Photolithographic process simulation is described in which fast computation of resultant intensity for a large number of process variations andor target depths is achieved by computation of a set of partial intensity functions independent of using a mask transmittance function, a plurality of illumination system modes, and a plurality of preselected basis spatial functions independent of. In accordance with the semiconductor device and the method for manufacturing the same of the present invention, carbon-based materials are used to form a sacrificial spacer, and at least one air void is formed after removing the sacrificial spacer, the overall dielectric constant of the spacer is effectively reduced. The other end of this arm supports the music deck upon which the music is placed. The display displays the measured amount of curing energy in real-time. In effect, a sideway HEMT is formed with the electron donor layer, the 2DEG region and the ohmic contact material increasing the concentration of electrons all along the contact between the lower semiconductor layer and the electron donor layer.