Non Equlibrium Green Functions NEGF Quantum Transport, Nanowires, Ballistic Effects Etc

Network for Computational Nanotechnology (NCN)

Non Equlibrium Green Functions NEGF quantum transport, nanowires, ballistic effects etc.

Gerhard Klimeck Network for Computational Nanotechnology (NCN) Purdue University

November 2, 2014 Intel technology roadmap Today: Non-planar 3D devices have better gate control!

Intel 22nm finFET 22nm = 176 atoms 8nm = 64 atoms

http://www.goldstandardsimulations.com/index.php/news/blog_search/simulation-analysis-of-the-intel-22nm-finfet/ http://www.chipworks.com/media/wpmu/uploads/blogs.dir/2/files/2012/08/Intel22nmPMOSfin.jpg Today: Non-planar 3D devices have better gate control!

Intel 22nm finFET 22nm = 176 atoms 8nm = 64 atoms

Atomistic Modeling => NEMO

nm Node 22 14 10 7 5 Node atoms 176 122 80 56 40 Critical atoms 64 44(?) 29(?) 20(?) 14(?) Electrons 160-190 64-80 30-38 18-23 11-15 Roadmap of finite atoms

nm Node 22 14 10 7 5 Node atoms 176 122 80 56 40 Critical atoms 64 44(?) 29(?) 20(?) 14(?) Electrons 160-190 64-80 30-38 18-23 11-15 Quantum dot research

nm Node 22 14 10 7 5 Node atoms 176 122 80 56 40 Critical atoms 64 44(?) 29(?) 20(?) 14(?) Electrons 160-190 64-80 30-38 18-23 11-15 Roadmap of finite electrons

nm Node 22 14 10 7 5 Node atoms 176 122 80 56 40 Critical atoms 64 44(?) 29(?) 20(?) 14(?) Electrons 160-190 64-80 30-38 18-23 11-15 Single electron effects in today’s transistors (2008) z Single atom transistors (2012)

The Physical Limit of Moore’s Law Challenges ahead on the road of ever cheaper transistors 20m 20m 19m

Number of 16m 28nm 20nm 16nm transistors / $ 11.2m 40nm The Economic 7.3m End of Moore’s Law? 65nm 4.4m 2.6m 90nm

130nm Transistor size

180nm 2002 2004 2006 2008 2010 2012 2014 2015

http://www.economist.com/news/21589080-golden-rule-microchips-appears-be-coming-end-no-moore The International Technology Roadmap for Semiconductors (ITRS)

ITRS Quick facts ITRS Groups

• Worldwide joint effort since 1998 • 16 chapters • Ensures cost-effective • Process integration and advancements in ICs Device and Structures (PIDS) • More than 1000 engineers/ • System and drivers scientists worldwide • Lithography • Most successful roadmap • Test • Packaging,

ITRS identifies technological challenges for the semiconductor industry over the next 15 years

Gerhard Klimeck ITRS has predicted successfully future technology trends

1000 2011 ITRS Technology Trends 1000 Pitch

0.7x every 65nm 100 2 years 45nm Gate Pitch (nm)

32nm 112.5 nm

100 - 1995 2000 2005 2010

Moore’s Law

Nanometers 10

ITRS MPU/ASIC Metal 1 ½ Pitch (nm) [historical trailing at -2yr cycle; extended to 2013 then 3yr cycle] Transistor Gate Technology ITRS MPU Printed Gate Length (GLpr) (nm) Power performance Management [3- yr cycle from 2011] Enabled by “Equivalent Scaling” ITRS MPU Physical Gate Length (nm) [begin 3.8- yr cycle from 2009] Year of Production 1 1995 2000 2005 2010 2015 2020 2025 2030 Year of Production Adopted from Alan Allan (www.itrs.net) Gerhard Klimeck Current ITRS predictions contradict latest experimental observations => Problem!

ITRS projects ITRS projection rising ON current with smaller devices Experiment

Experimental results indicate decreasing ON current

ITRS projections point in opposite direction than experimental observations why?

Gerhard Klimeck ITRS MASTAR

• MASTAR: Model for Assessment of cmoS Technologies And Roadmaps (Skotnicki et al.) » Analytical drift-diffusion model. • Basic assumptions » Short channel effects are controlled through reducing oxide thickness. reducing junction depth (bulk), body thickness (SOI/DG). increasing doping concentration in the channel. » On-current is improved in the future nodes through Mobility/velocity increase due to strain technology and ballistic transport. • Shortcomings/Challenges » No 2D electrostatics included. » Lumped element assumption. » Limited quantum effects included (no tunneling)

Gerhard Klimeck MASTAR compact model used by ITRS not suitable anymore for ultra-scaled devices

Non-atomistic MASTAR model does not match experiments

Recent Device MASTAR SS, DIBL, OUT

IN MASTAR: Analytical ION, SS, DIBL, SCE Lg, EOT, Tsi, Models Experiment VDD, εox ,

Drawbacks • No electrostatics calculation • Dependent on fitting parameters • Fails for ultra-scaled devices

Current MASTAR model lacks important physics inaccurate predictions

Gerhard Klimeck NEMO predicts ITRS trends in line with experimental observations

Atomistic modeling using NEMO yields correct device trends

NEMO Geometry dependent MASTAR enables properties ITRS-2011 atomistic Short Channel Effects NEMO modeling ITRS-2013 of S/D Tunneling

Experiment

Modern ultra-scaled devices necessitate atomistic modeling tools

Gerhard Klimeck Quantization and Anisotropy Need a full band – atomistic model (beyond m* or k•p)

[010]

(d) (b) (c)

kx kx Cut through Cut through the the ellipsoid 3nm kx line (x-y plane)

Small Device (L) => largeGerhard k= Klimeckπ /L => large anisotropy Band Projection in [100] Quantum Wells (concrete example for Si:P case, but generic for Si QW)

• 3D2D Si [100] quantum well -

+&-, ! ,( ' )

, # % + 0$

,(**+) .+**/

Gerhard Klimeck Band Projection in [100] Quantum Wells => [010] wire (concrete example for Si:P case, but generic for Si nanowires)

• 3D2D1D projection of Si [100] nanowire Si:P [100] Wire (

1 4

&!(' ) '#"$ & ,

'!'& &#$

'#%%&$ *&%%+ & Gerhard Klimeck Band Projection in [100] Quantum Wells => [110] wire (concrete example for Si:P case, but generic for Si nanowires)

• 3D2D1D projection of Si [100] nanowire Si:P [110] Wire

(

&!(' '#"$ ' ' +

'!'& &#$

'#%%&$ )&&%* & Gerhard Klimeck Band Projection in [010] and [110] Si Quantum Wires (concrete example for Si:P case, but generic for Si nanowires)

[100] [110]

Effective Mass variesGerhard Klimeck with Geometry! Quantum Confinement varies band structure and DOS

Gerhard Klimeck Quantum Confinement varies band structure and DOS

Geometry dependent properties

60%

Previously unconsidered Trade-Offs 33% => Details matter! Gerhard Klimeck Short channel effects degrade device performance

Short channel effects Gate

Source • Short channel effects • DIBL • S/D Tunneling Drain Drain • Shortening the channel increases control of drain on top-of-the- barrier

• DIBL and Sub threshold Slope (SS) increases with scaling

DIBL and SS increase with scaling

Gerhard Klimeck Gate Scaling Increases Tunneling Currents

S/D tunneling

Gerhard Klimeck S/D tunneling increases SS and is scaling dependent

S/D tunneling

• Cause: carrier passing through S/D tunneling thin potential barrier increases SS, degrades device performance and • Tunneling depends on increases with Potential barrier width scaling Carrier effective mass

• Tunneling is f(m*, LG) LG ↓ Tunneling ratio ↑ Body thinning reduce m* Tunneling ratio ↑

• Gate has to control the tunneling and thermionic current

LG ↓ SS ↑ Vth ↑ ION ↓ Gerhard Klimeck Summary: NEMO results for ITRS projections

Analytical model only NEMO atomistic model

MASTAR ITRS projection ITRS-2011

Experiment NEMO ITRS-2013

Experiment

ITRS problem shows growing relevance of atomistic modeling

Gerhard Klimeck DG UTB benchmark

DG 2020 and DG 2028 UTBs have been benchmarked

Parameter DG HP 2028 DG HP 2020

LG 5.1 nm 10.6 nm

Leff (0.8*LG) 4.1 nm 8.5 nm

Tsi (0.4*Leff) 1.64 nm 3.4 nm

Lead length 10 nm 10 nm 2E20/cm3 in leads, 1.47E20/cm3 in leads, Doping 1E15/cm3 in channel 1E15/cm3 in channel

EOT 0.41 nm (k=20.66) 0.59 nm (k=15.25)

Vdd 0.64 V 0.75 V Gerhard Klimeck DG HP 2020 - Results

OFF ON

Tunneling ratio @OFF state: 58%

Parameter NEMO5 OMEN Relative Difference

SS (mV/dec) 82.54 81.81 0.8 %

ION (µA/µm) 2826.5 2927.8 3.4 %

DIBL (mV/V) 108 102 5.8 %

Gerhard Klimeck DG HP 2028 - Results

OFF ON

OFF Tunneling ratio NEMO5: 97.27% OMEN: 97.68%

Parameter NEMO5 OMEN Relative Difference

SS (mV/dec) 102.74 98.12 4.7 %

ION (µA/µm) 1798.2 1788.2 0.56 %

DIBL (mV/V) 147 125 17.6 %

Gerhard Klimeck Modeling of modern semiconductor devices requires atomic-scale resolution

Intel roadmap Atomistic model of finFET device

22nm = 176 atoms Intel 22nm finFET 8nm = 64 atoms

Non-planar 3D devices have better control!

Gerhard Klimeck NEMO models realistic devices with atomistic resolution

Computational Nanoelectronics

NEMO can model • Quantum Dots • Nanowires • MOSFET • Impurities • Many more

18 years development: Texas Instruments, NASA JPL, Purdue

Gerhard Klimeck NEMO5 offers user-friendly GUI interface

3D geometric 1 representation

3 Crystal 2 visualization 1 Hierarchical 3 structure

Gerhard Klimeck Quantum transport is far from equilibrium

Dimensions Macroscopic Atomic

Diffuse Ballistic Quantum

Regime

Transport Drift / Diffusion Boltzmann Transport Non-equilibrium Green functions

UNIFIED MODEL

Σs

SILICON D μ1 H μ2 INSULATOR VG V D VG V D Σ1 Σ2 I

Gerhard Klimeck Journey through nanoelectronics tools: NEMO and OMEN

Tool Name NEMO-1D

Transport Yes

Dim. 1D

Atoms ~1000 [100] Crystal Cubic, ZB Strain -

Multiphysics - Parallel 3 levels Computing 23, 000 cores

Impact

4 top pubs cites: 545,157,128,82 Patents:2

Gerhard Klimeck 36 Journey through nanoelectronics tools: NEMO and OMEN

Tool Name NEMO-1D NEMO-3D

Transport Yes Yes

Dim. 1D any

Atoms ~1000 50 million [100] [100] Crystal Cubic, ZB Cubic, ZB Strain - VFF

Multiphysics - - Parallel 3 levels 1 level Computing 23, 000 cores 80 cores

Impact

4 top pubs cites: 4 pubs cites: 545,157,128,82 166,157,131,128 Patents:2 1 Nature Physics >100 groups

Gerhard Klimeck 37 Journey through nanoelectronics tools: NEMO and OMEN

Tool Name NEMO-1D NEMO-3D NEMO3Dpeta

Transport Yes Yes Yes

Dim. 1D any any

Atoms ~1000 50 million 100 million [100] [100] [100] Crystal Cubic, ZB Cubic, ZB Cubic, ZB, WU Strain - VFF VFF

Multiphysics - - - Parallel 3 levels 1 level 3 levels Computing 23, 000 cores 80 cores 30,000 cores

Impact

4 top pubs cites: 4 pubs cites: 2 pubs in Science, 545,157,128,82 166,157,131,128 Nature Nano 2012 Patents:2 1 Nature Physics 50 & 30 cites >100 groups

Gerhard Klimeck Journey through nanoelectronics tools: NEMO and OMEN

Tool Name NEMO-1D NEMO-3D NEMO3Dpeta OMEN

Transport Yes Yes Yes Yes

Dim. 1D any any any

Atoms ~1000 50 million 100 million ~140,000 [100] [100] [100] Any Crystal Cubic, ZB Cubic, ZB Cubic, ZB, WU Any Strain - VFF VFF -

Multiphysics - - - - Parallel 3 levels 1 level 3 levels 4 levels Computing 23, 000 cores 80 cores 30,000 cores 220,000 cores

Impact

4 top pubs cites: 4 pubs cites: 2 pubs in Science, Gordon Bell Prize 545,157,128,82 166,157,131,128 Nature Nano 2012 4 pubs cites Patents:2 1 Nature Physics 50 & 30 cites 135,59,54,30 >100 groups 1 patent

Gerhard Klimeck Journey through nanoelectronics tools: NEMO and OMEN

Tool Name NEMO-1D NEMO-3D NEMO3Dpeta OMEN NEMO5

Transport Yes Yes Yes Yes Yes

Dim. 1D any any any any

Atoms ~1000 50 million 100 million ~140,000 100 million [100] [100] [100] Any Any Crystal Cubic, ZB Cubic, ZB Cubic, ZB, WU Any Any Strain - VFF VFF - MVFF

Multiphysics - - - - Spin, classical Parallel 3 levels 1 level 3 levels 4 levels 4 levels Computing 23, 000 cores 80 cores 30,000 cores 220,000 cores 100,000 cores

Impact

4 top pubs cites: 4 pubs cites: 2 pubs in Science, Gordon Bell Prize New 2011- Few publ. 545,157,128,82 166,157,131,128 Nature Nano 2012 4 pubs cites Intel, Samsung, GF, Patents:2 1 Nature Physics 50 & 30 cites 135,59,54,30 IBM, LockheedMartin >100 groups 1 patent >100 research groups

Gerhard Klimeck 40 Journey through nanoelectronics tools: NEMOFirst and predictive OMEN First 10 million atom First peta-scale NEMOco NEGF tool electronic structure engineering

Tool Name NEMO-1D NEMO-3D NEMO3Dpeta OMEN NEMO5

Transport Yes Yes Yes Yes Yes

Dim. 1D any any any any

Atoms ~1000 50 million 100 million ~140,000 100 million [100] [100] [100] Any Any Crystal Cubic, ZB Cubic, ZB Cubic, ZB, WU Any Any Strain - VFF VFF - MVFF

Multiphysics - - - - Spin, classical Parallel 3 levels 1 level 3 levels 4 levels 4 levels Computing 23, 000 cores 80 cores 30,000 cores 220,000 cores 100,000 cores

Impact

Gerhard Klimeck 41 NEMO5 bridges the scale From ab-initio to realistic devices

NEMO Ab-initio TCAD

Goal Approach • Device performance with realistic extent, • Ab-initio (Bulk, small ideal superlattices) heterostructures, fields, etc. for novel materials • Map ab-initio to tight binding (binaries and superlattices) Problems • Current flow in ideal structures • Need ab-initio for new material properties • Study devices (perturbed by bias, disorder, • Ab-initio cannot model non-equilibrium phonons) • TCAD lacks real material physics

Gerhard Klimeck Modular framework structure supports expandability and code maintenance

S C A L E F R A M E W O R K I N F O

Atom positions Geometry • Valence Force Construction Field (VFF) ~10-50 million method for strain atoms

Atomistic Strain Relaxation

Valence electrons Piezoelectric Hamiltonian Electrical / • Piezoelectric Potential Construction Magnetic field effects ~0.5-10 million • Empirical tight atoms binding sp3d5s* Single Particle Optical Prop. + spin orbit States Electronic Str.

E-e interactions Many Body Optical Prop. • SCP: Interactions Electronic Str. Poisson + LDA Few states • Slater determinants

Gerhard Klimeck Transport capabilities of NEMO5

• Nonequilibrium Green’s function formalism (NEGF) Quantum transport • Quantum transmitting boundary method (QTBM) models • Top of the barrier model (ideal transistors in ON states)

• Ohmic and Schottky contacts Various physical Ideal (ballistic) and realistic (diffusive, structured) leads models Homogeneous and realistic strain Simple and fast phonon scattering model (under testing)

General simulation • 1D, 2D, 3D structures structures Heterostructures, arbitrary shapes, multiple contacts

5-level MPI • Random seeds, bias, energy, momentum, space parallelization

Quantum / semi- • Efficient solution for confined states classical simulation

Low rank • Mode space for effective mass, k.p and tight binding approximation • Alternative low-rank spaces under testing

Gerhard Klimeck NEMO handles different crystal structures

Atomistic crystal structures

• Simple-Cubic (for effective-mass band structure) • BCC, FCC (for metals) • Diamond (Si, Ge, MOSFETs, UTBs) • Zincblende (GaAs, InSb, TFETs, HEMTs, QDs) • Wurtzite (Nitrides, HEMTs, LEDs)

• Rhombohedral (Bi2Te 3, thermoelectrics) • Graphene (Bilayer Graphene, CNTs)

• Orthorhombic (C49, C54, TiSi2)

Gerhard Klimeck Realistic contact materials Metals in NEMO5

Cu nanowire (NEMO5) Modeling of metals

Challenges • Shrinking semiconductor device dimensions enhance influence of metallic leads • Metals have long range interactions beyond standard 1st nearest neighbor tight binding FCC Cu bandstructure (DFT vs. NEMO5) models NEMO5 • Include extended neighbor interactions • Verify bandstructure / transport in ideal metallic structures (Cu, Ag, Au, Al, Pb) Ef

Lines: FP-LAPW- DFT* Energy (eV) * Full Potential Linear Augmented Plane Wave Density Functional Theory Circles: NEMO5 fitted to FP-LAPW-DFT

Gerhard Klimeck Transport through Cu / Si interface

Transport Cu / Si interface Cu Si Complex Metal- semiconductor contact studied in NEMO5 Periodic BC in-plane

Model Bandstructure Transmission Cu: 2nd nearest 6 6 6 neighbor model Cu Si Si: 1st nearest 4 4 4 neighbor model 2 2 2

Energy(eV) Energy (eV) 0 Energy (eV) 0 0 -2 -2 -2 0 2 4 6 8 0 1 2 3 4 5 0 0.01 0.02 0.03 K (1/nm) K (1/nm) Transmission

Gerhard Klimeck NEMO allows modeling of arbitrary geometries

Simulation structures

• All models within NEMO5 can handle 1/2/3D and arbitrary geometries • Alloy disorder, random dopants, ternary alloys gate oxide source silicon drain Drain gate oxide Gate Source

Gerhard Klimeck NEMO allows modeling of arbitrary geometries

real contact

In53Ga47As D.-H. Kim, J. D. A. del Alamo, IEEE Trans. Elec. Dev. 57, 1504 (2010) In52Al48As nm InP

In52Al48As virtual contact Si δ-doping In53Ga47As InAs

In53Ga47As In Al As 52 48

Gerhard Klimeck 8 band k•p hamiltonian in NEMO5

Objective • Full 3D discretized 8 band k.p model E-k diagrams • Band structures of relaxed / strained bulk, quantum wells, wires and dots GaAs bulk GaAs 5nm QW • Electron / hole transport, Piezoelectric effects

Motivation • k.p has simple parameters / widely used • k.p is expected to be faster than TB • Band structures of optoelectronic devices around gamma point • Optical properties (absorption, gain)

Approach • Cond. band treated according to perturbation theory • Non parabolic valence bands modeled using Luttinger Bi2Se3 15nm QW GaSb/InAs/GaSb 15nm QW 50 formulation • Coupling between conduction and valence band included using Kane’s parameter

Simulation of Zinc blende, wurtzite and rhombohedral homogeneous and hetero structures or alloys Homogeneous strain and transport Results Results

Gerhard Klimeck NEMO5: Tunneling field effect transistor

Transport in band-to-band tunneling devices Tunneling between valence / conduction band geometry affects the device performance tunable via gate geometry

Gate drain extension

X Y undercut

Energy and spatially resolved current

Vg=-0.5V

Gerhard Klimeck General iterative lead contact self-energy

General solution scheme Divide lead into segments

• Add smooth damping potential , e.g. V(R) = exp(R) i V0 • Apply RGF on lead surface Green’s function (PhD thesis T. Kubis, http://nanohub.org/resources/8612)

Comparison: Sancho-Rubio vs Transfer Matrix Method ☺ Completely general approach (dimensions, Hamiltonian, lead structure) Requires incoherent scattering to speed up convergence (“dirty trick”) Requires iterative solution (not as fast as Transfer Matrix Method)

Gerhard Klimeck SiGe random alloys

Pure InAs

Alloy in device

Alloy everywhere

Device: 10nm

Example Results

• 3x3nm Si0.5Ge0.5 • General lead nanowire in sp3s* tight algorithm is able to binding represent randomness • Si and Ge atoms in leads randomly distributed • Randomness in leads • Results averaged over significantly lowers 50 samples current density (also vs. VCA) Gerhard Klimeck Silicon nanowire with charge impurities Channel Source Drain I-V Curve * x

4.8879 nm 5.431 nm 1E20 /cm3 10.3189 nm 1E20 /cm3 1E15 /cm3 Current (A) Current (A)

Center impurity Potential Objective Results Voltage • Accurately model effect of charge impurities • Simulations show largest effect when in nanowires impurity is in center of channel Approach • Virtually no effect when impurity is in the • Tight binding method with QTBM drain • Charge impurity and solved self-consistently • The inclusion of charge impurities lowers • Effect of the charge impurity’s location the VT shift but does not have much effect on the saturation current Gerhard Klimeck Transport modeling in piezoelectronic transistors

Device design and bulk band structure

Objectives • Quantum transport in Piezoelectronic Methods Transistor • Tight binding parameterization of • Generalized gradient approximation piezoresistive materials (SmSe, SmTe) (GGA) with spin-orbit (SO) coupling Impact • Hubbard-type on-site electron-electron repulsion U • ETB parameterization captures • Parameter mapping from DFT to ETB bandgap change with strain • Coherent Appl.transport Phys. Lett. by 102, NEGF 193501 (2013) successfully Gerhard Klimeck Transport modeling in piezoelectronic transistors

Bandgap modification due to strain

Experiment: Topological insulators Experiment

• Unique transport features of topological Motivation insulators (ballistic surface transport) NEMO5 • Question: surface conductance tunable? Science 325, 178 (2009)

• Charge self-consistent tight-binding Method (sp3d5s*) Schrödinger/Poisson (electron-core model) • Spin analysis and scattering rates

Agreement with experiment • warping of Fermi surface Results • spin polarized surface states

• Dirac hyperbolas in thin Bi2Te 3 layers Warping of the Fermi surface

Gerhard Klimeck NEMO is at the forefront of quantum computing

2012

2014

Gerhard Klimeck Single electron transport

Schematic of single atom transistor Coulomb diamond

IDS

VG G

E EF F VG VDS

VDS G

Gerhard Klimeck 59

Pushing towards the ultimate scaling limit Atomistic modeling of a single atom transistor

Deterministic single atom transistor Charge stability diagram • Atomic-scale fabrication precision • Hybrid atomistic/rate-equations model • Single P dopant charging energies • Modeling of Coulomb diamond

Single atom transistor

Potential profile modeling Lead density of states fluctuations • Comprehensive device modeling • Dopant placement effects in leads • Charging energies / gate control • Atomistic density of states fluctuations modeling

M. Füchsle, et. al. Nature Nanotechnology (2012)

Gerhard Klimeck Taking the first step towards scalable qubit arrays Spin-blockade and exchange in a double donor-dot device

From vision to real device

Device Specifications

• Two phosphorus donor clusters D1, D2 • Atomic-scale STM fabrication precision

• Independent gate control via G1,G2

Experimental Goals • Pauli Spin-blockade • Measurement of exchange-interaction

Modeling Goals • Atomistic donor-cluster characterization

• Determination of donor number in D1, D2

What is the number of donors in each donor cluster?

Gerhard Klimeck Characterization of donor clusters using atomistic modeling

Atomistic modeling of binding energies determines number of donors

Modeling Achievements Binding Energy Confidence Bands

• Donor clusters D1, D2 identified as 2P, 3P system • Atomistic modeling of different donor cluster configurations

D1 D2

Gerhard Klimeck Global impact of NEMO software pack

9 NEMO/OMEN based codes Last 12 months • 2,800 Users Systemic Education • 59,000 Simulation Runs 35 Klimeck tools >10,100 students, 718 courses Overall >33,000 users >64 universities • 18,400 Users >1,200,000 simulations • 354,000 Simulation Runs

Gerhard Klimeck NEMO5: support and discussion forum

• Post questions and look for answers in the NEMO5 discussion forum • Feedback/suggestions welcome • You can contribute to the code

• Intel enjoys privileged access and support • 2 biweekly phone meetings (formal report and work-call) • Fast response to ad- hoc message/queries

Gerhard Klimeck NEMO5 – a team’s code

NEMO5 is a team effort of individuals with varying

Knowledge

Cultural background

Responsibility

Involvement

Scientific Orientation

Gerhard Klimeck NEMO5 - Band structure engineering A solution for MOSFET scaling

From quantum mechanics to providing solutions for scaling

• Source to drain (S/D) tunneling below 20 nm gate length

• A solution is using heavier m* material or engineering Si for heavier mass. Light m* (Si) Heavy m* (Si)

Material’s property are geometry dependent.

Opportunities toGerhard solve Klimeck scaling issues Gerhard Klimeck 67 Wave function modeling of quantum dots in NEMO5

InAs / GaAs quantum dot

Ground State 1st Excited 2nd Excited 3rd Excited

E=1.123eV E=1.354eV E=1.523eV E=1.587eV

InAs

GaAs

Gerhard Klimeck Strain modeling in nanostructures using NEMO

Modeling of strain

• Atomistic description using valence force field (VFF) method • Structure relaxation by minimizing an energy functional that depends on bond angles and bond lengths • Various models for energy functional available

Displacement vector and zz-component of strain tensor, InAs quantum dot (~50 million InAs atoms)

Gerhard Klimeck Phonon modeling in NEMO5

NEMO5 Phonon modes • Same physical model as strain relaxation • Hessian of energy functional is reused as dynamical matrix

Results • Bulk phonon dispersion for GaN in Wurtzite phase • calculated using Keating VFF model + Coulomb interaction

Gerhard Klimeck Relaxation: Si/Ge/Si UTB transistor

Gate n++ Si intrinsic Ge n++ Si

8nm 8nm

Quick Facts Task 8x20nm Si/Ge/Si UTB transistor • Investigate 2 different boundary • 8nm Ge embedded in Si conditions • Source-Drain voltage: 0.5V • Fixed • ON Gate voltage: 0.5V • Open • OFF Gate voltage: -0.8V • Source-Drain temperature difference (for 20nm): 5K

Gerhard Klimeck UTB: Relaxation for open boundary conditions Ge atoms expand structure in x and y direction

Result Type Illustration

0.3 Displacement 0.15 dx (nm) 0

OPEN BC OPEN BC -0.15 -0.3 dy

3 1.5 Strain εxx component (%) 0

OPEN BC OPEN BC -1.5 -3 εyy

Gerhard Klimeck UTB: Relaxation for closed boundary conditions Ge atoms expand structure in x and only partly in y direction

Result Type Illustration

0.3 Displacement 0.15 dx (nm) 0

OPEN BC OPEN BC -0.15 -0.3 dy

0.3 0.15 Displacement dx (nm) 0

FIXED BC FIXED BC -0.15 -0.3 dy

Gerhard Klimeck UTB: Relaxation for closed boundary conditions Ge atoms expand structure in x and only partly in y direction

Result Type Illustration

0.3 0.15 Strain εxx component (%) 0

OPEN BC OPEN BC -0.15 -0.3 εyy

0.3 0.15 Strain εxx component (%) 0

FIXED BC FIXED BC -0.15 -0.3 εyy

Gerhard Klimeck Strain relaxation in thermal transport

Objective Illustrations • Understand heat flow mechanics in heterostructures • Study effects of strain relaxation in thermal transport

Approach • Harmonic Keating model for relaxation • Valence Force Field model for phonon dispersions Transmission (1/nm) Thermal conductance (W/K) • NEGF quantum transport simulations (bosons)

Results • Strain relaxation crucial in thermal transport - gives correct energy window for heat transport • Si/Ge interface blocks a lot of phonons due to phonon dispersions mismatch

Gerhard Klimeck