In this paper a framework for the analysis of a family of high order interpolative sigma-delta modulators is introduced. It is shown that a large number of high order architectures can be reduced to a diagonal form which facilitates the stability analysis of the system. In addition, the diagonal form is a canonical form which illustrates the equivalence of a variety of sigma-delta architectures. Architectural di erences are manifested as di erences in parameter values in the diagonal form, providing a convenient method of comparison between systems. It is also shown how transformation to the diagonal form may result in a reduction in order of a system. Finally, there is a brief discussion on the importance of diagonal systems as opposed to non-diagonal systems.
A hybrid directed self-assembly approach is developed to fabricate unprecedented servo-integrated bit-patterned media templates, by combining sphere-forming block copolymers with 5 teradot/in.(2) resolution capability, nanoimprint and optical lithography with overlay control. Nanoimprint generates prepatterns with different dimensions in the data field and servo field, respectively, and optical lithography controls the selective self-assembly process in either field. Two distinct directed self-assembly techniques, low-topography graphoepitaxy and high-topography graphoepitaxy, are elegantly integrated to create bit-patterned templates with flexible embedded servo information. Spinstand magnetic test at 1 teradot/in.(2) shows a low bit error rate of 10(-2.43), indicating fully functioning bit-patterned media and great potential of this approach for fabricating future ultra-high-density magnetic storage media.
Tunneling magnetoresistive (TMR) readers capable of 150 Gb/in 2 of areal density magnetic recording for hard disk drive were demonstrated with bit-error-rate performance. The head design used is basically a bottom type stack of Ta/PtMn/CoFe/ Ru/CoFe/oxide barrier/CoFe/NiFe/Ta cap with abutted hard bias stabilization. The electrical reader width is about 4 to reach a very high track density and shield-to-shield spacing is about 700 A for high linear density. On-track bit error floor is better than 10 5 at a linear density of 900 KBPI and the recording system noise is dominated by the media. The best areal density achieved (using 4 OTC reference level) is 143 Gb/in 2 using symmetric squeeze and 152 Gb/in 2 using asymmetric squeeze method, respectively. It was found that the TMR head has several decibels more signal-to-noise ratio gain over spin valve readers at 150 Gb/in 2 and beyond. The TMR head is also suitable for perpendicular recording application.Index Terms-Areal density, current-perpendicular-to-plane (CPP) geometry, perpendicular recording, signal-to-noise ratio (SNR), tunneling magnetoresistive (TMR) heads.
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