1. Network for Computational Nanotechnology (NCN) UC Berkeley, Univ.of Illinois, Norfolk State, Northwestern, Purdue, UTEP First time user guide for RTD-NEGF Samarth Agarwal, Mathieu Luisier, Zhengping Jiang, Michael McLennan, Gerhard Klimeck Samarth Agarwal

2. What are RTDs? Quantum transmission for a single barrier is less than one. Quantum transmission for a double barrier (or more) is equal to one at some energies. This is due to the resonant states present in the well region.

3. Samarth Agarwal What are RTD’s?...cont’d Current Voltage This fact enables RTDs to exhibit Negative Differential Resistance. NDR: Current is a decreasing function of voltage. Peak in current: Emitter fermi level(Green) is aligned with a resonance(Red). Trough in current: Emitter fermi level not aligned with a resonance.

4. Samarth Agarwal Purpose of the tool Schrodinger Equation: Using Green’s Functions for open systems Schrodinger Equation: Using Green’s Functions for open systems Poisson equation for Open Systems Poisson equation for Open Systems Self-consistently Open Systems: Charge can be exchanged at the boundary RTD-NEGF: Resonant Tunneling Diode Simulator using Non-equilibrium Green’s Fn.

5. Samarth Agarwal If you just hit simulate… The listed plots are generated.

6. Samarth Agarwal Default Outputs Conduction band: Bulk conduction band profile + electrostatic potential Normalized Current: Current as a function of energy Transmission Coefficient: Quantum transmission as a function of energy Conduction band: Bulk conduction band profile + electrostatic potential Normalized Current: Current as a function of energy Transmission Coefficient: Quantum transmission as a function of energy

7. Samarth Agarwal Geometry Two barrier transmission Triple barrier transmission Resonances in adjoining wells couple and split. (3nm barriers and 5nm long wells) Resonances in adjoining wells couple and split. (3nm barriers and 5nm long wells)

8. Samarth Agarwal Barrier Thickness I-V curve for default structure: Barrier thickness 5nm I-V curve: Barrier thickness reduced to 4.8nm Thicker barriers Greater Confinement in the well. Longer lifetime of resonances Lower Current

9. Samarth Agarwal Potential Models Linear Drop Thomas-Fermi Hartree No self-consistency. Quantum calculation on linearly varying potentials No self-consistency. Quantum calculation on linearly varying potentials Quantum calculation on potential determined self-consistently using semi-classical charge. Potential determined self-consistently using quantum mechanical charge.

10. Samarth Agarwal Potential Models with asymmetric structures Linear Drop Thomas-Fermi Hartree Default structure: Symmetric barriers Asymmetric barriers: Width of second barrier increased to 8nm. More charge accumulation in asymmetric structures. Hartree gives the most accurate description. More charge accumulation in asymmetric structures. Hartree gives the most accurate description.

11. Samarth Agarwal Reservoir relaxation model Energy Independent Exponential Decay Reservoir relaxation model: Treatment of optical potential below the conduction band edge. Optical potential: Necessary to include broadening of states.

12. Samarth Agarwal Reservoir Relaxation Models : Impact on I-Vs I-V curve: Default structure, Energy Independent relaxation model. Higher valley current. I-V curve: Default structure, Exponentially damped relaxation model. Lower valley current. Valley current dominated by scattering. Optical potential determined by relaxation models, represents scattering. Energy independent model predicts higher valley current, because of higher scattering.

13. Samarth Agarwal References For the Non-equilibrium Green’s function formalism: https://nanohub.org/topics/negf https://nanohub.org/topics/negf Simulation using tight-binding and NEGF: Quantum device simulation with a generalized tunneling formula, Gerhard Klimeck, Roger Lake, R. Chris Bowen, William R. Frensley, and Ted S. Moise, Appl. Phys. Lett. 67, 2539 (1995), DOI:10.1063/1.114451. Online courses: Quantum transport: https://nanohub.org/resources/6172, Fundamentals of Nanoelectronics: https://nanohub.org/resources/5346 https://nanohub.org/resources/6172https://nanohub.org/resources/5346 Comparison of tight-binding and transfer-matrices: https://nanohub.org/resources/pcpbt https://nanohub.org/resources/pcpbt