ELECTRONIC DEVICES

At the end of the course, the student will be able to understand and derive the electrical behavior of main silicon devices. He can also be able to use the derived models both for the component biasing and for the small signal analysis.  The student will be in the condition to understand the construction characteristics (process or design) of the silicon deices and how they affect the device performance, and can also analyze and understand the main manufacturing steps of the integrated technology devices.

1. Knowledge and understanding: the student will be able to understand the construction methods of and the operating principles of electronic devices (diodes, BJT, MOSFET).

2. Ability to apply knowledge and understanding: the student will be able both to derive the models of the semiconductor components, and to linearize them when the device is used inside a simple electronic circuit. The student will also be able to simulate, implement and test electronic circuits, firstly, modeled with open source simulation tools and, then, mounted on breadboard and characterized with laboratory instrumentations.

3. Making judgments: the student will be able to independently assess whether any devices meet the requirements for the applications on which they are working and make the necessary choices in order to adapt the device to the application itself.

4. Communication and learning skills: Upon completion of the course, the student is expected to acquire the ability to convey the knowledge acquired to their interlocutors in a clear and complete way and will also be able to rework the knowledge to extend it to situations not explicitly addressed, being also able to learn independently.

Teaching is carried out through lectures and laboratory activities. About half of the lessons are dedicated to numerical exercises, laboratory experiences and simulations conducted in presence.

If the course is taught in mixed or distance mode, the necessary changes may be introduced with respect to what was previously stated, in order to comply with the program provided and reported in the syllabus.

A good knowledge of the contents of Mathematical Analysis I is required with particular reference to the basic mathematics knowledge (such as limits, derivatives, integrals and functions study). Knowledge of the contents of Physics I and Physics II with regard to the techniques of analysis and modeling of physical phenomena and knowledge of the main electrical quantities are also required. Further topics, such as methods of analysis of linear circuits in the time and frequency domain (given in the course of Electrical Engineering) can be of valuable help in understanding the subject.

Attendance is strongly recommended. During the lessons, the student's presence will be recorded and monitored in order to allow the access to the midterm tests and for the final evaluation.

Physics of semiconductors

Electric field and potential. Current and current density. Thermal velocity of electrons. Drift current. Mobility coefficient. Ohm's law. Silicon as a semiconductor. Electrons and holes. Intrinsic concentration. Doped semiconductors. Types of doping and their effects. Mobility in doped semiconductors. Thermal equilibrium and the mass action law. Charge neutrality. Generation/recombination processes and injection of carriers. Low and high levels of injection. Recombination transient. Diffusion processes. Diffusion current. Einstein relationship. Continuity equation. Injected charge and profile of minority carriers. Potential in a non-uniform concentration material. Boltzmann equations. Fermi Potential.

Diodes

Pn junction. Space charge region. Abrupt junction analysis: electric field, potential, width of the depletion region. Analysis of the linear junction: electric field, potential, width of the depletion region. Nonequilibrium pn junction: potential barrier and carrier flows in direct and inverse polarization. Carriers at the edge of the depletion region. Long diode: profile of minority carriers, current density. Short diode: profile of minority carriers, current density, transit times. Current-voltage characteristic of the pn junction. Second order effects: low and high levels of injection. Temperature dependence. Capacitive effects: depletion capacitance, diffusion capacitance. Junction breakage and Zener diodes. Metal-semiconductor junctions: Schottky diodes and ohmic contacts. Static circuit models. Small-signal analysis. Low-frequency small-signal model. High-frequency small-signal model.

Bipolar transistors

Types of bipolar transistors: npn and pnp. The bipolar transistor in equilibrium. Operating regions. Analysis of the bipolar transistor in the forward active region. Current amplification in the common base configuration. Emitter efficiency. Base transport factor. Current amplification in the common emitter configuration. Current-to-voltage characteristic in the bipolar transistor: Forward and Reverse configuration. Ebers-Moll model. Simplification of the Ebers-Moll model: interdiction region, direct active region, inverse active region, saturation region. Second order effects: Early effect, β_F dependence on the collector current. Characteristic curves in the common emitter configuration. Capacitive effects: base-emitter capacitance, base-collector capacitance. Temperature dependence. Low-frequency small-signal models. High-frequency small-signal models. Transition frequency. Parasitic effects: distributed resistances and substrate capacitance.

MOS transistors

The MOS capacitor. Flat band potential. Effect of the gate-substrate voltage on the MOS capacitor. Operating regions: accumulation, depletion, weak inversion, strong inversion. Surface potential and operating regions. Threshold voltage of the MOS capacitor. The MOS transistor: operating principle. Current-to-voltage characteristic in the MOS transistor: analysis of the conduction channel. Expression of the drain current. Operating regions: interdiction, triode and saturation. Body effect. Channel length modulation. Capacitive effects: gate-source capacitance, gate-drain capacitance, drain-bulk and source-bulk capacitances. Low-frequency small-signal models. High-frequency small-signal models.

Planar technology (note)

Thermal oxidation. Thermal diffusion: Fick's law and diffusion profiles. Ionic implantation. Deposition of thin layers: chemical vapor deposition, physical vapor deposition. Annealing and gettering. Photolithography: masking, exposure and attack. Bipolar process. CMOS process.

Experiments aimed at a better understanding of the functioning of the studied electronic device are foreseen for each single topic treated. Among the various experiences there are: introduction to the simulation tool and the electronic instrumentation that will be used; characterization of passive components and their use in simple circuits (voltage and current dividers, first order passive integrators and derivators); characteristic curve of the diode and its application as a rectifier, variable capacitor and temperature sensor; characteristic curves of bipolar and MOS transistors and their applications as controlled switches and amplifiers. There are 5 laboratory activities.

Main Textbook

1.       G. Giustolisi, G. Palumbo, Introduzione ai Dispositivi Elettronici, Franco Angeli, 2005.

Other Textbooks

1.   R. S. Muller, T. I. Kamins, Dispositivi elettronici nei circuiti integrati, Bollati Boringhieri, 1993.

2.   S. Dimitrijev, Understanding semiconductor devices, Oxford University Press, 2000.

Total exam: Learning is verified through a final exam. It consists of a written test, lasting 2 hours, and an oral part. The written test, preliminary to the oral part, consists of 5 numerical exercises that cover the contents of the course. Each question is assigned a score from 0 to 6 which takes into account the correctness of the procedure, the clarity of the presentation and the correctness of the calculations.

Students who achieve a grade lower than 15 are not admitted to the oral part. The result of the written part is published on the main page of the department. Students who have accumulated more than two absences during the laboratory exercises will have a limitation on the final evaluation. The oral part consists of questions concerning all the program treated. The student have to demonstrate adequate understanding, mastery of the topics discussed and clarity of exposition. The final evaluation will take into account the result of both the written and oral parts.

Mid-term tests: Students with less than 20% absences during each module of the course can access the in mid-term evaluation, consisting of a written part and the related oral part that will cover topics of elements of semiconductor and diode physics. If positively passed, the final test, always carried out through a written part and an oral part, will only cover the verification of the topics related to bipolar and MOS transistors.

The assessment method is identical to that described for the total exam.

The verification of learning can also be carried out remotely, if the conditions require it.

To ensure equal opportunities and in compliance with current laws, interested students may request a personal interview in order to plan any compensatory and/or dispensatory measures based on educational objectives and specific needs. Students can also contact the CInAP (Centro per l’integrazione Attiva e Partecipata - Servizi per le Disabilità e/o i DSA) referring teacher within their department.

Prove Einstein's relationship

Obtain the continuity equation.

Given a pn junction, assuming the step approximation is valid, derive the trend of the electric field and potential.

Find the current-voltage relationship in a long-base diode.

Given a pnp-type BJT transistor, derive the expressions of the profiles of the minority carriers in the three regions.

Given an n-p-n type BJT transistor, derive the expression of the base transport factor.

Describe what is due to the Early effect in the BJT transistor.

Given a MOS capacitor with a p-type substrate, derive the expression of the threshold voltage.

Obtain the current-voltage relationship for an n-channel MOS transistor in the triode region.