Advances in the Spherical Harmonic–Boltzmann–Wigner approach to device simulation

Abstract Recent advances in the Spherical Harmonic Boltzmann method of device modeling are presented. A new surface scattering model and improved numerical interpolation schemes have been developed. The method is shown to be capable of calibrating an entire deep submicron process to provide I – V characteristics and substrate current self-consistently. Substrate currents agree with experiment over a complete process without any fitting parameters. Applications to a 50 nm MOSFET predict well-behaved device operation. The method requires approximately ten minutes to self-consistently calculate a MOSFET bias point and provide the device distribution function. The spherical harmonic method has been extended to account for quantum mechanical effects by applying it to the Wigner equation. We treat the Wigner equation as a quantum correction to the Boltzmann equation thereby making the spherical harmonic approach a natural method of solution.