  Impedance matching and heat management are important factors influencing
performance of THz sources. In this work we analyze thermal and radiative
properties of such devices based on mesa structures of a layered
high-temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. Two types
of devices are considered, containing either a conventional large single
crystal, or a whisker. We perform numerical simulations for various geometrical
configurations and parameters and make a comparison with experimental data for
the two types of devices. It is demonstrated that the structure and the
geometry of both the superconductor and the electrodes are playing important
roles. In crystal-based devices an overlap between the crystal and the
electrode leads to appearance of a large parasitic capacitance, which shunts
THz emission and prevents impedance matching with open space. The overlap is
avoided in whisker-based devices. Furthermore, the whisker and the electrodes
form a turnstile (crossed-dipole) antenna facilitating good impedance matching.
This leads to more than an order of magnitude enhancement of the radiation
power efficiency in whisker-based, compared to crystal-based devices. These
results are in good agreement with presented experimental data.
