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This tool simulates transport in RTDs using the Non-equilibrium Green’s Function method. The simulation methodology is based on 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: Two different potential models: 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.
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. Ver 1.3.3 In the previous versions a bug used to show up as soon as the user selected a negative applied bias (some plots used to disappear or to show wrong results). This bug is now fixed. Ver 1.3.3 The algorithm that creates the energy range for the simulation has been generalized to handle reverse and backward applied biases. Ver 1.3.4 A bug used to occur when the resonance finder was set to off. This is now fixed. Ver 1.3.5 The resonances sorting algorithm has been modified ans is now faster. Ver 2.0 Powered by NEMO5 simulator which is entirely C++ based. Ver 2.0 A new tab named Multiscale Domain has been added to choose where the charge will be treated semi-classically or quantum mechanically. Ver 2.0 Resonance Finder tab now has more options to control the solvers used for locating resonance energies. Ver 2.0 Resonance vs voltage plots have been improved by incorporating a C based modified resonance curve recognition algorithm. This displays continuous variation of resonance energies involved in resonant tunneling with the applied bias. Option to view these as scatter plots is also available. Ver 2.0 For semi-classical Thomas-Fermi model, charge in the barrier & quantum well regions is fixed to be at 0. Ver 2.1 A new tab with adaptive energy grid options has been added. Ver 2.1 The resonance finder tab has a new option to combine resonance finder’s grid with NEGF energy grid. Ver 2.1.1 The unit for current in the current voltage characteristic has been corrected and is now A/cm2.
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 except the monolayer spacing
Known issues with this release: When resonance finder is turned off, an incorrect IV is shown even if the adaptive grid option is turned on.
|H. Park||... NEGF solver, NEMO5 development and supervision for Version 2.0|
|Z. Jiang||... Resonance finding algorithm used in Version 2.0|
|A. Akkala||... Rappture GUI modification and integration with NEMO5, New C based Resonance Curve Recognition Algorithm in Version 2.0|
|S. Steiger, M. Povolotskyi, T. Kubis||... NEMO5 development|
|JM Sellier||... Adaptive grid refinement, Debug, Creation of new plots, Improvement of existing plots, Creation of composite plots, Resonance Curve Recognition Algorithm, prior to Version 2.0|
|Y. Tan||... Numerical technique used to curtail round-off errors in resonance finder in Version 2.0|
|S. Kim||... Online support and Maintenance, Version 2.0 and prior|
|M. Luisier, S. Agarwal||... Core effective mass simulation engine in matlab, prior to Version 2.0|
|M. McLennan, G. Klimeck||...GUI design, direction 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).
Cite this work
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).
Hong-Hyun Park; Zhengping Jiang; Arun Goud Akkala; Sebastian Steiger; Michael Povolotskyi; Tillmann Christoph Kubis; Jean Michel D Sellier; Yaohua Tan; SungGeun Kim; Mathieu Luisier; Samarth Agarwal; Michael McLennan; Gerhard Klimeck; Junzhe Geng (2014), "Resonant Tunneling Diode Simulation with NEGF," http://nanohub.org/resources/rtdnegf. (DOI: 10.4231/D3CN6Z099).