Determining the thermal diffusivity in microcalorimeter absorbers and its effect on detector response

An x-ray microcalorimeter consists of an absorber and a thermometer connected to each other, and to a heat sink, via well defined thermal conductances. The standard theoretical derivation of energy resolution treats the absorber and thermometer as point elements that are internally isothermal. In reality, the finite size and internal diffusivity of the absorber and thermometer prevents these elements from instantly achieving a uniform temperature, leading to a variation in observed pulse shapes as a function of the interaction's position within the absorber. These variations result in a distortion of the detector response and a subsequent degradation of the energy resolution. This paper presents diffusivity measurements for x-ray microcalorimeters fabricated at the NASA/GSFC. Using a diffusion model we developed, we show quantitatively how a 2 eV Gaussian response is distorted into a non-Gaussian profile roughly 12 eV wide at an energy of 6 keV for an absorber diffusivity of 104 μ m2 μs. We then present a method for eliminating the effect of pulse shape variation on the detector energy response with a modified optimal filter approach.