quantum and semi-classical transport in rtds using nemo 1-d
DESCRIPTION
Quantum and semi-classical transport in RTDs using NEMO 1-D. Gerhard Klimeck Jet Propulsion Laboratory, California Institute of Technology [email protected] (818) 354 2182 http://hpc.jpl.nasa.gov/PEP/gekco - PowerPoint PPT PresentationTRANSCRIPT
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) 354 2182
http://hpc.jpl.nasa.gov/PEP/gekco
This research was carried out by at the Jet Propulsion Laboratory, California Institute of 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.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
Res
onan
ce
Find
er
Hybrid
C, FORTRAN
FORTRAN90
Software EngineeringObject-Oriented Principles
Graphical
User Inte
rface
Material Param.
Database
Batch Run
InterfaceLibrary of Examples
NovelGrid Gen.
Documentation
Tool
Band-
structure
Chargin
g
InterfaceRoughness
Phonons
Alloy
Disord
er
IonizedDopants
Physics
FormalismGreen 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.
• • ••• •
Impurity
Phonon
InterfaceElectron
Transport/Engineering
Quantum Mechanics / Physics
20/50/ 2
Tes
tmat
rix
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
.
0123
0 0.5 1 1.5 2Voltage (V)
Experiment
Simulat ion
Oscillationin NDR
.
-1-0.500.5
Energy (eV)
04080120160200240280Length (nm)
Density of StatesDensity of States
leftreservoir
rightreservoir
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
Device
F
L
F
R
LeftReservoir
RightReservoir
Σ
RB
Σ
< B
Σ
RB
Σ
< B
n+ contact
n+ contact
E − H0
− Σ
RB
( )G
<
= Σ
< B
G
A
E − H0
− Σ
RB
( )G
R
= 1
Dynamics
KineticsHow good is the reservoir assumption?
Flat Fermi Level -> Zero Current
Gerhard Klimeck Applied Cluster Computing Technologies Group
Couple NEGF in Central Device toDrift-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
€
Jn = niμ i∇E i
Gerhard Klimeck Applied Cluster Computing Technologies Group
Current Voltage Characteristic
• Compare µ=infinite, µ=20,000cm2/Vs, µ=10cm2/Vs
• Low mobility -> similar to series resistance Vapplied = Vinternal+R I->stretch of voltage axis -> bi-stability
Gerhard Klimeck Applied Cluster Computing Technologies Group
“Resistance” is not Constant!
• Compare µ=infinite, µ=20,000cm2/Vs, µ=10cm2/Vs
• Low mobility -> similar to series resistance Vapplied = Vinternal+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=20,000cm2/Vs, µ=10cm2/Vs
• Low mobility -> similar to series resistance Vapplied = Vinternal+R I->stretch of voltage axis -> bi-stability
Gerhard Klimeck Applied Cluster Computing Technologies Group
High Mobility V=0.32V
• µ=20,000cm2/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=10cm2/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.