The intrinsic carrier density n_i of crystalline silicon is an essential parameter for the simulation of electrical and thermal behavior of silicon devices. At 300 K, a value of n_i= 9.65 x10^9 cm^-3 has been determined by extensive experimental studies. However, the temperature dependence of this parameter remains to be verified. In this work, we propose a new expression n_i=1.541x10^15.T^1.712exp[-E0g/(2kT)] thanks to an updated fit of experimental data. Polynomial fits of (m*_dc/m_0)^(3/2) and (m*_dv/m_0)^(3/2) are also proposed to model N_C and N_V.