# SEMICONDUCTOR DEVICES

## Learning outcomes of the course unit

The aim of this course is providing the students with the basic knowledge of the fundamental physical mechanisms underlying the operation of the most important semiconductor devices.

## Prerequisites

The student must be familiar with the notions of mathematics, phyiscs, chemistry, electrical and electronic engineering provided by the Laurea course in Electronic Engineering.

## Course contents summary

1) Introduction.

Semiconductors under equilibrium conditions. Mass action law. Fermi-Dirac and Maxwell-Boltzmann distributions. Density of states, Fermi level and intrinsic Fermi level. Free carriers, mobility, saturation velocity. Drift-diffusion model.

2) Metal-semiconductor junctions.

Metal-semiconductor junction under equilibrium conditions, forward bias and reverse bias. Interface states and Fermi level pinning. Ohmic contacts.

3) PN junctions.

Non-uniform doping distributions. The PN junction at equilibrium. Debye length. Reverse bias. Capacitance of a reverse-biased diode. Avalanche and Zener breakdown. Continuity equations. Shockley-Hall-Read recombination. Auger and surface recombination. I-V characteristics of the PN diode. Long-base and short-base diodes. Validity of the low-injection and quasi-equilibrium approximations. G-R currents in forward and reverse bias. Diffusion capacitance.

4) Bipolar Junction Transistors (BJTs).

Forward-active region. Base transport factor. Emitter efficiency. Reverse active region, saturation, off-state. Early effect. Integrated BJTs. Low-current effects. High-injection effects: Kirk effect, base resistance. Base transit time. Frequency limitations: fT and fMAX.

5) MOS Transistor (MOSFET).

Ideal MOS systems. Band structure. Accumulation, depletion, inversion, strong inversion. Threshold voltage and body effect. C-V characteristics of the ideal MOS system. Non-ideal MOS systems: cahrges in the oxide and at the interface. MOS transistors. Body effect. Bulk charge effect. Threshold voltage adjustment. Sub-threshold current. Short-channel and narrow-channel effects. Source/drain charge sharing. Drain-induced barrier lowering. Sub-surface punch-through. Mobility reduction. Velocity saturation. Drain current in short-channel MOSFETs. Effects of scaling on short-channel MOSFETs. Electric field in the saturated velocity region: quasi-2D model. Hot carrier effects: substrate and gate currents.

6) Energy bands in semiconductors

Crystalline structure and periodic potential. Schroedinger equation. Energy bands. Reduced-zone plot. Quantum states and materials classification. Si and GaAs band structures. Crystal momentum and effective mass. Constant-energy surfaces. Effective-mass Schroedinger equation.

7) Charge carriers

Generation of electrons and holes. Recombination. Carrier concentrations. Si DOS effective mass.

8) Thermal equilibrium

Collisions and scattering. Fermi level. Equilibrium carrier concentrations. Mean unidirectional velocity of an equilibrium distribution.

9) Charge transport

Boltzmann equation. Drift-diffusion model. Hydrodynamic model.

10) Solar cells

Absorption and generation. Photocurrent. Photovoltage. Maximum power point and conversion efficiency.

## Course contents

1) Introduction.

Semiconductors under equilibrium conditions. Mass action law. Fermi-Dirac and Maxwell-Boltzmann distributions. Density of states, Fermi level and intrinsic Fermi level. Free carriers, mobility, saturation velocity. Drift-diffusion model.

2) Metal-semiconductor junctions.

Metal-semiconductor junction under equilibrium conditions, forward bias and reverse bias. Interface states and Fermi level pinning. Ohmic contacts.

3) PN junctions.

Non-uniform doping distributions. The PN junction at equilibrium. Debye length. Reverse bias. Capacitance of a reverse-biased diode. Avalanche and Zener breakdown. Continuity equations. Shockley-Hall-Read recombination. Auger and surface recombination. I-V characteristics of the PN diode. Long-base and short-base diodes. Validity of the low-injection and quasi-equilibrium approximations. G-R currents in forward and reverse bias. Diffusion capacitance.

4) Bipolar Junction Transistors (BJTs).

Forward-active region. Base transport factor. Emitter efficiency. Reverse active region, saturation, off-state. Early effect. Integrated BJTs. Low-current effects. High-injection effects: Kirk effect, base resistance. Base transit time. Frequency limitations: fT and fMAX.

5) MOS Transistor (MOSFET).

Ideal MOS systems. Band structure. Accumulation, depletion, inversion, strong inversion. Threshold voltage and body effect. C-V characteristics of the ideal MOS system. Non-ideal MOS systems: cahrges in the oxide and at the interface. MOS transistors. Body effect. Bulk charge effect. Threshold voltage adjustment. Sub-threshold current. Short-channel and narrow-channel effects. Source/drain charge sharing. Drain-induced barrier lowering. Sub-surface punch-through. Mobility reduction. Velocity saturation. Drain current in short-channel MOSFETs. Effects of scaling on short-channel MOSFETs. Electric field in the saturated velocity region: quasi-2D model. Hot carrier effects: substrate and gate currents.

6) Energy bands in semiconductors

Crystalline structure and periodic potential. Schroedinger equation. Energy bands. Reduced-zone plot. Quantum states and materials classification. Si and GaAs band structures. Crystal momentum and effective mass. Constant-energy surfaces. Effective-mass Schroedinger equation.

7) Charge carriers

Generation of electrons and holes. Recombination. Carrier concentrations. Si DOS effective mass.

8) Thermal equilibrium

Collisions and scattering. Fermi level. Equilibrium carrier concentrations. Mean unidirectional velocity of an equilibrium distribution.

9) Charge transport

Boltzmann equation. Drift-diffusion model. Hydrodynamic model.

10) Solar cells

Absorption and generation. Photocurrent. Photovoltage. Maximum power point and conversion efficiency.

## Recommended readings

Suggested textbooks

R. S. Muller, T. I. Kamins, P. K. Ko, “Device Electronics for Integrated Circuits,” 3rd Edition, John Wiley & Sons, 2003. ISBN: 0-471-42877-9

D. L. Pulfrey, "Understanding modern transistors and diodes," Cambridge University Press, 2010. ISBN: 978-0-521-51460-6.

Other useful books

W. A. Harrison, “Applied quantum mechanics,” World Scientific, 2000, ISBN: 9810243758.

P. Hofmann, "Solid State Physics - An Introduction," Wiley-VCH, 2008, ISBN: 978-3-527-40861-0

## Teaching methods

The course consists in a series of classroom lectures.

## Assessment methods and criteria

Oral exam.