  This paper considers a system of two parallel quantum Hall layers with total
filling factor $0$ or $1$. When the distance between the layers is small
enough, electrons and holes in opposite layers form inter-layer excitons, which
have a finite effective mass and interact via a dipole-dipole potential.
Results are presented for the chemical potential $\mu$ of the resulting bosonic
system as a function of the exciton concentration $n$ and the interlayer
separation $d$. Both $\mu$ and the interlayer capacitance have an unusual
nonmonotonic dependence on $d$, owing to the interplay between an increasing
dipole moment and an increasing effective mass with increasing $d$. A phase
transition between superfluid and Wigner crystal phases is shown to occur at $d
\propto n^{-1/10}$. Results are derived first via simple intuitive arguments,
and then verified with more careful analytic derivations and numeric
calculations.
