Optical Critical Dimension Metrology
Active · PhDSemiconductor process control needs geometry, not pictures. Optical critical dimension metrology reads the geometry of a periodic structure out of the light it diffracts, so nothing has to be cleaved, coated or destroyed to be measured.
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The problem
Below roughly a hundred nanometres, the features that matter to a process engineer are smaller than the wavelength used to inspect them. A microscope cannot resolve them; a cross-section SEM can, but the wafer is destroyed and the answer arrives hours later. Neither is compatible with in-line control of a running process.
The information is nevertheless still present in the reflected field. A periodic grating redistributes incident light into discrete diffraction orders whose angles follow sin θₘ = sin θᵢ + mλ/Λ, and whose amplitudes depend on the exact profile of the line: its width, its height, the angle of its sidewall, the rounding at its top corner. Geometry is encoded in intensity, not in position.
How I measure it
A collimated broadband beam illuminates the grating at oblique incidence and the specular or first-order response is collected across wavelength and polarisation. That spectrum is the measurement; on its own it is not yet an answer.
The answer comes from inverting a forward model. I solve Maxwell's equations for a parameterised profile using rigorous coupled-wave analysis, expanding the periodic permittivity in Fourier harmonics and matching fields across layer boundaries, then vary critical dimension, height and sidewall angle until the simulated spectrum matches the measured one. The fitted parameters are the reported measurement.
The practical difficulty is that this inverse problem is not always well conditioned. Different profiles can produce nearly identical spectra, so much of the work is choosing wavelength ranges, incidence angles and polarisation states in which the parameters of interest are genuinely separable, and quantifying how much of the residual is real structure rather than model error.
Why it matters
A measurement that is non-destructive, fast and optical can sit inside the process loop rather than beside it. That changes what process control can be: every wafer measured instead of a sampled few, and profile drift caught while it is still correctable.
Methods & tools
- Broadband spectroscopic scatterometry bench
- RCWA forward solver (MATLAB)
- Inverse fitting and regression analysis
- Polarisation and angle-resolved acquisition
Figure: measured spectral signature of a periodic grating, with the RCWA forward-model fit overlaid.