Particles and antiparticles in compex field

 P: 46 Hi. I am confused about something related to the creation of particles/antiparticles in a complex scalar field. I read in the literature that $\phi(x)|0\rangle$ describes the creation of a particle at point $x$. But given that $$\phi(x) = \int \frac{d^3 p}{\sqrt{(2\pi)^3 2E_p}} \left(a(p)e^{-ipx}+b^\dagger (p)e^{ipx}\right)$$ then in $\phi(x)|0\rangle$ only the $b^\dagger(p)$ term contributes, i.e. $$\phi(x)|0\rangle= \int \frac{d^3 p}{\sqrt{(2\pi)^3 2E_p}}e^{ipx} b^\dagger(p)|0\rangle$$ from which it seems that an anti-particle (created by $b^\dagger(p)$) is created at $x$.