  The conversion of energy of electrons produced by a radioactive source into
electricity in a Si and SiC $\textit{p-n}$ junctions is modeled. The features
of the generation function describing the electron-hole pair production by an
electron flow and the emergence of a "dead layer" are discussed. The collection
efficiency, $Q$, describing the rate of electron-hole pair production by
incident beta particles, is calculated taking into account the presence of the
"dead layer". It is shown that in the case of high-grade Si $\textit{p-n}$
junctions, the collection efficiency, $Q$, of electron-hole pairs created by a
high-energy electrons flux, e.g. Pm-147 beta flux, is close or equal to 1 in a
wide range of electron energies. For SiC junctions, $Q$ is large enough (about
1) only for electrons with relatively low energies of about 5 keV, as produced,
e.g., by a tritium source, and decreases rapidly with further increase of
electron energy. The conditions, under which the influence of the "dead layer"
on the collection efficiency is negligible, are determined. The open-circuit
voltage is obtained for realistic values of the minority carriers' diffusion
coefficient and lifetime in Si and SiC $\textit{p-n}$ junctions irradiated by a
high-energy electrons flux. Our calculations allow us to estimate the
attainable efficiency of betavoltaic elements.
