Formulation of Macroscopic TransportModels for Numerical Simulationof Semiconductor Devices

Abstract

According to different assumptions in deriving carrier and energy flux equations, macroscopic semiconductor transport models from the moments of the Boltzmann transport equation (BTE) can be divided into two main categories: the hydrodynamic (HD) model which basically follows Bløtekjer's approach [1, 2], and the Energy Transport (ET) model which originates from Strattton's approximation [3, 4]. The formulation, discretization, parametrization and numerical properties of the HD and ET models are carefully examined and compared. The well-known spurious velocity spike of the HD model in simple nin structures can then be understood from its formulation and parametrization of the thermoelectric current components. Recent progress in treating negative differential resistances with the ET model and extending the model to thermoelectric simulation is summarized. Finally, we propose a new model denoted by DUET (Dual ET)which accounts for all thermoelectric effects in most modern devices and demonstrates very good numerical properties. The new advances in applicability and computational efficiency of the ET model, as well as its easy implementation by modifying the conventional drift-diffusion (DD) model, indicate its attractiveness for numerical simulation of advanced semiconductor devices

Hierarchy of simulation approaches for hot carrier transport in deep submicron devices

“…One can find in the literature a wide variety of approaches that originate from the moments of the Boltzmann equation, and which differentiate themselves mainly in the approximations or simplifications made to obtain practical implementations [50][51][52][53][54][55]. We will examine in detail the two formulations that have more relevance today, and that best exemplify the capabilities of the moment method.…”

“…In the first approach (hydrodynamic model) [50] the moments are initially performed and then average relaxation times for the momentum and energy continuity equations are introduced. In the other approach (energy transport model) the collision term in the Boltzmann equation is first formulated in terms of a microscopic relaxation time for the distribution function and then the moments are based on this approximated equation [51][52][53][54].…”

“…In this approach a microscopic relaxation time τ for the distribution function is assumed in the Boltzmann equation [51,52]. By decomposing f into its even and odd parts, f 0 and f 1 [53,54], and using the microscopic relaxation time approximation (∂f 1 /∂t) coll = −f 1 /τ , the odd part of the steady-state Boltzmann equation becomes…”