  The quest for safe high-energy batteries with "5V-class" cathodes and lithium
metal anodes drives research into solid electrolytes. However, reasons for the
large charge transfer resistances -- the major bottleneck of all-solid-state
batteries -- are still debated. In this article, we explore the processes in
incompressible solid electrolytes between blocking electrodes by theory-based
continuum modeling and numerical simulations. We investigate the experimentally
observed wide space-charge-zones in solid electrolytes, which are a possible
cause for the high interfacial resistances. On time scales relevant for battery
applications, we reduce our model equations. Analytic and numeric calculations
predict and study the actual structure of space-charge-layers in solid
electrolytes. To illustrate these dynamics and validate our model,
computational results are presented and compared with experimental
observations. Analog to semiconductors, we determine the material dependent,
asymmetric space-charge-layer width in the low temperature limit approximately.
This allows us to make an explicit statement about the influence of defect
concentrations and dielectric properties on the width of the
space-charge-layers in homogeneous solid electrolytes.
