Drift and diffusion in semiconductors
A semiconductor is not diffusion or drift-based, those are two phenomena always taking place in the same semiconductor. Considering electrons as carriers (but the same can be said for holes), the current density in a semiconductor can be expressed by the drift-diffusion transport equation:

$$
\vec{J}_n=q\mu_nn\vec{E} + qD_n\vec{\nabla}n
$$
where \$q\$ is the elctron charge, \$\mu_n\$ the electrons mobility, \$n\$ the electron concentration and \$D_n\$ the diffusion coefficient. Thus, according to which term in the sum dominates the other you could say that a certain current is produced by diffusion or drift, but that's a matter of the ՝՝circumstances'', it's not the semiconductor which is diffusion or drift-based.

If you applied a strong electric field, the drift term would dominate; if no field is applied then the current is due only to the \$n\$ concentration gradient.

Hoping that what I said is clear enough, I want to make one final note: don't be fooled into thinking that without an electric field you would obtain a constant current depending only on how you doped your semiconductor; when electrons start to flow into the domain with less \$n\$ concentration, they ՝՝leave behind'' positively ionized atoms, which contributes in generating a potential difference and thus an electric field, until the diffusion term is compensated and there is no net flux of carriers.