On the experimental determination of the Fano factor in Si at soft X-ray wavelengths

We have investigated the experimental determination of the Fano factor in silicon using a low-noise CCD detector. We have tested the hypothesis of Fraser et al. (Nucl. Instr. and Meth. A 350 (1994) 365) that the distribution of secondary electrons generated by low-energy X-ray interactions is not normally distributed, leading to an asymmetry in the electron number distribution with energy. This in turn, leads to systematically low values of the Fano factor when derived using a traditional analysis of the energy resolution function. Based on measurements taken at the Daresbury Synchrotron Radiation Source (SRS) we find that monoenergetic energy-loss distributions are indeed non-Gaussian to a similar degree predicted by Fraser et al. (1994). The Fano factors determined from a probability analysis of the pulse height data are typically (0.155±0.002) which are significantly different from the value of (0.143±0.001) derived from a Gaussian decomposition of the energy resolution function. The results are in excellent agreement with the theoretical values of ∼0.158 derived from the photoionization theory of Fraser et al. (1994). Lastly, we show that for practical detection systems, failure to correct for a finite energy threshold can also lead to an underestimate in the derived value of F—by as much as ∼5% in the present case.