A semiconductor device noise model in the framework of semiclassical transport and Pauli's exclusion principle is presented. Terminal current noise is modeled as a direct consequence of electron scattering taking place inside the device at the microscopic level. The approach directly connects electron scattering rates of semiclassical transport theory with the current spectral density at the device terminals. It is shown that the spectral density of steady-state current fluctuations can be obtained from the transient solution of the Boltzmann transport equation with special initial conditions. This formulation is inherently suitable for deterministic solution techniques, for instance, the computationally efficient spherical harmonics method. Approximating the instantaneous value of the occupation number by the occupation probability, this model is able to account for Pauli's principle and at the same time describe the behavior of the electron ensemble in terms of independent entities. As a practical demonstration, the model is employed to compute the current noise spectral density due to generation recombination and acoustic and optical phonon scattering for bulk n-type silicon material. Additionally, in order to add more physical insight and to verify results, the model is also employed to compute the low-frequency current spectral density as a function of the electric field and temperature, respectively. The results show good agreement with low-frequency noise measurements reported in literature.