Transcript Network for Computational Nanotechnology (NCN) Purdue, Norfolk State, Northwestern, MIT, Molecular Foundry, UC Berkeley, Univ.

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 Goud
Network for Computational Nanotechnology (NCN)
Electrical and Computer Engineering
11/28/2011
Beyond CMOS
For the last 3 decades CMOS scaling driven by Moore’s law has been
the norm
Scaling challenges
 Leakage effects – High k dielectrics
 Gate control – Non-planar structures
 Variability – Process improvement
 Mobility – Strain, III-V
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)
A.Arun Goud
ITRS 2009 - Emerging
Research Devices
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 –
1dhetero
Brillouin zone viewer
A.Arun Goud
Quantum device – RTD (GaAs/AlGaAs)
First demonstrated by Chang, Esaki and Tsu (1974)
Grown using MBE
Vertical devices  current flows along growth direction
IV characteristics
showing NDR
I
n+ GaAs
(b)
n GaAs
z
AlxGa1-xAs
GaAs
AlxGa1-xAs
Iv
L < Phase coherence
length
(a)
Vp
n GaAs
(b)
A.Arun Goud
Vv
V
Peak to Valley Current Ratio = Ip/Iv (figure of merit)
Requirements  Large Ip, low Iv.
n+ GaAs
(a)
(c)
Ip
(c)
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)

(a) Ultra-high switching speeds
(b) Not transit time limited
(c) Low voltage
Multi-Functional devices -
Digital circuit
applications?
YES!
Peak current should be larger than leakage
currents of read/write FETs
Else there is unwanted state transition
Simulation models needed.
6T SRAM memory cell
A.Arun Goud
Should be Physics driven instead of
RTD latch
compact model
So why are RTDs not widespread
 2 terminal  No isolation
 Low drive capabilities. Peak current, PVR must be increased
 Device variations from die to die
More importantly,
Compatibility with mainstream Si technology?
 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…
So is the emphasis laid on RTDs totally unfounded?
Advances in MBE, integration techniques  Viable way to integrate RTDs
with mainstream processes is likely (InP based RTD/HEMTs already exist)
Perfect Lab for studying quantum phenomena - Physics involved and
Simulation techniques devised will be useful for analyzing other devices too
A.Arun Goud
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
a) Charge - 1. Thomas-Fermi method
• Energy resolved charge profiles
2. Hartree method (NEGF)
b) Transport - NEGF
A.Arun Goud
RTD modeling – Thomas-Fermi
The converged potential is
used by NEGF solver to
calculate current
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
A.Arun Goud
RTD modeling - Hartree
Charge treated
semiclassically in terminals
Quantum charge calculated
in Quantum region
Current calculated only in
Non-equilibrium region
A.Arun Goud
NEGF - Quantum Charge and Current
1. RGF method
2. Dyson’s equation
3. iη relaxation model
EQ 
NEQ
(Right contact will be
ignored in this
explanation )
gN,N = GN,N
Mimics broadening just
as imaginary part of
Only 1st and Nth column of G are needed
A.Arun Goud
Simulation flow – Thomas-Fermi
Described in
previous slide
A.Arun Goud
Simulation flow - Hartree
A.Arun Goud
Thomas-Fermi vs Hartree
IV
CB profile
PVR = 2
Well charge vs Bias
Hartree
Thomas-Fermi
Quantization  Low
charge density => Low
potential energy
Well charge  CB
raises to block further
flow of charges into
well
Resonance drops below Ec slower w.r.t bias in
Hartree method than in Thomas-Fermi method
Hartree Vp > TF Vp
A.Arun Goud
Approximations made
Parabolic transverse dispersion
• Higher order subband minima are overestimated
=> 2nd and further turn-on voltages are overestimated
J. Appl. Phys. 81 (7),
1997
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 RTDs
Scattering self-energies also for incoherent simulation
A.Arun Goud
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
A.Arun Goud
From Esaki diodes to RTDs to RITDs
Esaki diode operation -
I
V
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
In the case of RTD’s,
Barriers are not effective in reducing valley current – low PVR
Barriers and well are undoped – low capacitance 
A.Arun Goud
We
need a
mix

Esaki diode + RTD = RITDs
InAs/AlSb/GaSb RITD
Exhibit larger PVR at 300K than RTDs by reducing valley
current.
- Type II broken gap
- Interband like Esaki diode
InAs non-parabolicity
Mixing of CB, VB states
Multiband model is needed for proper description.
A.Arun Goud
Tight binding Hamiltonian
Form Bloch sum of localized orbitals in the transverse plane
σ1
σ2
v
…
α  Cation or anion orbitals (10 for sp3s*)
σ  Layer index
…
||
Wavefunction is expressed in terms of planar orbitals in
each layer
Δ=a0/2
z
Real space Schroedinger equation
can be transformed to this basis using
Open boundary
conditions using NEGF
A.Arun Goud
Cation
Anion
RITD multiband simulation IV
1. Thomas-Fermi charge
model
PVR = 50
2. sp3s* TB model with spin
orbit coupling
3. Numerical k|| integration
to compute current
Valley region is broad because effectively electrons
see bandgap of AlSb+GaSb+AlSb layers
A.Arun Goud
J(kx) at Vp and Vv
kx,ky grid  (0.15,0.15) * 2π/a
ky
a = 0.6058 nm
2π/a = 10.37 /nm
0 1 2 3 4
kx
Majority of the current is due to tunneling through Г state
A.Arun Goud
Energy resolved electron density
At peak voltage
At valley voltage
A.Arun Goud
1dhetero
Application
Design and study of
electrostatics within HEMTs
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
Outputs
1. Energy band diagram
Gate
2. Potential
Schroedinger
domain
3. Resonances
4. Wavefunction magnitude squared
5. Sheet density, doping density
6. Resonance vs voltage
Sheet charge density
 Analytical method – Parabolic transverse dispersion
 Numerical – Transverse dispersion from TB calculation used
A.Arun Goud
Bulk
Poisson domain
Users
281
Simulation
Sessions
1421
(WCT– 104 days)
http://nanohub.org/1dhetero/usage
Brillouin Zone viewer
Application
Visualization of 1st Brillouin
zones for lattice system
 Cubic (SC,BCC,FCC)
 Hexagonal (Wurtzite)
 Honeycomb (Graphene)
 Rhombohedral (Bi2Te3)
Input
Translational vectors
Lattice constant
Output
1st Brillouin zone
Real space unit cell
Users
61
Simulation
Sessions
157
(WCT – 5 days)
http://nanohub.org/brillouin/usage
A.Arun Goud
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 simulation
A coherent InAs/AlSb/GaSb RITD was simulated using NEMO5 with sp3s*
SO model
1dhetero tool
Simulation tool for the study and design of 1D heterostructures using a
choice of substrates
Brillouin zone viewer
Simulation tool for visualizing the 1st Brillouin zones of cubic, hexagonal,
honeycomb and rhombohedral lattice systems.
A.Arun Goud
Acknowledgements
Advisory committee
Prof. Gerhard Klimeck
Profs. Mark Lundstrom, Vladimir Shalaev
NEMO5 developers
Sebastian Steiger – 1dhetero, Brillouin and for answering other questions
Hong-Hyun & Zhengping Jiang – RTD NEGF, NEGF simulation technqiues
Tillmann 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 installation
Derrick Kearney
Rappture support
George Howlett
Cheryl Haines
Vicky Johnson
Scheduling appointments, handling
paperwork
Funding agencies – NSF, SRC, NRI
A.Arun Goud
Thank You!
A.Arun Goud
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
(Bulk like)
In Well
(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
A.Arun Goud
IV at 0K
Under equilibrium
CB Profile,
resonance
position
Relative position of Well subband &
E-kx dispersion in emitter
No overlap between well
suband level & emitter bulk
level => No tunneling
channel
kx, ky that
take part in
tunneling
A.Arun Goud
Contribution
to current
IV at 0K
V < Peak voltage Vp
CB Profile,
resonance
position
Relative position of Well subband &
E-kx dispersion in emitter
Some well suband levels &
emitter bulk levels overlap =>
Tunneling channel
kx, ky that
take part in
tunneling
A.Arun Goud
Contribution
to current
IV at 0K
V = Peak voltage Vp
CB Profile,
resonance
position
Relative position of Well subband &
E-kx dispersion in emitter
Maximum overlap of well
suband levels & emitter
bulk levels => Current is at
its max.
kx, ky that
take part in
tunneling
A.Arun Goud
Contribution
to current