A theory of ${\mathrm{sp}}^3$-bonded substitutional deep impurity levels in periodic $N_1$×$N_2$ GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As superlattices predicts that as the thickness t(GaAs) of each GaAs layer is reduced below a critical value (≲17 Å or $N_1$≲6 for x=0.7) common shallow donor impurities such as Si cease donating electrons to the conduction band and instead become deep traps.

This happens because the deep levels associated with point defects in either GaAs or ${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As layers (when measured relative to the valence-band maximum of GaAs) are much less sensitive to changes of the alloy composition or layer thicknesses of the superlattice than the superlattice band edges, particularly the conduction-band edge. For some compositions x, dopants such as Si are shallow donors in N×N GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As superlattices but deep traps in ${\mathrm{Al}}_{(\mathrm{x}/2)}$${\mathrm{Ga}}_{1\mathrm{-}(\mathrm{x}/2)}$As alloy (the alloy obtained by disordering the superlattice). The band gap and band edges of the superlattice, and hence the ionization energies of deep levels, depend strongly on the layer thickness t(GaAs) but only weakly on t(${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As). The $T_2$- and $A_1$-derived deep levels (of the bulk point group $T_d$) are split and shifted, respectively, near a GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As interface: the p-like $T_2$ level splits into an $a_1$ ($p_z$-like) level, a $b_1$ [($p_x$+$p_y$)-like] level, and a $b_2$ [($p_x$-$p_y$)-like] level of the point group for any general superlattice site ($C_{2v}$), whereas the s-like $A_1$ bulk level becomes an $a_1$ (s-like) level of $C_{2v}$. The order of magnitude of the shifts and splittings of deep levels at a GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As interface is 0.1 eV, depends on x, and becomes very small for impurities more than about three atomic planes away from an interface. Deep levels in the GaAs quantum wells experience level shifts due to (i) penetration of their wave functions into the more electropositive ${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As layers, (ii) the band offset, and (iii) quantum confinement.

The cation vacancy, when brought close to a GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As interface, may undergo a shallow-deep transition. These predictions are based on a periodic superslab calculation for unit superslabs with total thickness t(GaAs)+t(${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As) as large as 102 Å or $N_1$+$N_2$=36 two-atom-thick layers. The Hamiltonian is a tight-binding model in a hybrid basis that is a generalization of the Vogl model and properly accounts for the nature of interfacial bonds. The deep levels are computed by using the theory of Hjalmarson et al. and the special-points method. Our results indicate that some normally shallow donors, such as Si, can become deep levels at certain sites in the superlattice as a result of local fluctuations in alloy composition x or layer thickness t(GaAs).

• Received 20 October 1988

DOI:https://doi.org/10.1103/PhysRevB.38.10677