  A system very similar to a dielectric barrier discharge, but with a simple
stationary DC voltage, can be realized by sandwiching a gas discharge and a
high-ohmic semiconductor layer between two planar electrodes. In experiments
this system forms spatiotemporal and temporal patterns spontaneously, quite
similarly to e.g., Rayleigh-Benard convection. Here it is modeled with a simple
discharge model with space charge effects, and the semiconductor is
approximated as a linear conductor. In previous work, this model has reproduced
the phase transition from homogeneous stationary to homogeneous oscillating
states semiquantitatively. In the present work, the formation of spatial
patterns is investigated through linear stability analysis and through
numerical simulations of the initial value problem; the methods agree well.
They show the onset of spatiotemporal patterns for high semiconductor
resistance. The parameter dependence of temporal or spatiotemporal pattern
formation is discussed in detail.
