  We consider the effect of the finite size in the ab-plane on the surface
density of states (DoS) in clean d-wave superconductors. In the bulk, the DoS
is gapless along the nodal directions, while the presence of a surface leads to
formation of another type of the low-energy states, the midgap states with zero
energy. We demonstrate that finiteness of the superconductor in one of
dimensions provides the energy gap for all directions of quasiparticle motion
except for \theta=45 degrees (\theta is the angle between the trajectory and
the surface normal); then the angle-averaged DoS behaves linearly at small
energies. This result is valid unless the crystal is 0- or 45-oriented (\alpha
\ne 0 or 45 degrees, where \alpha is the angle between the a-axis and the
surface normal). In the special case of \alpha=0, the spectrum is gapped for
all trajectories \theta; the angle-averaged DoS is also gapped. In the special
case of \alpha=45, the spectrum is gapless for all trajectories \theta; the
angle-averaged DoS is then large at low energies. In all the cases, the
angle-resolved DoS consists of energy bands that are formed similarly to the
Kronig-Penney model. The analytical results are confirmed by a self-consistent
numerical calculation.
