An analytical thermal model for MR heads

In this work, we present an analytical study of temperature rise due to Joule heating in magnetoresistive heads. Using a transmission-line type model and proper boundary conditions, we derived an analytical formula, including thermal resistance, finite track width and conducting lead effects. Results show the temperature rise due to Joule heat is non-uniform along the MR track width direction: the temperature rise has its peak at the center and decreases rapidly off the track. The averaged temperature rise, which is what one measures experimentally, is 20% lower than the maximum temperature rise at 2 μm track width. Although the temperature distribution also depends on thermal conductivities of both MR and lead materials, it more strongly depends on the thickness and thermal conductivity of the gap dielectric material