TRAPEZOIDAL BACK BIAS AND TRILAYER READER GEOMETRY TO ENHANCE DEVICE PERFORMANCE

Abstract

A magnetoresistive sensor having a trilayer sensor stack with two ferromagnetic freelayers separated by a nonmagnetic spacer layer is disclosed. The sensor is biased with a back biasing magnet adjacent a back of the trilayer sensor. The back biasing magnet, the trilayer sensor stack, or both have substantially trapezoidal shapes to enhance the biasing field and to minimize noise. In some embodiments, the trilayer sensor or back bias magnet have a shape designed to stabilize a micromagnetic “C” shape or concentrate magnetic flux in the trilayer sensor stack.

Description

BACKGROUND

In a magnetic data storage and retrieval system, a magnetic recording head typically includes a reader portion having a magnetoresistive (MR) sensor for retrieving magnetically encoded information stored on a magnetic disc. Magnetic flux from the surface of the disc causes rotation of the magnetization vector of a sensing layer or layers of the MR sensor, which in turn causes a change in electrical resistivity of the MR sensor. The sensing layers are often called “free” layers, since the magnetization vectors of the sensing layers are free to rotate in response to external magnetic flux. The change in resistivity of the MR sensor can be detected by passing a current through the MR sensor and measuring a voltage across the MR sensor. External circuitry then converts the voltage information into an appropriate format and manipulates that information as necessary to recover the information encoded on the disc.

MR sensors have been developed that can be characterized in three general categories: (1) anisotropic magnetoresistive (AMR) sensors, (2) giant magnetoresistive (GMR) sensors, including spin valve sensors and multilayer GMR sensors, and (3) tunneling giant magnetoresistive (TGMR) sensors.

Tunneling GMR (TGMR) sensors have a series of alternating magnetic and non-magnetic layers similar to GMR sensors, except that the magnetic layers of the sensor are separated by an insulating film thin enough to allow electron tunneling between the magnetic layers. The resistance of the TGMR sensor depends on the relative orientations of the magnetization of the magnetic layers, exhibiting a minimum for a configuration in which the magnetizations of the magnetic layers are parallel and a maximum for a configuration in which the magnetizations of the magnetic layers are anti-parallel.

For all types of MR sensors, magnetization rotation occurs in response to magnetic flux from the disc. As the recording density of magnetic discs continues to increase, the width of the tracks as well as the bits on the disc must decrease. This necessitates increasingly smaller MR sensors as well as narrower shield-to-shield spacings. As MR sensors become smaller in size, particularly for sensors with dimensions less than about 0.1 micrometers (μm), the sensors have the potential to exhibit an undesirable magnetic response to applied fields from the magnetic disc. MR sensors must be designed in such a manner that even small sensors are free from magnetic noise and provide a signal with adequate amplitude for accurate recovery of the data written on the disc.

GMR and TGMR readers can use the resistance between the freelayer and a reference layer to detect media stray fields so as to read back stored information. Magnetization of the reference layer is fixed through an antiferromagnetic coupling interaction by a ferromagnetic pinned layer which is again pinned by antiferromagnetic (AFM) material. The reference and the pinned layer, together with the antiferromagnetic coupling layer between them, are the so-called synthetic antiferromagnetic (SAF) structure. This kind of configuration has two major disadvantages. The first one is high shield-to-shield spacing due to the complicated multi-layer structure. The continued reduction of the shield-to-shield spacing requirement is limited by the emerging instability of individual layers in the sensor as they become thinner. For example, the pinning strength of the AFM materials decreases with a reduction in their thickness. As a consequence, weakly pinned SAF structures lead to an increase of sensor noise when the reference layer is not satisfactorily pinned. The second disadvantage of traditional GMR and TGMR sensors is their low sensitivity because the freelayer is the only response layer. Reducing the free layer thickness correspondingly reduces the sensitivity.

Trilayer readers with dual free-layers are one solution to address these issues. In a trilayer structure, two free-layers with easy axes of magnetization in a scissor orientation are used to detect media magnetic flux. Synthetic antiferromagnetic (SAF) and antiferromagnetic (AFM) layers are not needed and free layer biasing comes from the combination of backend permanent magnet and demagnetization fields when both freelayers have ends at the air bearing surface. However, the biasing field from the back end magnet decays rapidly away from the magnet. The freelayer portion of the trilayer sensor in the vicinity of the air bearing surface (ABS) suffers from insufficient bias and the magnetization scissor angle is open too much.

SUMMARY

A magnetoresistive sensor includes a trilayer sensor stack comprising two ferromagnetic freelayers separated by a nonmagnetic spacer layer with a front width proximate an ABS, and a back width distal from an ABS and a back biasing magnet with a trapezoidal shape with a front width and a back width. The front width of the biasing magnet is adjacent the back width of the trilayer sensor stack and is about the same as the back width of the sensor stack. The back width of the biasing magnet is larger than the front width. The trilayer sensor stack can have a rectangular shape or a trapezoidal shape wherein the back width is larger than the front width. The trapezoidal shape concentrates the magnetic field at the front of the biasing magnet in the vicinity of the sensor stack. The trapezoidal shape also encourages “C” type micromagnetic magnetization patterns in the trilayer sensor stack, minimizing signal noise due to “C” to “S” switching during sensor operation.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a schematic diagram showing micromagnetic magnetization patterns in a rectangular sample.

FIG. 1B is a schematic diagram showing a “C” type micromagnetic magnetization pattern in the sample of FIG. 1A.

FIG. 1C is a schematic diagram showing an “S” type micromagnetic magnetization pattern in the sample of FIG. 1A.

FIG. 1D is a schematic showing a “C” type micromagnetic magnetization pattern in a trapezoidal sample.

FIG. 2 is a top view of a first example of a read head in accord with the present invention.

FIG. 3 is an ABS view of the read head in FIG. 2 in accord with the present invention.

FIG. 4A is a schematic top view of the trilayer sensor in FIG. 2 showing biasing in the absence of external bit flux.

FIG. 4B is a schematic top view of the trilayer sensor in FIG. 4A under the influence of a first state of data.

FIG. 4C is a schematic top view of the trilayer sensor in FIG. 4A under the influence of a second state of data.

FIG. 5 is a top view of a second example of a read head in accord with the present invention.

FIG. 6 is an ABS view of the read head in FIG. 5 in accord with the present invention.

FIG. 7A is a schematic top view of the trilayer sensor in FIG. 5 showing biasing in the absence of external bit flux.

FIG. 7B is a schematic top view of the trilayer sensor in FIG. 7A under the influence of a first state of data.

FIG. 7C is a schematic top view of the trilayer sensor in FIG. 7A under the influence of a second state of data.

FIGS. 8A-8K illustrate the fabrication steps to produce the read head illustrated in FIGS. 2 and 3.

FIGS. 9A-9K illustrate the fabrication steps to produce the read head illustrated in FIGS. 5 and 6.

DETAILED DESCRIPTION

The inventive shapes disclosed herein increase the performance of a reader by increasing the bias field at the front of a back bias magnet and by decreasing signal noise. The origin of these effects is shown in FIGS. 1A-1C. FIG. 1A illustrates possible micromagnetic magnetization patterns in a rectangular magnetic sample under a magnetization oriented generally from the left to right. Magnetization vectors 12′ and 14′ originate at the corners of the sample and are directed to the center where they converge at magnetization vector 10′. Magnetization vector 10′ diverges into vectors 16′ and 18′ as it approaches the right side of the sample. FIG. 1 shows all possible micromagnetic magnetization patterns. Two patterns are energetically favored. FIG. 1B illustrates a “C” pattern comprised of vectors 12′, 10′ and 16′. An alternative “C” pattern comprises vectors 14′, 10′ and 18′. FIG. 1C illustrates an “S” pattern comprised of vectors 12′, 10′ and 18′ or alternatively vectors 14′, 10′ and 16′. The energy difference between the “C” state and the “S” state is very small and during magnetic switching, thermally activated transitions between both patterns contribute to measurable sensor noise.

By changing the geometry of a magnetic element, one or the other of the “C” and “S” states can be energetically favored. FIG. 1D illustrates how the “C” state can be favored by a trapezoidal shape of the micromagnetic element. This shape will be used in what follows to tailor magnetization in the back bias permanent magnet of a trilayer reader as well as in the freelayers of the reader itself. Although trapezoidal geometries are discussed herein to favor “C” shape micromagnetic magnetization patterns, it should be noted that other geometries such as half moon shapes can be used to obtain similar beneficial results.

FIGS. 2 and 3 illustrate one aspect of the trilayer reader of the present invention. FIG. 2 is a top view of trilayer read head 10, and FIG. 3 is an ABS view of read head 10. Read head 10 comprises rectangular trilayer reader stack 20 (comprising ferromagnetic freelayers 22 and 24 and spacer layer 26) in front of trapezoidal back bias magnet 30. Magnetic side shields 40 and 42 abut both sides of bias magnet 30 and trilayer reader stack 20. Trilayer reader stack 20, bias magnet 30, and side shields 40 and 42 are separated from each other by insulating layer 50. Side shields 40 and 42 may also be replaced by an insulator preferably an oxide of aluminum.

The ABS view of trilayer read head 10 in FIG. 3 shows top shield 60, bottom shield 70 and side shields 40 and 42 adjacent trilayer reader stack 20 and insulator layer 50. Ferromagnetic freelayers 22 and 24 of trilayer reader stack 20 are separated by spacer layer 26. If spacer layer 26 is a nonmagnetic electrical conductor, read head 10 is a GMR head. If spacer layer 26 is a nonmagnetic electrical insulator, read head 10 is a TGMR head. Read head 10 can be a current perpendicular to plane (CPP) head wherein electrical contact is made to trilayer reader stack 20 through top shield 60 and bottom shield 70.

If spacer layer 26 is nonmagnetic, and electrically conducting, it may be fabricated from, for example, copper. If spacer layer 26 is nonconducting, it may be fabricated from, for example, aluminum oxide (Al₂O₃ or Al_xO where x may or may not be an integer) or magnesium oxide. Ferromagnetic layers 22 and 24 may be fabricated from magnetic material such as, for example, nickel-iron-cobalt (Ni—Fe—Co) compositions. The shield layers may be fabricated from, for example, a soft magnetic material such as nickel-iron (Ni—Fe). Back bias magnet 30 may be fabricated from a permanent magnet material such as, for example, a cobalt-platinum (Co—Pt) alloy.

The operation of read head 10, according to one aspect of the invention is described in conjunction with FIGS. 4A-4C. FIGS. 4A, 4B and 4C show top views of read head 10 with magnetization vector 30′ of back bias layer 30 oriented with respect to magnetization vectors 22′ and 24′ of freelayers 22 and 24 to achieve optimum response of freelayers 22 and 24 to external magnetic fields. In the absence of back bias magnetization, freelayer magnetization vectors 22′ and 24′ would be antiparallel and commonly parallel to the ABS. Under the bias of magnetization vector 30′, they arrange in a scissor orientation for optimum sensitivity. One benefit of the trapezoidal shape of back bias magnet 30 is that the smaller base near the back of trilayer reader stack 20 results in magnetic flux concentration in that region resulting in deeper penetration of the biasing field into reader stack 20 in the direction of the ABS.

FIGS. 4A-4C illustrate the effect of varying bit magnetization on recorded media on the magnetization directions 22′ and 24′ of first freelayer 22 and second freelayer 24 respectively. FIG. 4A shows trilayer reader stack 10 in a quiescent magnetic state when it is not under the influence of magnetic flux emanating from recording media. The angle of magnetization between first ferromagnetic freelayer 22 and second ferromagnetic freelayer 24 at the ABS is in a scissors relation for optimum sensor response. FIG. 4B is a top view of read head 10 showing trilayer reader stack 20 under the influence of a first state of data D1 corresponding to a positive bit. This first state of data causes the angle of magnetization between first freelayer 22 and second freelayer 24 to increase at the ABS. When this occurs, the resistance across trilayer reader stack 20 changes and is detected when a sense current is passed through trilayer reader stack 20. FIG. 4C is a top view of read head 10 showing trilayer reader stack 20 under the influence of a second state of data D2 corresponding to a negative bit. This second state of data causes the angle of magnetization between first freelayer 22 and second freelayer 24 to decrease at the ABS. As with the first state of data, the second state of data causes a change in resistance across trilayer reader stack 20 and is detected when a sense current is passed through trilayer reader stack 20.

FIGS. 5 and 6 illustrate another aspect of the invention. FIG. 5 is a top view of trilayer reader head 110, and FIG. 6 is an ABS view of read head 110. Read head 110 comprises trapezoidal trilayer reader stack 120 comprising ferromagnetic freelayers 122 and 124 and spacer layer 126 in front of trapezoidal back bias magnet 130. Magnetic side shields 140 and 142 are adjacent both sides of back bias magnet 130 and freelayer stack 120. Trilayer reader stack 120, back bias magnet 130, and side shields 140 and 142 are separated from each other by insulating layer 150. Side shields 140 and 142 may also be replaced by an insulator, preferably an oxide of aluminum. In this aspect of the invention, trilayer reader stack 120 has a trapezoidal shape. A benefit of the trapezoidal shape is that a “C” pattern of micromagnetic magnetization in reader stack 120 is preferred. The ABS view of trilayer read head 110 in FIG. 6 shows top shield 160, bottom shield 170 and side shields 140 and 142 adjacent trilayer reader stack 120 and insulator layer 150. Ferromagnetic freelayers 122 and 124 of trilayer reader stack 120 are separated by spacer layer 126. If spacer layer 126 is nonmagnetic, read head 110 is a GMR head. If spacer layer 126 is an insulator, read head 110 is a TGMR head. Read head 110 can be a current perpendicular to plane (CPP) head wherein electrical contact is made to trilayer reader stack 120 through top shield 160 and bottom shield 170.

If spacer layer 126 is nonmagnetic and electrically conducting, it may be fabricated from, for example, copper. If spacer layer 126 is nonconducting, it may be fabricated from, for example, aluminum oxide (Al₂O₃ or Al_xO where x may be not be an integer) or magnesium oxide. Ferromagnetic layers 122 and 124 may be fabricated from magnetic materials, such as, for example, nickel-iron-cobalt (Ni—Fe—Co) compositions. The shield layers may be fabricated from, for example, a soft magnetic material such as nickel-iron (Ni—Fe). Back bias magnet 130 may be fabricated from a permanent magnet material such as, for example, a cobalt-platinum (Co—Pt) alloy.

The operation of read head 110 according to one aspect of the invention is described in conjunction with FIGS. 7A-7C. FIGS. 7A, 7B and 7C show top views of read head 110 with magnetization vector 130′ of back bias layer 130 oriented with respect to magnetization vectors 122′ and 124′ of freelayers 122 and 124 to achieve optimum response of freelayers 122 and 124 to external magnetic fields. In the absence of back bias magnetization 130′, freelayer magnetization vectors 122′ and 124′ would be antiparallel and parallel to ABS 160. Under the back bias of magnetization 130′, they arrange in a scissor orientation for optimum sensitivity. A benefit of the trapezoidal shape of back bias magnet 130 is that the smaller base at trilayer reader stack 120 results in magnetic flux concentration in that region resulting in deeper penetration of the biasing field into reader stack 120 in the direction of the ABS.

FIGS. 7A-7C illustrate the effect of varying bit magnetizations on recorded media on the magnetization directions 122′ and 124′ of first freelayer 122 and second freelayer 124 respectively. FIG. 7A shows trilayer reader stack 120 in a quiescent magnetic state when it is not under the influence of magnetic flux emanating from recording media. The angle of magnetization between first ferromagnetic freelayer 122 and second ferromagnetic freelayer 124 at the ABS is in a scissors relation for optimum sensor response. FIG. 7B is a front view of read head 110 showing trilayer reader stack 120 under the influence of a first state of data D1 corresponding to a positive bit. This first state of data causes the angle of magnetization between first freelayer 122′ and second freelayer 124′ to increase at the ABS. When this occurs, the resistance across trilayer reader stack 120 changes and is detected when a sense current is passed through trilayer reader stack 120. FIG. 7C is a top view of read head 110 showing trilayer reader stack 120 under the influence of a second state of data D2 corresponding to a negative bit. This second state of data causes the angle of magnetization between first freelayer 122′ and second freelayer 124′ to decrease at the ABS. As with the first state of data, the second state of data causes a change in resistance across trilayer reader stack 120 and is detected when a sense current is passed through trilayer reader stack 120.

The operation of read head 110 is similar to that discussed for read head 10 and schematically illustrated in FIG. 4A-4C, with one exception. The trapezoidal shape of trilayer reader stack 120 encourages a “C” type of micromagnetic magnetization in freelayers 124 and 126. This forces the magnetization vectors into orientations parallel to the ABS and discourages the formation of “S” type micromagnetic magnetization patterns in the freelayers, thereby minimizing noise resulting from “C” type to “S” type switching behavior during operation.

The formation of reader 10 with trapezoidal back bias magnet 30 shown in FIGS. 2 and 3 is schematically illustrated in FIGS. 8A-8K. FIG. 8A shows a substrate coated with reader stack 220. The reader stack can be a GMR or a TGMR stack. In the next step, photoresist (PR) layer 260, covering the center portion of reader stack 220, is deposited as shown in FIG. 8B. In the next step, shown in FIG. 8C, exposed reader stack 220 has been removed by ion beam machining or etching or by other means known in the art. Following removal of exposed reader stack 220, insulating layer 250 is deposited on each side of reader stack 220 and PR layer 260 as shown in FIG. 8D. Insulating layer 250, as mentioned earlier, is preferably aluminum oxide and is preferably deposited by atomic layer deposition (ALD). In the next step permanent bias magnet 230 is then deposited as shown in FIG. 8E comprising reader stack 220 with bias magnets 230 above and below reader stack 220 separated from reader stack 220 by insulating layers 250. The structure in FIG. 8E is then covered with PR layer 260b with a narrow center width and wider ends as shown in FIG. 8F. The exposed structure not covered with PR layer 260b is then removed by ion beam machining or etching or other means known in the art as shown in FIG. 8G. Insulator layer 250 is then deposited on each side of the structure covered with PR layer 260b as shown in FIG. 8H. Side shields 240 and 242 are deposited to form the structure shown in FIG. 8I. Side shields 240 and 242 could be replaced with insulator layer 250 if needed. Removing PR layer 260b in FIG. 8I reveals the structure shown in FIG. 8J comprising rectangular reader stack 220 separated from side shields 240 and 242 and trapezoidal bias magnets 230 by insulating layer 250. Masking the top half of the structure shown in FIG. 8J and removing the remainder creates reader structure 10 shown in FIG. 8K comprising rectangular reader stack 220, side shields 240 and 242 and trapezoidal back bias magnet 230 separated from each other by insulating layer 250. Air bearing surface ABS is indicated in FIG. 8K.

The formation of reader 110 with trapezoidal back bias magnet 130 and trapezoidal reader stack 120 shown in FIGS. 5 and 6 is schematically illustrated in FIGS. 9A-9K. FIG. 9A shows a substrate coated with reader stack 320. The reader stack can be a GMR or a TGMR stack. Photoresist (PR) layer 360, covering the center portion of reader stack 320, is deposited as shown in FIG. 9B. In the next step, shown in FIG. 9C, exposed reader stack 320 has been removed by ion beam machining or etching or by other means known in the art. Following removal of exposed reader stack 320, insulating layer 350 is deposited on each side of reader stack 320 and PR layer 360 as shown in FIG. 9D. Insulating layer 350, as mentioned earlier, is preferably aluminum oxide and is preferably deposited by atomic layer deposition (ALD). In the next step, permanent bias magnet 330 is then deposited as shown in FIG. 9E comprising reader stack 320 with bias magnets 330 above and below reader stack 320 separated from reader stack 320 by insulating layer 350. The structure in FIG. 9E is then covered with PR layer 360b with a narrow center width and asymmetrically wider ends as shown in FIG. 9H. The exposed structure not covered with PR layer 360b is then removed by ion beam machining or etching or other means known to produce the structure shown in FIG. 9G. Insulator layer 350 is then deposited on each side of the structure in FIG. 9G to produce the structure shown in FIG. 9H. Side shields 340 and 342 are deposited on each side to form the structure shown in FIG. 9I. Side shields 340 and 342 could be replaced with insulator layer 350 if needed. Removing PR layer 360b in FIG. 9K reveals the structure shown in FIG. 9J comprising trapezoidal reader stack 320, side shields 340 and 342 and trapezoidal bias magnet 330. All are separated by insulating layer 350. Masking the top half of the structure shown in FIG. 9J and removing the remainder creates reader structure 110 shown in FIG. 9K comprising trapezoidal trilayer reader stack 320, side shields 340 and 342, and trapezoidal back bias magnet 330 separated from each other by insulating layer 350. Air bearing surface ABS is indicated in FIG. 9K.

While the invention has been described with reference to an exemplary embodiment(s), it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment(s) disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.

Claims

1. A magnetoresistive sensor comprising:

a trilayer sensor stack comprising two ferromagnetic freelayers separated by a nonmagnetic spacer; and

a back biasing magnet adjacent a back end of the trilayer sensor stack;

wherein at least one of the trilayer sensor stack and the back biasing magnet has a shape that stabilizes a micromagnetic “C” state or concentrates magnetic flux in the trilayer sensor stack.

2. The magnetoresistive sensor of claim 1 wherein the back bias magnet has a substantially trapezoidal shape.

3. The magnetoresistive sensor of claim 2 wherein the trilayer sensor stacks have a substantially trapezoidal shape.

4. The magnetoresistive sensor of claim 1 wherein the trilayer sensor stack has a substantially rectangular shape.

5. The magnetoresistive sensor of claim 1, wherein the nonmagnetic spacer layer of the trilayer sensor stack is an insulator layer and the trilayer sensor stack is a tunneling magnetoresistive sensor.

6. The magnetoresistive sensor of claim 1, wherein the biasing magnet provides vertical bias to the trilayer sensor stack.

7. The magnetoresistive sensor of claim 1, wherein the biasing magnet is a hard magnetic material.

8. The magnetoresistive sensor of claim 7, wherein the hard magnetic material is a cobalt-platinum based alloy or iron-platinum based alloy.

9. The magnetoresistive sensor of claim 1, wherein the back biasing magnet is isolated from the trilayer sensor stack by an insulating layer.

10. The magnetoresistive sensor of claim 1, wherein the ferromagnetic layers in the trilayer sensor stack are selected from the group consisting of nickel-iron, copper-iron, and nickel-iron-copper alloys.

11. The magnetoresistive sensor of claim 1, and further comprising:

lateral side shields adjacent both sides of the trilayer sensor stack and the back biasing magnet.

12. The magnetoresistive sensor of claim 11, wherein the lateral side shields are isolated from the trilayer sensor stack and the vertical biasing magnet by a side shield insulating layer comprising aluminum oxide.

13. A magnetoresistive sensor comprising:

a trilayer sensor stack comprising two ferromagnetic layers separated by a nonmagnetic spacer layer, and having a front width proximate an air bearing surface and a back width distal from the air bearing surface; and

a back biasing magnet adjacent the back width of the trilayer sensor stack, the back biasing magnet having a front width that is about the same as the back width of the trilayer stack, and a back width; wherein at least the back biasing magnet has a trapezoidal shape.

14. The magnetoresistive sensor of claim 13 wherein the back width of the trilayer sensor stack is larger than the front width of the trilayer stack.

15. The magnetoresistive sensor of claim 13 wherein the back biasing magnet provides bias to the trilayer sensor stack in a direction generally perpendicular to the air bearing surface.

16. The magnetoresistive sensor of claim 13 wherein the back width of the biasing magnet is larger than its front width.

17. The magnetoresistive sensor of claim 13 and further comprising:

lateral side shields adjacent both sides of the trilayer sensor stack and the back biasing magnet.

18. The magnetoresistive sensor of claim 13 wherein the back width of the trilayer sensor stack is about the same as the front width of the trilayer sensor stack.

19. A magnetoresistive sensor comprising:

a trilayer sensor stack comprising first and second free layers separated by a nonmagnetic spacer;

a permanent magnet located on an opposite side of the trilayer sensor stack as an air bearing surface, the permanent magnet having a front side width less than a back side width wherein a front side is closest to the trilayer sensor stack;

a first and second side shield adjacent the trilayer sensor stack and permanent magnet;

a top shield adjacent the first free layer; and

a bottom shield adjacent the second free layer.

20. The magnetoresistive sensor of claim 19, wherein the trilayer sensor stack has a front side width less than the back side width and a front side is closest to the air bearing surface.