Currently semiconductor devices are manufactured using the photolithographic process wherein light is past through a mask which forms a pattern of shadows on the surface of a wafer. The pattern of shadows is reduced in size using a lens. The patterns are etched into the wafer surface and used to form
circuits.
The process has a theoretical size limited by the wavelength of light. X-rays and electron beams have been proposed as alternatives to light since they have shorter wavelengths hence making smaller features, but they are harder to control. For example, neither can be focused with a lens.
To overcome this problem a diffraction grating could be used. The diffraction grating pattern would be the 2d Fourier Transform of the resultant image required.
Essentially this uses the interference of waves to create a focused image instead of a lens.
This would require a diffractive grating much larger than the image itself to reproduce the required detail (by capturing enough diffractive orders).
Manufacturing the diffraction grating would need to be smaller/sharper than a standard photolithographic mask, which could be made by electron beam lithography (EBL) or some nano-manufacturing technique.