# Writer Performance Optimization with Shingled Rounded Corner and Exchange Coupled Composite Media
## 2 Model Parameters and Methodology
### Combined Write-In Error Probability  
The combined write-in error probability (\(P_{write-in}\)) is one of the evaluation criteria for the write performance. The \(P_{write-in}\) is defined as the rate that the adjacent track bit is erased (\(P_{ensure}\)) and the current recording bit is not reversed (\(P_{recording\_bit}\)) when writing the current bit, which can be expressed by  
\[P_{write-in}\ =\ 1-(1-P_{ensure})\times(1-P_{recording\_bit}) \tag{3}\]  
Assuming that the statistical deviation is Gaussian distribution, the \(P_{ensure}\) and \(P_{recording\_bit}\) are given according to [13; 20].  
\[P_{ensure}\ =\ 0.5\times(1-erf(\frac{H_{sw}-H_{max\_ATE}}{\sigma_{H}\sqrt{2}})) \tag{4}\]  
\[P_{recording\_bit}\ =\ 0.5\times(1-erf(\frac{H_{recording}-H_{sw}}{\sigma_{H} \sqrt{2}})) \tag{5}\]  
where \(H_{sw}\) is the switching field of recording media, \(H_{max\_ATE}\) is the stray field of adjacent bit, \(H_{recording}\) is the writing field strength, \(\sigma_{\rm H}\), \(\sigma_{\rm H}\)' are the combined field variance of the adjacent bit and recording bit, respectively. The recording noise is mainly caused by three aspects, including: (1) writer synchronization, (2) intrinsic switching field distribution and demagnetizing field from the neighboring grains, and (3) cell spacing or size deviation. When the shingled writer moves across the recording bits along the down track direction and switches the media polarity, the adjacent track's bits could be potentially erased by the stray field. The combined field variance consists of 5% writer synchronization variance (\(\sigma_{time}\)), 3.5% grain anisotropy field distribution and demagnetizing field from neighboring grains (\(\sigma_{sw}\)), and 15% grain size deviation (\(\sigma_{filter}\)). Considering the recording noise discussed above, \(\sigma_{\rm H}\) and \(\sigma_{\rm H}\)' can be obtained by the quadratic sum of the three field variances.  
The switching field of the recording media (\(H_{sw}\)) is a critical factor affecting the BER. It needs to be ensured that \(H_{sw}\) is much smaller than the writing field (\(H_{recording}\)) to reverse the recording bit with a high possibility, and larger than the maximum adjacent track erasure field (\(H_{max\_ATE}\)) to avoid the potential reverse of adjacent bits. Figure 4 shows how the switching field affects the write performance. As illustrated, the combined write-in error probability (\(P_{write-in}\)) is sensitive to the switching field. A small dispersion of \(H_{sw}\) can lead to an abrupt change in BER. As mentioned in Equation (3), the smaller \(H_{sw}\) makes the recording bit be reversed more easily, and increases the erasure possibility of the adjacent  
Figure 3: EBW as function of the skew angle for single-phase media [Co/Ni]s(10 nm) and ECC media FePt(6 nm)/[Co/Ni]s(4 nm). Inset: the ABS view of pole tip, the skew angle is defined as the angle between recording track and normal direction of trailing side.  
track bit. The \(P_{\textit{{{{\it{ensure}}}}}}\) drops sharply along with the increase of \(H_{\textit{{{\it{sw}}}}}\) when \(H_{\textit{{{\it{sw}}}}}\) is smaller than 16.44 kOe, so the \(P_{\textit{{{\it{write-in}}}}}\) declines as well. In contrast, because the \(P_{\textit{{{\it{reporting}}}}}\)_hit increases rapidly along with the increase of \(H_{\textit{{{\it{sw}}}}}\) when \(H_{\textit{{{\it{sw}}}}}\) is larger than 16.44 kOe, the \(P_{\textit{{{\it{write-in}}}}}\) increases correspondingly. The results show that proper \(H_{\textit{{{\it{sw}}}}}\) is significant to guarantee the writing capability of the shingled writer, and simultaneously the media polarity can avoid being potentially switched by the stray field at the same write window. Therefore, \(L1_{0}\)-FePt(6 nm)/[Co/Ni]\({}_{5}\)(4 nm) (\(H_{\textit{{{\it{sw}}}}}\) = 16.44 kOe) is adopted as an appropriate ECC media to calculate EBW and the combined write-in error rate.