Nanoelectronic Modeling Lecture 20: NEGF in a Quasi-1D Formulation
27 Jan 2010 | Online Presentations | Contributor(s): Gerhard Klimeck, Samarth Agarwal, Zhengping Jiang
This lecture will introduce a spatial discretization scheme of the Schrödinger equation which represents a 1D heterostructure like a resonant tunneling diode with spatially varying band edges and effective masses.
Nanoelectronic Modeling Lecture 09: Open 1D Systems - Reflection at and Transmission over 1 Step
25 Jan 2010 | Online Presentations | Contributor(s): Gerhard Klimeck, Dragica Vasileska, Samarth Agarwal
One of the most elemental quantum mechanical transport problems is the solution of the time independent Schrödinger equation in a one-dimensional system where one of the two half spaces has a higher potential energy than the other. The analytical solution is readily obtained using a scattering matrix approach where wavefunction amplitude and slope are matched at the interface between the two half-spaces. Of particular interest are the wave/particle injection from the lower potential energy half-space.
Nanoelectronic Modeling Lecture 11: Open 1D Systems - The Transfer Matrix Method
31 Dec 2009 | Online Presentations | Contributor(s): Gerhard Klimeck, Dragica Vasileska, Samarth Agarwal, Parijat Sengupta
The transfer matrix approach is analytically exact, and “arbitrary” heterostructures can apparently be handled through the discretization of potential changes. The approach appears to be quite appealing. However, the approach is inherently unstable for realistically extended devices which exhibit electrostatic band bending or include a large number of basis sets.
Nanoelectronic Modeling Lecture 10: Open 1D Systems - Transmission through & over 1 Barrier
31 Dec 2009 | Online Presentations | Contributor(s): Gerhard Klimeck, Dragica Vasileska, Samarth Agarwal
Tunneling and interference are critical in the understanding of quantum mechanical systems. The 1D time independent Schrödinger equation can be easily solved analytically in a scattering matrix approach for a system of a single potential barrier. The solution is obtained by matching wavefunction values and derivatives at the two interfaces in the spatial domain. This simple example shows the extended nature of wavefunctions, the non-local effects of local potential variations, the formation of resonant states through interference, and quantum mechanical tunneling in its simplest form.
Comparison of PCPBT Lab and Periodic Potential Lab
10 Aug 2009 | Online Presentations | Contributor(s): Abhijeet Paul, Samarth Agarwal, Gerhard Klimeck, Junzhe Geng
This small presentation provides information about the comparison performed for quantum wells made of GaAs and InAs in two different tools. This has been done to benchmark the results from completely two different sets of tools and validate the obtained results. In this presentation we provide the motivation for this work, the input details and results obtained. The tools used for this purpose are Piecewise Constant Potential Barrier Tool(PCPBT) and Periodic Potential Lab. We provide ...