Simple model for multistability and domain formation in semiconductor superlattices

Negative differential conductivity is a well-known effect in semiconductor superlattices if a voltage is applied perpendicular to the layer structure. For highly doped superlattices, the appearance of electric-field domains has been found experimentally [H. T. Grahn et al., Phys. Rev. Lett. 67, 1618 (1991)]. In this paper we present a theoretical model which can explain these effects quantitatively. The model considers the lowest two subbands of the single quantum wells and includes resonant tunneling between adjacent wells, miniband conduction, and intersubband relaxation within each well. We obtain multistability of the current-voltage characteristic and various hysteretic transitions which arise upon sweeping the applied voltage, and which are associated with changes in the domain size.