Vertical power devices which include an insulated trench containing insulating material and a gate electrode, and related methods. A body region is positioned so that a voltage bias on the gate electrode will cause an inversion layer in the body region. A layer of permanent charge, at or near the sidewall of the trench, provides charge balancing for the space charge in the depleted semiconductor material during the OFF state. A conductive shield layer is positioned below the gate electrode in the insulating material, and reduces capacitive coupling between the gate and the lower part of the trench. This reduces switching losses. In other embodiments, a planar gate electrode controls horizontal carrier injection into the vertical conduction pathway along the trench, while a shield plate lies over the trench itself to reduce capacitive coupling.