The course aims to present an in-depth analysis of the most important devices used in modern electronics, focusing on the CMOS and the bipolar technology. Starting from the basic physics and the working principles of the devices, the course comes to discuss second-order effects impacting their performance in deca-nanometer technologies, addressing possible optimization rules.
1) Review of basic properties of semiconductor materials
Energy bands in a semiconductor material, energy-gap dependence on temperature, density of states. Thermodynamic equilibrium: Fermi-Dirac and Maxwell-Boltzmann statistics, Fermi level, charge-carrier concentration. Drift and diffusion of charge carriers, current transport, resistivity and sheet resistivity. Electrostatic potential in semiconductors: the non-linear Poisson equation, Debye length. Non-equilibrium conditions: quasi-Fermi levels, continuity equations, dielectric relaxation time, Shockley-Read-Hall theory for carrier generation/recombination via defect-assisted processes.
2) Two-terminal integrated devices
Device electrostatics under thermodynamic equilibrium: band diagram, built-in potential, electric field profile. Forward and reverse bias: band diagram, quasi-Fermi levels, potential drops and current components along the junction. Shockley ideal-diode equation. Wide-base and narrow-base diodes. Generation/recombination currents in the space-charge region. High injection levels and impact of the resistance of the quasi-neutral regions on the diode I-V curve. Gummel plot. Temperature dependence of the diode current-voltage characteristics. Small-signal model of the p-n junction.
Electrostatic analysis under equilibrium and non-equilibrium conditions. Current transport: Schottky's diffusion theory, Bethe's thermionic-emission theory, thermionic-emission-diffusion theory. Schottky effect. Tunneling ohmic contacts. Effect of interface states on the band diagram of the junction.
The MOS system: band diagram under equilibrium and in presence of an external gate bias. Working regimes of the device as a function of the gate bias. Calculation of the substrate charge vs. surface potential relation from the Poisson equation. Surface potential and substrate charge as a function of the gate bias. Weak inversion: exponential growth of the inversion charge in the channel with the gate bias. Strong inversion: estimation of the thickness of the inversion layer. Capacitance of an MOS structure: dependence on the gate bias and on the measurement frequency. Polysilicon gate: technological benefits, electrostatic drawbacks and impact on the threshold voltage of an n-MOS and of a p-MOS. MOS capacitor with ring: impact of the ring bias on device electrostatics, on threshold voltage and on the C-V curve. Oxide charge and interface states: impact on the C-V curve.
Long-channel MOSFETs: gradual-channel approximation, electrostatic analysis and calculation of the drain current. Current-voltage characteristics of a long-channel MOSFET above threshold; pinch-off condition at the drain. Small-signal model of the transistor and carrier transit time in the channel. Subthreshold conduction. Body effect. Temperature dependence of the transistor electrical parameters. Output resistance and channel length modulation. Short-channel MOSFET: electrostatics, short-channel effect, DIBL. Velocity saturation along the channel: mobility dependence on the longitudinal and transverse electric field, impact on the current-voltage characteristics of the device. MOSFET scaling: constant-field scaling and generalized scaling. Limits to constant-field scaling: subthreshold current and OFF-state power dissipation, silicon energy gap, short-channel effects, parasitic effects. Tox-Wdmax space for the design of scaled MOSFETs. Emerging scaling issues: statistical variability, leakage currents.
Bipolar junction transistor:
Structure, working principles and band diagram. Electric field in the quasi-neutral region of the base: non-uniform doping, high injection and parasitic resistance. Collector current in presence of non-uniform base doping, band-gap narrowing and SiGe base. Base current. Impact of the emitter and base parasitic resistances on the collector and base current. Dependence of beta on the collector current: drop of beta at high currents, Kirk effect, modulation of base conductivity; drop of beta at low currents, carrier recombination in the base/emitter depletion layer. Current-voltage characteristics of the BJT: saturation regime and forward-active regime. Early effect. Small-signal model of the BJT. Frequency response, cut-off frequency and its dependence on the collector current. Forward transit time. Advanced BJTs: polysilicon emitter and SiGe base.
- Fundamentals of semiconductors