Diamond Detectors for Ionizing Radiation - HEPHY

Chapter 4
Solid State Detector Theory
When a heavy charged particle traverses material, energy is mainly transfered due to
Coulomb interactions between the particle and the atomic electrons in the material. In
solids with an atomic lattice, which can be described by the band model, the electrons
are excited from the valence to the conduction band when the particle transfers enough
energy. This process is known as electron-hole generation. At very high incident particle
energies, also radiation is emitted when collisions occur, which is called bremsstrahlung.
4.1 Bethe-Bloch Theory
H.A. Bethe 1 and F. Bloch 2 developed a theory based on energy and momentum
conservation for the energy loss of charged particles other than electrons at high energies
(v c) traversing material, stated in terms of dE=dx, when radiative energy loss is
negligible [13, 14].
"
, 1 dE
dx =4N Ar 2 e m ec 2 z 2Z 1 1
A 2 2 ln 2m ec 2 2 2 T max
! #
, 2 , () (4.1)
I 2
2
Eq. 4.1 represents the dierential energy loss per mass surface density [MeV (g cm ,2 ) ,1 ],
where ze is the charge of the incident particle, N A , Z and A are Avogadro's number, the
atomic number and the atomic mass of the material, m e and r e are the electron mass and
e
its classical radius (
2
4 0 m ec
). T 2 max is the maximum kinetic energy which is still detected
in the material, I is the mean excitation energy, = v=c, = (1 , 2 ) ,1=2 and () is
a correction for the shielding of the particle's electric eld by the atomic electrons, the
density eect caused by atomic polarization.
For 0:1 < < 1:0, the dE=dx curves (g. 4.1) approximately fall proportionally to
,2 , then show a broad minimum at =3to 4 (decreasing with Z) and nally slowly
1 Hans Albrecht Bethe, *1906 in Strasbourg. Most of the time he worked with the Cornell University,
interrupted by sabbaticals leading him to CERN and other research centers. For his contributions
to the theory of nuclear reactions he was awarded the Nobel Prize in 1967.
2 Felix Bloch, *1905 in Zurich, y1983. He was working with a number of universities and research
centers, like Stanford and CERN. The Nobel Prize was awarded to him in 1952 for nuclear magnetic
precision measurements.
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