High voltage integrated circuit capacitors are disclosed. In an example arrangement. A capacitor structure includes a semiconductor substrate; a bottom plate having a conductive layer overlying the semiconductor substrate; a capacitor dielectric layer deposited overlying at least a portion of the bottom plate and having a first thickness greater than about 6 um in a first region; a sloped transition region in the capacitor dielectric at an edge of the first region, the sloped transition region having an upper surface with a slope of greater than 5 degrees from a horizontal plane and extending from the first region to a second region of the capacitor dielectric layer having a second thickness lower than the first thickness; and a top plate conductor formed overlying at least a portion of the capacitor dielectric layer in the first region. Methods and additional apparatus arrangements are disclosed.