Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2020 / Paper 1 / Section A(ii) / 3

A high-pressure Mercury arc lamp is a conventional source for proximity photolithography. An electric discharge excites Mercury vapour; radiative transitions produce strong spectral lines, selected by filters and delivered through collimating optics. Common lines are $365\mathrm{nm}$ (i-line) and $436\mathrm{nm}$ (g-line). The finite mask-wafer gap gives near-field Fresnel diffraction, rather than the far-field approximation. Diffracted light spreads into nominally dark regions, limiting the minimum printable feature.

With the proximity-resolution convention $w=k\sqrt{\lambda g}$, the maximum mask-wafer gap isFor $w=5\mu \mathrm{m}$ and $k=2$, $g_{\max }\simeq 17.1\mu \mathrm{m}$ at $365\mathrm{nm}$. If the g-line is used instead, $g_{\max }\simeq 14.3\mu \mathrm{m}$ at $436\mathrm{nm}$. The wavelength must be specified; the question's preceding choice of two lamp lines does not select a unique number. This estimate neglects extra loss of resolution from finite resist thickness, mask imperfections and angular illumination spread.

Projection lithography images a mask through reduction optics; its resolution scales approximately as $k_1\lambda /\mathrm{NA}$. It offers parallel exposure, high throughput and accurate repeat patterning, but small features demand short wavelengths, large numerical aperture, costly optics and high-quality masks, with a shrinking depth of focus.

Electron beam lithography directly writes a programmable pattern using a focused electron beam. Its much shorter wavelength and small probe permit nanometre-scale features without an optical mask, making it attractive for research prototypes, low-volume devices and mask fabrication. Its limitations are serial writing time, charging of insulating substrates, beam drift, field stitching and forward/backscattering proximity effects in electron-beam lithography. Electron wavelength alone does not set the resist resolution. E-beam is often preferable for a few very small custom structures; projection remains preferable for high-volume repeated manufacture.