  We propose to control of an electron-hole superfluid in semiconductor coupled
quantum wells and double layers of two-dimensional (2D) material by an external
periodic field. This can either be created by the gates periodically located
and attached to the quantum wells or double layers of 2D material or by the
Moir\'e pattern of two twisted layers. The dependence of the electron-hole
pairing order parameter on the temperature, the charge carrier density, and the
gate parameters is obtained by minimization of the mean-field free energy. The
second order phase transition between superfluid and electron-hole plasma,
controlled by the external periodic gate field, is analyzed for different
parameters.
