Electronic conductance of a two-dimensional electron gas in the presence of periodic potentials

We utilize mode-matching and transfer-matrix methods to study the transport properties of an electron through two-dimensionally modulated periodic potentials. The model structures treated here are finite-size one- and two-dimensional arrays of quantum boxes (lateral surface superlattice) and antidots. The structure is divided into a chain of uniform waveguide sections in the direction of current flow, and mode matching is imposed across the boundaries. The transfer-matrix technique is utilized to obtain the transmission probability for the composite superlattice structures. Energy dependences of the two-terminal conductance are presented in terms of the transition from one-dimensional to two-dimensional transport. Increasing the number of quantum boxes in the lateral surface superlattice shows that Lorentzian-shaped transmission resonances in a single quantum box are brought together to form a Bloch band structure. Complete reflections over broad energy ranges, due to the formation of minigaps, and a strong resonant behavior due to discrete states in minibands are observed in the energy dependence of the conductance. For the antidot lattice, the formation of the Bloch band structure is found to arise as a drop in the conductance. If attractive scattering centers are embedded in a two-dimensional electron gas, transmission resonances due to quasibound states are observed.