  It has recently been shown that if we take into account a class of higher
derivative corrections to the effective action of heterotic string theory, the
entropy of the black hole solution representing elementary string states
correctly reproduces the statistical entropy computed from the degeneracy of
elementary string states. So far the form of the solution has been analyzed at
distance scales large and small compared to the string scale. We analyze the
solution that interpolates between these two limits and point out a subtlety in
constructing such a solution due to the presence of higher derivative terms in
the effective action. We also study the T-duality transformation rules to
relate the moduli fields of the effective field theory to the physical
compactification radius in the presence of higher derivative corrections and
use these results to find the physical radius of compactification near the
horizon of the black hole. The radius approaches a finite value even though the
corresponding modulus field vanishes. Finally we discuss the non-leading
contribution to the black hole entropy due to space-time quantum corrections to
the effective action and the ambiguity involved in comparing this result to the
statistical entropy.
