Your Project Title Here Your Research Theme Here

6 downloads 20088 Views 2MB Size Report
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