  We propose a kinetic theory to describe the power dependence, $I_{PC}(P)$, of
the photocurrent (PC) lineshape in optically pumped quantum dots at low
temperatures, in both zero and finite magnetic fields. We show that there is a
crossover power $P_c$, determined by the electron and hole tunneling rates, at
which the photocurrent spectra become strongly influenced by the dot kinetics,
and no longer reflect the exciton lifetime in the dot. For $P>P_c$, we show
that the photocurrent saturates due to the slow hole escape rate (in e.g.,
InGaAs/GaAs dots), whereas the line-width increases with power: $\Gamma \propto
\sqrt{P}$. We also analyze to what measure the spin-doublet lineshape of the
photocurrent studied in a high magnetic field reflects the degree of circular
polarization of the incident light.
