= Raman peak-position map
{c}
{title2=$\widetilde\nu_{\rm peak}(x,y)$}
A <Raman peak-position map> assigns to each sample position the fitted <Raman shift> of a selected spectral band. Starting from position-resolved spectra, the analysis estimates $\widetilde\nu_{\rm peak}(x,y)$ and displays its spatial variation. It answers a different question from a <Raman band-area map>, which records an integrated spectral intensity. Manufacturer documentation uses fitted band position to reveal structural variation, including strain-related changes in a silicon-carbide wafer.<What Raman images can reveal by Renishaw>[Silicon-carbide wafer example; “How can I analyse Raman images?”, curve-fit parameters]{ref}
For a simple isolated <Gaussian function> band above background $B$,
$$
I(\widetilde\nu)-B(\widetilde\nu)
=H\exp\!\left[-\frac{(\widetilde\nu-\widetilde\nu_0)^2}{2s^2}\right],
$$
the fitted center $\widetilde\nu_0$ is the peak position. A maximum chosen from discrete channels can instead jump in steps of the channel spacing. Fitting uses the neighboring samples too, although its result still depends on the line-shape model, background and noise. <Raman peak-fit uncertainty> belongs with the resulting map.
For an explicitly hypothetical band, suppose a reference region is at1000.0cm⁻¹ and another region at1000.5cm⁻¹. The shift difference is0.5cm⁻¹. If an independently established local stress calibration were $\Delta\widetilde\nu=K\sigma$ with $K=2\,\mathrm{cm^{-1}/GPa}$, that model would imply0.25GPa. The coefficient is illustrative, not a material constant asserted for the manufacturer's wafer. A quantitative stress map requires the applicable <measurement calibration> and control of other causes of spectral change.
Overlapping bands can move the maximum of their sum when only their relative intensities change. A stable center estimate must therefore track a specified band rather than interpret every maximum shift as strain. Instrument drift, temperature and laser-induced heating can also affect position. Retaining the underlying spectra and fit results makes it possible to test those interpretations rather than rely only on the map's colours.
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