Network for Computational Nanotechnology NCN UC Berkeley Univ

Network for Computational Nanotechnology (NCN) UC Berkeley, Univ. of Illinois, Norfolk State, Northwestern, Purdue, UTEP Thermoelectric effects in ultra-scaled semiconductor devices Role of electronic and lattice properties Abhijeet Paul Network for Computational Nanotechnology & School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA. email: paul 1@purdue. edu Abhijeet Paul & Gerhard Klimeck 1

Why thermoelectricity ? ? ? Nasty Problems g in !! s ea on! r nc luti I l po r ne e g !!! sin and a re em c In d IEA, WEO, 2008 Green energy Production by thermoelectricity ! gy Automobile waste heat thermoelectric power generation DEER ng i as e cr In Gelsinger et. al ISSCC 2001 On chip thermoelectric cooling (Bi. Te SL) Choudhary et. al, Nature nano. (2009) www. tellurex. com Green Solutions from thermoelectricity !!! Abhijeet Paul IC t!! a he 2

What inspired present research ? ? ? Electronic structure in nanostructures? 20 1 0 20 0 0 19 90 Dresselhaus et. al, DOS engg. 19 8 0 19 7 0 19 60 Bi. Te, Pb. Te Phonons in nanostructures ? ? Th Bulk er ZT ~1 m Treatment of alloys at atomic level ? ? oe Fr lec om tri B Pb. Te ? ? ? c M ulk to at ? ? LAST Ddots ZT > 3 Na er Atomic 3 level treatment ial 1< ZT < n ? de ostr crucial to understand uc ve Bi. Te/Pb. Te tur lo nano-scale thermoelectric properties the pm es Qwell Si /Si. Ge … en t Y. Superlattice NW SL ea rl in e Si Nanowires Si. Ge/Si QDot Superlattice 3 Abhijeet Paul (Bi, Sb), (Te, Se), Pb. Te, Phonon Glass Electron crystal Begin Semiconductor use 19 50 Atomic scale interface treatment ? ?

Outline of the talk • Introduction to Thermoelectricity – Basics – Material Development – Research vectors • Approach for thermoelectric (TE) analysis. • Research milestones – Results for Silicon nanowires – Scientific Outreach • Future Proposal – Investigation of Si. Ge nanowire superlattices as TE material. • Summary Abhijeet Paul 4

Assessing thermoelectric efficiency: ZT Coefficient of Performance Heat energy removed from cold side Heat energy added to hot side Abhijeet Paul Large Scale Refrigeration Small refrigeration systems ZT = 4 ‘The Holy grail’ Small Scale Refrigeration TE can replace existing Vapor cooling technology !! 5

Composition of Figure of Merit (ZT) Generation of potential difference due to applied temperature difference `Seebeck Coefficient’. Generation of temperature difference due to applied potential difference `Peltier Coefficient’ Measure of thermoelectric power generation (High) Measure of thermoelectric cooling (High) ‘Thermoelectric Figure of Merit’ unitless quantity obtained at temp `T’. Defined by Ioffe in 1949. Ability of material to conduct electricity `Electrical Conductance’ Measure of charge flow (High) Large COP High ZT large G Abhijeet Paul Ability of material to conduct heat energy `Thermal Conductance’ Measure of heat flow (Low) Both electrons (ke)and lattice(kl) carry heat. large S and small κ desired !!! 6

Material of choice for thermoelectricity TE Parameters Materials Electrical Conductivity (G) Thermal Conductivity (κ) Seebeck Coefficient (S) Very High Insulators Semiconductors Low High ~107 S/m Metals ~ 10μV/K ~102 W/m-K Extremely low (~10 -10 S/m) High Moderate High Low 10 -3 S/m ~120 μV/K ~10 W/m-K Low ~10 -2 -10 -4 W/m-K Semiconductors most suitable TE material. Allow separate control of G (electrons) and κ (phonons). Abhijeet Paul 7

ZT enhancement… Enhance Power factor (S 2 G) by electronic structure modification. 1990 s Nanostructures provide DOS modification. 3 D Phonon scattering Reduce thermal conductivity by phonon scattering. 1960 s 2 D 0 D DOS engineering Nanostructures and alloys increase phonon scattering. Nanostructures allow tuning of G, S and κ !!! Abhijeet Paul 1 D 8

Material Research ? ? ? Market Promising TE Materials Making research Economically viable Crucial R&D vectors Potential Markets [1] Ø Fabrication of nanostructures. §Consumer (35%) §Thin Films Ø Robust thermoelectric §Automobile (14%) §Nano-particles characterization §Telecom (16%) §Super Lattices Higher reliability Ø §Medical and Bio (12%) §Nano-composites Ø Better structural stability. §Industry (9%) §Nanowires Ø Efficient thermoelectric modules. §Semicon. Process (8%) §Quantum Dots § Ø Bulk and low cost production. Defense & space (6%) Research Ø Better simulation and analysis Economy $$$ tools. ? Abhijeet Paul Computer simulation an integral part to develop better TE materials and modules [1]Hachiuma & Fukuda ECT, 2007 9

Outline of the talk • Introduction to Thermoelectricity – Basics – Material Development – Research vectors • Approach for thermoelectric (TE) analysis. • Research milestones – Results for Silicon nanowires – Scientific Outreach • Future Proposal – Investigation of Si. Ge nanowire superlattices as TE material. • Summary Abhijeet Paul 10

How to analyze thermoelectric properties of materials ? O U T Tc V 1 Ie Th Material A IQ IN Material B V 2 Ie Steady-state linear thermoelectric (Onsager’s) relations [1, 2] Electric current Heat current Landauer’s Formula can be used to evaluate the transport parameters Abhijeet Paul [1] L. Onsager, Phys. Rev. 37 405 (1931). [2] G. D. Mahan, Many-body Physics. 11

Calculation of thermoelectric parameters G, S κe κl (Electronic) (Lattice) Landauer’s Integral Under zero current condition Landauer’s approach A suitable approach to calculate thermoelectric transport parameters in nanostructures. Abhijeet Paul 12

Phonon Integral Phonons need Both need • No. of modes, M(E). • Mean free path (λ). Electrons need • No Fermi Level • Bose Einstein distribution (bosons!!) • M(ω) Phonon dispersion. Accurate electronic & phonon dispersions must !!!. • Moment calculation near Fermi Level • Fermi Dirac distribution (fermions!!) • M(E) Electronic bandstructure. Electron Integral Abhijeet Paul 13

The approach for TE analysis es es ro pe rti ic P Thermoelectric analysis of semiconductors Transport Theory Modified Valence Force Field (MVFF) method. ti er op Pr ctr on ce Bottom Up tti Ele La Semi-empirical Tight-Binding (TB) method. Landauer’s approach and Green’s function method Three ingredients for TE analysis in nanostructures Abhijeet Paul 14

Outline of the talk • Introduction to Thermoelectricity – Basics – Material Development – Research vectors • Approach for thermoelectric (TE) analysis. • Research milestones – Results for Silicon nanowires – Scientific Outreach • Future Proposal – Investigation of Si. Ge nanowire superlattices as TE material. • Summary Abhijeet Paul 15

Why thermoelectric analysis of Si Nanowires (Si. NW) ? ? ? How to cool the heating ICs ? ? Silicon NW array (thermoelectric element) Heated IC Waste heat Electricity Two pronged advantage ØCool the chip. ØObtain electricity Abhijeet Paul Cooler Area Tcold Thot V Investigation of Si. NW TE properties crucial to explore more ideas !!! 16

Experimental realizations… High ZT p-type Si. NW waste heat conversion ZT ~1 @ 200 K Caltech, Nature, 451, 168, 2008 Thermal conductance reduction Silicon phonon mesh ZT ~0. 6 @ 300 K Berkeley, Nature, 451, 163, 2008 100 fold rise in Si. NW ZT compared to Bulk Si ZT (0. 01 @ 300 K)!!! κ ~ 1. 9 W/m-K Caltech, Nature nano. 2010, doi: 10. 1038/nnano. 2010. 149 100 fold reduction in Si nanomesh κ compared to Bulk Si (~148 W/m-K @ 300 K)!!! Nanostructuring (Si. NW) turns ‘lousy bulk Si’ to better TE material !! material. 17 Abhijeet Paul

Role of electronic structure on Thermoelectric properties 1. Atomistic confinemenet effects on the Seebeck coefficient (S) in Si. NWs. 2. Atomistic and uniaxial strain effect on thermoelectric powerfactor (S 2 G) of Si. NWs. DEVICE DETAILS: • Rectangular Si. NW [100], [110] and [111] channels. • Width (W) and height (H) varied from 2 to 14 nm. Electronic structure using Atomistic Tight Binding method. Abhijeet Paul S and G calculation using Landauer’s approach. 18

Atomistic Tight binding Approach : A short introduction Assemble TB Hamiltonian and obtain eigen energies Zinc blende unitcell <100> Y Z Nano-structure 19 Abhijeet Paul Atomic Orbital Interactions ADVANTAGES üAppropriate for treating atomic level disorder. üStrain treatment at atomic level. üStructural, material and potential variation at atomic level treated. 10 band nearest neighbor sp 3 d 5 s* model with spin orbit coupling. Electronic structure calculation in Si. NWs using Tight Binding [1] (TB) [1] Klimeck et. al CMES, 3, No. 5 (2002); 19

Effect of atomistic confinement on E(k): [100] Si. NW W confinement [100] Si. NW E(k) H confinement Conduction Band W=2, H=14 [0 -10] H D=4 [0 -10] W W Abhijeet Paul H and W confinement symmetric for [100] oriented wires 20 [001] H W=14, H=2

Effect of atomistic confinement on E(k): [110] Si. NW E(k) W=2, H=14 W=14, H=2 Conduction Band minima at Off-Γ D=2 [001] H H confinement D=4 [001] W confinement W [1 -10] W Abhijeet Paul H H confinement provides higher degeneracy (D=4) in [110] Si. NW. 21

Tuning S by confinement [100] X S 1 D V/K Both H and W confined for high S [110]X S 1 D V/K Only H confinement increases S Geometrical confinement a nice way to tune ‘S’ in Si. NWs. Abhijeet Paul 22

Maximum Ballistic Power Factor (PFmax) Components of Power Factor <111> has highest PFmax G 1 D/Area S 1 D • PF/Area improved for Si. NW with W/H < 6 nm. • PFmax saturates in larger Si. NW. Abhijeet Paul • Seebeck Coefficient is almost constant at PFmax. • G per area shows a saturation with <111> showing highest G/area value. • <111> shows maximum PF • W/H < 6 nm improves PF 23

Improvement in PF: Role of uniaxial strain ~5% ~115% n-type PF Ge. NW better due higher DOS L-valley. Compressive strain inc. DOS near Fermi level Improves PF. p-type PF Compressive/Tensile strain split VB dec. DOS near Fermi level degrades PF. Compressive uniaxial strain improves n-type ballistic PF. Abhijeet Paul 24

New results from the work ü Atomistic approach shows: Ø Width and height confinement not equivalent at atomic scale. Ø Crystal transport orientation crucial. ü Confinement direction important design high S devices. ü Si. NWs with W & H < 6 nm improvement in Ballistic PF. ü <111> orientated Si. NW best ballistic PF. ü Uniaxial Compressive strain improves n-type PF. Abhijeet Paul 25

Role of phonon dispersion on Thermoelectric properties 1. Phonon dispersion in bulk Si using Modified VFF. 2. Phonon dispersion in calculation in Si. NWs. 3. Effect of phonon dispersion on Si. NW lattice thermal properties. Si. NW DETAILS: • Rectangular Si. NW [100] channels • Width (W) and height (H) varied from 2 to 6 nm. Abhijeet Paul 26

Phonon dispersion calculation: Modified VFF (MVFF) model [A] Δr Old Keating [B] Model [1] [F] Δθ Long Range Bond-stretching(α) Bond-bending(β) [C] Short Range Δr Δθ Cross-bond stretch bend (γ) [2] Zunger et. al. 1999 Coulomb interaction Imp. for polar materials [2] Imp. For polar materials [2] [D] Δr 1 [E] Δr 2 Cross bond Stretching (δ) Δθ 1 Δθ 2 New combination of Interactions: Modified Valence Force Field Calculate phonons in zinc-blende materials. Coplanar bond bending(τ) Imp. for non-polar materials Abhijeet Paul ([3] Sui et. al, 1993) [1] Keating. Phys. Rev. 145, 1966. [2] PRB, 59, 2881, 1999. 27 [3] PRB, 48, 17938, 1993

What is the need for a new model? ? Keating VFF Model Over estimates optical modes Bulk Si Expt. (dots) [1] Over estimates acoustic modes at zone edges. Expt. Data, inelastic neutron scattering (80 K and 300 K). Abhijeet Paul New MVFF model matchs the dispersion very well in the entire Brillouin zone !!! Accurate phonon model crucial for correct calculation of phonon dispersion in nanostructures. [1] Nelsin et. al, PRB, 6, 3777, 1972. 28

Phonon dispersion in free-standing nanowires 1 D periodic [100] Si nanowire structure. [100] free Surface atoms free to standing Si. NW vibrate. Bulk Si Lot of flat bands (zero velocity) resulting in phonon confinement. qx [norm. ] X Strong phonon confinement responsible for different lattice properties in Si. NWs compared to bulk. Abhijeet Paul 29

Vibrational modes of free-standing [100] Si. NWs Flexural modes (1, 2) Bends the wire along the axis. Y Torsional modes (4) Z Rotates the wire along the axis. Y New vibrational modes appear in free-standing nanowires. X Abhijeet Paul Longitudinal modes (3) 30

Sound velocity in [100] free standing Si. NWs [1] q. Both longitudinal and transverse sound velocity is less in Si. NW. q. Phonon confinement results in flatter dispersions and hence smaller sound velocity. q. With increasing W/H Vsnd move towards bulk values. Abhijeet Paul Reduced sound velocity results in lesser dissipation of heat. A result of phonon confinement. [1] www. ioffe. ru/SVA/NSM/Semicond /Si/mechanic. html#Acoustic 31

Ballistic lattice thermal conductance(σball) in [100] Si. NW ~6 times reduction ~3 times reduction q. Higher temperature more phonon population inc. in thermal conductance. q. Thermal conductance drops with decreasing cross-section size. q~6 fold reduction in thermal conductance for ~3 fold increase in width (from 6 nm to 2 nm). Reduction in ballistic σl due to decreasing modes with cross-section size reduction. Abhijeet Paul 32

New things learnt from the work ü A new generalized model for phonon dispersion in zincblende semiconductors. ü Model benchmarked with expt. data. ü Free standing Si. NW show: Ø Very different phonon dispersion compared to bulk Si. Ø New flexural and torsional modes Ø Strong phonon confinement. ü Phonon confinement results in: Ø Reduction of both longitudinal and transverse sound velocity. Ø Reduction of thermal conductance in small Si. NWs. Abhijeet Paul 33

Outline of the talk • Introduction to Thermoelectricity – Basics – Material Development – Research vectors • Approach for thermoelectric (TE) analysis. • Research milestones – Results for Silicon nanowires – Scientific Outreach • Future Proposal – Investigation of Si. Ge nanowire superlattices as TE material. • Summary Abhijeet Paul 34

Global scientific outreach using nano. HUB. org Band. Structure Lab (Research Tool) Semiconductor Educational Tools Crystal Viewer Tool Periodic Potential lab • Calculates electronic bands in zinc-blende structures. • C/C++ based parallel code. 6 C/C++ and MATLAB based semiconductor physics tools developed. • Used in EE 305 (Semicond. Introduction) at Purdue University ØMost popular tool on nano. HUB. ØOver 3 K users. ØTill now ran 34503 simulations. ØHas been cited 28 times in research. Abhijeet Paul Ø Users (last 12 months) = 887 Ø Simulations (last 12 months) ~3 K Enabled dissemination of device physics knowledge globally. 35

Outline of the talk • Introduction to Thermoelectricity – Basics – Material Development – Research vectors • Approach for thermoelectric (TE) analysis. • Research milestones – Results for Silicon nanowires – Scientific Outreach • Future Proposal – Investigation of Si. Ge nanowire superlattices as TE material. • Summary Abhijeet Paul 36

Why to study Si-Ge superlattices ? ? Advantages of using Si. Ge: üAdvanced CMOS fabrication Allows precise thermal high quality Si. Ge structure. conductivity (κ) control. üEasy integration with Si κ 0. 9 W/m-K better heat recovery at chip (>100 fold reduction!!!) level. Nature mat. , 2010, doi: 10. 1038/NMAT 2752 ü Monolithic growth on Si higher energy conversion by thermal resistance reduction. üIn/cross plane tailoring optimize TE properties. Ge/Si(001) nanodots ZT ~ 3. 5@575 K [1] [2] Nanoscale Si. Ge structures will need atomic level understanding!!! Si. Ge structures provide high ZT. Abhijeet Paul [1] Harman et. al, Science, 80, 2002 [2]Wu et. al, Nano. Lett. , 2, 2002. 37

First steps towards future work… TE and thermal analysis Si. Ge nano-structures 2011 §Calculation of E(k) in Si. Ge alloys. §Transmission calculation in Si. Ge nanowires. §Lattice property calculations in Si-Ge structures. §Thermal transport in Si. Ge superlattices (1 D). Sept 2010 Some initial results are presented for the future directions Abhijeet Paul 38

Bandstructure Calculation in Si. Ge alloys: Virtual Crystal Approximation in TB Ge Si [1] Bond-length modification. Si. Ge “Virtual Atom” [2] On-site TB parameter modification. [3] Modification of coupling parameters 39 Tight-Binding based Virtual Crystal Approximation Abhijeet Paul TB-VCA

Benchmarking Bulk Band-structure Biaxial Comp. Stress Si. Ge bulk Relaxed Si. Ge bulk Si Ge Bulk Si • Cross-over at 85% Ge for relaxed Si. Ge Conduction band (CB) captured. • Valance Band Edge equal amount of change in relaxed and strained Si. Ge. • CB edge is almost constant for all Ge% for strained Si. Ge Bulk. First benchmark of experimental Si. Ge bandedges using TB-VCA. Work Published in IEEE EDL , 31, 2010. doi: 10. 1109/LED. 2010. 2040577 Abhijeet Paul 40

Cross-plane transmisson Transport in Si. Ge superlattice: Transmission results* Ge Conduction Band Si Superlattice Ideal Si Simulated Valence Si. Ge Band Nanowire Superlattice Radius = 3 nm Cross-plane Transmission • Strong reduction in cross-plane transmission due to material mismatch. Abhijeet Paul *This work in progress with Lang Zheng 41

Thermal transport in Si. Ge superlattices: Phonon NEGF* How does heat flow in nano-structures ? Simulated Nano-scale Si-Ge-Si device APPROACH Coherent phonon picture within NEGF* approach. Si Transmission Cont 1, T 1 Σ 1 Ge Cont 2, T 2 Dc Σ 2 1 D Spring Model representation of the device • Ge blocks the phonons. • Resonant states appear. Abhijeet Paul Channel Dc = channel dynamical matrix Work in progress for calculating energy density, phonon local temperature, etc. *NEGF = Non Equilibrium Green’s Function 42

Some open questions and probable solutions • How to handle alloy scattering in VCA for nanostructures? – Use of bulk scattering potential not adequate in nanostructures. – Use of random alloy method can provide solution. – Work going on in this direction with Saumitra Mehrotra. • Transmisison in Si. Ge super lattices: – What happens to inplane transmission? – What happens at other composition and widths ? – Work in progress with Lang Zeng. • Nanoscale thermal transport: – Is boundary condition (BC) with temperatures correct? – What is ‘temperature’ in non eqb. nanoscale systems? – Need BCs in terms of energy fluxes. – Work in progress with Dr. Tillmann Kubis and Dr. Mathieu Luisier. Abhijeet Paul 43

Outline of the talk • Introduction to Thermoelectricity – Basics – Material Development – Research vectors • Approach for thermoelectric (TE) analysis. • Research milestones – Results for Silicon nanowires – Scientific Outreach • Future Proposal – Investigation of Si. Ge nanowire superlattices as TE material. • Summary Abhijeet Paul 44

Summary • The current developments, challenges and opportunities in thermoelectricity introduced. • Thermoelectric analysis in semiconductor nanostructures: – Electronic structure and new lattice dynamics model with transport. • Electronic and lattice effects on Si. NWs TE properties: – Tuning Seebeck coefficient by geometry confinement. – Uniaxial strain improves n-type ballistic PF. – Reduction in ballistic thermal conductance due to phonon confinement. • Future research direction: – Analysis of thermoelectric and thermal effects in Si. Ge nanowire superlattices. Abhijeet Paul 45

Acknowledgements • Overall guidance and direction – Prof. Gerhard Klimeck and Prof. Mark Lundstrom, Purdue University, USA. – Prof. Leonid Rokhinson, Purdue University, USA (Ph. D committee member). • Theory and Code development – Dr. Mathieu Luisier, Purdue University, USA (OMEN/OMEN-BSLAB development). – Prof. Timothy Boykin, University of Alabama Huntsville, USA (Ph. D committee member, TB and solid state phys. theory) – Dr. Neophytos Neophytou, TU Wien, Austria (Initial MATLAB codes) • Discussions and work – Saumitra Mehrotra, Parijat Sengupta, Sunhee Lee, Lang Zeng, Dr. Tillmann Kubis, Raseong Kim and Changwook Jeong, Purdue University, USA • . Experimental Collaborators – Dr. Giuseppe Tettamanzi, TU Delft, Netherlands, Shweta Deora, IIT Bombay, India, Dr. Subash Rustagi, IME, Singapore. • Summer Undergrad students (for nanohub tools) – Junzhe Geng, Victoria Savikhin and Mohammad Zulkifli, Purdue University, USA • Funding and Computational Resources – MSD-FCRP, SRC, NSF and MIND for funding. – NCN and nano. HUB. org for computational resources. Abhijeet Paul 46

Thank You !!! All the group member for vital inputs and support. Everyone for attending the talk. Abhijeet Paul 47