Effects of the aspect ratio of a word line on the self-field in the presence of a keeper layer

The self-field from a word line containing a soft magnetic keeper layer in the geometry relevant to magnetic random access memory is calculated by using a finite-element method. A significant increase of the self-field is observed by the introduction of the soft magnetic keeper layer. Furthermore, the magnitude of the self-field is found to vary greatly with the aspect ratio of the word line in the presence of the keeper layer. In the aspect ratio range from 0.25 to 16 but at a constant cross-sectional area of 1 μm², the self-field initially increases with the increase of the aspect ratio, reaches a maximum at an aspect ratio of 4, and then decreases with the further increase of the aspect ratio. The present results emphasize the importance of optimizing the shape of a word line containing a soft magnetic keeper layer.