  Spin-orbit splitting of conduction band in HgTe quantum wells was studied
experimentally. In order to recognize the role of different mechanisms, we
carried out detailed measurements of the Shubnikov-de Haas oscillations in
gated structures with a quantum well widths from $8$ to $18$ nm over a wide
range of electron density. With increasing electron density controlled by the
gate voltage, splitting of the maximum of the Fourier spectrum $f_0$ into two
components $f_1$ and $f_2$ and the appearance of the low-frequency component
$f_3$ was observed. Analysis of these results shows that the components $f_1$
and $f_2$ give the electron densities $n_1$ and $n_2$ in spin-orbit split
subbands while the $f_3$ component results from magneto-intersubband
oscillations so that $f_3=f_1 - f_2$. Comparison of these data with results of
self-consistent calculations carried out within the framework of four-band
\emph{kP}-model shows that a main contribution to spin-orbit splitting comes
from the Bychkov-Rashba effect. Contribution of the interface inversion
asymmetry to the splitting of the conduction band turns out to be four-to-five
times less than that for the valence band in the same structures.
