klein gordon equation - What wavefunctions do the creation operator of a massive real scalar free field create?

A real scalar free field of mass $m$ can be represented as:

$$\hat\phi(\mathbf{x}) = \int \frac{d^3\mathbf{k}}{(2\pi)^3\sqrt{2\omega_{\mathbf{k}}}}\hat a_{\mathbf{k}}e^{i(\omega_{\mathbf{k}}t - \mathbf{k} \cdot \mathbf{x})} + \hat a^\dagger_{\mathbf{k}} e^{-i(\omega_{\mathbf{k}} t + \mathbf{k} \cdot \mathbf{x})},$$

where $\omega_{\mathbf{k}} = \sqrt{|\mathbf{k}|^2 + m^2}$.

What wavefunction does the creation operator $\hat a^\dagger_{\mathbf{k}}$ create from the vacuum state? Is it the momentum eigenstate $e^{i\mathbf{k}\cdot\mathbf{x}}$? If so, how can I show this?