Gerhard Klimeck Applied Cluster Computing Technologies Group Quantum and semi-classical transport in RTDs using NEMO 1-D Gerhard Klimeck Jet Propulsion.

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Presentation transcript:

Gerhard Klimeck Applied Cluster Computing Technologies Group Quantum and semi-classical transport in RTDs using NEMO 1-D Gerhard Klimeck Jet Propulsion Laboratory, California Institute of Technology (818) This research was carried out by at the Jet Propulsion Laboratory, California Institute of Technology under a contract with the National Aeronautics and Space Administration.

Gerhard Klimeck Applied Cluster Computing Technologies Group NEMO 1-D: A User-friendly Quantum Device Design Tool Resonance Finder Hybrid C, FORTRAN FORTRAN90 Software Engineering Object-Oriented Principles Graphical User Interface Material Param. Database Batch Run Interface Library of Examples Novel Grid Gen. Documentation Tool Band- structure Charging Interface Roughness Phonons Alloy Disorder Ionized Dopants Physics Formalism Green Function Theory & Boundary Cond. NEMO was developed under a government contract to Texas Instruments and Raytheon from >50,000 person hours of R&D 250,000 lines of code in C, FORTRAN and F90 NEMO 1-D maintained and NEMO 3-D developed at JPL ‘98-’02 (>12,000 person hours) under NASA funding. Since ‘02 NSA and ONR funding. Based on Non-Equilibrium Green function formalism NEMO in THE state-of-the-art heterostructure design tool. Used at Universities, Government Labs, Industry. Bridges gap between device engineering and quantum physics. Transport/ Engineering Quantum Mechanics / Physics 20/50/ 2 Testmatrix Good News! I mean great news! After 5 years of agony with Raytheon release problems: JPL can release the code to US institutions with a US government contract that requires / would benefit from NEMO use! er

Gerhard Klimeck Applied Cluster Computing Technologies Group NEMO Breakthrough: Simulations of Devices With Realistic Large Extent Calculate charge self-consistently in the left and right reservoir central device region Density of States left reservoir right reservoir Quantum Optical Switch

Gerhard Klimeck Applied Cluster Computing Technologies Group Generalized Boundary Conditions: Boundaries as a Scattering Problem Three Critical Simulation Domains: left reservoir, central device, right reservoir Dynamics Kinetics How good is the reservoir assumption? Flat Fermi Level -> Zero Current

Gerhard Klimeck Applied Cluster Computing Technologies Group Couple NEGF in Central Device to Drift-Diffusion Equation in Reservoirs Central Device Carriers injected from reservoirs, need Fermi level in left/right edge Fermi level not defined in central device. Current / Charge from NEGF Current imposed on reservoirs Reservoirs: Current imposed by central device Gradient of Fermi level at each site imposed by current. Charge from EGF and Fermi level Self-consistency: Poisson NEGF Drift-Diffusion

Gerhard Klimeck Applied Cluster Computing Technologies Group Current Voltage Characteristic Compare µ=infinite, µ=20,000cm 2 /Vs, µ=10cm 2 /Vs Low mobility -> similar to series resistance V applied = V internal +R I ->stretch of voltage axis -> bi-stability

Gerhard Klimeck Applied Cluster Computing Technologies Group “Resistance” is not Constant! Compare µ=infinite, µ=20,000cm 2 /Vs, µ=10cm 2 /Vs Low mobility -> similar to series resistance V applied = V internal +R I ->stretch of voltage axis -> bi-stability

Gerhard Klimeck Applied Cluster Computing Technologies Group Peak Current Depends Weakly on Mobility Compare µ=infinite, µ=20,000cm 2 /Vs, µ=10cm 2 /Vs Low mobility -> similar to series resistance V applied = V internal +R I ->stretch of voltage axis -> bi-stability

Gerhard Klimeck Applied Cluster Computing Technologies Group High Mobility V=0.32V µ=20,000cm 2 /Vs Potential difference only in the quantum well. High current state -> charge accumulation in well Low current state -> empty quantum well

Gerhard Klimeck Applied Cluster Computing Technologies Group Low Mobility V=0.35V µ=10cm 2 /Vs Potential difference in emitter and quantum well. High current state -> charge accumulation in well Low current state -> empty quantum well, accumulation in notch

Gerhard Klimeck Applied Cluster Computing Technologies Group Comparison to Experiment & Conclusions Experiment: Show I-V curves from two different devices from different wafers -> 15% peak current deviation Introduction of finite mobility has small effect on overall I-V curve for high performance RTDs Conclusion: Demonstrated coupling of drift diffusion to NEGF simulation. Flat Fermi levels in reservoirs a pretty reasonable assumption. Future work: Need to combine the intrinsic resistance simulation with a quantum capacitance calculation Need to look at low performance RTDs with long spacer layers and low carrier densities.