Determination of X-ray flux using silicon pin diodes

Abstract

Accurate measurement of photon flux from an X-ray source, a parameter required to calculate the dose absorbed by the sample, is not yet routinely available at macromolecular crystallography beamlines. The development of a model for determining the photon flux incident on pin diodes is described here, and has been tested on the macromolecular crystallography beamlines at both the Swiss Light Source, Villigen, Switzerland, and the Advanced Light Source, Berkeley, USA, at energies between 4 and 18 keV. These experiments have shown that a simple model based on energy deposition in silicon is sufficient for determining the flux incident on high-quality silicon pin diodes. The derivation and validation of this model is presented, and a web-based tool for the use of the macromolecular crystallography and wider synchrotron community is introduced.

Figure 1

Diagrammatic representation of a pin type diode, showing a typical P⁺–I–N⁺ (pin) layer arrangement.

Figure 2

Log–log plot of the photoelectric cross section, μ_pe/ρ_Si (units: cm² g⁻¹), of silicon as a function of incident X-ray energy.

Figure 3

Representative plot of uncorrected scintillator counts per second versus diode current (points). A Poisson distribution (line) was fitted to these data and the overall agreement shown here implies that the diode current (lower x-axis) was linear with incident flux (proportional to upper x-axis). In this case the incident photon energy was 11 keV, a silica glass target was used as a differential attenuator as described in the text, and the ratio of incident photons diverted to the scintillator over the diode current was 13911 counts s⁻¹ nA⁻¹. The inset highlights a clear deviation from the overall best-fit Poisson model when the SR570 amplifier was using an input impedance of 1 MΩ (blue dots), indicating that the diode became non-linear in this region. This non-linearity was due to the current divider detailed in §2.2.

Figure 4

Normalized sensitivity of diode PIN-10DPI as a function of tilt angle at different incident X-ray energies. Line plots of equation (5) (t _Si 401.9 ± 0.5 µm, t _w 0.33 ± 0.01 µm) are overlaid on the experimental points for each energy.

Figure 5

The ratio of the corrected scintillator count rate to current produced in the S100VL diode plotted against photon energy. Red error bars indicate the root-mean-square scatter of ten back-and-forth comparisons corrected for dead-time and window transmissions [equation (4)] while the blue line is the theoretical photoconversion ratio of the diode [equation (2)]. The theoretical photoconversion ratio is overlaid on the comparison, not fitted to the data. Note that the scatter in measured values is much greater at lower incident X-ray energies owing to the instability of the highly attenuated beam.

Figure 6

Photon flux calculated from equation (2) using the current observed from four diodes in the same X-ray beam as a function of X-ray energy. For details see Table 2 ▶. The energy dependence of the photon flux is a property of the undulator harmonics and the beamline optics and not of the pin diodes used.