A. Arun Goud Network for Computational Nanotechnology (NCN) Electrical and Computer Engineering
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Transcript of A. Arun Goud Network for Computational Nanotechnology (NCN) Electrical and Computer Engineering
Network for Computational Nanotechnology (NCN)Purdue, Norfolk State, Northwestern, MIT, Molecular Foundry, UC Berkeley, Univ. of Illinois, UTEP
NEGF Simulation of Electron Transport in Resonant Tunneling and
Resonant Interband Tunneling Diodes
A. Arun GoudNetwork for Computational Nanotechnology (NCN)
Electrical and Computer Engineering
11/28/2011
A.Arun Goud
Beyond CMOS
Scaling challenges Leakage effects – High k dielectrics Gate control – Non-planar structures Variability – Process improvement Mobility – Strain, III-V
For the last 3 decades CMOS scaling driven by Moore’s law has been the norm
ITRS 2009 - Emerging Research Devices
Another line of thought…Quantum mechanical effects Tunneling Interference Quantization, etc.
Emerging devices will have to utilize these effects while delivering high performance (high speed, low power consumption)
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Outline
Example of a quantum device – Resonant tunneling diode (RTD) Characteristics Applications…Why show interest in RTDs? Shortcomings...Why RTDs are not common? Simulation tool using NEMO5…To understand Physics behind RTDs NEGF formalism…A quantum formalism to calculate charge and current
Resonant interband tunneling diode (RITD) Alternative to RTDs Overcomes some drawbacks with RTDs Modeling of RITDs
Two other simulation tools –1dheteroBrillouin zone viewer
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Quantum device – RTD (GaAs/AlGaAs)
First demonstrated by Chang, Esaki and Tsu (1974)Grown using MBEVertical devices current flows along growth direction
n GaAsn GaAs
AlxGa1-xAsAlxGa1-xAs
GaAsGaAsAlxGa1-xAsAlxGa1-xAs
n+ GaAsn+ GaAs
n GaAsn GaAs
n+ GaAsn+ GaAs
L < Phase coherence length
z
V
I
(a) (b) (c)
(a)
(b)
(c)
VvVp
Ip
Iv
Peak to Valley Current Ratio = Ip/Iv (figure of merit)Requirements Large Ip, low Iv.
IV characteristics showing NDR
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Motivation - RTDs for digital applications
RTDs have been used for microwave circuits such as oscillators due to NDR.
Oscillations as high as 2.5 THz! (TCLG Sollner, Applied Physics Letters 43: 588)
6T SRAM memory cellRTD latch
(a) Ultra-high switching speeds (b) Not transit time limited(c) Low voltage
Digital circuit applications?
Multi-Functional devices -
YES!
Peak current should be larger than leakage currents of read/write FETsElse there is unwanted state transition
Simulation models needed.Should be Physics driven instead of compact model
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So why are RTDs not widespread
Compatibility with mainstream Si technology?
2 terminal No isolation
Low drive capabilities. Peak current, PVR must be increased
More importantly,
AlGaAs/GaAs, InGaAs/InAlAs, etc are popular choices but not compatible with Si technology and are expensive Si/SiGe RTDs have been demonstrated. Tend to have poor PVRs at 300K…
Advances in MBE, integration techniques Viable way to integrate RTDs with mainstream processes is likely (InP based RTD/HEMTs already exist)
Device variations from die to die
Perfect Lab for studying quantum phenomena - Physics involved and Simulation techniques devised will be useful for analyzing other devices too
So is the emphasis laid on RTDs totally unfounded?
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Contribution - RTD NEGF tool
Features - Coherent simulation of GaAs/AlGaAs RTDs - Charge density 1. Semiclassically (Thomas-Fermi)
2. Quantum self-consistent (Hartree)
- Effective mass Hamiltonian - NEGF formalism for transport Scattering/Relaxation in emitter reservoir NEMO5 driven
Output -• Energy band diagram, Resonance levels• Transmission coefficient• Well, Emitter quasi-bound |Ψ|2 • Current density• IV• Charge & sheet density profiles• Resonances vs voltage• Energy resolved charge profiles
a) Charge - 1. Thomas-Fermi method 2. Hartree method (NEGF)b) Transport - NEGF
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RTD modeling – Thomas-Fermi
Free charge density non-zero only in reservoirs
Thomas-Fermi expression
Solved iteratively with Poisson’s equation. BCs are φ(z=L)=V and φ(z=0)=0
The converged potential is used by NEGF solver to calculate current
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RTD modeling - Hartree
Charge treated semiclassically in terminalsQuantum charge calculated in Quantum regionCurrent calculated only in Non-equilibrium region
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NEGF - Quantum Charge and Current
gN,N = GN,N
Only 1st and Nth column of G are needed
1. RGF method2. Dyson’s equation3. iη relaxation model
EQ
NEQ
(Right contact will be ignored in thisexplanation )
Mimics broadening just as imaginary part of
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Simulation flow – Thomas-Fermi
Described in previous slide
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Simulation flow - Hartree
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Thomas-Fermi vs Hartree
Hartree
Thomas-Fermi
Quantization Low charge density => Low potential energy
Well charge CB raises to block further flow of charges into well
Hartree Vp > TF Vp
IVCB profile
Well charge vs Bias
Resonance drops below Ec slower w.r.t bias in Hartree method than in Thomas-Fermi method
PVR = 2
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Approximations made
Parabolic transverse dispersion• Higher order subband minima are overestimated => 2nd and further turn-on voltages are overestimated
Transverse energy and momentum are separable • T(E,k||) T(Ez) => Current calculation involves integration over only Ez
Full transverse dispersion and integration over k|| for exact analysis of coherent RTDsScattering self-energies also for incoherent simulation
J. Appl. Phys. 81 (7), 1997
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Recap
Resonant tunneling diode (RTD) Characteristics…NDR Applications…Memory Shortcomings...Low PVR at 300K Simulation tool…To understand Physics behind RTDs NEGF formalism…To calculate current
Is there a way to increase PVR?...We can draw inspiration from the Esaki diode
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From Esaki diodes to RTDs to RITDs
Esaki diode operation -
1) High peak to valley current ratio due to drastic reduction in valley current
2) Major drawback - Heavily doped junctions difficult to produce - High capacitance which degrades speed of operation
V
I
In the case of RTD’s,
Barriers are not effective in reducing valley current – low PVR Barriers and well are undoped – low capacitance
We need a mix
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Esaki diode + RTD = RITDs
InAs/AlSb/GaSb RITD
Multiband model is needed for proper description.
- Type II broken gap- Interband like Esaki diode
Exhibit larger PVR at 300K than RTDs by reducing valley current.
InAs non-parabolicityMixing of CB, VB states
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Tight binding Hamiltonian
Form Bloch sum of localized orbitals in the transverse plane
z
||α Cation or anion orbitals (10 for sp3s*)σ Layer index
Δ=a0/2
σ1 σ2
v
… …
Wavefunction is expressed in terms of planar orbitals in each layer
Real space Schroedinger equation
can be transformed to this basis using
CationAnion
Open boundary conditions using NEGF
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RITD multiband simulation IV
Valley region is broad because effectively electrons see bandgap of AlSb+GaSb+AlSb layers
1. Thomas-Fermi charge model
2. sp3s* TB model with spin orbit coupling
3. Numerical k|| integration to compute current
PVR = 50
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0 1 2 3 4
J(kx) at Vp and Vv
a = 0.6058 nm2π/a = 10.37 /nm
kx,ky grid (0.15,0.15) * 2π/a
kx
ky
Majority of the current is due to tunneling through Г state
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Energy resolved electron density
At peak voltage
At valley voltage
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1dhetero
Features Schroedinger-Poisson solver 3 options for Hamiltonian- Single band- TB sp3s* with spin-orbit coupling- TB sp3d5s* with spin-orbit coupling Semiclassical density-Poisson option Choice of substrates
ApplicationDesign and study of electrostatics within HEMTs
Sheet charge density Analytical method – Parabolic transverse dispersion Numerical – Transverse dispersion from TB calculation used
Outputs1. Energy band diagram2. Potential3. Resonances4. Wavefunction magnitude squared5. Sheet density, doping density6. Resonance vs voltage
Gate Bulk
Schroedinger domain
Poisson domain
Users 281
SimulationSessions
1421 (WCT– 104 days)
http://nanohub.org/1dhetero/usage
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Brillouin Zone viewer
ApplicationVisualization of 1st Brillouin zones for lattice system Cubic (SC,BCC,FCC) Hexagonal (Wurtzite) Honeycomb (Graphene) Rhombohedral (Bi2Te3)
InputTranslational vectorsLattice constant
Output1st Brillouin zoneReal space unit cell Users 61
SimulationSessions
157(WCT – 5 days)
http://nanohub.org/brillouin/usage
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Summary
RTD NEGF Coherent simulation of GaAs/AlGaAs RTDs using effective mass model and NEGF for transport Relaxation in equilibrium reservoir modeled using imaginary optical potential term iη Future work – Implementation of self energy expressions for various scattering mechanisms, (111) wafer orientation
RITD multiband simulationA coherent InAs/AlSb/GaSb RITD was simulated using NEMO5 with sp3s* SO model
1dhetero toolSimulation tool for the study and design of 1D heterostructures using a choice of substrates
Brillouin zone viewerSimulation tool for visualizing the 1st Brillouin zones of cubic, hexagonal, honeycomb and rhombohedral lattice systems.
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Acknowledgements
Advisory committeeProf. Gerhard Klimeck Profs. Mark Lundstrom, Vladimir Shalaev
NEMO5 developersSebastian Steiger – 1dhetero, Brillouin and for answering other questions Hong-Hyun & Zhengping Jiang – RTD NEGF, NEGF simulation technqiuesTillmann Kubis & Michael Povolotskyi – NEMO5 simulation issues
All other members of the Nanoelectronic modeling group…Presentation skills
Xufeng Wang, JM Sellier – For code that went into 1dhetero
Steven Clark – Tool installationDerrick KearneyGeorge Howlett
Cheryl HainesVicky Johnson
Funding agencies – NSF, SRC, NRI
Rappture support
Scheduling appointments, handling paperwork
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Thank You!
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Coherent tunneling
Coherent tunneling –
Translational periodicity in the transverse direction
Two rules should be satisfied –
1) Total energy is conserved 2) Transverse momentum is conserved
In Emitter In Well(Bulk like) (2D subband)
Shaded disk in Fermi sphere indicates kx, ky states in emitter that take part in tunneling for a particular subband min. Eo in the well
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IV at 0K
Under equilibrium
CB Profile, resonance position
kx, ky that take part in tunneling
Contribution to current
Relative position of Well subband & E-kx dispersion in emitter
No overlap between well suband level & emitter bulk level => No tunneling channel
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IV at 0K
V < Peak voltage Vp
CB Profile, resonance position
Contribution to current
kx, ky that take part in tunneling
Relative position of Well subband & E-kx dispersion in emitter
Some well suband levels & emitter bulk levels overlap => Tunneling channel
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IV at 0K
V = Peak voltage Vp
CB Profile, resonance position
kx, ky that take part in tunneling
Contribution to current
Relative position of Well subband & E-kx dispersion in emitter
Maximum overlap of well suband levels & emitter bulk levels => Current is at its max.