  The carbon-oxygen white dwarf (CO WD) + He star channel has been thought to
be one of the promising scnarios to produce young type Ia supernovae (SNe Ia).
Previous studies found that if the mass-accretion rate is greater than a
critical value, the He-accreting CO WD will undergo inwardly propagating
(off-centre) carbon ignition when it increases its mass close to the
Chandrasekhar limit. The inwardly propagating carbon flame was supposed to
reach the centre by previous works, leading to the production of an oxygen-neon
(ONe) WD that may collapse into a neutron star but not an SN Ia. However, it is
still uncertain how the carbon flame propagates under the effect of mixing
mechanisms. In the present work, we aim to investigate the off-centre carbon
burning of the He-accreting CO WDs by considering the effect of convective
mixing. We found that the temperature of the flame is high enough to burn the
carbon into silicon-group elements in the outer part of the CO core even if the
convective overshooting is considered, but the flame would quench somewhere
inside the WD, resulting in the formation of a C-O-Si WD. Owing to the
inefficiency of thermohaline mixing, the C-O-Si WD may explode as an SN Ia if
it continues to grow in mass. Our radiation transfer simulations show that the
SN ejecta with the silicon-rich outer layer will form high-velocity absorption
lines in Si II, leading to some similarities to a class of the high-velocity
SNe Ia in the spectral evolution. We estimate that the birthrate of SNe Ia with
Si-rich envelope is ~ 10^(-4)/yr in our galaxy.
