Review of basic properties of semiconductor materials
- Energy bands in a semiconductor material, dependence of the energy gap on temperature, density of states for the conduction and valence bands;
- Thermodynamic equilibrium: Fermi-Dirac and Maxwell-Boltzmann statistics, Fermi level, concentration of electrons and holes;
- Current transport by drift and diffusion of charge carriers, resistivity and sheet resistivity;
- Electrostatic potential in a semiconductor material: non-linear Poisson equation, Debye length;
- Non-equilibrium conditions: quasi-Fermi levels, continuity equation for electron and holes, dielectric relaxation time, Shockley-Read-Hall theory for carrier generation/recombination via defect-assisted processes.
- Basic structure and 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 of the junction, high level of injection and parasitic resistances, Gummel plot, temperature dependence of the current-voltage characteristics of the device;
- Small-signal model of the p-n junction.
- Basic structure and device electrostatics 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;
- Impact of interface states on device operation.
- The MOS system: basic structure, working principles, band diagram under thermodynamic equilibrium and in the presence of a gate bias, working regimes of the device;
- Analysis of device electrostatics: calculation of the substrate charge as a function of the surface potential from the solution of the Poisson equation, surface potential and substrate charge as a function of the gate bias, threshold voltage;
- Small-signal capacitance: dependence on the gate bias (C-V curve), low-frequency, high-frequency and deep-depletion regimes;
- MOS capacitor with ring: split C-V, impact of the ring bias on device electrostatics, on threshold voltage and on the C-V curve;
- Oxide charge and interface states: impact on device electrostatics and on the C-V curve;
- Polysilicon gate: technological benefits, electrostatic drawbacks and impact on the threshold voltage of an n-MOS and of a p-MOS.
- The long-channel MOSFET: basic structure of the device, working principles, gradual-channel approximation, electrostatic analysis and calculation of the depletion and inversion charge in the channel under subthreshold and strong-inversion conditions, general expression for the drain current;
- Current-voltage characteristics of the long-channel MOSFET above threshold: ohmic, parabolic and saturation regimes, pinch-off condition at the drain, band diagram and quasi-Fermi levels along the channel, small-signal model of the transistor, output resistance in the saturation regime and channel length modulation, carrier transit time in the channel, body-effect;
- Subthreshold conduction in the long-channel MOSFET: carrier diffusion from source to drain, subthreshold current, subthreshold slope, carrier generation in the channel, transcharacteristics of the transistor;
- Dependence of the electrical characteristics of the device on the oxide thickness, on substrate doping and on temperature, impact of oxide charge and interface states on the drain current, source/drain parasitic resistances and capacitances;
- Short-channel MOSFET: electrostatics, short-channel effect, DIBL, velocity saturation along the channel and its impact on the current-voltage characteristics of the device, early saturation of the drain current due to velocity saturation at the drain;
- MOSFET scaling: constant-field scaling and generalized scaling, scaling trade-offs and constraints, high-k dielectrics, metal gate, Tox-Wdmax space for the design of scaled MOSFETs, FinFETs and advanced MOSFET structures, relevant scaling issues in nanoscale devices, statistical variability, leakage currents.
Bipolar junction transistor (BJT)
- Basic structure of the device, working principles, current gain, collector current of the prototype transistor;
- Electric field in the quasi-neutral base region: non-uniform doping, high injection, band-gap narrowing and engineering of the base material, expressions for the collector current;
- Base current: shallow emitter and deep emitter;
- Dependence of the current gain of the transistor on the collector current, Gummel plot, carrier recombination in the base/emitter depletion layer, parasitic resistances, Kirk effect, modulation of the base conductivity;
- 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;
- Evolution of device parameters, advanced device structures, polysilicon emitter, SiGe base.