disk. 
     Conventional slider fabrication techniques place limitations on the design of the slider ABS. There is, however, an ongoing need for slider designs that improve performance of magnetic storage systems. 
     SUMMARY 
     Disclosed herein are methods for manufacturing sliders for use in a hard disk drive, including a method comprising removing a first portion of material from a wafer, the first portion of material comprising substrate; and, using an additive fabrication technique, forming at least a portion of a feature of the slider in a first location formerly occupied by at least some of the first portion of material. In some embodiments, removing the first portion of material from the wafer comprises lapping or ion milling. In some embodiments, the additive fabrication technique comprises three-dimensional (3D) printing, stereo lithography, fused deposition modeling, selective laser sintering, or multi-jet modeling. In some embodiments, at least a portion of the feature is hollow. 
     In some embodiments, the material is a first material, and forming the at least a portion of the feature of the slider using an additive fabrication technique comprises laying down two or more layers of a second material, wherein the second material is the same as or different from the first material. 
     In some embodiments, forming the at least a portion of the feature of the slider using an additive fabrication technique comprises three-dimensional (3D) printing the at least a portion of the feature. 
     In some embodiments, the method further comprises removing a portion of the feature. In some such embodiments, removing the portion of the feature comprises ion milling or lapping. In some such embodiments, the method further comprises depositing a coating. 
     Also disclosed herein is non-transitory computer-readable storage medium storing one or more machine-executable instructions that, when executed, cause at least one processor to remove a first portion of material from a wafer, the first portion of material comprising substrate; and using an additive fabrication technique, form at least a portion of a feature of a slider for use in a hard disk drive in a first location formerly occupied by at least some of the first portion of material. In some embodiments, at least one of the machine-executable instructions is stored as a computer-aided design (CAD) file or as a stereolithography (STL) file. In some embodiments, when executed by the at least one processor, the one or more machine-executable instructions further cause the at least one processor to add a read/write head to the slider. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The disclosure herein is illustrated by way of example, and not by way of limitation, in the figures of the accompanying drawings, in which like reference numerals refer to similar elements and in which: 
         FIG. 1  illustrates several components of an exemplary hard disk drive in accordance with some embodiments. 
         FIG. 2A  illustrates an exemplary slider having a mask applied in a prior-art fabrication process. 
         FIG. 2B  illustrates the exemplary slider of  FIG. 2A  after the removal of portions not protected by the mask. 
         FIG. 2C  illustrates the back surface of the exemplary slider of  FIG. 2B . 
         FIG. 2D  illustrates a cross-section of the exemplary slider illustrated in  FIGS. 2B and 2C . 
         FIG. 2E  illustrates a cross-section of an exemplary slider created by removing additional material from the slider shown in  FIGS. 2B and 2C . 
         FIGS. 3A through 3C  illustrate different views of an exemplary slider having an air-bearing surface with four levels. 
         FIG. 4A  illustrates a cross-section of an exemplary slider in accordance with some embodiments. 
         FIG. 4B  illustrates a feature of a slider. 
         FIG. 4C  illustrates a feature of a slider. 
         FIG. 5A  illustrates a cross-section of an exemplary slider in accordance with some embodiments. 
         FIG. 5B  illustrates a feature of a slider. 
         FIG. 5C  illustrates a feature of a slider. 
         FIG. 6  illustrates a cross-section of an exemplary slider in accordance with some embodiments. 
         FIG. 7  illustrates a cross-section of an exemplary slider in accordance with some embodiments. 
         FIG. 8  illustrates a cross-section of an exemplary slider in accordance with some embodiments. 
         FIG. 9  illustrates a cross-section of an exemplary slider in accordance with some embodiments. 
         FIG. 10  illustrates a cross-section of an exemplary slider in accordance with some embodiments. 
         FIG. 11  illustrates an exemplary slider having features in accordance with some embodiments. 
         FIG. 12  is a flowchart illustrating a process for fabricating a slider in accordance with some embodiments. 
         FIGS. 13A through 13I  illustrate cross-sections of an exemplary slider during the fabrication process represented by the flowchart of  FIG. 12 . 
         FIG. 13J  illustrates the ABS function corresponding to the slider cross-section shown in  FIG. 13I . 
         FIGS. 14A through 14H  illustrate cross-sections of another exemplary slider during the fabrication process represented by the flowchart of  FIG. 12 . 
         FIG. 14I  illustrates the ABS function corresponding to the slider cross-section shown in  FIG. 14H . 
     
    
    
     DETAILED DESCRIPTION 
     The following description is made for the purpose of illustrating the general principles of the present disclosure and is not meant to limit the inventive concepts claimed herein. Furthermore, particular embodiments described herein may be used in combination with other described embodiments in various possible combinations and permutations. 
       FIG. 1  illustrates several components of an exemplary hard disk drive  500  in accordance with some embodiments. The magnetic hard disk drive  500  includes a spindle  515  that supports and rotates a magnetic disk  520 . The spindle  515  is rotated by a spindle motor (not shown) that is controlled by a motor controller (not shown) that may be implemented in electronics of the hard disk drive  500 . A slider  525 , which is supported by a suspension and actuator arm  530 , has a combined read and write magnetic head  540 . The head  540  may include only one read sensor, or it may include multiple read sensors. The read sensors in the head  540  may include, for example, one or more giant magnetoresistance (GMR) sensors, tunneling magnetoresistance (TMR) sensors, or another type of magnetoresistive sensor. An actuator  535  rotatably positions the suspension and actuator arm  530  over the magnetic disk  520 . The components of the hard disk drive  500  may be mounted on a housing  545 . It is to be understood that although  FIG. 1  illustrates a single disk  520 , a single slider  525 , a single head  540 , and a single suspension and actuator arm  530 , hard disk drive  500  may include a plurality (i.e., more than one) of disks  520 , sliders  525 , heads  540 , and suspension and actuator arms  530 . 
     In operation, the actuator  535  moves the suspension and actuator arm  530  to position the slider  525  so that the magnetic head  540  is in a transducing relationship with the surface of the magnetic disk  520 . When the spindle motor rotates the disk  520 , the slider  525  is supported on a thin cushion of air known as the air bearing that exists between the surface of the disk  520  and an air-bearing surface of the slider  525 . The head  540  may be used to write information to multiple tracks on the surface of the disk  520  and to read previously-recorded information from the tracks on the surface of the disk  520 . Processing circuitry  510  provides to the head  540  signals representing information to be written to the disk  520  and receives from the head  540  signals representing information read from the disk  520 . The processing circuitry  510  also provides signals to the spindle motor to rotate the magnetic disk  520 , and to the actuator  535  to move the slider  525  to various tracks. 
     To read information from the magnetic disk  520 , the slider  525  passes over a region of the disk  520 , and the head  540  detects changes in resistance due to magnetic field variations recorded on the disk  520 , which represent the recorded bits. 
     The slider  525  has a gas-bearing surface that faces the surface of the disk  520  and counteracts a preload bias that pushes the slider toward the disk  520 . For convenience, in this document the gas-bearing surface is referred to as the air-bearing surface (ABS) and the gas is generally referred to as “air,” although it is to be understood that the gas used in a hard disk drive  500  may be a gas other than air (e.g., the gas may be helium). For simplicity, throughout this disclosure, the surface of the slider  525  that faces or that will eventually face the disk  520  is referred to as the ABS. 
     As the disk  520  rotates, the disk  520  drags air under the slider  525  and along the ABS in a direction approximately parallel to the tangential velocity of the disk  520 . As the air passes under the ABS, air compression along the air flow path causes the air pressure between the disk  520  and the ABS to increase, which creates a hydrodynamic lifting force that counteracts the tendency of the suspension and actuator arm  530  to push the slider  525  toward the disk  520 . The slider  525  thus flies above the disk  520  but in close proximity to the surface of the disk  520 . To obtain good performance, it is desirable for the slider  525  to maintain a substantially constant flying height above the surface of the disk  520 . The degree of stability of the fly-height of the slider influences the performance of the magnetic head  540 . The design of the slider  525  ABS has an impact on the flying characteristics of the slider  525  and therefore the performance of the magnetic head  540 . 
     A conventional slider  525  ABS may include a pair of raised side rails that face the disk  520  surface. The raised side rails may be separated by an etched cavity and have tapered or stepped leading edges. Additional stepped surfaces may also be formed at various other locations on the slider  525  ABS. 
     Conventionally, the slider  525  is fabricated from a wafer using a photolithography process having two steps: (a) covering a portion of a surface of the wafer, and (b) removing substrate material from the exposed (i.e., not covered) surface of the wafer. Step (a) may be accomplished, for example, using a binary mask having hard edges to create a well-defined pattern in a photoresist layer that is applied to the wafer surface. Step (b) may be accomplished, for example, by lapping, etching, or milling (e.g., using an ion beam) to transfer the photoresist pattern to the wafer surface. The surface of the slider  525  to which the covering is applied and from which material is removed is the surface that will eventually face the disk  520  when the slider  525  is used in a disk drive  500 , i.e., the ABS. The steps (a) and (b) may be repeated multiple times to create different slider features. 
       FIGS. 2A through 2C  illustrate an exemplary slider  525 A being fabricated using a prior-art fabrication process having two steps as described above.  FIGS. 2A, 2B , and  2 C show a three-dimensional wafer  120  oriented according to the three-dimensional axes shown in  FIGS. 2A through 2C , which use rectangular coordinates in directions labeled as x, y, and z. It is to be understood that the labeling of the three axes as x, y, and z is arbitrary. Furthermore, it is to be understood that the use of a rectangular coordinate system is convenient because the wafer  120  initially has a cuboid shape, but other coordinate systems (e.g., polar, cylindrical, spherical) could be used instead, but might not be as convenient if the wafer  120  has a cuboid shape. Moreover, the x-, y-, and z-axes are oriented parallel and perpendicular to the surfaces of the wafer  120  shown in  FIG. 2A  for convenience and to simplify the explanations herein. 
     As illustrated in  FIG. 2A , before fabrication begins, the wafer  120  has a substantially flat initial surface  145  that lies in an x-y plane. The initial surface  145  is the surface of the wafer  120  from which material is removed to form an ABS having features such as those described previously (e.g., side rails, edges, stepped surfaces, etc.). The wafer  120  also has a substantially flat back surface  125 , shown in  FIG. 2C , which also lies in an x-y plane. Because material is not removed from the back surface  125  during fabrication, the back surface  125  remains substantially flat in the finished slider  525 A. 
     To create an exemplary slider  525 A from the wafer  120 , a mask  130 , shown in  FIG. 2A , is applied to the initial surface  145  to protect the regions of the initial surface  145  under the mask  130 . Material is then removed from the portion of the wafer  120  that is not protected by the mask  130 . There are many ways to accomplish the removal, such as, for example, by etching the initial surface  145  from a direction perpendicular to the initial surface  145  (i.e., from above the initial surface  145  as illustrated in  FIG. 2A ) or by using an ion mill with ions aimed at the initial surface  145  in the z-direction. As a result of the removal of material from the wafer  120 , only the portion of the initial surface  145  protected by the mask  130  remains intact. 
       FIG. 2B  shows the slider  525 A after regions of the wafer  120  not protected by the mask  130  have been removed from the z-direction (e.g., by directing an ion beam at the initial surface  145  from above the wafer  120 ). As shown in  FIG. 2B , the portion of the wafer  120  that was under the mask  130  remains intact, whereas material from the wafer  120  that was not under the mask  130  has been removed. Assuming for the sake of example that the slider  525 A is now complete, the ABS  140  is the three-dimensional surface that includes the portion of the initial surface  145  previously protected by the mask  130  (i.e., the portion of the initial surface  145  that remains after removal of material from the wafer  120 ) and the newly-created surface in the wafer  120 , which is recessed from the plane that contained the initial surface  145 . Thus, the ABS  140  of  FIG. 2B  has two levels,  155 A and  155 B. 
     As shown in  FIG. 2B , the slider  525 A has transitions in the z-direction between the levels  155 A (i.e., regions of the wafer  120  formerly covered by the mask  130 ) and  155 B (i.e., the now-exposed regions of the wafer  120  from which material was removed). For example,  FIG. 2B  labels two z-direction transitions  150 A and  150 B, although there are, of course, many other z-direction transitions shown. 
       FIG. 2D  shows a cross-section  160 A of the exemplary slider  525 A illustrated in  FIGS. 2B and 2C . The cross-section  160 A is taken parallel to the z-axis and perpendicular to the back surface  125  (i.e., the cross-section is made vertically, perpendicular to the x-y plane based on the orientation of the axes in  FIG. 2B ) along the dashed line  170  shown on the level  155 A of the slider  525 A illustrated in  FIG. 2B . For ease of explanation, as shown in  FIG. 2D , the cross-section  160 A has been taken in an x-z plane defined by the axes illustrated in  FIGS. 2A and 2B . Therefore, the cross-section  160 A illustrates how the ABS  140  varies along the z-axis as a function of the value along the x-axis at whatever fixed value of y is represented by the line  170  in  FIG. 2B . 
     As used herein, the term “single-valued function” means a relation f(x) for which, for all possible values of x, f(x) has exactly one value or a discontinuity. 
     As used herein, the term “multi-valued function” means a relation f(x) for which, for at least one possible value of x, f(x) has two or more distinct nonzero values. For purposes of the definition of multi-valued function herein, a discontinuity does not have two or more distinct nonzero values. 
     The terms “single-valued function” and “multi-valued function” as used herein are mutually exclusive. A single-valued function cannot be a multi-valued function, and a multi-valued function cannot be a single-valued function, even if, in some range of x values, the multi-valued function has all of the properties of a single-valued function. In other words, as used herein, a function can be either a single-valued function or a multi-valued function, but not both. 
     As will be appreciated by a person having ordinary skill in the art, as used herein, the terms “function,” “single-valued function,” and “multi-valued function” do not necessarily comport with those terms as they may be used in mathematics. For example, in mathematics the terms “function” and “single-valued function” typically mean a relation in which for each input there is exactly one output. Here, a single-valued function may also include a discontinuity, meaning that for a selected value of x at which a discontinuity occurs, the single-valued function f(x) evaluates to many values in a range defined by the discontinuity. 
     The term “ABS function” is used herein to describe the characteristics of a portion of the ABS  140  in a two-dimensional plane made by taking a cross-section of the slider  525  parallel to the z-axis and perpendicular to the x-y plane (i.e., the plane defined by the back surface  125 , assuming the back surface  125  is substantially flat). Using the orientation of axes presented herein, i.e., with the initial surface  145  and back surface  125  lying in parallel x-y planes, the ABS function describes how the ABS  140  varies in the z-direction along a selected axis in an x-y plane. The ABS function does not include any portion of the back surface  125 . 
     Using the definitions provided above, an ABS function in which, for all possible input values along the selected axis in the x-y plane, the ABS function has exactly one value or a discontinuity is a single-valued function. In other words, the ABS function is a single-valued function if, for all possible input values along the selected axis in the x-y plane, the ABS function has exactly one value or a discontinuity. In contrast, an ABS function having at least one input value along the selected axis in the x-y plane for which the ABS function has two or more distinct nonzero z-values is a multi-valued function. Thus, the ABS function is a multi-valued function if, for at least one input value along the selected axis in the x-y plane, the ABS function has two or more distinct nonzero z-values. It is to be appreciated that an ABS function need not be continuous, as some of the exemplary new slider embodiments herein will illustrate. 
       FIG. 2D  shows the ABS function  180 A resulting from the exemplary cross-section  160 A. For clarity, the ABS function  180 A is shown in bold. As is evident from  FIG. 2D , the ABS function  180 A is a piecewise linear function. As explained previously, for ease of explanation, the cross-section  160 A is taken parallel to the x-axis at a selected value of y, and therefore the axis in the x-y plane is simply an x-axis. As shown by the vertical dashed line  165  in  FIG. 2D , which may be positioned anywhere along the x-axis, for any selected value of x along the cross-section  160 A, the ABS function  180 A has either exactly one z-value, or there is a vertical transition, i.e., a discontinuity, at that value of x. For example, as shown in  FIG. 2D , when the value of x is X 1 , the ABS function  180 A has exactly one nonzero z-value, Z 1 . When the value of x is X 2 , the ABS function  180 A has a discontinuity and evaluates to all values between Z 1  and Z 4 . Therefore, the ABS function  180 A is a single-valued function. 
     Although  FIG. 2D  shows only one exemplary cross-section of the slider  525 A illustrated in  FIG. 2B , as will be understood by those having ordinary skill in the art after reading and understanding the disclosures herein, the ABS function  180  resulting from any cross-section  160  of the slider  525 A illustrated in  FIG. 2B  made parallel to the z-axis and perpendicular to an x-y plane will be a single-valued function. This ABS function  180  will be a single-valued function regardless of the orientation of the cross-section  160  with respect to the x- and y-axes (i.e., regardless of which axis in the x-y plane is selected); as long as the cross-section  160  is made parallel to the z-axis (i.e., perpendicular to the x-y plane), the resulting ABS function  180  will be a single-valued function. 
     It is to be appreciated that the value of y that coincides with the line  170  in  FIG. 2B  is arbitrary. The line  170  could be moved to another value of y along the y-axis, and the resulting cross-section  160  would have similar characteristics to the cross-section  160 A shown in  FIG. 2D . Specifically, the resulting cross-section  160  would have an ABS function  180  that is a single-valued function. Furthermore, the line  170  could be oriented parallel to the y-axis instead of parallel to the x-axis, thereby defining a cross-section  160  in the y-z plane instead of in the x-z plane as shown in  FIG. 2C . In this case, too, the resulting cross-section  160  would have similar characteristics to the cross-section  160 A shown in  FIG. 2D ; in other words, that cross-section  160  would also have an ABS function  180  that is a single-valued function. It is also to be appreciated that, as shown in  FIG. 2B , the line  170  is parallel to the y-axis, and therefore represents a single value of y, only for ease of explanation and presentation. A cross-section  160  taken parallel to the z-axis and perpendicular to any arbitrary axis in the x-y plane would have similar characteristics to the cross-section  160 A shown in  FIG. 2D  (i.e., would have an ABS function  180  that is a single-valued function) but could be more complicated to describe using the axes shown in  FIGS. 2A through 2C  because both the value of x and the value of y could vary along the cross-section  160 . 
     As explained above,  FIG. 2B  illustrates an exemplary slider  525 A created using only one mask  130 , but additional masks may be applied to the slider  525 A shown in  FIG. 2B  to create additional features or contours. For example, a different mask may be applied to the slider  525 A of  FIG. 2B  to cover not only the region formerly covered by the mask  130 , but also additional exposed areas of the wafer  120 , and additional material may subsequently be removed from the wafer  120 . Alternatively, a mask that does not entirely cover the region covered by the mask  130  may be applied, and material from the portion of the wafer  120  formerly protected by the mask  130  may then be removed along with material from elsewhere on the wafer  120 . After the removal of material unprotected by each mask, yet another mask may be applied and yet more material removed, and so on. 
       FIG. 2E  illustrates a cross-section  160 B of an exemplary slider (not shown) created by removing additional material from the wafer  120  shown in  FIG. 2B . Like the cross-section  160 A of  FIG. 2D , the cross-section  160 B is taken in the z-direction, parallel to the z-axis and perpendicular to an x-y plane (e.g., the x-y plane that coincides with the back surface  125 ) along a selected axis in the x-y plane. For ease of explanation, the cross-section  160 B has been taken parallel to the x-axis (and perpendicular to the y-axis) and therefore, like the cross-section  160 A of  FIG. 2D , lies in an x-z plane defined by the axes illustrated in  FIGS. 2A through 2C . Therefore, the cross-section  160 B illustrates how the ABS function  180 B varies (in the direction of the z-axis) as a function of the value along the x-axis at a selected value of y. Again, for clarity, the ABS function  180 B is shown in bold. As shown by  FIG. 2E , although the ABS function  180 B has more contours and transitions than the ABS function  180 A, the ABS function  180 B is still a single-valued function because for any selected value of x at which the line  165  may be located, the ABS function  180 B has exactly one nonzero value or a discontinuity. 
       FIGS. 3A through 3C  illustrate a more complicated exemplary slider  525 B created by a prior-art process in which the steps of applying a mask and removing material from unprotected regions of the wafer  120  have been executed three times to create an ABS  140  having four levels. The slider  525 B has six surfaces: the back surface  125  (shown in  FIG. 3C ), a leading-edge surface  121  (shown in  FIGS. 3A and 3C ), a trailing-edge surface  122  (shown in  FIG. 3B ), an inner-radius surface  123  (shown in  FIGS. 3A and 3C ), an outer-radius surface  124  (shown in  FIG. 3B ), and an ABS  140  (shown in  FIGS. 3A and 3B ). In the exemplary slider  525 B shown in  FIGS. 3A through 3C , the leading-edge surface  121 , trailing edge surface  122 , inner-radius surface  123 , and outer-radius surfaces  124  are substantially perpendicular to the back surface  125 . The leading-edge surface  121  and trailing-edge surface  122  are substantially parallel to each other, and the inner-radius surface  123  and outer-radius surface  124  are substantially parallel to each other. The leading-edge surface  121  and trailing-edge surface  122  are both substantially perpendicular to both of the inner-radius surface  123  and the outer-radius surface  124 . In some embodiments, the leading-edge surface  121 , trailing-edge surface  122 , inner-radius surface  123 , and outer-radius surface  124  may be substantially perpendicular to at least a portion of the ABS  140 . 
     A first level  142  of the ABS  140  is the level of the ABS  140  that will be closest to the disk  520  when the slider  525 B is incorporated into a disk drive  500 . A second level  144  is the level that will be the next-closest to the disk  520 . A fourth level  148  is the level that will be furthest from the disk  520 , and a third level  146  is the level that will be next-furthest from the disk  520 . 
     The slider  525 B shown in  FIGS. 3A through 3C  may be fabricated as follows. First, a mask having the shape of the first level  142  is applied to a cuboid wafer  120 , as previously described in the discussion of  FIGS. 2A through 2C . Material down to the surface of the second level  144  is then removed from the wafer  120 , creating a two-level ABS  140 . Next, a mask having the shape that is the union of the shape of the first level  142  and the second level  144  is applied to the ABS  140 , and material not protected by the mask is removed from the wafer  120 , creating a three-level ABS  140  that includes the third level  146 . Finally, a mask having the shape that is the union of the shapes of the first level  142 , the second level  144 , and the third level  146  is applied to the ABS  140 , and material not protected by the mask is removed from the wafer  120  to create the fourth level  148 , as shown in  FIGS. 3A and 3B . 
     Although the process of protecting a portion of the wafer  120  and removing material from the unprotected portion of the wafer  120  may be repeated multiple times with masks having different sizes and shapes to create a relatively complex ABS  140 , such as the exemplary ABS  140  shown in  FIGS. 3A through 3C , prior-art fabrication methods only allow for the removal or preservation of wafer  120  material. As a result, when a slider  525  is fabricated using prior-art techniques, in which material is removed from a particular direction, along a particular axis (assumed herein to be the z-axis using the orientation of axes shown in  FIGS. 2A through 2C ) perpendicular to the plane in which the back surface  125  lies (assumed herein to be the x-y plane), the ABS function  180  for any cross-section  160  taken perpendicular to the plane of the back surface  125  is a single-valued function. One can verify by inspection of  FIGS. 3A through 3C  that even more sophisticated sliders having multiple levels and more complex shapes have ABS functions  180  that are single-valued functions. Any cross-section  160  of the exemplary slider  525 B illustrated in  FIGS. 3A through 3C  taken perpendicular to the x-y plane of the back surface  125  will result in an ABS function  180  that is a single-valued function. 
     Because prior-art slider fabrication processes only allow the removal of material from one direction, previously-existing slider fabrication methods impose significant limitations on the design of sliders  525 . As a consequence, existing slider designs can have several drawbacks, including a tendency to collect lubricant, which affects the aerodynamics of a slider  525 . Lubricant pickup occurs when lubricant coated on the surface of the disk  520  collects on the ABS  140 . Once collected on the ABS  140 , the lubricant tends to interfere with the fly-height of the slider  525 , causing the slider  525  to have a tendency to fly at an inconsistent height, which results in degraded magnetic interfacing between the slider  525  and the disk  520 . 
     Another problem with existing slider designs is that, because existing slider designs are constrained by prior-art fabrication processes, they impose limits on the types of features sliders  525  may have. New hard disk drive concepts, such as ultra-thin hard disk drives and heat-assisted magnetic recording (HAMR), need more functionalities from spacing control by ABS and thermal mechanical designs. The features that could provide these functionalities simply cannot be created economically—or, in some cases, at all—using prior-art fabrication techniques. These limitations affect designers&#39; ability to create sliders  525  having more optimal aerodynamic and other properties. 
     A related application, identified above and incorporated by reference herein, discloses novel slider  525  designs that improve upon prior-art designs. These new slider  525  designs have novel ABS features that provide numerous advantages, such as, for example, low vibration during self-servo write and operation, low spacing sensitivity to intermolecular force, balanced head transfer between the reader and writer, fast takeoff from thermal fly-height control (TFC) touchdown, increased robustness to particle and lubrication interference, and low spacing sensitivity to flatness change. Unlike prior-art sliders, these new sliders  525  have at least one ABS function  180  that is a multi-valued function. In other words, there is at least one cross-section  160  taken perpendicular to the plane in which the substantially flat back surface  125  of the slider  525  lies (i.e., the x-y plane with the axes oriented as described for  FIGS. 2A through 2C ; in other words, the cross-section  160  is taken parallel to the z-axis shown in  FIGS. 2A through 2C ) for which the ABS function  180  is a multi-valued function. These novel slider  525  designs include slider features that were previously impossible, impractical, too expensive, or too time-consuming to create. 
       FIG. 4A  illustrates an ABS function  180 C of a slider cross-section  160 C in accordance with some embodiments assuming axes oriented as shown in  FIGS. 2A-2C and 3A-3C . For clarity, the ABS function  180 C is shown in bold. For convenience, the cross-section  160 C has been taken parallel to the x-axis at a particular value along the y-axis and therefore lies in an x-z plane. Thus, the cross-section  160 C illustrates how the ABS function  180 C varies in the direction of the z-axis as a function of the value along the x-axis at a selected value of y. In embodiments in which the leading-edge surface  121  and the trailing-edge surface  122  are substantially parallel, the cross-section  160 C is likewise substantially parallel to the leading-edge surface  121  and the trailing-edge surface  122 . Likewise, in embodiments in which the inner-radius surface  123  and the outer-radius surface  124  are substantially parallel to each other and substantially perpendicular to the leading-edge surface  121  and the trailing-edge surface  122 , the cross-section  160 C is substantially perpendicular to the inner-radius surface  123  and the outer-radius surface  124 . 
     The cross-section  160 C intersects a feature  190 . The feature  190  may be, for example, a rectangular channel or tunnel that extends for some distance in the y-direction of the slider  525 , as illustrated in  FIG. 4B .  FIG. 4B  shows an exemplary embodiment of the feature  190  from the y-z plane assuming that the selected value of y at which the cross-section  160 C of  FIG. 4A  was taken is Y 1 , shown in  FIG. 4B . Alternatively, as another example, the feature  190  may be a recessed area of the slider  525  that extends for some distance along the y-direction of the slider  525 .  FIG. 4C  illustrates an exemplary recessed area viewed in the y-z plane.  FIG. 4C  also shows the value Y 1  at which the cross-section  160 C of  FIG. 4A  was assumed to have been taken. It is to be understood that although  FIG. 4C  illustrates a rectangular opening for the recessed area, the opening may have any arbitrary shape that corresponds to the feature  190  of the ABS function  180 C shown in  FIG. 4A . It is to be appreciated that there are myriad slider characteristics in a y-z plane (e.g., uniform or non-uniform characteristics) that would result in the exemplary feature  190  of  FIG. 4A  in an x-z plane, and the examples shown in  FIGS. 4B and 4C  are not intended to be limiting. 
     Referring again to  FIG. 4A , the exemplary ABS function  180 C is a multi-valued function because there is at least one value of x for which the ABS function  180 C has at least two distinct nonzero values. Specifically, the ABS function  180 C has at least two distinct nonzero values at the locations along the x-axis intersecting the feature  190 . For example, at the value of x corresponding to the location of the line  165 , the ABS function  180 C has three distinct values: Z 2 , Z 3 , and Z 4 . 
     As would be appreciated by a person having ordinary skill in the art, the feature  190  would be impossible, impractical, too expensive, or too time-consuming to create using prior-art fabrication techniques. 
       FIG. 5A  illustrates an ABS function  180 D of a slider cross-section  160 D in accordance with some embodiments. Again, for clarity, the ABS function  180 D is shown in bold. For convenience, the cross-section  160 D has been taken parallel to the x-axis at a particular value along the y-axis and therefore lies in an x-z plane defined by the axes illustrated in  FIGS. 2A-2C and 3A-3C . Therefore, the cross-section  160 D illustrates how the ABS function  180 D varies in the direction of the z-axis as a function of the value along the x-axis at a selected value of y. In embodiments in which the leading-edge surface  121  and the trailing-edge surface  122  are substantially parallel, the cross-section  160 D is likewise substantially parallel to the leading-edge surface  121  and the trailing-edge surface  122 . Likewise, in embodiments in which the inner-radius surface  123  and the outer-radius surface  124  are substantially parallel to each other and substantially perpendicular to the leading-edge surface  121  and the trailing-edge surface  122 , the cross-section  160 D is substantially perpendicular to the inner-radius surface  123  and the outer-radius surface  124 . 
     The cross-section  160 D intersects a feature  192 . The feature  192  may be, for example, a non-rectangular (e.g., semi-circular, cylindrical, irregularly-shaped, etc.) channel or tunnel that extends for some distance along the y-direction of the slider  525 , as illustrated in  FIG. 5B .  FIG. 5B  shows an exemplary embodiment of the feature  192  from a y-z plane assuming that the selected value of y at which the cross-section  160 D of  FIG. 5A  was taken is Y 1 , shown in  FIG. 5B . Alternatively, the feature  192  may be, for example, a recessed area of the slider  525  that extends for some distance along the y-direction of the slider  525 . The recessed area may have any arbitrary shape that creates the feature  192  of the ABS function  180 D shown in  FIG. 5A .  FIG. 5C  illustrates an exemplary recessed area viewed in a y-z plane.  FIG. 5C  also shows the value Y 1  at which the cross-section  160 C of  FIG. 5A  was taken. Although  FIG. 5C  illustrates a slider characteristic having a fairly regular shape, the feature  192  need not be the result of a slider characteristic having a regular shape. The slider characteristic may have any shape that results in the feature  192  shown in  FIG. 5A . It is to be appreciated that there are myriad slider characteristics in a y-z plane that would result in the exemplary feature  192  of  FIG. 5A  in an x-z plane, and the examples shown in  FIGS. 5B and 5C  are not intended to be limiting. 
     Referring again to  FIG. 5A , the exemplary ABS function  180 D is a multi-valued function because there is at least one value of x for which the ABS function  180 D has at least two distinct nonzero values. Specifically, the ABS function  180 D has at least two distinct nonzero values at the locations along the x-axis intersecting the feature  192 . For example, at the value of x corresponding to the location of the line  165 , the ABS function  180 D has three distinct values: Z 4 , Z 5 , and Z 6 . 
     As would be appreciated by a person having ordinary skill in the art, the feature  192  would be impossible, impractical, too expensive, or too time-consuming to create using prior-art fabrication techniques. 
       FIG. 6  illustrates an ABS function  180 E of a slider cross-section  160 E in accordance with some embodiments. Again, for clarity, the ABS function  180 E is shown in bold. For convenience, the cross-section  160 E has been taken parallel to the x-axis at a particular value along the y-axis and therefore lies in an x-z plane defined by the axes illustrated in  FIGS. 2A-2C and 3A-3C . Therefore, the cross-section  160 E illustrates how the ABS function  180 E varies in the direction of the z-axis as a function of the value along the x-axis at a selected value of y. In embodiments in which the leading-edge surface  121  and the trailing-edge surface  122  are substantially parallel, the cross-section  160 E is likewise substantially parallel to the leading-edge surface  121  and the trailing-edge surface  122 . Likewise, in embodiments in which the inner-radius surface  123  and the outer-radius surface  124  are substantially parallel to each other and substantially perpendicular to the leading-edge surface  121  and the trailing-edge surface  122 , the cross-section  160 E is substantially perpendicular to the inner-radius surface  123  and the outer-radius surface  124 . 
     The cross-section  160 E intersects a feature  194 , which is a protrusion in the x-direction of the slider  525 . For example, the feature  194  may be a rail, having a uniform or a non-uniform shape, which extends for some distance in the y-direction of the slider  525 , as shown in  FIG. 6 . Alternatively, the feature  194  may be a bump, a dome, or a protrusion having a non-uniform shape. It is to be appreciated that there are myriad slider characteristics that would result in the exemplary feature  194  of  FIG. 6  in an x-z plane, and the examples provided herein are not intended to be limiting. 
     The exemplary ABS function  180 E is a multi-valued function because there is at least one value of x for which the ABS function  180 E has at least two distinct nonzero values. Specifically, the ABS function  180 E has at least two distinct nonzero values at the locations along the x-axis intersecting the feature  194 . For example, at the value of x corresponding to the location of the line  165 , the ABS function  180 E has three distinct values: Z 1 , Z 7 , and Z 8 . 
     As would be appreciated by a person having ordinary skill in the art, the feature  194  would be impossible, impractical, too expensive, or too time-consuming to create using prior-art fabrication techniques. 
       FIG. 7  illustrates an ABS function  180 F of a slider cross-section  160 F in accordance with some embodiments. Again, for clarity, the ABS function  180 F is shown in bold. Note that the ABS function  180 F is discontinuous. For convenience, the cross-section  160 F has been taken parallel to the x-axis at a particular value along the y-axis and therefore lies in an x-z plane defined by the axes illustrated in  FIGS. 2A-2C and 3A-3C . Therefore, the cross-section  160 F illustrates how the ABS function  180 F varies in the direction of the z-axis as a function of the value along the x-axis at a selected value of y. In embodiments in which the leading-edge surface  121  and the trailing-edge surface  122  are substantially parallel, the cross-section  160 F is likewise substantially parallel to the leading-edge surface  121  and the trailing-edge surface  122 . Likewise, in embodiments in which the inner-radius surface  123  and the outer-radius surface  124  are substantially parallel to each other and substantially perpendicular to the leading-edge surface  121  and the trailing-edge surface  122 , the cross-section  160 F is substantially perpendicular to the inner-radius surface  123  and the outer-radius surface  124 . 
     The cross-section  160 F intersects a feature  196 , which, in the embodiment illustrated in  FIG. 7 , is a cavity or tunnel along the x-direction that extends into the slider  525  in the y-direction. Although  FIG. 7  illustrates a rectangular cavity or tunnel, the feature  196  may have any convenient size and shape. For example, the feature  196  may have a uniform or a non-uniform shape that extends, uniformly or non-uniformly, for some distance parallel to the x- and z-axes of the slider  525  and that extends in some uniform or non-uniform way into the slider  525  in the y-direction (i.e., parallel to the y-axis). As another example, the feature  196  may have a first size and shape at a first value of y (e.g., Y 1 , not shown) and a second size and shape at a second value of y (e.g., Y 2 , not shown). In other words, the feature  196  may have an irregular shape and/or a non-uniform size that may change depending on where the cross-section  160 F is taken. It is to be appreciated that there are myriad slider characteristics that would result in exemplary features (e.g., uniform or non-uniform cavities or tunnels) similar to the feature  196  of  FIG. 7  in an x-z plane, and the examples provided herein are not intended to be limiting. 
     The feature  196  is part of the ABS  140 , and therefore the ABS function  180 F includes the feature  196 , even though the resultant ABS function  180 F is discontinuous (i.e., the portion of the ABS function  180 F corresponding to the feature  196  does not intersect the rest of the ABS function  180 F). The exemplary ABS function  180 F is a multi-valued function because there is at least one value of x for which the ABS function  180 F has at least two distinct nonzero values. For example, the ABS function  180 F has at least two distinct nonzero values at the locations along the x-axis intersecting the feature  196 . For example, at the value of x corresponding to the location of the line  165  shown in  FIG. 7 , the ABS function  180 F has three distinct values: Z 4 , Z 9 , and Z 10 . 
     As would be appreciated by a person having ordinary skill in the art, the feature  196 , and features having characteristics similar to the characteristics of feature  196 , would be impossible, impractical, too expensive, or too time-consuming to create using prior-art fabrication techniques. 
       FIG. 8  illustrates an ABS function  180 G of a slider cross-section  160 G in accordance with some embodiments. Again, for clarity, the ABS function  180 G is shown in bold. For convenience, the cross-section  160 G has been taken parallel to the x-axis at a particular value along the y-axis and therefore lies in an x-z plane defined by the axes illustrated in  FIGS. 2A-2C and 3A-3C . Therefore, the cross-section  160 G illustrates how the ABS function  180 G varies in the direction of the z-axis as a function of the value along the x-axis at a selected value of y. In embodiments in which the leading-edge surface  121  and the trailing-edge surface  122  are substantially parallel, the cross-section  160 G is likewise substantially parallel to the leading-edge surface  121  and the trailing-edge surface  122 . Likewise, in embodiments in which the inner-radius surface  123  and the outer-radius surface  124  are substantially parallel to each other and substantially perpendicular to the leading-edge surface  121  and the trailing-edge surface  122 , the cross-section  160 G is substantially perpendicular to the inner-radius surface  123  and the outer-radius surface  124 . 
     The cross-section  160 G intersects a feature  198 , which, in the embodiment illustrated in  FIG. 8 , manifests as a protrusion in the x- and z-directions. Although  FIG. 8  illustrates a cylindrical protrusion, the feature  198  may have any convenient shape. For example, the feature  198  may have a uniform or a non-uniform shape that extends for some distance parallel to the x-, y-, and z-axes of the slider  525 . It is to be appreciated that there are myriad slider characteristics that would result in features similar to the feature  198  of  FIG. 8  in an x-z plane, and the examples provided herein are not intended to be limiting. 
     The exemplary ABS function  180 G is a multi-valued function because there is at least one value of x for which the ABS function  180 G has at least two distinct nonzero values. For example, the ABS function  180 G has at least two distinct nonzero values at the locations along the x-axis intersecting the feature  198 . For example, at the value of x corresponding to the location of the line  165 , the ABS function  180 G has three distinct values: Z 1 , Z 11 , and Z 12 . 
     As would be appreciated by a person having ordinary skill in the art, the feature  198 , and features having characteristics similar to the characteristics of feature  198 , would be impossible, impractical, too expensive, or too time-consuming to create using prior-art fabrication techniques. 
     The ABS functions  180  corresponding to sliders  525  having the exemplary features  190 ,  192 ,  194 ,  196 , and  198  are all multi-valued functions having, at most, three values of f(x) for at least one value of x. It is also possible for a slider  525  to have an ABS function having more than three values of f(x) for at least one value of x.  FIG. 9  illustrates such an embodiment of an ABS function  180 H having five values for at least one input value. Again, for clarity, the ABS function  180 H is shown in bold. For convenience, the cross-section  160 H has been taken parallel to the x-axis at a particular value along the y-axis and therefore lies in an x-z plane defined by the axes illustrated in  FIGS. 2A-2C and 3A-3C . Therefore, the cross-section  160 H illustrates how the ABS function  180 H varies in the direction of the z-axis as a function of the value along the x-axis at a selected value of y. In embodiments in which the leading-edge surface  121  and the trailing-edge surface  122  are substantially parallel, the cross-section  160 H is likewise substantially parallel to the leading-edge surface  121  and the trailing-edge surface  122 . Likewise, in embodiments in which the inner-radius surface  123  and the outer-radius surface  124  are substantially parallel to each other and substantially perpendicular to the leading-edge surface  121  and the trailing-edge surface  122 , the cross-section  160 H is substantially perpendicular to the inner-radius surface  123  and the outer-radius surface  124 . 
     The cross-section  160 H intersects a feature  191 , which, in the exemplary embodiment illustrated in  FIG. 9 , results from two “shelves” extending in the x- and y-directions from a vertical surface (i.e., in the z-direction) of the slider  525 . It is to be appreciated that there are myriad slider characteristics that would result in the exemplary feature  191  of  FIG. 9  in an x-z plane, and the examples provided herein are not intended to be limiting. 
     The exemplary ABS function  180 H is a multi-valued function because there is at least one value of x for which the ABS function  180 H has at least two distinct nonzero values. For example, the ABS function  180 H has at least two distinct nonzero values at the locations along the x-axis intersecting the feature  191 . For example, at the value of x corresponding to the location of the line  165 , the ABS function  180 H has five distinct values: Z 1 , Z 11 , Z 12 , Z 13 , and Z 14 . 
     It is to be understood that the ABS function  180  may also have more than five distinct values. The examples of features and the ABS functions  180  corresponding to those features presented herein are not intended to be limiting. 
     It is also to be understood that the ABS function  180  may have exactly two distinct values for certain input values along the selected axis in the x-y plane. As just one example, the slider  525  may have “wings” or “winglets” protruding from the inner-radius surface  123  and/or outer-radius surface  124 . Such features could result in a slider  525  having enhanced or different aerodynamic properties than, for example, a slider  525  that has a more cuboid overall shape.  FIG. 10  illustrates an ABS function  180 J of a slider cross-section  160 J in accordance with some embodiments. Again, for clarity, the ABS function  180 J is shown in bold. For convenience, the cross-section  160 J has been taken parallel to the x-axis at a particular value along the y-axis and therefore lies in an x-z plane defined by the axes illustrated in  FIGS. 2A-2C and 3A-3C . Therefore, the cross-section  160 J illustrates how the ABS function  180 J varies in the direction of the z-axis as a function of the value along the x-axis at a selected value of y. In embodiments in which the leading-edge surface  121  and the trailing-edge surface  122  are substantially parallel, the cross-section  160 J is likewise substantially parallel to the leading-edge surface  121  and the trailing-edge surface  122 . Likewise, in embodiments in which the inner-radius surface  123  and the outer-radius surface  124  are substantially parallel to each other and substantially perpendicular to the leading-edge surface  121  and the trailing-edge surface  122 , the cross-section  160 J is substantially perpendicular to the inner-radius surface  123  and the outer-radius surface  124 . 
     The cross-section  160 J intersects a feature  199 , which, in the embodiment illustrated in  FIG. 10 , is a wing-shaped protrusion in the x-direction from the inner-radius surface  123 . It is to be understood that a similar-shaped protrusion could also extend from the outer-radius surface  124 . Although  FIG. 10  illustrates a wing-shaped protrusion, the feature  199  may have any convenient shape. For example, the feature  199  may have a uniform or a non-uniform shape that extends for some distance parallel to the x-axis and y-axis of the slider  525 . It is to be appreciated that there are myriad slider characteristics that would result in features similar to the feature  199  of  FIG. 10  in an x-z plane, and the examples provided herein are not intended to be limiting. 
     The exemplary ABS function  180 J is a multi-valued function because there is at least one value of x for which the ABS function  180 J has at least two distinct nonzero values. For example, the ABS function  180 J has at least two distinct nonzero values at the locations along the x-axis intersecting the feature  199 . For example, at the value of x corresponding to the location of the line  165 , the ABS function  180 J has exactly two distinct values: Z 11  and Z 12 . At some other locations along the x-axis intersecting the feature  199 , the ABS function  180 J has exactly three distinct values, namely Z 1 , Z 11 , and Z 12 . 
     As would be appreciated by a person having ordinary skill in the art, regardless of the shapes and characteristics of the features  190 ,  191 ,  192 ,  194 ,  196 ,  198 , and  199 , these features would be impossible, impractical, too expensive, or too time-consuming to create using prior-art fabrication techniques. The features  190 ,  191 ,  192 ,  194 ,  196 ,  198 , and  199 , and myriad other features, may be created, however, using the novel methods of fabricating sliders  525  having extended three-dimensional (E3D) air-bearing surfaces as disclosed herein. The E3D ABS surfaces can include, for example, the exemplary slider features described above. The methods enable the fabrication of an E3D ABS design by combining, in some embodiments, lapping, additive manufacturing, and ion mill etching. 
       FIG. 11  illustrates an exemplary slider  525 C having features  200 A through  200 F in accordance with some embodiments. As shown in  FIG. 11 , each of the features  200 A through  200 F is illustrated as a cavity or tunnel similar to the feature  196  shown in  FIG. 7 . It is to be appreciated, however, that the features  200 A through  200 F may have nonrectangular and/or non-uniform shapes (e.g., arbitrary shapes), and they may be protrusions or cavities, such as shown and discussed in the context of the examples provided in  FIGS. 4 through 10 . As will be understood by a person having ordinary skill in the art in view of the disclosures herein, there are myriad possible size, shapes, and characteristics of features  200 A through  200 F. The examples provided herein are not intended to be limiting. 
     One can verify by inspection that the slider  525 C of  FIG. 11  includes multiple cross-sections  160  that have ABS functions  180  that are multi-valued functions. For example, there are multiple cross-sections  160  of the slider  525 C of  FIG. 11  that, when taken perpendicular to the x-y plane defined by the substantially flat back surface  125  (not shown), will result in an ABS function  180  that is a multi-valued function. The lines  205 ,  210 ,  215 ,  220 , and  225  identify several exemplary locations at which a cross-section  160  made perpendicular to the plane of the back surface  125  (i.e., perpendicular to the x-y plane and parallel to the z-axis shown) will result in an ABS function  180  that is a multi-valued function. The lines  205 ,  210 ,  215 ,  220 , and  225  are shown having arbitrary orientations in the x-y plane. Therefore, the lines  205 ,  210 ,  215 ,  220 , and  225  also have arbitrary orientations with respect to the leading-edge surface  121 , trailing-edge surface  122 , inner-radius surface  123 , and outer-radius surface  124  (not shown in  FIG. 11 ; refer to  FIGS. 3A-3C ). Of course, a cross-section  160  may be parallel or perpendicular to the leading-edge surface  121 , trailing-edge surface  122 , inner-radius surface  123 , or outer-radius surface  124 , and such cross-section  160  may also have an ABS function  180  that is a multi-valued function. 
       FIG. 12  is a flowchart illustrating a process  300 , in accordance with some embodiments, to manufacture sliders  525  having ABS functions  180  that are multi-valued functions. At  305 , the process begins. At  310 , an area of the wafer  120  where a feature (e.g., one of features  190 ,  191 ,  192 ,  194 ,  196 ,  198 , or  199 , or any other feature that would be impossible, impractical, too expensive, or too time-consuming to create using prior-art fabrication techniques) is to be created is prepared. In some embodiments, the area of the wafer  120  where the feature is to be created is prepared by removing a first portion of material from the wafer  120 , the first portion of material comprising part of the substrate. 
     Step  310  may be accomplished using conventional techniques. For example, lapping may be used to remove a desired amount of material from the wafer  120 . In some embodiments, the resulting cavity in the wafer  120  is 3-5 microns deep. 
       FIGS. 13A and 13B  illustrate step  310  of the process  300  in accordance with some embodiments.  FIG. 13A  is a substrate side view of a cross-section  160 K of a wafer  120  that is in fabrication to become a slider  525 . The cross-section  160 K is in the y-z plane, assuming that the x-, y-, and z-axes are as oriented in  FIGS. 2A-2C and 3A-3C . The wafer  120  includes a substrate  350  that initially has a uniform height  302  in the z-direction. An overcoat  355  has been applied to the substrate  350  at what will eventually be the trailing edge surface  122  of the slider  525 . 
       FIG. 13B  is a substrate side view of the cross-section  160 K of the wafer  120  after the wafer  120  has been processed in step  310 . As illustrated in the exemplary embodiment of  FIG. 13B , material has been removed from the substrate  350  to prepare the wafer  120  for step  315  of the process  300 . 
     Referring again to  FIG. 12 , in step  315 , an additive manufacturing technique is used to create a three-dimensional (3D) object within the prepared region of the wafer  120 . Many additive manufacturing techniques exist. They include, for example, three-dimensional (3D) printing, whereby a 3D printer controlled by a processor executing machine-executable instructions produces, by successively laying down thin layers of material, a physical 3D object from digital blueprints. In some embodiments, the machine-executable instructions are stored as a stereolithography (STL) file, which is a triangulated representation of a 3D surface geometry (e.g., a computer-aided design (CAD) model). The 3D objects created using 3D printing technologies may have myriad shapes and geometries, including the shapes and geometries of the exemplary slider  525  features described above. 
     In some embodiments, the additive manufacturing technique is stereo lithography, in which a perforated platform is positioned just below the surface of a vat of liquid photo-curable polymer. When an ultraviolet laser traces the first slice of an object on the surface of the liquid polymer, a thin layer of the polymer hardens. The perforated platform is then lowered slightly, and the laser traces out and hardens the next slice. The procedure is repeated until the complete object has been created, at which time the object is removed from the vat of liquid, drained of excess liquid, and cured. 
     In some embodiments, the additive manufacturing technique is fused deposition modeling, in which a hot thermoplastic is extruded from a temperature-controlled print head to produce an object. 
     In some embodiments, the additive manufacturing technique is selective laser sintering (SLS), in which an object is built using a laser to selectively fuse together successive layers of material, such as, for example, powdered wax, ceramic, metal, nylon, or another suitable material. 
     In some embodiments, the additive manufacturing technique is multi jet modeling (MJM), in which an object is built from successive layers of powder using an inkjet-like print head that sprays on a binder solution that glues only the required granules together. 
     It is to be appreciated that other additive manufacturing processes may be used to create E3D slider ABS features, and the examples provided herein are not intended to be limiting. 
       FIGS. 13C through 13E  illustrate the exemplary cross-section  160 K during step  315  of the process  300 . In  FIG. 13C , material  360  has been deposited using an additive manufacturing technique in the area from which material was removed from the substrate  350  in step  310 . The material  360  may be the same as, similar to, or different from the material from which the substrate  350  is made. In some embodiments, the material  360  has properties that facilitate a strong bond between the material  360  and the substrate  350 . 
     In  FIG. 13D , additional material  360  has been deposited using additive manufacturing. As illustrated by the exemplary embodiment of  FIG. 13D , the use of additive manufacturing enables the creation of non-uniform shapes. It is to be understood that the shape illustrated in  FIG. 13D  is merely exemplary and is not meant to be limiting. 
     In  FIG. 13E , yet more material  360  has been deposited using additive manufacturing to complete step  315  of the process  300 . As illustrated in  FIG. 13E , there is a cavity in the material  360  after the completion of the additive manufacturing step  315 . As will be appreciated by those having ordinary skill in the art, creating a cavity in a slider, such as the one illustrated in  FIG. 13E , would not be possible using conventional slider fabrication techniques. The use of additive manufacturing enables the creation of slider features in various shapes and sizes that could not be created economically—or at all—using conventional slider fabrication techniques. The feature illustrated in  FIG. 13E  has an arbitrary size and shape. It is to be understood that the use of additive manufacturing techniques enables the creation of a wide variety of shapes in a wide variety of sizes, including the exemplary features  190 ,  191 ,  192 ,  194 ,  196 ,  198 , and  199 . The examples shown herein of the features that may be created using additive manufacturing techniques are not intended to be limiting in any way. 
     Although step  315  of the process  300  is illustrated in  FIGS. 13C through 13E  as being accomplished in three steps, it is to be appreciated that the number of additive manufacturing steps required to complete step  315  of process  300  may be more or fewer than three. Furthermore, the number of additive manufacturing steps may depend, for example, on the type of additive manufacturing used and how one defines an “additive manufacturing step.” If one considers the creation of a single layer to be one additive manufacturing step, then the number of manufacturing steps required to complete step  315  of the process  300  may be very large. 
     Referring again to  FIG. 12 , in step  320 , the wafer  120  is processed to finish the slider  525 . In some embodiments, the processing in step  320  uses conventional techniques, such as ion milling and/or lapping. In some embodiments, step  320  includes adding a read/write head  540  to the slider. 
       FIGS. 13F through 13I  illustrate step  320  of the process  300  in accordance with some embodiments.  FIG. 13F  illustrates the cross-section  160 K of the exemplary slider  525  after a first ion milling step. As shown in  FIG. 13F , material has been removed both from the substrate  350  and from the material  360 . Thus, a portion of the created feature has been removed.  FIG. 13G  illustrates the cross-section  160 K of the exemplary slider  525  after a second ion milling step, and  FIG. 13H  illustrates the cross-section  160 K of the exemplary slider  525  after a third ion milling step. 
       FIG. 13I  illustrates the cross-section  160 K of the slider  525  after a coating has been deposited and the slider  525  has been finished. In some embodiments, the slider  525  is finished by an additional lapping step. It is to be understood that step  320  may be accomplished using more or fewer steps than shown herein. Moreover, conventional techniques other than or in addition to those disclosed herein may be used. 
       FIG. 13J  illustrates the ABS function  180 K of the slider cross-section  160 K illustrated in the embodiment of  FIG. 13I . The ABS function  180 K is a multi-valued function because there is at least one value of y for which the ABS function  180 K has at least two distinct nonzero values. For example, the ABS function  180 K has at least two distinct nonzero values of z at the locations along the y-axis intersecting the feature created by the material  360 . For example, at the value of y corresponding to the location of the line  175 , the ABS function  180 K has three distinct values. 
     Returning to  FIG. 12 , at  325 , the process ends. 
       FIGS. 14A through 14H  illustrate the use of the exemplary process  300  shown in  FIG. 12  to create another exemplary slider.  FIGS. 14A and 14B  illustrate step  310  of the process  300  in accordance with some embodiments.  FIG. 14A  is a substrate side view of a cross-section  160 L of a wafer  120  that is in fabrication to become a slider  525 . Like the cross-section  160 K of  FIG. 13A , the cross-section  160 L is in the y-z plane, assuming that the x-, y-, and z-axes are as oriented in  FIGS. 2A-2C and 3A-3C . The wafer  120  includes a substrate  350  that initially has a uniform height  302  in the z-direction. An overcoat  355  has been applied to the substrate  350  at what will eventually be the trailing edge surface  122  of the slider  525 . 
       FIG. 14B  is a substrate side view of the cross-section  160 L of the wafer  120  after the wafer  120  has been processed in step  310 . As illustrated in the exemplary embodiment of  FIG. 14B , material has been removed from the substrate  350  to prepare the wafer  120  for step  315  of the process  300 . 
       FIGS. 14C through 14E  illustrate the exemplary cross-section  160 L during step  315  of the process  300 . In  FIG. 14C , material  360  has been deposited using an additive manufacturing technique in the area from which material was removed from the substrate  350  in step  310 . As explained previously, the material  360  may be the same as, similar to, or different from the material from which the substrate  350  is made. In some embodiments, the material  360  has properties that facilitate a strong bond between the material  360  and the substrate  350 . 
     In  FIGS. 14D and 14E , additional material  360  has been deposited using additive manufacturing to complete step  315  of the process  300 . As illustrated in  FIG. 14E , there is a cavity in the material  360  after the completion of the additive manufacturing step  315 . As will be appreciated by those having ordinary skill in the art, creating a cavity in a slider, such as the one illustrated in  FIG. 14E , would not be possible using conventional slider fabrication techniques. The use of additive manufacturing enables the creation of slider features in various shapes and sizes that could not be created economically—or at all—using conventional slider fabrication techniques. It is to be understood that the shape of the cavity illustrated in  FIG. 14E  is merely exemplary and is not meant to be limiting. 
       FIGS. 14F through 14H  illustrate step  320  of the process  300  in accordance with some embodiments.  FIG. 14F  illustrates the cross-section  160 L of the exemplary slider  525  after a first ion milling step. As shown in  FIG. 14F , material has been removed both from the substrate  350  and from the material  360 . Thus, a part of the feature created using the additive manufacturing technique has been removed.  FIG. 14G  illustrates the cross-section  160 L of the exemplary slider  525  after a second ion milling step. 
       FIG. 14H  illustrates the cross-section  160 L of the slider  525  after a coating has been deposited and the slider  525  has been finished. In some embodiments, the slider  525  is finished by adding a read/write head  540  to the slider and/or by performing an additional lapping step. It is to be understood that step  320  may be accomplished using more or fewer steps than shown herein. Moreover, conventional techniques other than or in addition to those disclosed herein may be used. 
       FIG. 14I  illustrates the ABS function  180 L of the slider cross-section  160 L illustrated in the embodiment of  FIG. 14H . The ABS function  180 L is a multi-valued function because there is at least one value of y for which the ABS function  180 L has at least two distinct nonzero values. For example, the ABS function  180 L has at least two distinct nonzero values of z at the locations along the y-axis intersecting the feature created using the material  360 . For example, at the value of y corresponding to the location of the line  175 , the ABS function  180 L has three distinct values. 
     Referring back to  FIG. 11 , each of the exemplary features  200 A through  200 F may be a cavity as shown in the ABS function  180 L of  FIGS. 14H and 14I , and each may be created using the fabrication process  300 . 
     It is to be appreciated in view of the disclosures herein that it is possible to fabricate an entire slider using only additive manufacturing techniques. In other words, in reference to  FIG. 12 , the steps  310  and  320  may be eliminated, and the entire slider may be fabricated using only an additive manufacturing technique as indicated by step  315 . 
     In the foregoing description and in the accompanying drawings, specific terminology has been set forth to provide a thorough understanding of the disclosed embodiments. In some instances, the terminology or drawings may imply specific details that are not required to practice the invention. 
     To avoid obscuring the present disclosure unnecessarily, well-known components (e.g., of a disk drive) are shown in block diagram form and/or are not discussed in detail or, in some cases, at all. 
     Unless otherwise specifically defined herein, all terms are to be given their broadest possible interpretation, including meanings implied from the specification and drawings and meanings understood by those skilled in the art and/or as defined in dictionaries, treatises, etc. As set forth explicitly herein, some terms may not comport with their ordinary or customary meanings. 
     As used in the specification and the appended claims, the singular forms “a,” “an” and “the” do not exclude plural referents unless otherwise specified. The word “or” is to be interpreted as inclusive unless otherwise specified. Thus, the phrase “A or B” is to be interpreted as meaning all of the following: “both A and B,” “A but not B,” and “B but not A.” Any use of “and/or” herein does not mean that the word “or” alone connotes exclusivity. 
     To the extent that the terms “include(s),” “having,” “has,” “with,” and variants thereof are used in the detailed description or the claims, such terms are intended to be inclusive in a manner similar to the term “comprising,” i.e., meaning “including but not limited to.” The terms “exemplary” and “embodiment” are used to express examples, not preferences or requirements. 
     The terms “over,” “under,” “between,” and “on” are used herein refer to a relative position of one feature with respect to other features. For example, one feature disposed “over” or “under” another feature may be directly in contact with the other feature or may have intervening material. Moreover, one feature disposed “between” two features may be directly in contact with the two features or may have one or more intervening features or materials. In contrast, a first feature “on” a second feature is in contact with that second feature. 
     The drawings are not necessarily to scale, and the dimensions, shapes, and sizes of the features may differ substantially from how they are depicted in the drawings. Furthermore, the use, labeling, and orientation of the x-, y-, and z-axes are for convenience and to facilitate the explanations provided herein. 
     Moreover, although the exemplary wafers  120  and sliders  525  have cuboid shapes, other wafer  120  and slider  525  shapes may be used without departing from the spirit and scope of this disclosure. 
     Although specific embodiments have been disclosed, it will be evident that various modifications and changes may be made thereto without departing from the broader spirit and scope of the disclosure. For example, features or aspects of any of the embodiments may be applied, at least where practicable, in combination with any other of the embodiments or in place of counterpart features or aspects thereof. Accordingly, the specification and drawings are to be regarded in an illustrative rather than a restrictive sense.