  The Bardeen-Cooper-Schrieffer (BCS) condensation and the Bose-Einstein
condensation (BEC) are the two extreme limits of the ground state of the paired
fermion systems. We report crossover behavior from the BCS condensation to the
BEC realized in the two-dimensional (2D) superconductor, electron doped layered
material ZrNCl. The phase diagram, established by simultaneous experiments of
resistivity and tunneling spectra under the ionic gating, demonstrates the
pseudogap phase at the low doping regime. In the low carrier density limit,
$T_{\rm BKT}$ (Berezinskii-Kosterlitz-Thouless transition temperature for 2D
superconductors) scales as $T_{\rm BKT}/T_{\rm F} = 0.12$, where $T_{\rm F}$ is
the Fermi temperature, which is consistent with the theoretical upper bound
expected in the BCS-BEC crossover regime. The present results indicate that the
gate-doped semiconductor provides an ideal platform for the 2D BCS-BEC
crossover without any added complexity, such as magnetic orders and density
waves.
