We calculate the operating parameters of a transition edge sensor that is mounted on a thin dielectric membrane with the assumption that the phononic heat transport in the membrane is ballistic. Our treatment uses the correct phonon modes from elasticity theory (Lamb-modes), and spans the transition from 3D to 2D behavior. The phonon cooling power and conductance have a global minimum as function of membrane thickness, which leads to an optimal value for the membrane thickness with respect to noise equivalent power at a fixed operating temperature. The energy resolution of a calorimeter will not be affected strongly, but, somewhat counterintuitively, the effective time constant can be reduced by decreasing the membrane thickness in the 2D limit.
@article{arxiv.cond-mat/0702542,
title = {Optimal operation of transition-edge sensors on ballistic membranes},
author = {T. Kühn and I. J. Maasilta},
journal= {arXiv preprint arXiv:cond-mat/0702542},
year = {2007}
}