Channel Characterization and Performance Evaluation ... - IEEE Xplore

IEEE TRANSACTIONS ON MAGNETICS, VOL. 49, NO. 2, FEBRUARY 2013

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Channel Characterization and Performance Evaluation of Bit-Patterned Media Maria Yu Lin , Moulay Rachid Elidrissi , Kheong Sann Chan , Kwaku Eason , Melissa Chua , Mohamed Asbahi , Joel K. W. Yang , Naganivetha Thiyagarajah , and Vivian Ng Data Storage Institute (DSI), Agency for Science, Technology and Research (A*STAR), Singapore 117608 Institute Material Research and Engineering (IMRE), Agency for Science, Technology and Research (A*STAR), Singapore 117602 Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576 Bit-patterned media (BPM) is a promising approach to push back the onset of the superparamagnetic limit faced by conventional continuous granular media. Today, BPM islands can be fabricated at densities higher than can be characterized by existing methods and full bit-patterned media recording (BPMR) is still a long way off. In this work, we rely on simulations to predict how such islands would perform in a real recording scenario. The grain flipping probability (GFP) model is trained via micromagnetic simulations and reproduces the magnetic profiles used to generate readback signals for channel simulations. The geometrical parameters to the micromagnetic simulations, such as the island size variations and island position jitter are characterized from measurements of islands fabricated via e-beam at various channel densities. Index Terms—Bit-patterned media (BPM), grain flipping probability (GFP) model, hard disk drives (HDDs), jitter characterization, magnetic recording, micromagnetic simulations, signal processing.

I. INTRODUCTION

B

IT Patterned Media Recording (BPMR) [1]–[3] is a candidate technology proposed to extend the a real density growth capability of magnetic recording systems. In conventional granular magnetic recording (CGMR), bits of information are recorded onto a number (today, around 15) of randomly distributed magnetic grains. The challenge for the granular media approach is that the randomness of the grains leads to media noise. A certain minimum number of grains per bit are required to maintain the media signal to noise ratio (SNR) at an adequate level. This requires smaller grains as the bits are shrunk. Eventually, the grains need to be so small that they become either thermally unstable, or unwriteable by the head, as described in the well-known media-trilemma. In BPMR, instead of randomly positioned grains, they are ordered into a well-defined lattice of magnetic islands. The lattice is typically either rectangular, or hexagonal. In this work we consider hexagonal lattices because of the closer packing achieved for a given minimum island pitch. Because of this ordering, the media SNR is no longer determined by the number of grains per bit, but by the geometrical and magnetic distributions of the islands instead. In [4], processes for fabricating high-density BPM and using magnetic-force microscopy (MFM) for characterization of bits up to 1.9 Tera bit per square inch (Tbpsi) have been proposed. Currently, we are able to produce BPM islands at close to 3 Tbpsi, using scanning electron microscope (SEM) for characterization of the bits. Although the characterization resolution

Manuscript received July 27, 2012; revised September 07, 2012; accepted October 22, 2012. Date of current version January 22, 2013. Corresponding author: M. Y. Lin (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2012.2226708

still needs to be improved, we can evaluate the channel performance based on the jitter measurements from lower densities. In this paper, BPM with a hexagonal lattice array and a bit aspect ratio are fabricated, characterized and used in micromagnetic simulations. The GFP model has been proposed in [5], [6], reproducing micromagnetic simulation output at rates that are able to support readback signals for channel simulations. The GFP model characterizes a multidimensional look-up table (LUT) with probabilities of grains or islands flipping under various conditions. The parameters defining these conditions form the dimensions of the LUT are chosen with the intention that the parameters with the most influence on the probability, are used in the LUT. In [5], [6], the (downtrack) position and (crosstrack) position of the island actual location with respect to the write head of the island and the immeposition, the anisotropy field diate previous bit pattern have been used as the key parameters defining a 4-dimensional GFP LUT. Dong and Victora [7] derived specifications for a 2.3 bit aspect ratio (BAR) bit patterned exchange coupled composite bit error rate (ECC) media and head, that demonstrates at 4 Tbpsi density with a 4 nm fly height, 5% switching field distribution, 5% timing and 5% jitter errors. The write-head used in [7] is also used in [5], [6] and this work. In [5], [6], [8], low-density parity-check (LDPC) coded read channel performance using an analytical channel model, the GFP model and micromagnetic models for BPMR systems at 4 Tbpsi have been evaluated for different magnetic distributions and position jitters. In this work, we rely on simulations to predict how fabricated BPM would perform using measured island size and position variations as inputs to the micromagnetic model. To generate sufficiently long readback signal, we create BPM island arrays in a hexagonal lattice with the same position jitters and size variation statistics. Next, micromagnetic simulations were run to model the writing process over a hexagonal lattice, and

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Fig. 2. Block diagram of coded channel.

Fig. 1. Block diagram showing the processes involved in obtaining the results.

the GFP model for BPMR was characterized. We then assumed a 2D-Gaussian read head sensitivity model to produce the long readback waveform for channel performance evaluation. Our purpose is to investigate the user densities achievable on the various densities of BPM assuming realistic jitters and size distributions. For higher channel densities with larger jitter, more redundancy in the code is needed. Using today’s fabrication processes, we are thus able to predict the highest optimum channel density that gives the most density to the user after error correction. In Section II, the system setup is summarized. In Section III, we describe the bit-patterned media’s fabrication process and the characterization results of the position jitter and size variation from the SEM images. In Section IV, we describe the micromagnetic and GFP models used to generate the readback signal for channel evaluation at the various a real densities (AD). These two models are used in the writing process and rely on the head field distribution from [7] and are described in Section IV-C. To obtain the readback signal, a Gaussian read head sensitivity (RHS) function is used and is described in Section IV-F. In Section V, we describe the detection and decoding schemes used, followed by the channel error rate results discussed in Section VI. We conclude the paper in Section VII. II. SYSTEM SETUP The processes involved in getting the empirical data from fabrication into our simulations are depicted in Fig. 1. First the media is fabricated via e-beam lithography. Images of the media samples are acquired through SEM. The pictures from the SEM are then processed to obtain statistics on the island size and position jitters. Media with the same statistics are then created for micromagnetic simulations. Parameter table files that hold information for micromagnetic simulations are precomputed. Then preliminary micromagnetic simulations are run to optimize , and , where is the media anisotropy constant and and are the offset position of the write head with respect to the ideal island center in the downtrack and crosstrack direction. Then, mass micromagnetic simulations are run, from which the GFP LUT can be characterized. Once characterized, the GFP can reproduce waveforms with the same probability statistics which are used in channel simulations, from which the frame error rate (FER) is estimated.

Fig. 3. Original SEM image of BPMR media at 1.54 Tbpsi density (left), 2.29 Tbpsi density (middle) and 2.91 Tbpsi density (right).

Fig. 2 shows the system block diagram for the signal processing simulations. The user data is encoded into channel data with a code rate which is then passed to the channel model. The channel model is decomposed into the writer model (the GFP) and the reader model. Convolution with the read-head sensitivity function produces the readback waveform with the corresponding SNR. For the channel simulations, the equalizer and target responses are jointly optimized for each density and the raw bit error rate (bER) is measured after the detector, while the FER is measured after the decoder. III. BIT PATTERNED MEDIA FABRICATION PROCESS JITTER CHARACTERIZATION

AND

The processes for fabricating high-density BPM beyond 1.5 Tbpsi are described in [4]. Using high-resolution electron-beam lithography, robust silicon oxide resist structures were patterned onto a Si substrate in a hexagonal array with center-to-center distances as small as 15 nm. By depositing the Co/Pd multilayers directly onto the resist structures, and avoiding the etching process, the resulting bits have perpendicular anisotropy and structure densities close to that of the lithographic step. SEM images of the resulting magnetic islands are shown in Fig. 3 for three densities. A. SEM Images and Jitter Characterization In the current work, we characterize the geometrical properties (jitter and size variation) of the fabricated media at various densities. Fig. 4 shows the SEM image with pixel values greater than a specified threshold in light red (light grey) at the same three densities as Fig. 3. Once the pixels belonging to an island are identified, the jitter and size variations were obtained by locating the edges of each island in a raster-scan. The thresholds are chosen by minimizing the difference between the given island pitch values when BPM are fabricated and the measured island pitch values. The measured island pitch values are obtained from the SEM by setting a threshold and

LIN et al.: CHANNEL CHARACTERIZATION AND PERFORMANCE EVALUATION OF BIT-PATTERNED MEDIA

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Fig. 4. The SEM image of BPMR media at 1.54 Tbpsi density (left), 2.30 Tbpsi density (middle) and 2.91 Tbpsi density (right) with pixels above a threshold marked in light red (light grey).

TABLE I FABRICATED BPM PARAMETERS AND THE CORRESPONDING CHARACTERIZED DIAMETERS AFTER THRESHOLDING THE SEM IMAGES Fig. 5. Jitter versus density plot. Dotted blue curves are the sigmas of the absolute jitter while the solid red curves are the sigmas as a percentage of the island pitch. is for position jitter while is for size jitter.

then measuring the average island pitch in pixels and then converting it to nm by multiplying the resolution in nm/pixel. After the island pitch value is measured, we compare it with the given value and adjust the threshold such that the estimation error is minimized. The minimization process is stopped after the estimation error is less than or equal to 5%. After the estimation error is minimized, we measure the diameter in pixels and convert it to nm. Table I tabulates the island pitch values for generating the BPM, the corresponding area density, the measured diameter, the estimated island pitch values and the estimation errors. The size jitter is defined as the sigma-of-the-diameter/average-diameter. The position jitter is the sigma-of-the-position/ average-island-pitch-value. Fig. 5 shows the jitter measured corresponding to the same thresholds used in Fig. 4. The measured jitter in Fig. 5 is more sensitive to the threshold for high densities than for low densities. This is because the profile of the islands reflected to the SEM image is sharper for lower densities than higher densities. The gathered statistics were then used to generate media for simulations. For example, at 1.54 Tbpsi a real density, a bit aspect ratio (BAR) of 0.866, an average island diameter of 14.4 nm, position jitter of 5.9% and size variation of 8.4% were used to generate the media. Consistent with the fabricated media, the micromagnetic simulations are run on a hexagonal lattice configuration with nominal values of , . From Figs. 3 and 4, the jitter can be seen to increase with increasing densities. Fig. 5, shows the absolute jitter in nm (left axis) and the relative jitter (right axis). The absolute jitters remain relatively constant for densities from 0.5 Tbpsi to 1.9 Tbpsi while the jitter percentages increase with density in the

Fig. 6. Sample output of the micromagnetic simulations. Red (light) islands are positively magnetized, blue (dark) islands are negatively magnetized. The media is generated with downtrack and crosstrack pitches of 22 nm and 19.05 . Subfigure (a) shows the nm, respectively, at 1.54 Tbpsi and results from simulations with zero size, position and magnetic distributions, , , while subfigure (b) is the result with , ), ( , ).

same range, due to reduced island pitch. Beyond 1.9 Tbpsi both the position and size variations rapidly increase using the current fabrication and SEM characterization methods. It should be noted that at the higher densities, the existing jitter characterization and SEM methods may be less accurate. It is not clear how much of this jitter increase is due to the fabrication and how much is due to the characterization errors, SEM noise and resolution limitations. The SEM image resolution is 1.2 pixel/nm. Optimization of the threshold value (which determines the island edges) can help to improve the measurement, however the resulting jitter ( 20%) at the highest densities is still considered too large for successful channel detection. IV. CHANNEL MODEL A. Micromagnetic Model The micromagnetic simulations that were carried out, model the response of the bit patterned media islands to the fields. The equation solved is the Landau-Lifshitz-Gilbert (LLG) equation, given by (1)

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Fig. 7. WIE rate as a function of


,

and

.

where is the magnetization, is a modified gyromagnetic ratio , given by , where ( in SI units) is the magnetic permeability of free space, and is the gyromagnetic ratio. is the total effective magnetic field, summing the contributions from the external write-head, the uni-axial crystalline anisotropy, and the magnetostatic interactions. Exchange coupling between islands is assumed to be negligible due to the large nonmagnetic spacing between the islands. In (1), is the Gilbert damping constant and is the saturation magnetization. Equation (1) is solved for each island, computing the magnetization of the media at each time instant in the presence of an external head field that moves over the media modulated by the written bit pattern. A 5th order adaptive Runge-Kutta solver is used in our simulations to numerically solve (1). B. GFP Model Fig. 6 depicts sample BPM islands after micromagnetic simulations with 0% geometrical and magnetic variations shown on the left and with 5.9% position and 8.4% diameter variation on the right at 1.54 Tbpsi. The black triangles indicate the position and polarity of the written bits. The written-in-error (WIE) is computed by comparing the magnetized media polarity with respect to the polarity of the written bits. For example, if an up triangle (positive bit) is on top of a red (grey positive) island, then it means the island is correctly magnetized. It can be observed in Fig. 6 that the write head location (i.e. the center of the write pole) is not exactly centered on each island, but has been optimized such that the probability of a WIE after writing three tracks is minimized. Also note this is a shingled magnetic recording (SMR) simulation. The target tracks of the SMR write process are tracks 1, 2, and 3. Fig. 6 shows results of the SMR write processes with the three target tracks written and track 4 of media is being magnetized while writing the track 3. Comparing the written bits with the island magnetization pattern, we found that for both cases, there is no WIE for all the 72,000 bits of data that we have simulated. This shows that when the jitter is not large, BPM can achieve similar WIE performance as the ideal case when there is no jitter. The GFP LUT consists of a 4-D numerator and a 4-D denominator array of identical sizes. The numerator array counts the number of islands (with the given parameter values) that have flipped in the given bit interval, while the denominator array counts the number of islands that could flip in the given bit-interval. The quotient of the numerator to denominator array is the probability LUT, referred to as the GFP.

C. Write Head Field and Media The write head used in these experiments was designed for 2.3:1 aspect ratio ECC BPMR media with the parameters described in [7]. The current evaluation of BPMR performance at the various densities, uses the same head. The head was designed for 4 Tbpsi with and a crosstrack/downtrack pitch of 19.26 nm/8.37 nm, respectively. As mentioned, the media was fabricated using a hexagonal lattice and thus the BAR was maintained at 0.866. This achieves the highest possible a real density for a given island pitch. For 1.54 Tbpsi media, the crosstrack pitch is 19.05 nm which is narrower than the crosstrack pitch that the head was optimized for. This leads to adjacent track erasure (ATE). Therefore, in order to allow writing with a fixed head field, we adopt SMR as the writing scheme. This is reasonable from a technology roadmap standpoint. Today, SMR is being considered by most hard drive vendors. For densities below 1.54 Tbpsi, the write-head is not likely to magnetize the adjacent track and SMR is likely not required. However, our simulations use the same writer at all densities and transition seamlessly between the two cases. D. Head/Media Alignment and

Selection

To maintain the bit aspect ratio (BAR) at 0.866 while mini, and was performed. mizing the WIE, a search of Fig. 7 shows the measured WIE as a function of , and . The , and are optimized such that the probability of correctly writing the targeted island is as close to 100% as possible, while the probability of writing the the last downtrack bit and the adjacent track bits are as close to 0% as possible. The WIE has several different sources depending on the values of , and . The left plot of Fig. 7 shows WIE as a function of and with . The WIE is seen to increase with increasing which is in the positive downtrack direction. This source of WIE is thus due to failure to write the targeted island. The WIE also increases with increasing on the same plot, because increasing makes it harder to write the target island. In the middle plot of Fig. 7, we plot WIE vs and with . The WIE increases with increasing which is in the direction of the last written track. This WIE is the ATE occurring and thus it increases with reducing . The last plot in Fig. 7, shows the WIE as a function of and with . The optimal values that we choose for these parameters after the search are , and .


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Fig. 8. WIE rate versus channel density.

Fig. 8 shows the characterized WIE over the tested densities. There are two curves in the figure, one corresponding to WIE measured from micromagnetic simulations and the other from the GFP model. This figure demonstrates that the GFP model is doing a sufficient job modeling the errors that are observed in the micromagnetic simulations. At lower densities, after the optimization, the WIEs are zero at all densities. This is also artifact as we are only able to run a limited number of bits for micromagnetic simulations due the fact that it takes approximately 25 s to simulate writing 1 bit. We have simulated 48 runs of 1500 bits each or 72000 bits to obtain these plots, thus WIE rates below 1.38 e-5 will not be visible on this plot. The sudden jump in WIE from 1.86 Tbpsi pitch to 2.29 Tbspi is due to the jump in jitters in the measurements of the fabricated media, in agreement with Fig. 5.

Fig. 9. Probability footprints of the GFP LUT for and 20 nm. The axes denote the and positions of the island centers relative to the writer in nm. Each pixel corresponds to a 2 nm bin. The top figure depicts higher density simulations at 18 nm island pitch while the the bottom figure depicts lower density simulations at 20 nm island pitch. The (0, 0) position corresponds to the head position at the end of writing the target island.

E. GFP Characterization Results

F. Read Head Sensitivity Model

Fig. 9 shows the probability footprints of the GFP LUT for (above) and 20 nm (below). The footprints are obtained by summing the 4-D LUT over the and pattern bins in the numerator and denominator arrays, leaving 2D arrays in just and . These arrays are then divided to obtain the 2D probability footprints averaged over the and pattern bins. It can be observed in Fig. 9 that for the smaller island pitch, the probability of islands on the adjacent track, and the nearest downtrack island on the current track have a larger probability of flipping. The probability of adjacent track writing in the higher density case also demonstrates the necessity for shingled writing. The LUT shows that islands on the leading edge in the downtrack direction are also flipped during micromagnetic simulations. However, they are not important as they will be overwritten in the next few bit-intervals. The islands on the trailing edge are going to remain after the head has passed. In shingled writing, only islands on one side should be overwritten and such islands are affected as seen in Fig. 9. We optimized the and such that only one side of the adjacent track can be flipped for shingled writing, and that the total WIE is minimized after three tracks are written.

After the writing process is completed, the readback signal is obtained by convolving the island magnetization pattern with a Gaussian read head sensitivity (RHS) function. The downtrack and crosstrack of the Gaussian are proportional to the downtrack and crosstrack pitches for each density. The crosstrack sigma was chosen such that is equal to the track pitch, meaning that we are operating in the “negligible intertrack-interference (ITI)” case. The downtrack was chosen such that which is a standard used in today’s read head response. Here is 25% to 75% rise time of a transition response, and is the bit interval. Electronics noise, modeled by 30 dB additive white Gaussian noise (AWGN), is then added to the readback signal after the convolution. V. DETECTION AND DECODING SCHEMES In this study, channel bit detection is performed by the Bahl, Cocke, Jelinek and Raviv (BCJR) [9] detector and random LDPC codes [10]. The BCJR detects the channel bits by computing log-likelihood ratio (LLR) probabilities from the equalized readback signal, and a 5 taps monic-contraint generalized partial response (GPR) target.

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TABLE II ISLAND SIZE JITTER, POSITION JITTER AND

AND

VARIATIONS

Fig. 11. FER for LDPC coded BPMR channel using 4096 codeword length over different densities. There are more legends than curves in this figure as the FERs corresponding to grain pitches 30 nm and 35 nm have FERs 1 e-3 and are not visible on the plot.

Fig. 10. FER for LDPC coded BPMR channel using 4096 codeword length for the 8 situations tabulated in Table II. There are more legends than curves shown in this figure because four of the curves have FERs 1 e-3 and are not visible on the plot.

The error correction codes used in this paper are random LDPC codes whose generator and parity-check matrices are obtained using the software package from [10]. We use irregular codes with 20% of the columns with weight of 2, 70% with weight 3 and 10% with weight 5. The parity check matrices are randomly constructed, while avoiding length 4 cycles. For all simulations, we test 4096 codeword length, with code rates ranging from 0.5 to 0.9688 to determine the code rate at which the FER drops drastically. VI. PERFORMANCE EVALUATION RESULTS A. Investigation of Island Size Variation, Position Jitter and , Variations for a Constant AD To investigate the impact of island size variation, position and , we simulated the 8 situjitter, and the influence of ations in Table II. Fig. 10 plots the FER performance of these 8 different situations at an . The region where the FER starts to drop determines the code rate at which the system transitions from nonworking to working and due to the nature of the shape of the curve, is termed the waterfall region. The plots in this figure determine the code rates needed at the given position, size and magnetic distributions. The code rates in turn determine the a real density overhead that needs to be paid in order to achieve

“error-free” recording. Higher code rates indicating less overhead. Fig. 10 shows the resulting curves corresponding to (filled) and (open). The four curves correspond to the various position and size jitters tested in this simulation. It can be observed that the curves are slightly to the left of the corresponding curves, indicating the code rate loss incurred by going from 0% to 2% magnetic distributions at the given geometrical distributions. The two curves corresponding to 0% size jitter are not visible as the error rates are already very low. It can also be seen from Fig. 10 that the BPMR system performs well at 1.54 Tbpsi for all tested combinations of variances. The maximum code rate lost is less than 3% for the case with 5.9% position jitter and 8.4% size jitter and . Another key observation from this simulation is that 2% distributions on the magnetic parameters has negligible impact on the performance. B. Performance Evaluation for Different Recording Densities Next, we evaluate the performance of BPMR at the different recording densities using the jitters measured from the fabricated media for densities between 0.5 Tbpsi and 2.29 Tbpsi with . Simulations at the highest density (2.91 Tbpsi) failed at all tested code rates due to the excessive jitter, and are not shown here. Fig. 11 plots the FER for LDPC coded BPMR channel using 4096 codeword length over the various densities characterized. A large loss in performance is observed for the 18 nm island pitch media, which is again attributed to the large increase in jitters that produce large WIEs at this density. The other densities have code rates fairly close to 1 indicating a system with reasonable coding overhead. There are still errors observed at these other densities due to the intersymbol interference (ISI), media noise (island size and position jitter) and the AWGN. However at the lowest densities, the error rate drops so low that we are not able to observe them on this plot.


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From this study, we can observe that the critical parameters which limit the user density include the size and position jitters. When the jitters are too large, the WIE rate can be large even after certain optimization of , and . In this case, more redundancy will be required and that reduces the code rate and subsequently the user density. The coded performance is highly correlated to the WIE performance which is in turn dependent on the optimization of writing head positioning, the island location alignment, for each density, as well as the jitters inherent in the media. Further advanced optimization of the nominal design could be helpful to improve the system performance further. REFERENCES Fig. 12. User density versus channel density.

Fig. 12 shows the user density after the coding overhead is accounted for, at each channel density tested. In these tests, the largest density available to the user with is around 1.8 Tbpsi using the e-beam fabrication techniques. VII. CONCLUSION AND FUTURE WORK We have characterized the geometrical variations from real BPM media fabricated via e-beam lithography and have used the results in micromagnetic simulations. These are then used to train the GFP channel model and the channel performance using this model has been evaluated. For the densities tested, the largest density that is available to the user was found to be around 1.8 Tbpsi, at a corresponding channel density of 1.86 Tbpsi. Investigation of island size variation, position jitter and , variations for a constant a real density at 1.54 Tbpsi shows that the BPMR system performs well at 1.54 Tbpsi a real density with 5.9% position jitter, 8.4% size jitter and . The code rate loss, due to the jitters, and , is less than 3%. This means that if the manufacturing process is able to fabricate BPM to maintain jitter levels not exceeding these levels then the channel performance is acceptable.

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