  Tunneling between opposite surfaces of topological insulator thin film
populated by electrons and holes is considered. We predict considerable
enhancement of tunneling conductivity by Cooper electron-hole pair fluctuations
that are precursor of their Cooper pairing. Cooper pair fluctuations lead to
the critical behavior of tunneling conductivity in vicinity of critical
temperature with critical index \nu=2. If the pairing is suppressed by disorder
the behavior of tunneling conductivity in vicinity of quantum phase transition
is also critical with the index \mu=2. The effect can be interpreted as
fluctuational internal Josephson effect and it is general phenomenon for
electron-hole bilayers. The peculiarities of the effect in other realizations
of electron-hole bilayer are discussed.
