  We investigated macroscopic quantum tunneling (MQT) of
Bi$_2$Sr$_2$CaCu$_2$O$_y$ intrinsic Josephson junctions (IJJs) with two device
structures. One is a nanometer-thick small mesa structure with only two or
three IJJs and the other is a stack of a few hundreds of IJJs on a narrow
bridge structure. Experimental results of switching current distribution for
the first switching events from zero-voltage state showed a good agreement with
the conventional theory for a single Josephson junction, indicating that a
crossover temperature from thermal activation to MQT regime for the former
device structure was as high as that for the latter device structure. Together
with the observation of multiphoton transitions between quantized energy levels
in MQT regime, these results strongly suggest that the observed MQT behavior is
intrinsic to a single IJJ in high-$T_c$ cuprates, independent of device
structures. The switching current distribution for the second switching events
from the first resistive state, which were carefully distinguished from the
first switchings, was also compared between two device structures. In spite of
the difference in the heat transfer environment, the second switching events
for both devices were found to show a similar temperature-independent behavior
up to a much higher temperature than the crossover temperature for the first
switching. We argue that it cannot be explained in terms of the self-heating
owing to dissipative currents after the first switching. As possible
candidates, the MQT process for the second switching and the effective increase
of electronic temperature due to quasiparticle injection are discussed.
