Transcript 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,

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
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.
Samarth Agarwal
What are RTD’s?...cont’d
Current
This fact enables RTDs to exhibit Negative Differential Resistance.
Peak in current:
Emitter fermi
level(Green) is
aligned with a
resonance(Red).
NDR: Current is a
decreasing function of
voltage.
Trough in current:
Emitter fermi level
not aligned with a
resonance.
Samarth Agarwal
Voltage
Purpose of the tool
RTD-NEGF: Resonant Tunneling Diode Simulator using Non-equilibrium Green’s Fn.
Schrodinger Equation:
Using Green’s Functions
for open systems
Self-consistently
Open Systems: Charge can be
exchanged at the boundary
Samarth Agarwal
Poisson equation for
Open Systems
If you just hit simulate…
The listed plots
are generated.
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
Samarth Agarwal
Geometry
Two barrier
transmission
Triple barrier
transmission
Resonances in adjoining wells couple and split.
(3nm barriers and 5nm long wells)
Samarth Agarwal
Barrier Thickness
Thicker
barriers
I-V curve: Barrier
thickness
reduced to 4.8nm
I-V curve for default
structure: Barrier
thickness 5nm
Greater
Confinement in
the well.
Longer
lifetime of
resonances
Lower
Current
Samarth Agarwal
Potential Models
Linear Drop
Thomas-Fermi
No self-consistency.
Quantum calculation
on linearly varying
potentials
Quantum calculation on
potential determined
self-consistently using
semi-classical charge.
Samarth Agarwal
Hartree
Potential determined
self-consistently using
quantum mechanical
charge.
Potential Models with asymmetric structures
Linear Drop
Thomas-Fermi
Hartree
Default structure:
Symmetric barriers
More charge
accumulation in
asymmetric structures.
Hartree gives the most
accurate description.
Asymmetric barriers:
Width of second
barrier increased to
8nm.
Samarth Agarwal
Reservoir relaxation model
Exponential
Decay
Energy
Independent
Reservoir relaxation model: Treatment of optical
potential below the conduction band edge.
Samarth Agarwal
Optical potential:
Necessary to
include broadening
of states.
Reservoir Relaxation Models : Impact on I-Vs
Valley current
dominated by
scattering.
Optical potential
determined by
relaxation models,
represents
scattering.
Energy independent
model predicts
higher valley
current, because of
higher scattering.
Samarth Agarwal
I-V curve: Default
structure, Energy
Independent
relaxation model.
Higher valley
current.
I-V curve: Default
structure,
Exponentially
damped
relaxation model.
Lower valley
current.
References
• For the Non-equilibrium Green’s function formalism:
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
• Comparison of tight-binding and transfer-matrices:
https://nanohub.org/resources/pcpbt
Samarth Agarwal