  We investigate the role of lattice polarization in determination of induced
carrier density at the $n$-type interface of LaAlO$_3$ overlayer on SrTiO$_3$
(001) by carrying out density-functional-theory calculations. When no oxygen
vacancy or defect is present, the magnitude of polarization screening in the
LaAlO$_3$ layers is found to be correlated with the carrier charge induced at
the interface. For the interfaces with a few LaAlO$_3$ layers, the induced
charge carrier is compensated by the electrostatic screening and consequently
its density remains far less than 0.5 electrons per unit cell.
