Determination of lateral diffusivity in single pixel X-ray absorbers with implications for position dependent excess broadening

An ideal microcalorimeter is characterized by a constant energy resolution across the sensor's dynamic range. Any dependence of pulse shape on the position within the absorber where an event occurs leads to a degradation in resolution that is linear with event's energy (excess broadening). In this paper we present a numerical simulation that was developed to model the variation in pulse shape with position based on the thermal conductivity within the absorber and between the absorber, sensor, and heat bath, for arbitrarily shaped absorbers and sensors. All the parameters required for the simulation can be measured from actual devices. We describe how the thermal conductivity of the absorber material is determined by comparing the results of this model with data taken from a position sensitive detector in which any position dependent effect is purposely emphasized by constructing a long, narrow absorber that is readout by sensors on both ends. Finally, we present the implications for excess broadening given the measured parameters of our X-ray microcalorimeters.