Course Unit Page


This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

Quality education Affordable and clean energy

Academic Year 2021/2022

Learning outcomes

The aim of the course is to develop the required background to address the study of nanoscale semiconductor devices. At these dimensional limits, the occurrence of quantum mechanical effects related with carrier confinement becomes important, and the gate length turns out to be comparable, or smaller, than the carrier mean-free path. These effects require a re-examination of the physical models to be used for the interpretation and prediction of the device characteristics. The course is thus going to introduce the basic foundations of quantum mechanics and semiconductor physics, as well as the treatment of non-equilibrium transport in semiconductors. The mathematical model is thus based on the coupled Schroedinger and Poisson equations, to be solved with the boundary conditions characterizing the specific device geometry and morphology. Modern semiconductor devices will be studied using both the classical transport model based on drift-diffusion, as well as the quantum-mechanical model under the assumption of ballistic transport. The student will thus become aware of the limitations of the obtained solutions by comparing the different results provided by the two models.

Course contents

The evolution of the microelectronic technologies has led to the fabrication of integrated systems containing some billions of elementary transistors with linear dimensions of the order of ten of nanometer which, in many cases, are smaller than, or comparable with, the electron mean-free path. The miniaturization process of electron devices has thus reached a level which makes the classical treatment of carrier transport in semiconductors no longer adequate. The drift-diffusion transport model is in fact based on the opposite assumption, namely that the electric field within the device changes over a space scale much larger than the carrier mean-free path, and over a time scale much longer than the average time between collisions. Also, the structural confinement of the carriers is responsible for novel quantum-mechanical effects, such as energy quantization and, thus, the splitting of the conduction and valence bands into a multiplicity of sub-bands with a smaller dimensionality. Finally, direct source-to-drain and band-to-band tunneling effects are going to play an ever increasing role. In view of the previous considerations, a re-examination of the classical methodologies currently used for the analysis of electron devices becomes mandatory.

The course of Nanoelectronics aims to address such a need, and to investigate the properties of carrier transport in nanometric-scale structures, also referred to as mesoscopic systems. This term means that these systems are still large with respect to the atomic dimensions, so as to make it possible using the concepts of band structure, Bloch waves, equivalent hamiltonian and effective mass but, at the same time, smaller or comparable with the electron mean-free path. The concept of local quasi-equilibrium is thus abandoned and so is the description of carrier transport via the concepts of mobility and diffusivity. The nature of the new constitutive equations becomes strongly non-local and the importance of the boundary conditions, by which the device under investigation is isolated from the neighboring circuit, increases.

The course of Nanoelectronics aims to provide the attending students the conceptual tools required to face the study of nanometer-scale electron devices. The complexity of the quantum equations makes the development of compact models more difficult, and forces us to adopt numerical techniques for their solution. Therefore, the course is going to include, within its program, the study of the main numerical methods for the solution of the Schrödinger equations with either closed and open boundaries, for which the non-equilibrium Green's function (NEGF) formalism has become very popular.

The devices to be studied are going to include, due to their practical importance, ultra-thin body (UTB) silicon-on-insulator (SOI) transistors, silicon nanowire field-effect transistors (NW-FETs) and multi-gate (MG) FETs, announced by Intel as the basic components of their technology node at 22 nm and beyond. The course will examine as well heterostructure devices based on III-V semiconductors, the interest of which for logic applications is currently increasing at research level. A theme of great current interest is the development new device concepts for the fabrication of FETs with a steep transition between the off- and the on-state, with the aim to reduce the supply voltage and to cut down power consumption. Among these novel devices, the band-to-band tunnel transistors (BTB-TFETs) and the superlattice-based FETs make it possible the achievement of inverse subthreshold swings much smaller than (kBT/q) ln(10) = 60 mV/dec, due to their ability to filter out high-energy electrons.


S. Datta: "Electronic Transport in Mesoscopic Systems", Cambridge University Press
S. Datta: "Quantum Transport: Atom to Transistor", Cambridge University Press
D. H. Ferry, S. M. Goodnick: "Transport in Nanostructures", Cambridge University Press
M. Lundstrom: "Fundamentals of Carrier Transport", Cambridge University Press
M. Rudan: "Physics of Semiconductor Devices", Springer

Teaching methods

Traditional lectures are delivered in the classroom, illustrating the most important physical concepts of the discipline. The required calculations leading to the main results are carried out at the blackboard. Occasionally, slides are used for a better presentation of images, not otherwise reproducible on the blackboard.

Assessment methods

The assessment of the student learning will occur via oral examination.

Teaching tools

A number of textbooks are suggested for consultation, and personal notes of the teacher are delivered to the students.

Office hours

See the website of Giorgio Baccarani