A no solid bed extruder screw for processing a material to a molten state has a body with a helical thread having pushing and trailing surfaces, the body extending longitudinally between feed and discharge ends. A channel for receiving the material to be processed is formed between the body outer surface and an outer diameter of the thread bounded by the pushing surface and the trailing surface. A volume of the channel decreases in a plurality of revolutions of the thread in a direction from the feed end to the discharge end. A channel depth between the pushing surface and the trailing surface decreases for a first portion of the channel toward the feed end and increases for a second portion of the channel toward the discharge end. At least one of the channel portions has a constant width and includes varying width sub-channels.