The Kronig-Penney model has been widely used to explore the characteristics of electrons in a periodic potential as this model provides one with perhaps the simplest instance of Bloch states. This model and its relation with superlattices has also been used in recent times to provide an implementation of the physics of random and quasiperiodic systems. It is because of its importance and wide applicability that we focus our attention on the Kronig-Penney model to investigate the imperfect finite superlattices. There exist many theoretical methods developed for description of disordered systems such as Monte-Carlo simulation

truncated rate equation

perturbative approach

Wannier-Stark levels etc. However

provides an easy way (tranfer matrix) that is very valid for studying the electronic states of imperfect finite SLS. Tranfer matrix method can be turned out to be more convenient for computer than the conventional formalism

which is based on effective mass approximation and Bastard’s boundary condition. The barrier and well can be represented by matrixes and the wave functions at any two positions inside the superlattice are connected by a product of transfer matrixes. The sequence of the matrixes matches the arrangement of the barriers and wells. No matter how the barrier and well change

we need only to modify the matrixes of barrier and well. We mainly discuss the electronic states of finite SLS with intentional random barriers or well widths by means of a transfer matrix method. The transmittance and its localized wave function of SLS with random potentials were calculated and also the transmittance and electronic eigenfunction of SLS with random well widths were calculated. The results are compared with those obtained from ordered SLS. We can observe discrete localized states of finite SLS with intentional random barriers or well widths. Our simulated results indicate that electronic states are sensitive to both the intentional random barriers and well widths. Especially when well widths randomly vary in a range of (9.1～10.9) nm for SLS discussed in this paper

we find that the subband begins to disappear. In recent decades the physical community and scientists in related fields have shown an increasing interest in the structure and properties of disordered condensed systems. It’s clear that the method developed in this paper can be extended easily to solve some other kinds of problems caused by disordered systems such as localized states

extended states

mobility edges and so on.