Electronic properties of the Kronig - Penney model with semi-infinite lattice of random potential barriers

By using the transfer matrices technique a problem on incidence of the Bloch wave on a semi-infinite one-dimensionallattice of δ-function potential barriers of random strength (the modified Kronig-Penney model) is solved. It is shown that anarbitrarily small uncorrelated perturbation of the periodic potential makes the propagation of undamped Bloch waves characteristic for the classical Kronig-Penney model into the lattice impossible. The extinction length of the Bloch wave is calculated.