  We describe the design, fabrication, and operation of a novel
surface-electrode Paul trap that produces a radio-frequency-null along the axis
perpendicular to the trap surface. This arrangement enables control of the
vertical trapping potential and consequentially the ion-electrode distance via
dc-electrodes only. We demonstrate confinement of single $^{40}$Ca$^+$ ions at
heights between $50~\mu$m and $300~\mu$m above planar copper-coated aluminium
electrodes. We investigate micromotion in the vertical direction and show
cooling of both the planar and vertical motional modes into the ground state.
This trap architecture provides a platform for precision electric-field noise
detection, trapping of vertical ion strings without excess micromotion, and may
have applications for scalable quantum computers with surface ion traps.
