Quantum and semi-classical transport in RTDs using NEMO 1-D

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

[email protected]

(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.


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


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


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


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


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


“Resistance” is not Constant!




Peak Current Depends Weakly on Mobility




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


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


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.

Documents

Quantum and semi-classical transport in RTDs using NEMO 1-D