Understanding the Detection Limits of a Vertically Packed Anisotropic Magnetoresistive Sensor System

In this work, we study the integration of anisotropic magnetoresistive (AMR) sensors in large arrays using a vertically packed architecture aiming at understanding the feasibility of increasing the sensor volume at a minimal footprint. The AMR elements were measured individually at different packing levels (from level <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${M} =1$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${M} =4$ </tex-math></inline-formula>) allowing the correlation of topography and roughness on each sensing layer with changes in key parameters of the R(H) curves, such as AMR(%), R, magnetic saturation field (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${H} _{\mathbf {Sat}}$ </tex-math></inline-formula>), and sensitivity. Overall, for the studied geometry and designs, an increase in R is observed, leading to a slight decrease in AMR (from 2.4% to 2.2%), whereas magnetically, a linear increase in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${H} _{\mathbf {Sat}}$ </tex-math></inline-formula> is found (from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\approx }3$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\approx }8$ </tex-math></inline-formula> mT). Calculated interlevel dipolar coupling is in good agreement with the experiments, indicating an expected linear increase in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${H} _{\mathbf {Sat}}$ </tex-math></inline-formula> of around 1.46 mT per level for the chosen geometry and spacer thickness. Finally, we compare the detectivity of the simple and compact architectures under external fields.