Fano-limited X-ray CCD energy resolution ($\Delta E_{\mathrm{FWHM}}=2\sqrt{2\ln 2}\sqrt{FwE}$)

A photon of energy $E$ fully absorbed in silicon produces on average $E/w$ electron-hole pairs, with variance $FE/w$ rather than necessarily a Poisson variance. Thus ${\sigma }_E=\sqrt{FwE}$ and Gaussian FWHM is $2\sqrt{2\ln 2}{\sigma }_E$. Representative silicon values $w\simeq 3.65$ eV and $F\simeq 0.12$ give about $156$ eV FWHM at $10$ keV. read noise in split-event pixels, trapping and gain errors broaden that limit; optical pixel size alone does not specify the energy resolution.^[ref]