A Study of X-Ray Response of the TES X-Ray Microcalorimeter for STEM

Abstract

TES microcalorimeters show a nonlinear pulse-height-to-energy relation, reflecting their nonlinear resistance-to-temperature relation on the transition edge. In some of TES applications, such as energy dispersive X-ray spectroscopy, a wide energy range (e.g. 0.5–15 keV) and a good energy calibration (e.g. within a few eV) are required. We have studied the method to calibrate the nonlinear pulse-height-to-energy and to correct for it in the data analysis. We irradiated a TES microcalorimeter with three radio isotopes simultaneously to obtain continuum-free line spectra covering from 3.3 to 17.8 keV. X-ray lines from those isotopes are, respectively, a line complex containing fine structures and/or satellite lines, which cannot be fully separated with TES microcalorimeters. Thus, a special treatment is necessary. We first established a method to estimate the relation between PHA (pulse height analyzed value by optimum filtering) and X-ray energy of the line complex precisely: we assumed that the relation could be approximated with a linear function, $\text{PHA} = aE +b$ , locally in the narrow energy range containing one of the line complex, and determined $a$ and $b$ from the model fit of the PHA spectrum of the line complex. Then, from the PHA-to-energy relations of six line complexes, we determined an approximation formula which represented the global PH-to-energy relation. We then applied the global relation to convert PHA values of all pulses to energy equivalent value, which we call PI (pulse invariant). We then fitted the PI spectra with the model function to check the consistency of energy. We have done these processes starting from two different forms of data; TES current as a function of time, and TES resistance as a function of time. The nonlinearity of PHA-to-energy was smaller for TES resistance pulses, and a better energy calibration is obtained. We found that the PI spectra obtained from TES resistance pulses reproduced the X-ray energies within $\pm 3$ eV uncertainty, while the uncertainties becomes as large as 10 eV for the PI spectra obtained from TES current pulses.