Photolithographic LED fabrication using phase-shift mask

A method of forming a light-emitting diode (LED), comprising:

• performing a single photolithographic exposure to photolithographically expose photoresist supported by a semiconductor substrate to form therein an array of photoresist posts having a second spatial frequency, the single photolithographic exposure including passing illumination light once through a phase-shift mask having a two-dimensional pattern comprising first and second phase-shift regions that are spaced apart by an opaque background section and that have a sub-resolution dimension and a sub-resolution spatial frequency, wherein the single photolithographic exposure has a numerical aperture of 0.5 or less and an imaging wavelength defined by a mercury line;
• processing the photoresist to form an array of substrate posts that defines a roughened substrate surface and that have substantially the sub-resolution dimension and substantially the sub-resolution spatial frequency of the first and second phase-shift regions;
• and
• forming a p-n multilayer structure atop the roughened substrate surface to form the LED, wherein the roughened substrate surface acts to scatter light generated by the p-n multilayer structure to increase an amount of light emitted by the LED as compared to the LED having an unroughened substrate surface.