The dynamics of the current and the electron number in quantum-dot tur
nstile devices, in which the heights of the tunneling barriers are mod
ulated by external rf signals, is studied theoretically within the adi
abatic approximation. The displacement current is more accurately quan
tized than the tunneling currents flowing through both the left and th
e right barriers, since the leakage current is compensated. We find nu
merically that an electron tunnels through the barrier before its heig
ht reaches the minimum value. The tunneling phases of rf signals, at w
hich an electron can actually tunnel, change as the amplitude of rf si
gnals and the barrier height and width are varied. We also discuss the
conditions for the current quantization, The dc I-V curve which We ob
tain shows a plateau at each quantized current nef with width e(2)/C Delta E and sharp steps between neighboring plateaus. Whenever the de
current is quantized, the change of the number of electrons in the qu
antum dot during one half-period of rf signal is an integer.