3. Let $F_{1}$ and $F_{2}$ be the left and right foci of the ellipse $C$:
$$
\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a>b>0)
$$

If there exists a point $P$ on the ellipse $C$ such that $P F_{1} \perp P F_{2}$, then the range of the eccentricity $e$ of the ellipse is $\qquad$
3. $\left[\frac{\sqrt{2}}{2}, 1\right)$.

Let $A$ be the upper vertex of the ellipse $C$.
According to the problem, we have
$$
\begin{array}{l}
\angle F_{1} A F_{2} \geqslant 90^{\circ} \Rightarrow \angle F_{2} A O \geqslant 45^{\circ} \\
\Rightarrow c \geqslant b \Rightarrow a \leqslant \sqrt{2} c \Rightarrow \frac{\sqrt{2}}{2} \leqslant e<1 .
\end{array}
$$