Aug 17, 2008 - (K3) to make a good design choice. ⢠Act 1: Can the Peak-to-Valley Ratio in RTDs be increased? What is the origin of the valley current in ...
Network for Computational Nanotechnology (NCN) Berkeley, Univ.of Illinois, Norfolk State, Northwestern, Purdue, UTEP
NanoElectronic MOdeling NEMO Gerhard Klimeck Dallas (UTD, TI, Raytheon) (1994-1998) NASA JPL, Caltech (1998-2003) Purdue (2003 - …) Gerhard Klimeck
Presentation Outline • Outline Inspired by L. P. Kadanoff: Excellent computer simulations are done for a purpose. The most valid purposes are » (K1) to explore uncharted territory, » (K2) to resolve a well-posed scientific or technical question, or » (K3) to make a good design choice.
• Act 1: Can the Peak-to-Valley Ratio in RTDs be increased? What is the origin of the valley current in RTD’s? (K2) • Act 2: What are the design alternatives? (K3) • Act 3: Million atom electronic structure? Will it matter? (K1) • Act 4: Can we simulate transport in million atoms systems? (K1)
Gerhard Klimeck
UT D
NANOTECHNOLOGY ENGINEERING
Current
Current Density (104 A/cm2)
Basic Operation of a Resonant Tunneling Diode Sb1780 Sb 1781 R=8.8Ω Nominal Size 07/20/07 ml 4 Exp InGaAs/AlAs System 08/17/08 3
PVR
2
1
0 0
Voltage
Conduction band diagrams for different voltages and the resulting current flow
0.2
0.4 0.6 0.8 Applied Bias (V)
1
1.2
12 different I-V curves: 2 wafers, 3 mesa sizes, 2 bias directions PVR – Peak-to-Valley-Ratio 1994: Best experiment PVR=80 => On-Off-Ratio should to be >1,000 1994: What is the valley current physics? 1997: Can overlay experiment and theory. What are the key insights?
Resonant Tunneling Diodes in 1994 Potential: • THz operation – limited only by tunneling time • NDR => fast oscillations • NDR => stable latches, digital logic Challenges: • Valley current too high => high “off” state current • No production-like experiments => repeatability issues • No generally accepted device modeling theory ⇒Nanoelectronic Modeling – NEMO ⇒Software tool that: • Quantitative modeling • Predictive design • Physics-based understanding Gerhard Klimeck
State-of-the-art RTD Modeling and Simulation Knowledge 1994 Knowledge / Availability: • 1-D Poisson Schrödinger » » » »
Quantum transmitting boundary conditions (QTBM), flatband (Lent) Single band, effective mass, no scattering (“everyone”) Multiple Sequential Scattering (Roblin) Tight binding, no scattering (Boykin, Ting)
• Density Function » Single band, no scattering, time dependent (Ferry)
• Wigner Function » Single band with empirical scattering (Frensley)
• NEGF » Single band with scattering (Lake) » Single band with charge self-consistency (Klimeck)
• SCATTERING is the source of the valley current Limitations: • Tiny device simulation domains – no extended contact regions • No realistic scattering models • Computation too expensive for engineering (we can build this in one month) • No predictive theory, modeling, and simulation Gerhard Klimeck
Available and Explored Theories • The non-equilibrium Green function formalism underlies NEMO. • All of the approaches shown were considered. • Approaches in light blue were dropped. Approaches in dark blue were incorporated. Non-Equilibrium Statistical Mechanics Direct Evaluation of
< ψ+(r',t')ψ(r,t) > Quantum Monte Carlo
Non-Equilibrium Green Function Formalism
Density Matrix
Ensemble Averaged
Multiple Sequential Scattering Time Averaged
Single Particle Schrödinger
ψ(r) Gerhard Klimeck
Stochastic Schrödinger
ψ(r) (Electrons) φ(r) (Phonons)
UT D
NANOTECHNOLOGY ENGINEERING
NEMO Breakthrough: Simulation of extended RTDs 0 .5
20 nm GaAs ND = 2 1018 cm-3 200 nm GaAs ND = 2 1015 cm-3 18 nm GaAs 5 nm Al0.4Ga0.6As 5 nm GaAs 5 nm Al0.4Ga0.6As 18 nm GaAs 200 nm GaAs ND = 2 1015 cm-3 20 nm GaAs ND = 2 1018 cm-3
0
C
- 0 .5
0
100
200 300 D is t a n c e (n m )
Density Densityof ofStates States
400
500
UT D
NANOTECHNOLOGY ENGINEERING
Generalized Boundary Conditions: Boundaries as a Scattering Problem • •
Left and right regions are treated as reservoirs. Quantum structure of reservoirs is included exactly.
Σ
100mev ~ 4kT
Gerhard Klimeck
Network for Computational Nanotechnology
0.1
nanoHUB.org
Effects of Band Non-Parabolicity on I-V Characteristics
online simulations and more
Resonator Resonator
.
k1 = 2 π
>100meV
L
k0
Ec
=
π L
L Length • • • •
parabolic non-parabolic
Second state lowered by >100mev ~ 4kT Second diode turn-on at lower voltages Valley current mostly due to thermal excitations k0 about equal - Why is peak current different? Gerhard Klimeck
Network for Computational Nanotechnology
Full Bandstructure
Realistic Material Properties: • Non-parabolic • Coupled conduction and valence bands • States outside the zone center, X, L
Gerhard Klimeck
Full Bandstructure vs. Parabolic Bands
2
h 2 E= * k 2m Realistic Material Properties: • Non-parabolic • Coupled conduction and valence bands • States outside the zone center, X, L Typical Assumption: • Parabolic bands
Gerhard Klimeck
Parabolic bands
Band Wrapping
X-States
Atomistic Representation is the Key! Current
Atomistic
Basis Sets
Concepts Voltage
s px py pz 5x d 2x spin
• • • • • • • • • • •
Usually considered a device This is also a new material!
Empirical Tight Binding makes the connection between Quantitative Engineering: Design, Analysis, Synthesis materials and devices! Gerhard Klimeck
.
UT D
NANOTECHNOLOGY ENGINEERING
4 Stack RTD with Spacer Variation V1911 #2 Added 2ml to the Barriers - No Spin-orbit
Vary VarySpacer Spacer Length Length
35000
40000
Current Density (A/cm2)
Exp. Forward Bias Exp. Reverse Bias sp3s full band
50000
20/47/47/47/20
30000 20000
30000 25000
58/47/47/47/58
20000 15000 10000 5000
10000
0 0
0 0
0.2
0.4 0.6 Applied Bias (V)
0.8
0.4 0.6 Applied Bias (V)
0.8
1
V1911 #4 Added 2ml to the Barriers - No Spin-orbit
Exp. Forward Bias Exp. Reverse Bias sp3s full band
10000 Exp. Forward Bias Exp. Reverse Bias sp3s full band
9000
15000
Current Density (A/cm2)
Current Density (A/cm2)
0.2
1
V1911 #3 Added 2ml to the Barriers - No Spin-orbit 20000
Four nominally symmetric devices: 20/47/47/47/20 A [1] 58/47/47/47/48 A [2] 117/47/47/47/117 [3] 200/47/47/47/200 [4]
Exp. Forward Bias Exp. Reverse Bias sp3s full band
V1911 #1 Added 2ml to the Barriers - No Spin-orbit 60000
Current Density (A/cm2)
InGaAs
InGaAs
InAlAs
InGaAs
InAlAs
W
W
40000
117/47/47/47/117 10000
5000
8000 7000 6000
200/47/47/47/200
5000 4000 3000 2000 1000
0 0
0.2
0.4 0.6 Applied Bias (V)
0.8
1
0 0
0.2
0.4 0.6 Applied Bias (V)
0.8
1
UT D
NANOTECHNOLOGY ENGINEERING
4 Stack RTD with Well Width Variation
W InGaAs
W
InAlAs
InAlAs
InGaAs
W
InGaAs
Vary VaryWell Well Width Width
20/47/29/47/20
•
•
20/47/35/47/20
Three nominally symmetric devices: 47/29/47 A [1] 47/35/47 A [2] 47/47/47 A [3] One asymmetric device: 35/47/47 A 20/47/47/47/20
20/35/47/47/20
.
UT D
NANOTECHNOLOGY ENGINEERING
4 Stack RTD with Well Width Variation Asymmetric Device #4
Vary VaryWell Well Width Width
Exp. Forward Bias sp3s full band
50000
Current Density (A/cm2)
Current Density (A/cm2)
InGaAs
InGaAs
InAlAs
InGaAs
InAlAs
W
W
V1909 #1 Forw. Bias Added 2ml to the Barriers No Spin-orbit
60000
40000 30000 20000 10000
•
Three nominally symmetric devices: 47/29/47 A [1] 47/35/47 A [2] 47/47/47 A [3] One asymmetric device: 35/47/47 A [4]
40000 30000 20000 10000 0
0 0
•
V1909 #1 Forw. Bias Added 2ml to the Barriers - No Spin-orbit 60000 Exp. Forward Bias sp3s full band 50000
0.2
0.4 0.6 Applied Bias (V)
0.8
Reverse Bias
1
0
0.2
0.4 0.6 Applied Bias (V)
Forward Bias
0.8
1
State-of-the-art RTD Modeling and Simulation Knowledge 1998 Knowledge: • Scattering inside RTD » Only important at low temperatures » Not important for room temperature, high performance
• Scattering inside extended contacts » Of critical importance at any temperature
• Charge self-consistency » Critical everywhere, contacts and central device
• Bandstructure – atomistic device resolution » Critical for understanding high temperature, high performance devices
• NEGF is the baseline of an industrial strength simulator Availability: • An engineering modeling and design tool for 1D heterostructures • Experimentally verified – analysis and design Gerhard Klimeck
Valley Current Bottom Line: Thermionic Emission – No Way Out!
• Design circuits and devices that are aware of it! • Dramatically reduce the total current density => 5 barriers • Use RTD as a latch, use HFET as switch => 2 US Patents on tunneling memory
Gerhard Klimeck
The next challenge: Full 3D atomistic modeling for realistic devices Designed Optical Transitions
Sensors
Atomic Orbitals size: 0.2nm
Structure (millions of atoms)
Nanoscale Quantum States (Artificial Atoms, size 20nm)
Quantum Dot Arrays
Computing
Approach: Problem: •Use local orbital description for individual Nanoscale device simulation requirements: • Cannot use bulk / jellium descriptions, need atoms in arbitrary crystal / bonding configuration description of the material atom by atom •Use s, p, and d orbitals => use pseudo-potential or local orbitals • Consider finite extent/transport, not infinitely Use genetic algorithm to determine material parameter fitting periodic •Compute mechanical strain in the system. => local orbital approach •Develop efficient parallel algorithms to • Need to include about one million atoms. generate eigenvalues/vectors of very large => need massively parallel computers matrices (N=40million for a 2 million atom • The design space is huge: choice of system). materials, compositions, doping, size, •Develop prototype GUI for (NEMO-3D) shape. => need a design tool gekco
High Performance Computing Group
Valley Splitting Physics Flat Quantum Well
8nm Si QW Goswami2004
Why is the experimental valley splitting so much smaller? d a/2
Well Understood Gerhard Klimeck
w
θ
Si
10 nm
16 nm
15
nm
Effect of disorder on valley-splitting step roughness
Elect. – 1.2 million atoms
150 nm
Rough steps
Gerhard Klimeck
Kharche et al. Appl. Phys. Lett. 90, 092109 (2007)
Effect of disorder on valley-splitting step roughness and alloy disorder
Si SiGe
Elect. – 2 million atoms
v
16 nm
SiGe
Strain – 10 million atoms
Δ [μeV]
10 nm
15
nm
80
Alloy disorder
Expt
20
Ideal
0
2
3 B [T] No SiGe buffer
Si
100
Alloy disorder
40
SiGe
150 nm
60
4
80
Expt Alloy+Step disorder
40 20 0
v
60
Rough steps Δ [μeV]
Δv [μeV]
80
3 B [T]
Gerhard Klimeck
Expt
40
Step disorder
20
Ideal 2
60
4
0
Ideal 2
3
4
B [T]
Kharche et al. Appl. Phys. Lett. 90, 092109 (2007)
Moving towards the peta-scale
NEMO 1-D with NEGF NEMO 3-D with millions of atoms Gerhard Klimeck
OMEN
OMEN
Gerhard Klimeck
NEMO 1994-98: Texas Instruments => NEMO 1D • 50,000 person hours, 250,000 code lines • 3,000 pages documentation » Automated like doxygen • Design (minutes), research tool (days) • Patents on tunneling memory 1998-2003: JPL/NASA => NEMO 3D • 12,000 person hours • HPC development in 1D and 3D • NEMO 3D open source! • Tune asis against bulk experiments 2003-… Purdue/NCN • Multimillion atoms simulations => matching experimental data! • Scaling to 23,000 cores • OMEN Gerhard Klimeck
686 users Qdot Lab
Presentation Outline • Outline Inspired by L. P. Kadanoff: Excellent computer simulations are done for a purpose. The most valid purposes are » (K1) to explore uncharted territory, » (K2) to resolve a well-posed scientific or technical question, or » (K3) to make a good design choice.
• Act 1: Can the Peak-to-Valley Ratio in RTDs be increased? What is the origin of the valley current in RTD’s? Thermionic Emission! • Act 2: What are the design alternatives? Design ultra-low current RTD with small PVR. • Act 3: Million atom electronic structure? Will it matter? Yes, we can match experimental data!
NO! (K2) (K3) (K1)
• Act 4: Can we simulate transport in million atoms systems? (K1) I think so, OMEN is being implemented! Gerhard Klimeck
Question 1
Gerhard Klimeck
Question 2
Gerhard Klimeck
Question 3
Gerhard Klimeck
