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Review of the Physics
of Semiconductor Detectors Interaction of Ionizing Radiation with Semiconductor
Detectors Heavy charged particles lose energy by Coulomb interaction with the electrons and the nuclei of the absorbing materials. The collision of heavy charged particles with free and bound electrons results in the ionization or excitation of the absorbing atom, whereas the interaction with nuclei leads only to a Rutherford scattering between two types of nuclei. Thus the energy spent by the particle in electronic collisions results in the creation of electron-hole pairs, whereas the energy spent in nuclear collisions is lost to the detection process. The concepts of specific ionization loss dE/dx and of range R can be used to summarize the interaction of heavy charged particles in semiconductor detectors when nuclear collisions are unimportant. The specific ionization loss measures the amount of energy lost by the particle per unit-length of its track; the range indicates how deeply the particle penetrates the absorbing material. Figure 1 shows the stopping power as a function of the energy, and Fig. 2 shows the range as a function of the energy in silicon and in germanium for alpha particles, protons, and deuterons. Nuclear collisions can become an important part of the energy loss process, especially in the case of heavy ions and fission fragments. The theory describing this process is too complicated for a brief summary. We refer the reader to specialized literature such as the IEEE Transactions on Nuclear Science and the references footnoted here.1, 2Finally, it should be mentioned that channeling effects (the steering of charged particles in open regions in the lattice) can reduce the specific ionization loss. Again, we refer the reader to the referenced literature for details on this particular phenomenon.1, 2 ElectronsThe interaction of electrons with matter is similar to the interaction of heavy particles, with the following differences: 1. Nuclear collisions are not part of the interaction because of the very light electron mass.2. At energies higher than a few MeV, radioactive processes (bremsstrahlung) must be considered in addition to the inelastic electron collision. 3. Again because of their light mass, electrons are so intensely scattered that their trajectory in the material is a jagged line; therefore, the concept of range as previously used cannot be applied. Rather, the concept of zero-transmission range is introduced. This is done by means of absorption experiments, which permit definition of the absorber thickness resulting in zero-electron transmission at a given energy. Figure 3 shows the zero-transmission range as a function of energy in silicon and germanium.Gamma and X Rays The interaction of ionizing electromagnetic radiation with matter is different from the processes previously mentioned, and the concept of ranges and specific ionization loss cannot be applied. Only the three most important absorption processes are considered: the photoelectric effect, the Compton effect, and the pair-production effect. The corpuscular description of electromagnetic radiation is the most appropriate for these effects, as one photon in a well-collimated beam of No photons disappears at each interaction. The attenuation of the photon beam can be described by a simple exponential law
where N is the remaining photons in the beam after traversing distance x, and the absorption coefficient µ is the sum of three terms due to the three above-mentioned processes. In the photoelectric interaction, the photon ejects a bound electron from an atom. All of the photon energy, hu is given to the atom, which ejects the electron with an energy hu – E1 , where E1 is the binding energy of the electron. The excited atom then releases energy E1 by decaying to its ground state. In this process, the atom releases one or more photons (and possibly an electron, called an Auger electron). The cross section of the photoelectric effect increases rapidly with the atomic number Z and decreases with increasing energy. The Compton effect is essentially an elastic collision between a photon and an electron; during this interaction, the photon gives a fraction of its energy to the electrons, and its frequency u is therefore decreased. The cross section for this effect decreases with increasing energy, but the decrease is less rapid than for the photoelectric effect.In the pair-production effect, a high-energy photon near a nucleus gives up its energy to produce an electron-positron pair. The photon energy goes into the rest-mass energy and the kinetic energy of the electron-positron pair. The minimum energy necessary for this effect is set by elementary relativistic considerations at the value of 1.022 MeV, an amount equivalent to two electron rest masses. The cross section P for pair production increases with energy. Up to energies of 10 MeV, the P/Z ratio remains constant with energy.2 At higher energies, the cross section starts to decrease for increasing values of the atomic number. Figure 4 summarizes values of the linear absorption coefficients of the above-mentioned effects as a function of gamma-ray energy for silicon and germanium.
1
Radiation Detection and Measurement (2nd
Edition) by Glenn F. Knoll, New York: John Wiley and Sons, 1989, and Semiconductor
Detectors, edited by G. Bertolini and A. Coche, North Holland Publishing Co., 1968
(distributed in the U.S. by American Elsevier Publishing Co.), New York City.
Fig. 1. Stopping Power vs. Energy for Protons, Deuterons, and Alpha Particles in Si and Ge.
Fig. 2. Proton, Deuteron, and Alpha Particle Ranges in Si and Ge.
Fig. 3. Zero Transmission Range vs. Energy for Electrons in Si and Ge.
Fig. 4. Linear Absorption Coefficients vs. Gamma-Ray Energy for Si and Ge. |
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