Local density of states in double-barrier resonant-tunneling structures. II. Finite-width barriers

The local density of states (DOS) in the quantum-well region of a double-barrier resonant-tunneling structure is calculated for the case of zero applied bias. As the barrier potential $V_0$ goes to zero, the local DOS approaches an $E^{1/2}$ behavior; as $V_0$ goes to infinity, a staircaselike local DOS is obtained. A one-dimensional DOS, characterized by a fixed momentum transverse to the barriers, goes like $E^{\mathrm{-}1/2}$ as $V_0$ goes to zero and like a series of δ functions in the limit of infinite $V_0$. The behavior of these local-DOS functions is examined for physically realizable structures.