# Numerical Simulation of the Head/Disk Interface for Patterned Media

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## Abstract

The use of patterned media is a new approach proposed to extend the recording densities of hard disk drives beyond 1 Tb/in.^{2}. Bit-patterned media (BPM) overcome the thermal stability problems of conventional media by using single-domain islands for each bit of recorded information, thereby eliminating the magnetic transition noise (Albrecht et al., Magnetic Recording on Patterned Media, 2003). Considering steady state conditions, we have transferred the pattern from the disk surface onto the slider surface and have investigated the pressure generation due to the bit pattern. To reduce the numerical complexity, we have generated the bit pattern only in the areas of the slider near the trailing edge, where the spacing is small. Cylindrical protrusions were modeled using very small mesh size on the order of nanometers to obtain the flying characteristics for the entire slider air bearing surface (ABS) using the “CMRR” finite element Reynolds equation simulator (Duwensee et al., Microsyst Technol, 2006; Wahl et al., STLE Tribol Trans, 39(1), 1996). The effect of pattern height, pattern diameter, slider skew angle, and slider pitch angle on flying height of a typical slider is investigated. Numerical results show that the flying height decreases for a patterned slider and the change in flying height is a function of the pattern height and ratio of the pattern diameter to the pattern pitch. In comparison to discrete track media, the flying height loss is larger for a patterned slider disk interface for the same recessed area of pattern.

## Keywords

Bit-patterned media Patterned slider Magnetic data storage Slider air bearing Finite element method## 1 Introduction

Patterned media for hard disk drives can be used in the form of discrete tracks or discrete bits. In discrete track recording (DTR), the bits are stored on discrete circumferential tracks on the disk. In bit-patterned media, each bit is stored on a single magnetic domain or “island” [1]. Magnetic transitions no longer occur between random grains as in conventional media, since distinct boundaries between islands are formed both in the circumferential and the radial directions on the disk. Several investigations have been published that discuss the head/disk interface for patterned media. Wachenschwanz et al. [2] reported an increase in the signal to noise ratio (SNR) and a better write efficiency for discrete track type of patterned media. Head/disk interfaces for patterned media are complicated to manufacture and pose challenging problems from a tribological viewpoint. The air bearing domain in bit-patterned media is highly influenced by the existence of surface features on the disk. Island-like cylindrical structures on the disk surface in the radial and circumferential directions change the air bearing pressure contours of the head/disk interface compared to a conventional head/disk interface with a “smooth” disk. Duwensee et al. [3] studied the influence of discrete track pattern on pressure generation in slider bearings. They reported that very high and localized air bearing pressure peaks occur in discrete track head/disk interfaces, and that the slider pitch angle was independent of the DTR parameters.

Gui et al. [4] and Fua et al. [5] studied padded sliders and reported that padded sliders have benefits in terms of reducing head/disk interactions and friction during contact start stop. Li et al. [6] studied the pressure of pattern on two-rail slider bearings and found that patterned sliders showed better stiction properties than unpatterned sliders. They also found that an increase in the pattern pitch and pattern height decreases the flying height. Tagawa et al. [7] investigated the effect of longitudinally grooved slider surfaces on the flying behavior of a two-rail slider flying over a smooth disk surface. Tagawa and Mori [8], [9] extended the work reported in [7] to head/disk interface for patterned media. They considered surface patterns that were on the order of 5–20 μm in width and length direction and 10–40 nm for the pattern height. They determined the pressure distribution for a two-rail, positive pressure slider and observed an increase in the flying height due to surface pattern. In a more recent investigation, Duwensee et al. [10] have numerically studied the head/disk interface for DTR. They investigated the effect of groove depth on the flying height and flying attitude for a constant ratio of groove width to groove pitch. They proposed an empirical expression for the flying height loss as a function of groove depth, groove pitch, and groove width. Their calculation used a very fine mesh discretization in the region of the slider air bearing surface (ABS) that is closest to the disk. A typical model consisted of 2.7 × 10^{6} finite elements, 1.3 × 10^{6} nodes, and required large computer memory.

Alternative techniques such as homogenization and Direct Simulation Monte Carlo (DSMC) methods have also been implemented to study the influence of surface pattern on the slider or disk surface. Buscaglia and Jai [11] applied homogenization techniques for the Reynolds equation, specifically for ultra-thin gas films with arbitrary Knudsen numbers. They considered fine but periodic surface structures on the slider disk interface. They presented the spacing between slider and disk as the sum of a low frequency contribution that is unknown and a high frequency contribution whose dependence on the low frequency is assumed to be known. The high frequency part represents the periodic spacing variations due to surface features on the disk or on the slider. The unknown part must be computed during the numerical solution of the generalized Reynolds equation. Homogenization techniques allow a coarser domain discretization than direct simulation methods. The problem size is small since only one period of the surface texture is considered due to periodicity. Also the authors show very good agreement qualitatively for the pressure fields between homogenized solution and the direct solution. The important feature of the homogenization technique is that the computation time is reduced without loss in average pressure prediction due to surface features. However, the local resolution of the pressure distribution of the air bearing is reduced due to homogenization. If details of the pressure distribution on the order of the surface features are of importance, the homogenization technique is not suitable. Alexander et al. [12] and Huang et al. [13, 14] applied the DSMC method to check the validity of the modified Reynolds equation for high Knudsen number flow in “smooth” head/disk interfaces in two and three dimensions, respectively. They reported that the DSMC method compared close to the simulation results obtained by solving the Reynolds equation. Duwensee et al. [15] have used the DSMC method to study the pressure generation in a nano slider covering one groove and land region for DTR type disk.

In the present article, we present a direct numerical simulation that investigates the head/disk interface for patterned media by considering the entire slider ABS with ability to resolve the pressure gradients caused by nanometer high periodic surface patterns. A finite-element-based solution of the Reynolds equation is used to obtain the steady state flying characteristics of the patterned head/disk interface. The steady state flying behavior of typical proximity recording sliders with surface patterns and the effect of pattern pitch, diameter and height is investigated for five sub-ambient pressure slider bearings. In areas of high pressure and low spacing, a very fine mesh is selected to investigate the effect of the ultra small features and determine the influence of pattern on the air bearing pressure. In areas of higher spacing, a coarser finite element mesh was chosen, since the influence of surface features is decreasing with increasing spacing. The numerical approach is similar to that used by Duwensee et al. [10] in the study of the head/disk interface for discrete track media. Finally, the flying height change due to bit pattern is compared with the results for DTR [10].

## 2 Simulation Model

*d*, height

*h*, and pitch

*p*. The protrusions are uniformly distributed representing the pattern from the disk in the radial and circumferential directions.

*p*’ denotes the pattern pitch, ‘

*d*’ denotes the pattern diameter, and ‘

*h*’ denotes the pattern height. The same pitch

*p*is used both in the length and the width directions of the slider. The nearest distance between two pattern features in both the length and the width directions of the slider is ‘(

*p*−

*d*)’.

*p*is the pressure,

*h*is the spacing between the slider and the disk, μ is the dynamic viscosity of air,

*U*and

*V*are the velocity components in the

*x*and

*y*directions, respectively.

In the initial calculation, a fairly large pattern diameter of 3 μm was used for the slider shown in Fig. 1 to obtain the pressure generation around the pattern features. Large diameter pattern features were chosen for visualizing the effect of pattern on air bearing pressure.

For the four femto designs shown in Fig. 3, pattern heights between 0 and 40 nm (0 < *d* < 40 nm) were investigated. A pattern diameter between 200 and 800 nm was used with a constant pattern pitch of 1000 nm. In addition, the influence of skew angle (ranging from 0° to 20°), the effect of slider pitch angle, and the effect of pattern diameter were investigated. Due to the small pattern features on the trailing edge center pad, a very fine mesh discretization was required. A uniform mesh density over the complete ABS would result in numerical models with several tens of millions of nodes. To reduce the model size, a non-uniform mesh was used for the simulation. Very small elements were used in the area where the pattern features are present and increasingly larger sized elements elsewhere. In particular, about 30–50 elements were created for each individual pattern. The number of pattern features on the trailing edge center pad of the femto slider designs was on the order of 5000–8000. For example, slider design 3 (Fig. 3c) had a center trailing pad area of about 140 × 40 μm resulting in 5600 pattern features. The total number of nodes and elements for this slider model was on the order of 0.7 × 10^{6} and 1.4 × 10^{6}, respectively.

## 3 Numerical Simulation Results

To investigate the effect of pattern height, pattern diameter, slider skew, and pitch angles on flying height, a parametric study was performed.

*h*is plotted in Fig. 8 for a ratio of

*d*/

*p*= 0.5. We observe that the flying height decreases linearly as a function of the pattern height. That trend is similar for all four slider designs.

*d*/

*p*= 0.5 can be estimated by subtracting ΔFH from the flying height on a conventional smooth head/disk interface. The dotted line in Fig. 8 was obtained using the following equation:

*h*” is not only the pattern height, it is also the depth of the recessed areas around the pattern. For a given ratio of

*d*/

*p*, change in flying height (which is a function of pressure) is directly proportional to “

*h*”. However, when the

*d*/

*p*ratio is varied as in Fig. 9, non-linear effects are observed. In fact the change in flying height fits well with a quadratic function and is later shown to be an area effect. We observe the higher order effects due to the surface patterns because of the use of direct simulation compared to homogenized solution in [20].

Figure 9 shows the change in flying height as a function of the pattern diameter. The change in flying height is plotted as a function of the ratio *d*/*p*. The dashed horizontal line in Fig. 9 corresponds to the non-patterned case. In Fig. 9, the pattern diameter was varied between 200 and 800 nm keeping the pattern pitch constant at 1000 nm. From Fig. 9 we observe that the change in flying height is non-linear as a function of the pattern diameter. The solid, dotted, and dashed lines in Fig. 9 represent a quadratic fit for a pattern height of 5, 10, and 15 nm, respectively.

*d*/

*p*= 0.5). A linear decrease in the trailing edge center spacing is observed with increasing pattern height, indicating that Eq. 2 applies also for non-zero skew cases.

*d*/

*p*, and the slider skew angle. From Fig. 11, we conclude that the presence of pattern with diameter on the order of several nanometers does not affect the pitch angle of the slider body.

## 4 Discussion and Summary

Comparing this equation to our simulation results for a bit-patterned slider disk interface, we observe that the groove depth of discrete track disks is analogous to the pattern height of a bit-patterned disk, and that the groove width is analogous to the area recessed around a pattern feature. In addition, the groove pitch is similar to the pattern pitch. For a DTR interface, the flying height loss is linearly proportional to the groove depth and the ratio of groove width to groove pitch for any value of groove depth and groove width for a constant groove pitch [10]. This is due to the fact that the length of the groove and the land regions of the discrete track are the same and that the groove pattern is unidirectional.

A non-linear change in flying height was observed for a bit-patterned slider disk interface when the pattern diameter was varied. The change in flying height was found to be a quadratic function of the pattern diameter. This result is to be expected since a change in the pattern diameter not only changes the pattern profile along the width of the slider, but also along the length of the slider. For the DTR interface, a change in width changes the pattern profile only along the width of the slider. For a range of different pattern diameters and pitch ratios, a functional relationship would have to be written as ΔFH = *f*(*h*) × *f*(*d*/*p*). The value of *f*(*d*/*p*) is different for various ratios of pattern diameter to pattern pitch.

*w*/

*p*. For the patterned slider disk interface, a similar area ratio can be obtained as:

For smaller pattern diameters, the change in flying height increases by larger amplitude for the bit-patterned interface compared to the DTR interface, as the recessed area ratio increases.

## 5 Conclusions

- 1.
High pressure peaks occur locally over each pattern feature. These high pressure areas are likely to cause lubricant loss over the bit areas.

- 2.
From the parametric analysis of several femto slider designs, it was found that the slider flying height decreases linearly with increasing pattern height. The flying height decreases quadratically with the ratio of

*d*/*p*. - 3.
The flying height loss of a discrete bit-patterned media is a linear function for small values of pattern height keeping pattern diameter and pattern pitch constant.

- 4.
The slider pitch angle was found to be independent of pattern height, slider design, and skew angle.

- 5.
The flying height loss is larger for a bit-patterned slider disk interface compared to a discrete track interface for the same recessed area of pattern.

## Notes

### Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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