84200 - Physics of Semiconductor Devices, Memories and Sensors M I.C.

Course Unit Page


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

Quality education Industry, innovation and infrastructure

Academic Year 2019/2020

Learning outcomes

Knowledge about the fundamentals of quantum mechanics and band theory of solids; knowledge about the physical phenomena underlying the transport of charged carriers in solids and about the basic semiconductor devices and solid-state memories. Competencies: (general) to have critical understanding of technical and scientific tools; communication skills; to be able to work in an international context; (specific) to understand the methods for investigating advanced solid-state devices and memories; to determine the important microscopic and macroscopic parameters involved in the functioning of such devices. Detailed contents: introductory part where the basic relations of quantum mechanics are shown; theory of bands in crystals and transport theory; mathematical model of semiconductor devices and its application to the description of the basic devices (p-n junction, bipolar transistor, MOS capacitor, MOS transistor), and application of the latter as memories. Resistive memories. Interaction of radiation with matter, absorption of light, basic optical sensors (photo diode, photo capacitor); lattice vibrations, derivation of the macroscopic elastic properties of solids and applications (e.g., energy-harvesting devices, gyroscopes); use of MOS transistors as chemical sensors in liquids. Performance metric of devices.

Course contents


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. The use of such concepts can not be disposed of, they actually constitute the cultural basis of the course itself.

Course contents

Presentation and aims of the course. Schedule. Notions that should already be known to the Students. Exams. Contents. References.

Introduction to crystals. Direct lattice. Characteristic vectors. Translational vectors. Wigner-Seitz cell. Description of the crystal structure of silicon and III-V compounds. Translational operators. Periodic operators. Bloch theorem and Bloch functions. Periodicity of the eigenvalues of the translational operators. Krönig-Penney model. Hint about the calculation of the dispersion relation in three dimensions. Definition of the effective-mass tensor. Wave packets in a periodic potential. Symmetry of the eigenvalues. Energy bands. Example: silicon. Density of states in the phase space. Density of states in energy for a parabolic band. Form of the dispersion relation of the conduction and valence bands for Ge, Si, and GaAs. Distribution function. Density of states in the general case. Definition of hole concentration. Qualitative discussion about conductors, insulators, and semiconductors at equilibrium. Calculation of the intrinsic concentration. Fermi integrals and exponential approximation for them. Examples of the parameters determining the gap and intrinsic concentration in Ge, Si, and GaAs. Definition of the average velocity of electrons and holes. Comments. Equivalent Hamiltonian. Dynamics of an electron in a crystal. Effective-mass theorem. Effect of the dopants. Calculation of the extrinsic concentrations in the uniform case. The case of non degeneracy and complete ionization. Examples of band diagrams for silicon. Compensation effect. The non-uniform case. The Poisson equation. Liouville theorem. Boltzmann transport equation (BTE). Relaxation time. Moments' method. Moment of order zero of the BTE. Physical meaning of the terms appearing in the moment of order zero. Moment of order one of the BTE. Simplification of some terms. Electron-temperature tensor. Closure condition. Moment of order one of the BTE in the parabolic-band approximation. Mathematical model of semiconductor devices. Boundary conditions of the model of semiconductor devices. Examples of numerical methods for solving the semiconductor equations. Thermal recombination-generation term. Auger recombination and impact ionization. Optical generation. Concept of laser. Perturbation constant in time. Conservation of energy. Example of the screened Coulomb perturbation. Calculation of the relaxation time due to the Coulomb perturbation.Derivation of the screened Coulomb perturbation. Harmonic perturbation. Contribution to mobility due to collisions with phonons, ionized impurities, and interfaces. Matthiessen's rule. Examples of numerical simulation of mobilities, and comparison with experiments. Mathematical model of semiconductors. Application of the model to the description of the basic devices: p-n junction, bipolar transistor, MOS capacitor, MOS transistor. Application of some of the above devices as memories. Resistive memories. Interaction of radiation with matter. Absorption of light, basic optical sensors: photo diode, photo capacitor. Lattice vibrations. Derivation of the macroscopic elastic properties of solids. Applications to devices: energy-harvesting, gyroscopic effect. Use of MOS transistors as chemical sensors in liquids.


Refer to the website http://www-micro.deis.unibo.it/cgi-bin/user?rudan

Teaching methods

Lessons + Exercises.

Needless to say, attending all classes is fundamental.

For the sake of the Commission entitled to Programme's certification, the Teacher hereby declares that lessons and exercises conform to the learning's objectives.

Assessment methods

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

To timely identify the level of knowledge necessary to fulfill the course's requirements, and remembering that the Italian law prescribes that exams are public, students are firmly invited to be present at other students' exams well before the date of their own.

Teaching tools

Slides. Notes. Books. Material posted in the website, including the audio recording of the lessons of the Academic Year 2018-2019.


Links to further information


Office hours

See the website of Massimo Rudan