Apparatus for high productivity combinatorial (HPC) processing of semiconductor substrates and HPC methods are described. An apparatus includes a showerhead and two or more pressure-controlled one-way valves connected to the showerhead and used for controlling flow of different processing gases into the showerhead. The pressure-controlled one-way valves are not externally controlled by any control systems. Instead, these valves open and close in response to preset conditions, such as pressure differentials and/or flow differentials. One example of such pressure-controlled one-way valves is a check valve. These valves generally allow the flow only in one direction, i.e., into the showerhead. Furthermore, lack of external controls and specific mechanical designs allow positioning these pressure-controlled one-way valves in close proximity to the showerhead thereby reducing the dead volume between the valves and the showerhead and also operating these valves at high temperatures.