Screening effects on theD−system in semiconductors

A calculation of the binding energy of a $D^{-}$ ion, defined as the energy required to remove one of the two electrons from the $D^{-}$ ion to infinity in the presence of other free carriers, is reported. It is assumed that the effective interactions between the constituents of the $D^{-}$ ion are described by Thomas-Fermi potentials. The variation of the binding energy of the $D^{-}$ ion as a function of the screening parameter $\delta$ is calculated with the use of a variational approach. Results with the use of a fairly general trial wave function show the binding energy of a $D^{-}$ ion goes to zero for $a\delta =0.87\mathrm{}$ where $a$ is the Bohr radius of an isolated neutral donor. The binding energy of a neutral donor itself in the presence of free carriers goes to zero for $a\delta =1.2\mathrm{}$. The relative significance of these two values is discussed. Some possible experimental situations where this system may be studied are pointed out.