 Negative sheet on a positive volume-charged slab

Place a fixed sheet of charge density $-\sigma$ at $z=0$ and a uniform fixed volume charge $\rho$ in $-d<z<0$. With no imposed uniform background field, the above-sheet and below-slab fields are $\pm (\rho d-\sigma )/(2{ϵ}_0)$. The interior field is the title expression, obtained by adding the slab's linear field to the sheet's constant field. If $0<\sigma <\rho d$, it vanishes at $z=-(d+\sigma /\rho )/2$, inside the lower half of the slab. At the sheet it jumps down by $\sigma /{ϵ}_0$, while it remains continuous at the slab's uncharged lower face.