In this paper, the formulation of unified transport model is reviewed along with its implementation in a three-dimensional device simulator. The model features an accurate description of the energy exchange among electrons, holes and lattice, and is therefore suitable for self-consistently simulating thermal effects and non-stationary phenomena, as well as their possible interactions. Despite the model complexity, it is shown that the computational effort required for its solution is reasonably close to more conventional approaches. Application examples are also given, in which both unipolar and bipolar devices are simulated, discussing the relative importance of different phenomena and highlighting the simultaneous occurrence of carrier and lattice heating.

In this paper, a "hydrodynamic" version of the three-dimensional code HFIELDS-3D is used to achieve a detailed knowledge on the distribution of the substrate current inside a recessed-oxide MOSFET. The physical model features a temperature-dependent formulation of the impact-ionization rate, allowing non-local effects to be accounted for. The discretization strategy relies on the Box Integration scheme and uses suitable generalizations of the Scharfetter-Gummel technique for the energy-balance equation. The simulation results show that the narrow-channel effect has a different impact on drain and substrate currents. Further three-dimensional effects, such as the extra heating of the carriers at the channel edge, are demonstrated.

A spherical-harmonics expansion method is used to find approximate numerical solutions of the Boltzmann Transport Equation in the homogeneous case. Acoustic and optical phonon scattering, ionized impurity scattering as well as an energy band structure fitting the silicon density of states up to 2.6 eV above the conduction-band edge are used in the model. Comparisons with Monte Carlo data show excellent agreement, and prove that detailed information on the high-energy tail of the distribution function can be obtained at very low cost using this methodology.