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Why does the amount of electric charge collected in a semiconductor detector indicate X-ray energy?

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detector output connected to a measuring circuit — radiation measurement Figure 1: (A) A simple equivalent circuit for the development of a voltage pulse at the output of a detector. R represents the resistance and C the capacitance of the circuit; V(t) is the time (t)-dependent voltage produced. (B) A representative current pulse due to the interaction of a single quantum in the detector. The total charge Q is obtained by integrating the area of the current, i(t), over the collection time, t_c. (C) The resulting voltage pulse that is developed across the circuit of (A) for the case of a long circuit time constant. The amplitude (V_max) of the pulse is equal to the charge Q divided by the capacitance C.

In a semiconductor detector, the amount of electric charge collected is proportional to the energy of the incident X-ray photon because of the way the material interacts with radiation at the atomic level.1

When an X-ray photon is absorbed by the semiconductor, it transfers its energy to electrons bound in the valence band. This energy is sufficient to promote these electrons across the band gap into the conduction band, creating electron-hole pairs.12

Because a specific, predictable amount of energy is required to create each electron-hole pair—on average, about three times the material's band-gap energy—the total number of pairs generated is directly linked to the total energy deposited by the X-ray. Under the influence of an applied electric field, these charge carriers drift toward electrodes, generating a current pulse. Since the total charge collected is the sum of these individual pairs, it serves as a direct measure of the original X-ray photon's energy.21