Stochastic Carrier Dynamics in Semiconductor Superlattices

We explore a new regime of hot carrier dynamics, in which electrons in a superlattice miniband exhibit a unique type of stochastic motion when a magnetic field is tilted at an angle θ to the superlattice axis. Remarkably, the dynamics of a miniband electron in a tilted magnetic field reduce to a one-dimensional simple harmonic oscillator, of angular frequency ωC cos θ, where ωC is the cyclotron frequency, driven by a time-dependent plane wave whose angular frequency equals the Bloch frequency ωB. At bias voltages for which ωB = nωC cos θ, where n is an integer, the electron orbits change from localised Bloch-like trajectories to unbounded stochastic orbits, which diffuse rapidly through intricate web patterns in phase space. To quantify how these webs affect electron transport, we make drift-diffusion calculations of the current–voltage curves including the effects of space-charge build up. When the magnetic field is tilted, our simulations reveal a large resonant peak, which originates from stochastic delocalisation of the electron orbits. We show that the corresponding quantised eigenstates change discontinuously from a highly localised character when the system is off resonance to a fully delocalised form when the resonance condition is satisfied. PACS numbers: 73.20.At, 73.21.C