# 35359 - Microelectronics M

### Course Unit Page

• Teacher Susanna Reggiani

• Credits 6

• SSD ING-INF/01

• Language Italian

• Campus of Bologna

• Degree Programme Second cycle degree programme (LM) in Electronic Engineering (cod. 0934)

• Course Timetable from Feb 20, 2023 to Jun 06, 2023

### SDGs

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

## Learning outcomes

To illustrate the fabrication methods for the integrated circuits and the functioning of the most important semiconductor devices.

## Course contents

Prerequisites

Basic concepts of mathematics and physics acquired from earlier courses. Basic concepts about the electron devices. In this course, further mathematical and physical concepts, not necessarily elementary, will be used. They will be explained as necessary during the lessons.

Introduction

Description of the course. Schedule and office hours. Basic concepts assumed to be already acquired from earlier courses. Exam assessment. Course contents. Bibliography.

Contents

General description of the Microelectronics Industries. Main fabrication processes for the realization of integrated circuits.

Crystal lattice. Definition of characteristic vectors. Elementary cell. Direct and reciprocal lattices. First Brillouin zone. Face-centered cubic lattice. Miller indices. Examples: diamond and zinc-blende structures. Particle dynamics in a periodic potential. Form of the conduction and valence band of silicon, germanium, and gallium arsenide. Transitions: intra-valley, inter-valley, direct inter-band, trap-assisted inter-band transitions. Fermi statistics.

Density of states in the k space and in the phase space. Effective mass. Dispersion relation E(k) in a crystal. Density of states in energy. Bands in conductors, insulators, and semiconductors. Dependence of conductivity on temperature. Form of the constant-energy surfaces of Ge, Si, GaAs.

Distribution function. Example of calculation of the density of states. Concept of hole. Calculation of the intrinsic concentration at equilibrium. Estimate of the position of the Fermi level. Dependence of the intrinsic concentration on temperature. Relevant parameters for Ge, Si GaAs. Qualitative explanation of the contribution of electron and holes to the current density of a semiconductor. Calculation of the position of the Fermi level. Average velocity and current density of the electrons and of the holes.

Dynamics of electrons and holes in the parabolic-band approximation. Doped semiconductor of the donor or acceptor type. Compensation effect. Calculation of the equilibrium concentrations. Non-degeneracy and complete-ionization approximations. Effect of temperature and dopant concentration on the position of the Fermi level. Intrinsic, saturation and freeze-out conditions of the dopants. Non-uniform dopant distribution. Expressions of the equilibrium concentrations of electrons and holes. Poisson equation in the semiconductor in the equilibrium and non-equilibrium cases.

Continuity equations. Quasi-static approximation. Mathematical model of semiconductor devices. Definition of the quasi-Fermi potentials. Boundary conditions of the model Trap-assisted transitions. Deduction of the SRH net-recombination rate. Limiting cases of it: depletion and weak-injection conditions. Auger recombination and impact ionization. Direct generations of thermal and optical type. Limiting case of strong ionization. Form of the optical generation inside the material. Macroscopic mobility models: collisions with the lattice, the ionized impurities and the interfaces. Dependence of mobility on temperature, total impurity concentration and field component normal to a boundary. Matthiessen rule. Example of a macroscopic mobility model. Results of mobility calculations obtained from the solution of the Boltzmann transport equation.

Applications: p-n junction: structure and qualitative form of the electric potential. Solution of the Poisson equation at equilibrium: neutral regions and space-charge regions. Drift and diffusion component of the current density. Effect of the contacts. Qualitative functioning of the p-n junction. Full depletion of the space-charge region in the reverse-bias condition. Shockley theory. Weak-injection condition and decoupling of the neutral zones. Current-voltage relation of the p-n junction; dominance of the diffusive current density for the minority carriers in the neutral zones. Shockley boundary conditions. Reverse bias: form of the charge density, electric field and electric potential. Calculation of the width of the space-charge region. Barrier capacitance of the p-n junction. Chynowetz model for the impact-ionization coefficients. Avalanche condition.

Bipolar transistor. Qualitative description. Calculation of the currents. Ebers and Moll model. Equivalent circuit. Optimization of the current gain.

MOS capacitor. Neutral zone and space-charge zone. Relation between charge in the semiconductor and surface potential in the different functioning regimes. Solution of the Poisson equation in the MOS capacitor with a constant substrate doping. Flat-band, depletion and inversion conditions. Approximate relations between charge per unit area and surface potential based on the full-depletion and ACE approximations. Differential capacitance of the MOS capacitor.

MOS transistor. Calculation of the drain current. Gradual-channel approximation and calculation of the steady-state characteristics. Saturation voltage. The linear-parabolic model. Low-frequency differential parameters. Limits of the gradual-channel approximation. Solution of the Poisson equation in the channel in a non-equilibrium case. Surface potential at the source and drain ends of the channel.

D. A. Neamen, Semiconductor Physics and Devices, IRWIN, 1992.

G. Soncini, Tecnologie microelettroniche, Boringhieri, 1986.

W. Maly, Atlas of IC Technologies: an Introduction to VLSI
Processes, The Benjamin-Cummings Publishing Co., 1987.

M. Rudan, Tavole di Microelettronica, Pitagora, 3ª Ed., 2001.

M. Rudan, Physics of Semiconductor Devices, Springer, 1a
edizione 2015, 2a edizione 2018.

M. Sze, Semiconductor Devices — Physics and Technology,
Wiley, 1985.

E. De Castro, Fondamenti di Elettronica — Fisica elettronica ed
elementi di teoria dei dispositivi, UTET, 1975.

E. De Castro, Teoria dei dispositivi a semiconduttore, Pàtron,
1983.

G. Baccarani, Dispositivi MOS, Pàtron, 1982.

## Teaching methods

Lessons and practice.

## Assessment methods

Oral examination. Numerical rating between 0 and 30. The examination is passed if the rating is equal to, or larger than 18.

## Teaching tools

Teaching material: slides, notes and examples of exercises with solutions will be available to students via the distribution list or in https://www.unibo.it/sitoweb/susanna.reggiani/contenuti-utili

## Office hours

See the website of Susanna Reggiani