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semiconductor nanodevices

Physics of semiconductor nanoelectronic devices

D. Svintsov

The course provides an introduction to the physics and modeling of contemporary semiconductor nanoelectronic devices, particularly focusing on devices for large integrated circuits based on silicon and emerging materials. The course starts with the discussion of electric properties of p-n junctions and drift-diffusive transport in semiconductors. A significant part of the course is devoted to the physics of the field-effect transistors and their scaling laws. The crossover from classical electron transport in large devices to the quantum ballistic and tunneling transport in nanoscale devices is analyzed in detail. The performance limits of the silicon nanotransistors are discussed, followed by the discussion of alternative high-mobility materials. The problem of power consumption in ultrafast circuits is addressed, and the operating principles of the ultralow-power tunneling and nano-mechanical switches are presented. To conclude the course, an introduction to the novel structures based on graphene and layered two-dimensional materials is given highlighting their possible applications in nanoelectronics.

Preliminary syllabus:
  1. Overview of the transport models for semiconductors. Boltzmann kinetic equation. Collision integrals for various scattering mechanisms (impurity, phonon, carrier-carrier). Relaxation-time approximation. Macroscopic (drift-diffusion and hydrodynamic) transport equations derived from Boltzmann equation. Limits of applicability for macroscopic transport equations and Boltzmann equation to nanoscale devices. Quantum kinetic equation.
  2. Semiconductor p-n junctions. Distribution of electrostatic potential, depletion layer. Transport under forward and reverse bias: quasi-Fermi levels and carrier recombination. Volt-ampere characteristic of an ideal p-n junction: Shockley formula. Deviations from an ideal characteristics: role of space charge, recombination in depletion layer. Avalanche and tunnel breakdown.
  3. Metal-oxide-semiconductor field-effect transistors (MOSFETs). Electrostatics of the MOS structure and field effect in semiconductors. Solutions of the Poisson equation in the depletion and accumulation modes. MOSFET structure and operation principle. Derivation of the current-drain voltage and current-gate voltage dependencies from drift-diffusion equations. MOSFET operation regimes: subthreshold, linear, current saturation. Logic gates based on MOSFETs (NOT, AND, OR) and their characteristics. Overview of MOSFET fabrication process.
  4. Performance limits of MOSFETs and scaling laws. Cutoff frequency of MOSFET: derivation from time-dependent drift-diffusion equations. Dependence of cutoff frequency on the channel length. Operating voltage of MOSFET and its dependence on gate insulator thickness. High-k gate oxides. Crossover from drift-diffusion to ballistic transport in short-channel devices. Effects of short-channel on MOSFET electrostatics: drain-induced barrier lowering and subthreshold slope degradation. Novel MOSFET architectures (double-gate, gate-all-around) for improved electrostatic control.
  5. Emerging low-power nanoelectronic switches. Power consumption of MOSFET and scaling laws for power consumption. Subthreshold slope of gate characteristic as a figure of merit for MOSFET power efficiency. Thermionic limit of subthreshold slope for MOSFETs and Schottky-barrier FETs. Structure and operating principle of interband tunneling transistor. Models of electron tunneling in semiconductors: direct and phonon-assisted tunneling. Limits of subthreshold slope for tunnel FETs: band tail tunneling and trap-assisted tunneling. Tunnel FETs based on low-dimensional materials and density-of-states switching. Alternative low-power digital switches (nanomechanical switches and impact-ionization MOSFETs).
  6. High-performance transistors based on III-V materials. Intrinsic electron mobility in bulk III-V materials and MOSFETs based on bulk III-V’s. Problems of electron-hole asymmetry, dopant activation and formation of ohmic contacts. Fermi level depining for improved contact resistivity in III-V MOSFETs. Two-dimensional electron gas formation in heterostructures based on III-V materials. “Remote doping” and improved electron mobility in FETs based on two-dimensional electron gas. Novel effects in high-mobility transistors: self-excitation of plasma waves and resonant response to the high-frequency radiation.
  7. Quantum effects in extremely scaled MOSFETs. Formation of two-dimensional electron gas in accumulation layer of MOSFETs. Transverse quantization and subband formation in quasi-one dimensional silicon nanowires. Landauer-Buttiker approach to electron transport in one-dimensional channels and conductance quantization. Self-consistent solution of Poisson and Schrodinger equations as a basis for modeling of nanoscale transistors. Inclusion of inelastic electron scattering into quantum transport models. Nonequilibrium Green’s function formalism.
  8. Electronic devices based on novel carbon materials. Electronic structure of graphene and carbon nanotubes: quasi-relativistic electron dispersion. Suppression of backscattering as a prerequisite of high electron mobility. Mobility degradation in graphene on different substrates. Performance limits of graphene and carbon nanotube FETs. Absence of band gap in 2d graphene, Klein tunneling, and problem of ON/OFF ratio in graphene transistors. Modifications of graphene (bilayers, nanoribbons) possessing band gap. Novel layered structures based on graphene, boron nitride, and transition metal chalcogenides. Vertical and lateral tunnel transistor based on graphene-boron nitride structures. Resonant tunneling in layered two-dimensional systems.

  1. S. Sze and K. Ng “Physics of semiconductor devices”, John Willey & Sons, 2007
  2. S. Datta “Quantum transport: atom to transistor”, Cambridge University Press, 2005
  3. L. Venema “Silicon electronics and beyond”, Nature 479, p. 309, 2011
  4. T. Enoki and T. Ando “Physics and chemistry of graphene”, Pan Stanford Publishing, 2013
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