A Hybrid Drift Diffusion Model: Derivation, Weak Steady State Solutions and Simulations

Abstract

Abstract. In this paper we derive a new hybrid model for drift diffusion equations. This model provides a description of the quantum phenomena in the parts of the device where they are relevant, and degenerates to a semiclassical model where quantum effects are negligible, so that the system can be considered classically. The study of quantum correction to the equation of state of an electron gas in a semiconductor with the assumption of localized quantum effects leads to a further condition on the classical-quantum interface. Moreover, we prove the existence of weak solutions for our hybrid model. Finally, we present numerical results for different devices, by means of Colsys software.

Stationary solutions for a new hybrid quantum model for semiconductors with discontinuous pressure functional and relaxation time

“…We only remark that a priori DT can be positive, negative or zero. In comparison with the hybrid model presented in Chiarelli et al [9] and Di Michele et al [10,12], in the present paper the electron temperature T can be different in the quantum and classical sub-domains. In particular, we have Q = 0 and T Q = T c in the classical region, whereas in the quantum region we have Q = 1 and T Q = T q .…”

“…In this section we present a new hybrid quantum hydrodynamic model accounting for a discontinuous pressure functional and the relaxation time. The hybrid model has been basically derived using the approach proposed in Ancona and Iafrate [25] for the standard fully quantum system, and recently used in Chiarelli et al [9] Michele et al [10][11][12] in the context of quantum hybrid models for semiconductors. In the present paper we introduce and study the one-dimensional case on the bounded domain O = ½0, 1.…”

“…We recall the quantum effect function Q : O ! ½0, 1, introduced in Chiarelli et al [9] and Di Michele et al [10,11], which is a smooth function that indicates where the internal energy depends on the gradient of the charge density.…”

“…A similar strategy was also employed in Di Michele et al [8] with application to electrolyte-oxide-semiconductor (EOS) devices. In the present paper, instead of using two different models in the classical and in the quantum domain, we adopt the fully hybrid approach firstly introduced in Chiarelli et al [9] and then developed in Di Michele et al [10][11][12]. In particular, we improve the results in Di Michele et al [10] allowing some parameters of the problem, namely the temperature T and the relaxation time t, to be non-constant, assuming different values within the classical and quantum domains.…”

“…This work is divided into four sections. In the first one we recall the model introduced in Chiarelli et al [9] for a quantum drift-diffusion model, and derive the new hybrid model taking into account the discontinuous pressure functional and the relaxation time. In the second section we summarize the main results, then in the third we discuss the existence of smooth solutions to the regularized problem called the HÀQ q HD model.…”