  Two issues related to the microwave surface impedance Z_s of MgB_2 thin film
are discussed in this Letter, both being significant for potential microwave
applications. At first, a correlation between Zs and Alpha = Xi/l was found,
where Xi is the coherence length, and l is the mean free path. The surface
resistance Rs decreases with Alpha at moderate and large values of Alpha and
saturates when Alpha approaches one. The values of the penetration depth at
zero temperature Lamda(0) for different films could be well fitted by Lamda_L
(1+Alpha)^(1/2), yielding a London penetration depth Lamda_L of 33.6 nm. The
second issue is to find a temperature niche for possible microwave
applications. Between 10K and 15K, our best MgB_2 films possess the lowest Rs
values compared with other superconductors such as NbN, Nb3Sn and the
high-temperature superconductor YBCO.
