In a semiconductor, the number density of intrinsic charge carriers at $27^{\circ} \mathrm{C}$ is $1.5 \times 10^{16} / \mathrm{m}^3$. If the semiconductor is doped with impurity atoms, the hole density increases to $4.5 \times 10^{22} / \mathrm{m}^3$. The electron density in the doped semiconductor is $\_\_\_\_$ $\times 10^9 / \mathrm{m}^3$.