Simulate transport in RTDs using the Non-equilibrium Green's Function method. The simulation methodology is following the concepts of the NEMO 1-D simulation tool. The embedded single band physics is decribed in detail in the Applied Physics Letters citation listed below.

Features:

• three different potential models:
• linear potential drop,
• semi-classical Thomas Fermi potential, and
• Hartree quantum charge-selfconsistent potential.
• relaxation in the reservoirs incorporated through a simple relaxation model.
• automatic determination of the AlGaAs barrier height.
• 2-barrier and multi-barrier devices.

Upgrades from previous versions:

• Computational speed dramatically improved through computations in C rather than Matlab. Computation times for a single bias point are now down to about 1 second compared to several minutes. Matlab is notoriously bad in "for" loops, but the RGF (Recursive Green Function algorithm) cannot be vectorized in a matlab friendly fashion. So a lower-most C call was implemented that now performs the RGF for many energies in C.
• Current density plots as a function of energy are added to the outputs. They are also augmented by a normalized running integral, which helps to identify, "where" in energy the current contributions are.
• The adaptive grid is now set to be more selective and appears to resolve very narrow resonances much better.
• A possible non-convergence has been avoided by setting an upper bound for the energy nodes that can be added by the adaptive grid.
• Local Density of states and energy resolved charge profile plots have now been added.
• A possible discrepancy between the quantum and semi-classical charge at the boundaries has been corrected. This discrepancy occurred at very small decay lengths of the optical potential.
• Ver 1.1.1 has Local Density of states and energy resolved charge profile plots that conserve the integral value of the quantities in energy.
• Ver 1.1.2 has camera angles predefined for surface plots.
• Ver 1.1.2 enables the user to turn off the time consuming surface plots
• Ver 1.1.2 runs faster by avoiding frequent hard-disk access
• Ver 1.1.3 Boundary conditions at interfaces corrected for the effective mass hamiltonian. It is now based on the formulation of Frensley.
• Ver 1.1.3 New GUI options that allow the user to control the resonance finder and the adaptive grid generator
• Ver 1.1.3 The device geometry/construction is now more flexible.
• Ver 1.1.3 Resonances are now plotted based on the output of the resonance finder, if it is turned on.
• Ver 1.1.3 Resonances as a function of bias are also displayed if the resonance finder is turned on.
• Ver 1.1.4 The Energy Mesh Refinement algorithm has been improved, some bugs have been fixed. A typical simulation time has been reduced from 50 seconds to 30 seconds.
• Ver 1.1.5 The mesh refiner has been improved and use much less points to refine the energy grid.
• Ver 1.1.6 Convergence criteria have been improved.
• Ver 1.1.7 A resonance width plot has been added.
• Ver 1.1.7 A resonance wave function has been added.
• Ver 1.1.7 Resonances in the undoped part of the emitter are also resolved.
• Ver 1.1.8 Charge balance problem in the emitter and collector has been resolved for small etas.
• Ver 1.1.9 Broadening in boundary conditions corrected. Energy range of integration for zero eta refined.
• Ver 1.1.9 A plot for the effective mass dependent on the position has been added.
• Ver 1.1.9 The output log has been modified. It now reports a information table about the device simulated.
• Ver 1.1.9 The convergence of the poisson solver has been improved by adopting a dampened oscillation scheme.
• Ver 1.1.10 A plot for sheet density has been added.
• Ver 1.2.0 Material parameters modified. In particular the Energy Conduction Band of AlGaAs is now assumed to have a quadratic form (1-x)*Eg(GaAs)+x*Eg(AlAs)-x*(1-x)*C where C=0.086*(300-Temp)/(300-77).
• Ver 1.2.0 Adaptive grid moved to the 4pt scheme.
• Ver 1.2.0 An algorithm for the recognition of resonance curves has been implemented. Three plots have been added (two are optional scatter plots) showing the resonances and widths curves with different colors depending on the position of the resonances (red and green=centre of the barrier, light red and light green=otherwise).
• Ver 1.2.0 A new plot reporting the not-normalized current has been added as optional. It is reachable from the Advanced tab.
• Ver 1.2.0 A new composite plot has been added (as default) showing the conduction band in linear scale and the transmission and current in log scale.
• Ver 1.3.0 The composite plot of the precedent version has been greatly improved.
• Ver 1.3.0 A new plot showing currents and transmission has been implemented and added.
• Ver 1.3.0 A new composite plot has been implemented and added showing (in 6 charts) the electrostatic potential, the current and transmissions (normalized to one), the resonance energies (normalized to one), the electron density, the sheet density curves, the IV curve.
• Ver 1.3.1 New composite plot showing the conduction band, the resonances and the current.
• Ver 1.3.1 The outputs have been totally reordered. Some plot labels have been modified too.
• Ver 1.3.1 A new view input/output has been implemented.
• Ver 1.3.1 The bands+transmission+currentdensity composite plot has been modified. The current voltage curve has been added.
• Ver 1.3.1 A new composite plot showing bands+transmission+IV has been created and added.
• Ver 1.3.1 A material and structure data table has been added.
• Ver 1.3.2 A small bug has been fixed in the original 6 chart plot (when the quantum charge is set to ON)
• Ver 1.3.2 A new 6 chart plot has been added with a zoomed energy range where the current flows.

Theory - Transport with Non-Equilibrium Green Functions:

Prof. Datta is providing information on the NEGF formalism and its applications in a designated Topics page with tutorials, research seminars, research publications, Ph.D. theses, and simulation tools. To understand the critical elements of the boundary conditions that treat the relaxation in the reservoirs we recommend that users read through the following publication.

• Quantum Device Simulation with a Generalized Tunneling Formula, Gerhard Klimeck, Roger K. Lake, R. Chris Bowen, William R. Frensley and Ted Moise, Appl. Phys. Lett., Vol. 67, p.2539 (1995).

This RTD tool uses some of the concepts of the NEMO 1-D simulation tool. Unfortunately we cannot release NEMO 1-D as such on the nanoHUB and we are in the process of recreating some of its capabilities here. The first release of this nanoHUB tool has some severe limitations compared to NEMO 1-D. A more comprehensive understanding of the NEMO 1-D simulation capabilities can be gained from reading the following publications:

• Quantitative Resonant Tunneling Diode Simulation, R. Chris Bowen, Gerhard Klimeck, Roger Lake, William R. Frensley and Ted Moise, J. of Appl. Phys., Vol. 81, 3207 (1997).
• Single and multiband modeling of quantum electron transport through layered semiconductor devices, Roger Lake, Gerhard Klimeck, R. Chris Bowen and Dejan Jovanovic, J. of Appl. Phys., Vol. 81, 7845 (1997).

Tool Limitations:

• single effective mass model, no sophisticated multiband models;
• no transverse momentum integration;
• no exchange and correlation potential;
• GaAs / AlGaAs material system;
• no material parameters are exposed to the users for possible changes

Known issues with this release:

• resonances are identified only by peaks in the transmission. There is no true spatial resolution and resonances in the triangular emitter well might be identified as central device resonance.

Luisier, Agarwal	... core effective mass simulation engine in matlab
JM Sellier	...Adaptive grid refinement, Debug, Creation of new plots, Improvement of existing plots, Creation of composite plots, Resonance Curve Recognition Algorithm
Zhengping Jiang	...C-functions in Matlab to speed up code in RGF and resonance finding
McLennan, Klimeck	...GUI design and output requirements

NCN@Purdue, MSD FCRP

• Quantum Device Simulation with a Generalized Tunneling Formula, Gerhard Klimeck, Roger K. Lake, R. Chris Bowen, William R. Frensley and Ted Moise, Appl. Phys. Lett., Vol. 67, p.2539 (1995).
• Quantitative Resonant Tunneling Diode Simulation, R. Chris Bowen, Gerhard Klimeck, Roger Lake, William R. Frensley and Ted Moise, J. of Appl. Phys., Vol. 81, 3207 (1997).
• Single and multiband modeling of quantum electron transport through layered semiconductor devices, Roger Lake, Gerhard Klimeck, R. Chris Bowen and Dejan Jovanovic, J. of Appl. Phys., Vol. 81, 7845 (1997).

Researchers should cite this work as follows:

• The simulation procedure and physics are described in the the following citation: Quantum Device Simulation with a Generalized Tunneling Formula, Gerhard Klimeck, Roger K. Lake, R. Chris Bowen, William R. Frensley and Ted Moise, Appl. Phys. Lett., Vol. 67, p.2539 (1995).

• Jean Michel D Sellier, Samarth Agarwal, Mathieu Luisier, Zhengping Jiang, Michael McLennan, Gerhard Klimeck (2018), "Resonant Tunneling Diode Simulation with NEGF," https://nanohub.org/resources/rtdnegf. (DOI: 10.4231/D32J68433).

  BibTex | EndNote

1. ANTSY
2. nanoelectronics
3. NCN@Purdue Supported
4. NEGF
5. resonant tunneling diodes
6. rtd