We analyze the dynamics of charge distributions in weakly coupled. doped, d
e voltage biased semiconductor superlattices subject to voltage steps of di
fferent sizes. Qualitatively different current responses to voltage switchi
ng processes have been observed experimentally. We explain them by invoking
distinct scenarios for electric-held domain formation, validated by numeri
cal simulations. Furthermore, we investigate the transient from an unstable
to a stable point in the current-voltage characteristics after a steplike
or ramplike increase of the external voltage.