Screened Coulombic impurity bound states in semiconductor quantum wells

The ground bound state of Coulombic impurity screened by free carriers in a quantum well versus the free-electron concentration nₑ is calculated for several well thicknesses. Zero temperature and electric quantum limit are assumed. The random-phase-approximation dielectric function is used to describe the screening effect. For a given well thickness the binding energy decreases with increasing electron concentration until a saturation is reached at large nₑ. The remaining binding is not negligible. At low temperature this may give rise to a freeze-out effect.