  We study the spin filling of a semiconductor quantum dot using excited-state
spectroscopy in a strong magnetic field. The field is oriented in the plane of
the two-dimensional electron gas in which the dot is electrostatically defined.
By combining the observation of Zeeman splitting with our knowledge of the
absolute number of electrons, we are able to determine the ground state spin
configuration for one to five electrons occupying the dot. For four electrons,
we find a ground state spin configuration with total spin S=1, in agreement
with Hund's first rule. The electron g-factor is observed to be independent of
magnetic field and electron number.
