Refinement of Transition-Edge Sensor Dimensions for the X-Ray Integral Field Unit on ATHENA

At NASA Goddard Space Flight Center, we have previously demonstrated a kilo-pixel array of transition-edge sensor (TES) microcalorimeters capable of meeting the energy resolution requirements of the future X-ray Integral Field Unit (X-IFU) instrument that is being developed for the Advanced Telescope for High ENergy Astrophysics (ATHENA) observatory satellite. The TES design in this array was a square device with side length of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$50 \,\mathrm{\upmu }\mathrm{m}$</tex-math></inline-formula> . Here, we describe studies of TES designs with small variations of the dimensions, exploring lengths, parallel to the current direction, ranging from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$75 \,\mathrm{\upmu }\mathrm{m}$</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">$50 \,\mathrm{\upmu }\mathrm{m}$</tex-math></inline-formula> and widths, perpendicular to the current direction, ranging from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$50 \,\mathrm{\upmu }\mathrm{m}$</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">$15 \,\mathrm{\upmu }\mathrm{m}$</tex-math></inline-formula> . We describe how these changes impact transition properties, thermal conductance and magnetic field sensitivity. In particular, we show that using a TES with a length of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$50 \,\mathrm{\upmu }\mathrm{m}$</tex-math></inline-formula> and width of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$30 \,\mathrm{\upmu }\mathrm{m}$</tex-math></inline-formula> may be a promising route to reduce the maximum time-derivative of the TES current in an X-ray pulse and reduce the sensitivity of the TES to magnetic field.