The radiation ionization energy epsilon(p), which is the mean energy e
xpended per electron-hole pair generated in a given material by an ion
izing radiation, is one of the most important parameters governing the
properties of radiation detectors based on this material. Since the a
dvent of semiconductor detectors in the 1950s, a great deal of experim
ental and theoretical work has been done to determine values of epsilo
n(p) for various crystalline semiconductors. After some review of the
theoretical models proposed for crystalline semiconductors, we present
a detailed study for an amorphous semiconductor. A microscopic Monte
Carlo calculation, taking into account the actual density of states, w
as performed in a-Si:H to study the energy sharing between ionization
and phonon production during hot carrier thermalization. This simulati
on yields values from 4.3 to 5.0 eV for epsilon p for reasonable value
s of the phonon emission mean free path lambda(r) in a-Si:H. This resu
lt is in agreement with experimental results of about 4.4 eV and are c
omparable to 3.63 eV in crystalline silicon, despite the larger 1.7-eV
gap.