### 2,014

The number of undergraduate students, 2014-15 school year.

Application of quantum mechanical concepts to electronics problems; detailed analysis of a calculable two-state laser system; incidental quantum ideas bearing on electronics. Course Information: 3 undergraduate hours. 3 graduate hours. Prerequisite: PHYS 485.

Credit in PHYS 485

Microelectronics and Photonics

In this course, quantum mechanical concepts are applied to practical problems in physics, electronics, chemistry, and electrical engineering. The goal of this course is to develop the quantum mechanical foundation for modern electronic devices (MEMS, lasers, transistors, LEDs, quantum size effects in FETs, optical communication, etc.).

Develop a basis for understanding the quantum mechanical aspects
of modern electronics (lasers, quantized Hall effect, field effect transistors, optical tweezers, etc.)

- time-independent Schrodinger equation
- quantum mechanical tunneling
- bound states and scattering
- transmission electron microscopy
- the energy spectrum of diatomic and aromatic molecules
- the band structure of one-dimensional crystalline and disordered solids
- the scattering time for electron transport in a crystal
- the quantized Hall effect in a two-dimensional electron gas
- perturbation theory and field quantization
- two-state lasers
- light pressure forces on atoms
- quantization of LC circuits
- Casimir forces

Develop a basis for understanding the quantum mechanical aspects of modern electronics (lasers, quantized Hall effect, field effect transistors, optical tweezers, etc.)

Topics:

- time-independent Schrodinger equation
- quantum mechanical tunneling
- bound states and scattering
- transmission electron microscopy
- the energy spectrum of diatomic and aromatic molecules
- the band structure of one-dimensional crystalline and disordered solids
- the scattering time for electron transport in a crystal
- the quantized Hall effect in a two-dimensional electron gas
- perturbation theory and field quantization
- two-state lasers
- light pressure forces on atoms
- quantization of LC circuits
- Casimir forces

Class notes

**Recommended:** H. Kroemer, *Quantum Mechanics for Engineering*, Material Science and Applied Physics, Prentice Hall, 1994.

Engineering Science: 3 credits

The objective of this course is introduce the quantum mechanical concepts needed to understand the operation of not only current nanoelectronic and nanophotonic devices and materials, but to understand the operating principles behind devices and materials still in their infancy. To this end, we will apply the principles of quantum mechanics to understand cutting edge next generation nanoelectronic devices and materials. This course combines the use of course textbooks with current literature to show how quantum principles are used not simply to understand traditional physics applications but to understand new physical effects and their potential applications in transformative new technologies.

By the completion of 21 lectures (halfway mark), the students should have been introduced to the following and be able to do:

- Demonstrate an understanding of Natural Units. (a,k)
- Understand Wave Particle Duality. (a)
- Be familiar with quantum computation: probability amplitudes and operators. (a,l)
- Know Wave Particle Duality. (a)
- Explain Probability Amplitudes, and Operators: Quantum Computation. (a,j,k,l)
- Apply The Time-Independent Schrödinger Equation. (a)
- Have seen Formalism: Observables. (a,l)
- Calculate The Uncertainty Principle, and Newton’s Second Law. (a,b)
- Formalisim: Dirac Bra-Ket Notation. (a)
- A Particle in a Square Well: Zero-point energy, Casimir Forces. (a,b,c,j,k)
- Three-dimensional Square well, Density of States. (a,l)
- Free Particles, Particle Currents, Wavepackets, and Uncertainty. (a)
- Be familiar with Gaussian Wavepackets and Quantum Measurement. (a,b,l)
- The Delta-Function Potential: Bound States. (a)
- The Delta-Function Potential: Scattering States and Tunneling. (a)
- Band Structure: From Free Electron to Bloch’s Theory. (a)
- Crystal Momentum and Effective Electron Mass. (a,b)
- The Kronig Penny Model. (a)
- Quantization due to Confinement by Simple Barriers: GaAs/AlGaAs Quantum Well. (a,l)
- One-dimensional Square-barrier: The Tunneling States. (a,b,c)
- The Propagation Matrix. (a,c,n)
- Demonstrate teamwork in completing homework assignments. (d,e)
- Perturbation Theory (Degenerate and Non-degenerate). (a)

By the end of the course (semester) students should be able to:

- Kronig-Penny model (revisited). (a,b,k)
- Calculations of the Transmission Coefficient: Resonant Tunneling. (a,b,j)
- Explain Transmission Electron Microscopy. (a,b,c,k)
- Use the Landauer Formula: Conductance Quantization. (a,b,l)
- Nondegenerate, Time-Independent Perturbation Theory (revisited)
- Apply Degenerate, Time-Independent (Stationary) Perturbation Theory (revisited) (a)
- Apply the Landauer theory to modern nanotransistors. (a,b,e,j,k)
- Understand Ballistic Conduction in Nanostructures. (a,c,j,k)
- Explain Electrons in Magnetic Fields: Aharonov-Bohm Effect. (a)
- Demonstrate an Understanding of Spin and its use in Modern Nanodevices. (a,b,c,e,j,k)
- Electrons in Magnetic Fields: Landau Levels and the Hall Effect. (a,b)
- The Quantum Hall Effect. (a,b,k)
- The harmonic oscillator (revisited): ladder operators. (a)
- Field Quantization: Phonons and Photons. (a)
- Topological Effects in 2D and 3D Materials. (a,b,c,j,k)
- Time-Dependent Perturbation Theory: Two-level Systems. (a)
- Charged Particle in a Harmonic Potential. (a)
- Apply Fermi’s Golden Rule:
- Explain Photon Emission and Absorption. (a)
- Understand Exchange and Correlation in Systems of Identical Particles. (a)
- Understand LASERs. (a,e)
- Photon Emission and Absorption. (a,b)
- Design A Simple, One-dimensional LASER. (a,b,c)

5/23/2013

DEPARTMENT OF ELECTRICAL

AND COMPUTER ENGINEERING

Copyright ©2015 The Board of Trustees at the University of Illinois. All rights reserved