Risorse bibliografiche
Risorsa bibliografica obbligatoria
Risorsa bibliografica facoltativa
Scheda Riassuntiva
Anno Accademico 2018/2019
Scuola Scuola di Ingegneria Industriale e dell'Informazione
Docente Chrastina Daniel , Sordan Roman
Cfu 10.00 Tipo insegnamento Corso Integrato

Corso di Studi Codice Piano di Studio preventivamente approvato Da (compreso) A (escluso) Insegnamento

Obiettivi dell'insegnamento

As modern technology moves ever further into the nanoscale, it becomes essential to extend fundamental solid-state physics knowledge to systems of reduced dimensionality. The tools developed to understand charge transport in high mobility 2-dimensional systems, such as semiconductor heterostructures and graphene, focus on the behaviour of electrons in solids in electric and magnetic fields. The study of the rich physics seen in these systems at low temperatures and high magnetic fields allows an understanding to be developed of state-of-the-art devices operating under everyday conditions, which is fundamental to the development of future technology.

Details of the first part of the integrated course are given on the "Nanodevice Characterization" page.

The second part of the course is focused on the extraordinary physical properties of graphene and their application in the development of graphene nanoelectronic devices. The main goal of this part of the course is to provide a comprehensive understanding of the state-of-the-art graphene ultrafast electronics and realistically evaluate possible applications of graphene in modern electronics. The course also presents the state-of-the-art methods for the fabrication of electronic devices at the nanoscale providing the comprehensive understanding of the fabrication methods used both in industry and research laboratories. 

Details of the second part of the integrated course are given on the "Graphene Nanoelectronics and Nanofabrication" page.

Risultati di apprendimento attesi

Following the Nanodevice Characterization course, the student understands the main physical phenomena relevant to low-dimensional semiconductor structures and devices, and how to recognise and evaluate these phenomena in terms of their manifestation in experimental results. 

The student understands how to extract important parameters and figures of merit from experimental transport data, and how to design experiments which can measure these data.

The student understands the main structural characterization methods used for semiconductor materials.


Follwoing the Graphene Nanoelectronics and Nanofabrication student understands:

  • the main physical properties of graphene and how they can be exploited to realize graphene electronic devices;
  • how to extract important parameters and figures of merit of graphene field-effect transistors (GFETs) both in dc and at high-frequencies;
  • the advantages and disadvantages of GFETs with respect to conventional Si transistor technology;
  • the suitable applications of graphene in electronics;
  • the state-of-the-art technologies for the fabrication of devices at the nanoscale, both used in research and industry.

Argomenti trattati

Nanodevice Characterization:

Linear transport theory: scattering mechanisms and screening, quantum and transport lifetimes.

The Boltzmann equation: relaxation time approximation, electrical and thermal conductivity and thermoelectric processes.

2-dimensional carrier gases: ballistic transport, high electron mobility transistors.

Weak magnetic fields at low temperature: weak localization.

Strong magnetic fields at low temperature: Landau levels, Shubnikov-de Haas oscillations, and the quantum Hall effect.

Strong magnetic fields at room temperature: parallel conduction channels and the mobility spectrum.

Vertical transport devices: the transfer matrix treatment of resonant tunnel diodes.

Methods of obtaining physical and structural information at the nanoscale: X-ray diffraction of thin films; High-resolution x-ray diffraction; Nanofocused x-ray beams at synchrotron light sources; Raman and micro-Raman spectroscopy in semiconductors; Tip-enhanced Raman spectroscopy; Micro-photoluminescence.


Graphene Nanoelectronics and Nanofabrication:

Introduction to carbon-based material

  • Allotropes and  hybridization of carbon
  • Band spectrum and massless Dirac fermions in graphene
  • The origin of high charge carrier mobility in graphene
  • Comparison with carbon nanotubes
  • Klein paradox and half-integer quantum Hall effect

Graphene field effect transistors (FETs)

  • The importance of high mobility in electronic devices and circuits
  • Comparison between graphene and conventional FETs
  • Ambipolarity of graphene FETs
  • Electrostatic doping in graphene electronic circuits
  • The importance of drain current saturation and voltage gain
  • Impact of contact resistance on the properties of graphene FETs
  • Scaling and short-channel effects
  • Impact of band gap opening in graphene on FET properties

Small-signal model of graphene FETs

  • Low-frequency AC small signal model of FETs (hybrid-pi model)
  • Determination of transconductance gm and output conductance gd

Voltage and current gain

  • Definition of voltage and current gains
  • Intrinsic voltage gain gm/gd and intrinsic current gain h21

High-frequency model of graphene FETs

  • Extrinsic high-frequency model of FETs
  • Phasors in electronic circuits

Cutoff frequency fT of graphene FETs

  • Intrinsic and extrinsic cutoff frequency fT of graphene FETs
  • Comparison of graphene and conventional FETsin terms of fT
  • h and Y parameter models of two-port networks
  • Cutoff frequency from Y parameters

Power gain and maximum frequency of oscillation fmax of graphene FETs

  • Definition of power gain
  • Intrinsic and extrinsic maximum frequency of oscillation fmax of graphene FETs
  • Comparison of graphene and conventional FETsin terms of fmax
  • S parameters of two-port networks

Graphene electronic circuits

  • Graphene Moore’s law
  • Voltage gain and multi-stage circuits
  • Noise margin
  • Static and dynamic power dissipation
  • Graphene electronic circuits: amplifiers, mixers, frequency multipliers, logic gates
  • Realistic gate delays and graphene ring oscillators

Nanodevice Fabrication

  • Introduction to lithography
  • Deep ultraviolet lithography
  • Resolution enhancement technologies
  • Extreme ultraviolet lithography
  • Electron beam lithography
  • Alternative lithographic technologies
  • Pattern transfer
  • Nanofabrication of graphene nanoelectronic devices and circuits


For Nanodevice Characterization the student will benefit from having already completed some courses in solid-state physics, for example Solid State Physics (096033) and Physics of Surfaces (096056).


For Graphene Nanoelectronics and Nanofabrication the student will benefit from having already completed some courses in solid-state physics, for example Solid State Physics (096033) and Electronics (096032). However, this is not obligatory.


Modalità di valutazione

For Nanodevice Characterization the student will be evaluated by oral examination according to the calendar of the course.

The student will be expected to discuss the physical phenomena which give rise to certain results or experimental effects, and what information regarding the characterization of the sample or device under test can be extracted from the experimental results. Emphasis is placed on the comprehension of real experimental data rather than calculation of simplified systems or reproduction of text-book derivations.


For Graphene Nanoelectronics and Nanofabrication the student will be evaluated by written examination according to the calendar of the course. The student will be expected to discuss the physical phenomena underlying applications of graphene in electronics, solve basic electronic circuits with graphene, extract transistor parameters and determine corresponding figures of merit.

Risorsa bibliografica facoltativaLuis E. F. Foa Torres, Stephan Roche, Jean-Christophe Charlier, Introduction to Graphene-Based Nanomaterials - From Electronic Structure to Quantum Transport, Anno edizione: 2014, ISBN: 9781107030831
Risorsa bibliografica facoltativaJuin J. Liou, Frank Schwierz, Hei Wong, Nanometer CMOS, Anno edizione: 2010, ISBN: 9814241083
Risorsa bibliografica facoltativaZheng Cui, Nanofabrication - Principles, Capabilities and Limits, Anno edizione: 2008, ISBN: 978-0-387-75576-2
Risorsa bibliografica facoltativaNeil W. Ashcroft and N. David Mermin, Solid State Physics, Editore: Thomson Learning
Risorsa bibliografica facoltativaJ. H. Davies, The Physics of Low-Dimensional Semiconductors, Editore: Cambridge University Press, Anno edizione: 1998

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Forme didattiche
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Laboratorio Informatico
Laboratorio Sperimentale
Laboratorio Di Progetto
Totale 100:00 150:00

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