Conditions of coexistence of Tamm and Shockley states in a superlattice with a perturbed surface

Conditions of electron surface-state existence are studied by means of the transfer matrix method in a semi-infinite superlattice with alloy concentration changing either abruptly (square potential) or gradually (sinusoidal potential). A small surface perturbation is introduced into the model by modifying the shape of surface potential well. The effect of this surface perturbation on Shockley (S) states is studied, with special attention paid to the threshold perturbation which destroys an existing S surface state by shifting it from the gap to a band; for Tamm (T) states, we search for the minimum perturbation value inducing a T surface state to appear. The results obtained show coexistence of Tamm and Shockley states within a precisely specified range of the model parameter values. The theory is applied to investigate S and T surface states coexistence in AlₓGa_1-xAs superlattice.