The availability of devices exploiting quantum effects is at the basis of the development of quantum electronics and quantum computing. The development of physical structures where quantum states can be prepared and manipulated is nowadays an active research field where new ideas, device concepts and physical implementations are developing day by day. Quantum engineers must be able to understand the operation principle of the main quantum devices as well as acquire the competences needed to keep the pace with the fast evolution in this field. The “Quantum devices” course is the introductory course of the Master Degree in Quantum engineering, first addressing the transition from the “classic devices” picture to the to “quantum devices” one. The course provides the theoretical background to understand and model the operation principles of the main quantum devices. It specifically aims at linking new electron device concepts to specific material properties of semiconductor and other nanotechnologies materials, allowing quantum operation. The course serves as the basis for the subsequent courses of the Master Degree, dedicated to qubit electronics, quantum communications and quantum computing.

Expected knowledge: - Understand and discuss the quantum limitation to device scaling in the framework of the current technological scenario - Acquire the mathematical and theoretical background to model quantum effects in electron devices ad in particular quantum confinement and quantum tunnelling - Understand and discuss the operation of advanced classic devices, highlighting the role of quantum effects - Understand and discuss the operation of the main quantum devices, and in particular quantum dots and resonant tunnel devices - Understand and discuss the fundamental physical properties relevant to quantum devices: spin, polarization, superconductivity - Understand the basic knowledge of superconducting quantum circuits. Expected competences and skills - Describe the FinFET operation and derive the characteristics in terms of analytical models - Describe the JLNT operation and derive the characteristics in terms of analytical models - Describe the TFET operation and derive the characteristics in terms of analytical models - Describe heterostructure devices - Describe the tunnel junctions characteristics in terms of analytical models - Describe Quantum blockade devices and Single electron transistors - Describe superconducting Quantum circuits and Qubit and SQUID operations in these quantum circuits - Develop codes to model FinFETs, TFETs, resonant diodes, single electron transistors - Compare devices in terms of quantum effects, operation and applications.

• Elementary physics (mechanics, thermodynamics, wave optics, fluidics, elements of structure of matter) • Elements of circuit theory and electronics (amplification, filtering, analog to digital conversion, …) • Elements of electronic devices (diode, BJT and CMOS transistor, band-gap concept): if this knowledge is not present the students will be asked to follow a self-learning activity with dedicated teaching material (slides, notes and video) + 10 hours in class.

Introduction (group A) - Advanced concepts on ballistic and quantum transport (5h). - Modelling Techniques for nanoscale devices: variability, statistical analysis, noise (3h theory + 2h lab) Introduction (group B) - Basics of semiconductors, band theory, electron transport (1.5 h) - The pn junction (3 h) - MOSFET transistors (5.5 h) From classic devices to quantum devices (23h) - Limits of device scaling, quantum effects in classic devices (3h) - Advanced MOSFETs, FINFETs (6h + 3h lab) - Nano transistors: JNTs, nanowires (2h) - Tunnel transistors (TFET) (6h + 3h lab) Quantum devices (19.5h) - Heterostructure devices and quantum confinement: quantum wells, quantum dots (1.5h) - Tunnel junctions, resonant tunnel devices, tunnelling models (3h + 3h lab) - Coulomb blockade device and single electron transistors (3h + 3h lab) - Silicon based qubits: basic concepts, spin, polarization (3h + 3h lab) Introduction to superconducting quantum circuits (7.5h): - the quantum Hamiltonian of a network of devices (3h) - LC resonator, transmission line, nonlinear resonator (Qubit), loops with Josephson junctions (SQUIDs) (4.5h)

The course is divided into three parts: 1) Introduction: 10 hours 2) Course body: 42.5 hours (33.5 theory + 9 lab) 3) Seminar part on superconducting quantum circuits: 7.5 hours The introduction is different for students coming from curricula providing a solid background on semiconductor devices (group A) and those who have no or insufficient knowledge in this field (group B). Before the course start, a preliminary assessment of the basic knowledge of semiconductor theory and the operation of elementary electron devices will be made by a multiple-choice quiz. Students will be then divided into groups A and B according to the quiz result, also taking into account their own choice. Students from group A will complement the preparation on electron devices with advanced topics on technological variability and quantum electron transport. These concepts, despite not necessary for the rest of this course, are of great relevance for a deeper understanding of quantum device fabrication and modelling issues. Students from group B will instead follow a specific path to bridge the gap in the basic electron device operation and modelling. The main course and seminar parts are instead common to all students. The course consists of lectures and lab sessions. Lectures cover the topics detailed in the Course Topics section and are delivered using slides on graphical tablet. The slides will be available to students in pdf format on the POLITO website at the beginning of the course. Laboratory practice sessions include software exercises where the students can work “hands on”, developing codes in MATLAB and/or using external software (NanoHub), to implement the theoretical concepts in significant case studies. The seminar dedicated to superconducting quantum circuits is tightly connected to similar parts specifically inserted in the courses of “Quantum Condensed Matter Physics “ and “Fundamentals of technological processes”, dedicated to the theory of superconductivity and the superconductor technology, respectively.

The teaching material includes the on slides for the lectures and the course notes. It will be distributed in pdf format by the teachers, and uploaded on the POLITO website before the course start. Some optional additive readings (i.e. fundamental historical papers, whitepapers, review papers, manuals, …) will be proposed by the teachers on the same above mentioned repository. Guidelines for the software Lab activity include notes and software templates.

Modalità di esame: Prova orale obbligatoria;

Exam: Compulsory oral exam;

... Criteria, rules and procedures for the examination The exams aims at assessing the ability of the student to 1) describe each quantum device analysed during the course in terms of operation principles, modelling and fabrication techniques 2) compare quantum devices with classic counterparts, highlighting the advantages and the challenges for their exploitation 3) compare the various quantum devices and their exploitation in the current electronics scenario 4) present and discuss the codes developed during the software lab 5) describe the basic ideas of superconducting quantum circuits Points 1) and 4) are essential to pass the exam. Points 2)-3)-5) are evaluated with growing marks in terms of depth of understanding and synthesis capability. The exam is oral with both open questions and short exercises. The total allotted time is 30-40 minutes for each student. No books, notes or any other didactic material is allowed. The exam results are communicated directly to the students at the end of the exam session.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.