2. 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 gekco@jpl.nasa.gov (818) 354 2182 http://hpc.jpl.nasa.gov/PEP/gekco 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.

3. 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 1993-97 >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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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.