A strong bias asymmetry of the spin-injection efficiency through an epitaxial Fe/GaAs Schottky tunnel contact is observed. Low-temperature post-growth thermal annealing is shown to strongly affect the spin-injection efficiency. The annealing leads either to a reduction or an enhancement. The spin accumulation is addressed electrically in a lateral spin-valve geometry using a non-local spin-valve setup at liquid helium temperatures. A spin-injection efficiency of up to 5.5% is estimated from experimental results. The electrical properties of the Schottky tunnel diode do not reflect the bias asymmetry and the changes in the spin-injection efficiency during annealing. Formation of spin-polarized interface states (IS) close to the Fermi-level is a possible explanation. The IS will not only radically affect the spin-injection but also the spin-detection process.