3.5.5.2. Detector Theory

In gas-flow and sealed detectors, X-rays produced from the sample ionize an inert detector gas, ejecting an outer shell electron to produce an electron-ion pair (Ar ® Ar⁺ + e^-). The first ionization potentials of the inert gases are small (less than 25 eV); however, the effective ionization potential that is required to produce an electron-ion pair is somewhat higher due to competing processes which absorb incident photon energy without causing ionization.

The average number of electron-ion pairs (n) produced by an X-ray is:

Consider: the energy of Cu-Ka is 8.04 keV, so, using Ar detector gas, n = 8040/26.4 = 304 primary electron-ion pairs. This number is too small to detect, but placing a potential across the gas from wire to tube wall produces amplification. The electrons produced by the incoming X-ray are accelerated towards the anode wire by the detector voltage and can in turn ionize other Ar atoms producing another electron-ion pair and so on (Figure 3.5.5.2a). This "avalanche" effect produces an amplification of the initial signal. The chain of ionizations causes a momentary voltage across the detector producing a pulse.

Figure 3.5.5.2a. Principle of detection of an X-ray photon. Incident X-rays ionize the Ar detector gas losing an average of 26.4 eV, then continue to ionize other atoms. The resulting secondary electrons are accelerated toward the detector wire, gaining sufficient energy to ionize other Ar atoms, producing an electron avalanches. The Ar ions are neutralized by electrons donated by methane molecules in the detector gas mix.

The amount of amplification produced by the gas depends on the amount of voltage applied to the detector (Figure 3.5.5.2b). At very low voltages in the region of undersaturation, the detector potential difference is too small to prevent recombination of electron-ion pairs formed by incident X-rays before they reach the collecting wire. At slightly higher voltages in the ionization chamber region, the potential is just sufficient to counter recombination so that the number of electron-ion pairs produced by X-rays equals the number reaching the anode wire, and the gain is 1. Further increases in the detector voltage produce the avalanche effect and significant gains. At voltages in the proportional counter region, the pulse height is proportional to the energy of the incident X-ray. Too high a voltage drives the detector out of the proportional region and into the Geiger region.

Figure 3.5.5.2b. The effect of increasing the applied anode voltage on (a) the gas amplification factor and (b) the observed count rate (ignoring pulse height analysis settings) for a gas proportional counter. Note the rapid increase in observed count rate at the threshold of Geiger breakdown (after Potts 1987).

Gain may be defined as:

Detector gains are typically on the order of 10⁴ to 10⁵. With a gain of 10⁴, the 304 EI pairs formed by a Cu-Ka X-ray produce 3.04 x 10⁶ electrons that reach the anode wire. The size of the resulting pulse can be calculated from:

The charge on a single electron is 1.6022 x 10^-19 coulomb, and a typical detector has a capacitance of 10^-10 farad. Thus, our Cu-Ka photon will generate a voltage of:

Recall that we've assumed a gain of 10,000! The resulting pulse is still very small and needs further electronic amplification.