Thomas-Fermi approximation in $p$-type δ-doped quantum wells of GaAs and Si

Thomas-Fermi calculations of the hole subband structure in $p$-type $\delta$-doped Si and GaAs quantum wells are carried out for different values of impurity concentration. Results are compared with previous self-consistent calculations and with some experimental reports, and very good agreement is found. In particular, the result of hole ground level from this model is exactly equal to the value reported for the experimental system with the smallest impurity spreading that has been achieved.