A plurality of layers of a first semiconductor material and a plurality of dots-in-a-fence barriers disposed in a stack between a first electrode and a second electrode. Each dots-in-a-fence barrier consists essentially of a plurality of quantum dots of a second semiconductor material embedded between and in direct contact with two layers of a third semiconductor material. Wave functions of the quantum dots overlap as at least one intermediate band. The layers of the third semiconductor material are arranged as tunneling barriers to require a first electron and/or a first hole in a layer of the first material to perform quantum mechanical tunneling to reach the second material within a respective quantum dot, and to require a second electron and/or a second hole in a layer of the first semiconductor material to perform quantum mechanical tunneling to reach another layer of the first semiconductor material.