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.
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