We study shallow-donor impurity states and the optical absorption spectra associated with transitions from the n = 1 valence subband to the donor impurities in a corner under an applied electric field. It is found that the energy contours for the impurity binding in the corner become closed when a suitable electric field is applied; this is similar to the impurity-state behaviour in quantum wires. When the electric field strength increases, the centre of the contours moves towards the corner and the centre impurity binding energy increases. The optical absorption spectra associated with donors in the corner are also similar to those of quantum wires when the electric field is applied, and the width of the absorption spectra increases with the increase in the electric field strength.