  We describe charging a quantum dot induced electrostatically within a
semiconducting graphene nanoribbon by electrons or holes. The applied model is
based on a tight-binding approach with the electron-electron interaction
introduced by a mean field local spin density approximation. The numerical
approach accounts for the charge of all the $p_z$ electrons and screening of
external potentials by states near the charge neutrality point. Both a
homogenous ribbon and a graphene flake embedded within the ribbon are
discussed. The formation of transport gaps as functions of the external
confinement potential (top gate potential) and the Fermi energy (back gate
potential) are described in good qualitative agreement with the experimental
data. For a fixed number of excess electrons we find that the excess charge
added to the system is, - depending on the voltages defining the work point of
the device: $(i)$ delocalized outside the quantum dot, - in the transport gap
due to the top gate potential $(ii)$ localized inside the quantum dot, - in the
transport gap due to the back gate potential or $(iii)$ extended over both the
quantum dot area and the ribbon connections, - outside the transport gaps. The
applicability of the frozen valence band approximation to describe charging the
quantum dot by excess electrons is also discussed.

Mesoscale and Nanoscale Physics