
Process Modeling
23 Aug 2011  Series  Contributor(s): Dragica Vasileska
This series on process modeling describes key process modeling steps such as implantation, diffusion, oxidation, etching, deposition, etc.

Nanoelectronics and Modeling at the Nanoscale
30 Jun 2011  Series  Contributor(s): Dragica Vasileska, Gerhard Klimeck
Nanoelectronics refers to the use of nanotechnology on electronic components, especially transistors. Although the term nanotechnology is generally defined as utilizing technology less than 100 nm in size, nanoelectronics sometimes refers to transistor devices that are so small that interatomic interactions and quantum mechanical properties need to be studied extensively.
In this tutorial various effects that occur at the nanoscale will be reviewed. Emphasis will be placed on how different …

From SemiClassical to Quantum Transport Modeling
10 Aug 2009  Series  Contributor(s): Dragica Vasileska
This set of powerpoint slides series provides insight on what are the tools available for modeling devices that behave either classically or quantummechanically. An indepth description is provided to the approaches with emphasis on the advantages and disadvantages of each approach. Conclusions are drawn about the applicability of each approach. There are additional teaching materials that can be found on the nanohub that give more indepth knowledge about each topic being addressed in this ...

Computational Electronics HW Set
24 Jul 2008  Series  Contributor(s): Dragica Vasileska, Gerhard Klimeck

Quantum Mechanics for Engineers: Podcasts
07 Jul 2008  Series  Contributor(s): Dragica Vasileska, Gerhard Klimeck, David K. Ferry
This course will introduce the students to the basic concepts and postulates of quantum mechanics. Examples will include simple systems such as particle in an infinite and finite well, 1D and 2D harmonic oscillator and tunneling. Numerous approximation techniques, such as WKB method, timedependent and timeindependent perturbation theory, variational methods and numerical solution methods of the 1D SchrÃ¶dinger equation, will be presented.
The importance of quantummechanics in todays life ...

Quantum Mechanics: Stationary Perturbation Theory
10 Jul 2008  Series  Contributor(s): Dragica Vasileska, Gerhard Klimeck
Stationary perturbation theory is concerned with finding the changes in the discrete energy levels and the changes in the corresponding energy eigenfunctions of a system, when the Hamiltonian of a system is changed by a small amount. In this section we provide reading material regarding stationary perturbation theory, slides and homework assignments.
Reading Material: Stationary Perturbation Theory
Reading Material: Stationary Perturbation Theory Examples and Stark Effect
Slides: ...

Quantum Mechanics: TimeDependent Perturbation Theory
10 Jul 2008  Series  Contributor(s): Dragica Vasileska, Gerhard Klimeck
Timedependent perturbation theory, developed by Paul Dirac, studies the effect of a timedependent perturbation V(t) applied to a timeindependent Hamiltonian H0. Since the perturbed Hamiltonian is timedependent, so are its energy levels and eigenstates. Therefore, the goals of timedependent perturbation theory are slightly different from timeindependent perturbation theory. We are interested in the following quantities: (1) The timedependent expected value of some observable A, for a ...

Quantum Mechanics: Harmonic Oscillator
09 Jul 2008  Series  Contributor(s): Dragica Vasileska, Gerhard Klimeck
The quantum harmonic oscillator is the quantum mechanical analogue of the classical harmonic oscillator. It is one of the most important model systems in quantum mechanics because an arbitrary potential can be approximated as a harmonic potential at the vicinity of a stable equilibrium point. Furthermore, it is one of the few quantum mechanical systems for which a simple exact solution is known.
The energy spectrum of a harmonic oscillator is noteworthy for three reasons. Firstly, the energies ...

Quantum Mechanics: WKB Approximation
09 Jul 2008  Series  Contributor(s): Dragica Vasileska, Gerhard Klimeck
In physics, the WKB (Wentzel–Kramers–Brillouin) approximation, also known as WKBJ (Wentzel–Kramers–Brillouin–Jeffreys) approximation, is the most familiar example of a semiclassical calculation in quantum mechanics in which the wavefunction is recast as an exponential function, semiclassically expanded, and then either the amplitude or the phase is taken to be slowly changing.
This method is named after physicists Wentzel, Kramers, and Brillouin, who all developed it in 1926. In ...

Quantum Mechanics: Hydrogen Atom and Electron Spin
09 Jul 2008  Series  Contributor(s): Dragica Vasileska, Gerhard Klimeck
A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positivelycharged proton and a single negativelycharged electron bound to the nucleus by the Coulomb force. The most abundant isotope, hydrogen1, protium, or light hydrogen, contains no neutrons; other isotopes contain one or more neutrons. This article primarily concerns hydrogen1.
The hydrogen atom has special significance in quantum mechanics and quantum field theory as a simple ...

Quantum Mechanics: Landauer's Formula
08 Jul 2008  Series  Contributor(s): Dragica Vasileska, Gerhard Klimeck
When a metallic nanojunction between two macroscopic electrodes is connected to a battery, electrical current flows across it. The battery provides, and maintains, the charge imbalance between the electrode surfaces needed to sustain steadystate conduction in the junction. This static nonequilibrium problem is usually described according to the Landauer picture. In this picture, the junction is connected to a pair of defectfree metallic leads, each of which is connected to its own distant ...

Quantum Mechanics: Periodic Potentials and KronigPenney Model
09 Jul 2008  Series  Contributor(s): Dragica Vasileska, Gerhard Klimeck
The KronigPenney model is a simple approximation of a solid. The potential consists of a periodic arrangement of delta functions, square well or Coulomb well potentials. By means of epitaxial growth techniques artificial semiconductor superlattices can be realized, which behave very similar to the assumptions of the KronigPenny model. To get better understanding of the KroinigPenney model, we provide written text, slides, homework assignments and access to the Periodic Potential Lab and the ...

Quantum Mechanics: Tunneling
08 Jul 2008  Series  Contributor(s): Dragica Vasileska, Gerhard Klimeck
In quantum mechanics, quantum tunnelling is a micro nanoscopic phenomenon in which a particle violates the principles of classical mechanics by penetrating a potential barrier or impedance higher than the kinetic energy of the particle. A barrier, in terms of quantum tunnelling, may be a form of energy state analogous to a "hill" or incline in classical mechanics, which classically suggests that passage through or over such a barrier would be impossible without sufficient energy. The two ...

Quantum Mechanics: Time Independent Schrodinger Wave Equation
07 Jul 2008  Series  Contributor(s): Dragica Vasileska, Gerhard Klimeck
In physics, especially quantum mechanics, the Schrödinger equation is an equation that describes how the quantum state of a physical system changes in time. It is as central to quantum mechanics as Newton's laws are to classical mechanics.
In the standard interpretation of quantum mechanics, the quantum state, also called a wavefunction or state vector, is the most complete description that can be given to a physical system. Solutions to Schrödinger's equation describe atomic and subatomic ...

Quantum Mechanics: Introductory Concepts
07 Jul 2008  Series  Contributor(s): Dragica Vasileska, Gerhard Klimeck, David K. Ferry
In this section of the Quantum Mechanics class we discuss the particlewave duality and the need for the quantization of energy to explain the blackbody radiation and the photoelectric effect. We provide reading material, slides and video, which in a very illustrative way, explain the most difficult concept in quantummechanics: the particlewave duality. A homework assignment, that teaches the students the quantization of the angular momentum and energy and also helps the students to better ...

Quantum Mechanics: Postulates
07 Jul 2008  Series  Contributor(s): Dragica Vasileska, Gerhard Klimeck
A physical system is generally described by three basic ingredients: states; observables; and dynamics (or law of time evolution) or, more generally, a group of physical symmetries. A classical description can be given in a fairly direct way by a phase space model of mechanics: states are points in a symplectic phase space, observables are realvalued functions on it, time evolution is given by a oneparameter group of symplectic transformations of the phase space, and physical symmetries are ...

Quantum Mechanics: Wavepackets
07 Jul 2008  Series  Contributor(s): Dragica Vasileska, Gerhard Klimeck
In physics, a wave packet is an envelope or packet containing an arbitrary number of wave forms. In quantum mechanics the wave packet is ascribed a special significance: it is interpreted to be a "probability wave" describing the probability that a particle or particles in a particular state will be measured to have a given position and momentum.
By applying the Schrödinger equation in quantum mechanics it is possible to deduce the time evolution of a system, similar to the process of the ...