We re-examine the idea that the origin of black-hole entropy may lie in the entanglement of
quantum fields between inside and outside of the horizon. Motivated by the observation that certain
modes of gravitational fluctuations in a black-hole background behave as scalar fields, we compute
the entanglement entropy of such a field, by tracing over its degrees of freedom inside a sphere. We
show that while this entropy is proportional to the area of the sphere when the field is in its ground
state, a correction term proportional to a fractional power of area results when the field is in a
superposition of ground and excited states. The area law is thus recovered for large areas. Further,
we identify location of the degrees of freedom that give rise to the above entropy.