Competition between leak aid quantized currents leads to the breakdown
of the current quantization as the frequency f of RF signal is smalle
r than the tunneling rate Gamma(leak). We find that when f > Gamma(lea
k), the de current is quantized, while tile much larger current than q
uantized current flows through the dot when f < Gamma(leak). We also f
ind new fine structures in the current plateaus resulting from the qua
ntized level spacing Delta E. These structures are washed out at the t
emperature k(B)T similar to Delta(E), though the quantized plateaus re
main. The quantized plateaus are washed out at k(B)T similar to e(2)/C
, where C is the capacitance of the dot.