Vittorio Romano

We propose a Schrödinger equation (SE) of arbitrary order for modeling charge transport in semiconductors operating in the ballistic regime. This formulation incorporates non-parabolic effects through the Kane dispersion relation, thereby extending beyond the conventional effective mass approximation. Building upon the framework introduced in Aliffi et al (2025 Z. Angew. Math. Phys. 76 155), we derive a hierarchy of models, each governed by a SE of increasing order. As in the standard second-order formulation, the problem is formulated on a bounded spatial domain with suitable transparent boundary conditions. These conditions are designed to simulate charge transport in a quantum coupler where an active region – representing the electron device – is connected to leads acting as reservoirs. We investigate several analytical properties of the proposed models and derive a generalized expression for the current, valid for any order. This formula includes additional terms that account for interference effects arising from the richer wave structure inherent in higher-order SEs, which are not captured by the effective mass approximation. Numerical simulations of a resonant tunneling diode illustrate the key features of the solutions and highlight the impact of the generalized formulation on device behavior.

Electron devices based on graphene have lately received a considerable interest; in fact, they could represent the ultimate miniaturization, since the active area is only one atom tick. However, the gapless dispersion relation of graphene at the Dirac points limits the possibility of using pristine graphene instead of traditional semiconductors in Field Effect Transistors (FET). For such a reason very accurate simulations are needed. In Nastasi & Romano, IEEE TED (2021) a graphene field effect transistor (GFET) has been proposed and simulated adopting a drift-diffusion model. Here, electron devices whose active area is made of monolayer graphene are simulated adopting as mathematical model the semiclassical Boltzmann transport equations (BTEs) in the bipolar case, coupled with the Poisson equation for the electric field. The system is solved by means of a discontinuous Galerkin (DG) approach (see Cockburn & Shu, J. Comp. Phys. (1998); Hesthaven & Warburton, 2008) with linear elements in the spatial coordinate and constant approximation for the wave-vector space, discretized with a polar mesh. The correct physical range for the distribution function is preserved with the maximum-principle-satisfying scheme introduced in Zhang & Shu, J. Comp. Phys. (2010). The adopted method reveals very robust and possesses a good degree of accuracy, making it particularly well suited for capturing the complex charge transport dynamics inherent to graphene-based devices. The results for suspended monolayer graphene and GFET constitute benchmark solutions for a rigorous assessment of the validity of macroscopic models, such as drift-diffusion and hydrodynamic ones.

The growing demand for better performance and lower thermal energy dissipation in nanoelectronic devices is the major driving force of the semiconductor industry’s quest for future generations of nanotransistors. Over the past 15 years, the miniaturization of silicon-based nanoelectronics predicted by Moore’s law has driven an aggressive scaling down of transistor structures, including materials, design, and geometries. In this regard, the electronic device community has expanded its focus to ultrascaled transistors targeting the 7-nm technology node and beyond. However, these emerging nanodevices also present thermal challenges that can limit carrier transport as a result of strong electron–phonon coupling. In this work, we investigate the physical origin of self-heating effects in an ultrascaled 5-nm silicon nanowire field-effect transistor. Based on a quantum hydrodynamic approach, we also provide an explanation of the phonon-drag contribution to thermal conductivity. We report the impact of the phonon-drag effect on the electrical and thermal performance of 5-nm gate-all-around silicon nanowire field-effect transistors. Our findings provide a new insight into the origin of self-heating as a result of mutual electron–phonon coupling. Furthermore, we demonstrate that the phonon-drag effect significantly reduces thermal conductivity by nearly 50% under high-bias conditions.

The main aim of this work is to optimize a Quantum Drift Diffusion model (QDD) (V. Romano, M. Torrisi, and R. Tracinà, “Approximate solutions to the quantum drift-diffusion model of semiconductors,” J. Math. Phys., vol. 48, p. 023501, 2007; A. El Ayyadi and A. Jüngel, “Semiconductor simulations using a coupled quantum drift-diffusion schrödinger-Poisson model,” SIAM J. Appl. Math., vol. 66, no. 2, pp. 554–572, 2005; L. Barletti and C. Cintolesi, “Derivation of isothermal quantum fluid equations with Fermi-Dirac and bose-einstein statistics,” J. Stat. Phys., vol. 148, pp. 353–386, 2012) by comparing it with the Boltzmann-Wigner Transport Equation (BWTE) (O. Muscato, “Wigner ensemble Monte Carlo simulation without splitting error of a GaAs resonant tunneling diode,” J. Comput. Electron., vol. 20, pp. 2062–2069, 2021) solved using a signed Monte Carlo method (M. Nedjalkov, H. Kosina, S. Selberherr, C. Ringhofer, and D. K. Ferry, “Unified particle approach to Wigner-Boltzmann transport in small semiconductor devices,” Phys. Rev. B, vol. 70, pp. 115–319, 2004). A situation of high non equilibrium regime is investigated: electron transport in a Resonant Tunneling Diode (RTD) made of GaAs with two potential barriers in GaAlAs. The range of the suitable voltage bias applied to the RTD is analyzed. We find an acceptable agreement between QDD model and BWTE when the applied bias is low or moderate with a threshold of about 0.225 V over a length of 150 nm; it is found out that the use of a field dependent mobility is crucial for getting a good description of the negative differential conductivity in such a range. At higher bias voltages, we expect that QDD model loses accuracy.

Some properties of the electron-electron collision operator in graphene are analyzed along with the evaluation of collision rate. Monte Carlo simulations complete the study and highlight the non-negligible role of the electron-electron scattering for an accurate evaluation of the currents and, as a consequence, of the characteristic curves.