We examine hot-electron transport with emphasis on the impact-ionization phenomena in crystalline Si using the Monte Carlo method. Contrary to the usual treatment of impact ionization exploiting the Keldysh formula ([Sov. Phys.---JETP 10, 509 (1960)] [Zh. Eksp. Teor. Fiz. 37, 713 (1959)]), a new impact-ionization model which takes account of the wave-vector dependence of the ionization threshold energies associated with a realistic band structure is introduced. The calculation results of impact-ionization properties such as ionization coefficient and quantum yield show excellent agreement with experimental data. The orientational independence of the ionization coefficient and the softness of the ionization threshold in bulk Si are also explained by our ionization model. The present simulations ensure that the approach employed here is a good candidate for correctly describing the impact-ionization mechanism.