Thermoelectric Energy Harvesting

Thermoelectric Energy Harvesting Prof Douglas Paul Director: James Watt Nanofabrication Centre University of Glasgow U.K.

The University of Glasgow Established in 1451 7 Nobel Laureates, 2 SI units, ultrasound, television, etc... 16,500 undergraduates, 5,000 graduates and 5,000 adult students 186M research income pa 400 years in High Street Moved to Gilmorehill in 1870 Neo-gothic buildings by Gilbert Scott

Famous Glasgow Scholars William Thomson (Lord Kelvin) James Watt William John Macquorn Rankine Rev Robert Stirling Rev John Kerr Joseph Black John Logie Baird Adam Smith

James Watt Nanofabrication Centre @Glasgow Vistec VB6 750m 2 (+150 m 2 ) cleanroom - pseudo-industrial operation 15 technicians + 4 PhD research technologists E-beam lithography Processes include: MMICs, III-V, Si/SiGe/Ge, integrated photonics, metamaterials, MEMS (microfluidics) Part of EPSRC III-V National Facility & STFC Kelvin-Rutherford Facility Commercial access through Kelvin NanoTechnology Süss MA6 optical lith http://www.jwnc.gla.ac.uk/ 14 RIE / PECVD / ALD 6 Metal dep tools 4 SEMs: Hitachi S4700 Veeco: AFMs

Electron Beam Lithography Capability 30 years experience of e-beam lithography Sub-5 nm single-line lithography for research 9 8 7 6 5 Measured linewidth vs dose HSQ 4 3 16000 20000 24000 28000 Dose (µc cm-2) 10nm Vistec VB6 Penrose tile: layer-to-layer alignment 0.46 nm rms Alignment allows 1 nm gaps between different layers: Vistec EBPG5 > nanoscience: single molecule metrology

200 nm gate length 10 nm wide, 50 nm tall nanowire 10 nm Width Si Nanowire FET

10 nm Wide Si Nanowire SET Depletion mode nanowire 1.4 K

Micro and Nanotechnology from Glasgow 1 nm nanogaps Nanoelectronics: 10 nm T-gate HEMT Optoelectronics: 1.55µm DFB laser Manufacture: AFM probes Hydrophobic patterns Healthcare: STEM cell interrogation metres 10 9 10 8 10 7 10 6 10 5 10 4 10 3 10 2 10 1 Sensing: Si nanowires III-V CMOS Environment: Microfluidics MEMS: THz optics 100 µm 2 mm

Thermoelectrics History History: Seebeck effect 1822 heat > electric current Peltier (1834): current > cooling Thomson effect: Thomson (Lord Kelvin) 1852

Thermoelectric Applications NASA Voyager I & II Peltier cooler: telecoms lasers Cars: replace alternator Micropelt BMW Temperature control for CO2 sequestration Buildings / industry temperature control autonomous sensing

Energy Harvesting for Remote Sensing Sports performance sensors Flood sensors Weather monitoring Aged well being sensors Radio Processor Sensor Energy harvester > 10 mw > 100 µw > 10 µw < 100 µw/cm 2!!! Battery free autonomous sensors: ECG, blood pressure, etc.

Background Thermal Physics Fourier thermal transport Joule heating Q = appleart Q = I 2 R Area, A hot side, Th Q = heat (power i.e energy / time) Heat (energy/t) = Q L resistance, R I cold side, Tc Q = applea T c T h L

The Peltier Effect heat transfer, Q Hot reservoir Th Material 2 Material 1 electrons Material 2 Cold reservoir Tc I Peltier coefficient, = Q I units: W/A = V Peltier coefficient is the heat energy carried by each electron per unit charge & time

The Seebeck Effect Hot reservoir Th Material 2 Material 1 α => I V Material 2 Cold reservoir Tc Open circuit voltage, V = α (Th Tc) = α ΔT Seebeck coefficient, = dv dt units: V/K Seebeck coefficient = 1 x entropy ( Q transported with electron q T )

The Physics of the Thermoelectric Effect If we ignore energy dependent scattering (i.e. τ = τ(e)) then from J.M. Ziman = q 2R 3 (E) 2 (E) g(e) de df de E g(e) EF EF g(e) f(e) df(e) de (E EF) df(e) g(e) de = q 2 3T R (E) 2 (E) g(e) df de (E EF )de Thermoelectric power requires asymmetry in red area under curve

Semiconductor Example: SiGe Alloys Seebeck coefficient, α (µv K 1 ) Mott criteria ~ 2 x 10 18 cm 3 Degenerately doped p-si0.7ge0.3 α decreases for higher n For SiGe, α increases with T = 8 2 k 2 B 3eh 2 m T 3n 2 3 J.P. Dismukes et al., J. Appl. Phys. 35, 2899 (1964)

The Thomson Effect Hot reservoir Th dx Q I Cold reservoir Tc T dt α is temperature dependent dq dx = I dt dx x Thomson coefficient, β: dq = IdT units: V/K

The Kelvin Relationships Derived using irreversible thermodynamics = T = T d dt These relationships hold for all materials Seebeck, α is easy to measure experimentally Therefore measure α to obtain and

Carnot Efficiency for Thermal Engines heat input, Q1 turbine Wt Efficiency = net work output = heat input = W t Wcom Q1 water boiler Power station steam 1 st law thermodynamics (Q1 Q2) (Wt Wcom) = 0 Wcom compressor Condenser = Q 1 Q 2 Q 1 heat recovered, Q2 = 1 Q 2 Q 1

Carnot Efficiency Efficiency = = net work output heat input Δ = 1 Q 2 Q 1 Carnot: maximum η only depends on Tc and Th c = 1 T c T h Tc = 293 K = 20 C Higher temperatures give higher efficiencies

Peltier Effect, Heat Flux and Temperature If a current of I flows through a thermoelectric material between hot and cold reservoirs: Area, A hot side, Th Heat flux per unit area = ( = Peltier + Fourier ) Heat (energy/t) = Q current, I Q A = J but = T and applert J = I A cold side, Tc Q = IT appleart

Semiconductors and Thermoelectrics Seebeck effect: electricity generation heat source metal n p Th metal metal heat sink Tc Heat transfer Q Peltier effect: electrical cooling i.e. heat pump heat source metal n p Th metal metal heat sink Tc I I + Load Battery

Conversion Efficiency heat source metal n p Th η = power supplied to load heat absorbed at hot junction Power to load (Joule heating) = I 2 RL Rn Rp metal metal heat sink Tc I Heat absorbed at hot junction = Peltier heat + heat withdrawn from hot junction Peltier heat = I = IT h Load, RL I = (T h T c ) R+R L (Ohms Law) R = Rn + Rp Heat withdrawn from hot junction = applea (T h T c ) 1 2 I2 R NB half Joule heat returned to hot junction

Thermoelectric Conversion Efficiency η = = = power supplied to load heat absorbed at hot junction power supplied to load Peltier + heat withdrawn I 2 R L IT h +applea(t h T c ) 1 2 I2 R heat source metal n p Rn Rp Th metal metal heat sink Load, RL Tc I For maximum value d d( R L R ) = 0 T = 1 2 (T h + T c ) T h T c T h p p 1+ZT 1 1+ZT+ Tc T h max = Z = 2 where RappleA = 2 apple = Carnot x Joule losses and irreversible processes

Thermodynamic Efficiency Figure of merit 2 ZT = T Efficiency, 70 60 50 40 30 20 0 100 200 300 400 500 600 T H T T H Solar Stirling ZT-=-5 ZT-=-20 ZT-=-10 Nuclear Rankine Solar Rankine ZT-=-2 10 Today-ZT-=-0.7 0 300 400 500 600 700 800 900

Power Generation From Macro to Micro Efficiency (%) 35 30 25 20 15 10 5 0 Illustrative schematic diagram cross over Power level (W e ) Engines TE (ZT=2) TE today 10 2 10 0 10 2 10 4 10 6 At large scale, thermodynamic engines more efficient than TE ZT average for both n and p over all temperature range Diagram assumes high ΔT At the mm and µm scale with powers << 1W, thermoelectrics are more efficient than thermodynamic engines (Reynolds no. etc..) C.B. Vining, Nature Mat. 8, 83 (2009)

Application Reality Check NASA with finite Pu fuel for RTG requires high efficiency Automotive requires high power (heat is abundant) Industrial sensing requires high power (heat is abundant) Autonomous sensing requires high power (heat is abundant) As heat is abundant the issue is how to maximise power output NOT efficiency for most applications Power α 2 σ

Maximum Temperature Drop As the system has thermal conductivity apple a maximum ΔT can be sustained across a module limited by heat transport T max = 1 2 ZT2 c The efficiency cannot be increased indefinitely by increasing Th The thermal conductivity also limits maximum ΔT in Peltier coolers heat source metal n p Th metal metal heat sink Tc Higher ΔTmax requires better Z materials

Thermoelectric vs Doping of Semiconductors apple ZT 2 ZT apple el apple ph 10 17 10 18 10 19 10 20 10 21 Carrier density (cm 3 ) Electrical and thermal conductivities are not independent Wiedemann Franz rule: electrical conductivity thermal conductivity at high doping

Bulk Thermoelectric Materials Performance zt 1.4 n-type zt 1.4 p-type zt 1.2 1.2 TAGS Bi SiGe 1.0 2 Te Sb 3 2 Te 3 Yb 14 MnSb 11 1.0 PbTe CoSb 3 CeFe 4 Sb 12 0.8 0.8 PbTe SiGe 0.6 0.6 0.4 0.4 0.2 0.2 0 0 200 400 600 800 1,000 0 0 200 400 600 800 1,000 Temperature ( C) Temperature ( C) zt Nature Materials 7, 105 (2008) Bulk n-bi2te3 and p-sb2te3 used in most commercial thermoelectrics & Peltier coolers But tellurium is 9 th rarest element on earth!!! Bulk Si1-xGex (x~0.2 to 0.3) used for high temperature satellite applications

Main Strategies for Optimising ZT Reducing thermal conductivity faster than electrical conductivity: e.g. skutterudite structure: filling voids with heavy atoms Low-dimensional structures: Increase α by enhanced DOS h i 3q k2 B T dln(µ(e)g(e)) de ( = 2 ) E=E F Make apple and σ almost independent Reduce apple through phonon scattering on heterointerfaces Energy filtering: = k B q apple E c E F k B T + R 1 0 (E Ec) k B T R 1 0 (E)dE (E)dE enhance Y.I. Ravich et al., Phys. Stat. Sol. (b) 43, 453 (1971)

Seebeck Enhancement at Low Dimensions Increase α through enhanced DOS: h i = 2 3q k2 B T dln(µ(e)g(e)) de E=E F 3D bulk 2D quantum well 1D quantum wire 0D quantum dot g(e) g(e) g(e) g(e) E E EF EF EF EF E E α increasing M. Cutler & N.F. Mott, Phys. Rev. 181, 1336 (1969)

Phonons: Lattice Vibration Heat Transfer Frequency (THz) 16 14 12 10 8 6 4 2 TO LO LA SiGe TA 60 50 40 30 20 10 Energy (mev) optic modes - neighbours in antiphase δ+δ LO TO NB acoustic phonons transmit most thermal energy acoustic modes - neighbours in phase LA 0 Γ Δ wavenumber X 0 TA The majority of heat in solids is transported by acoustic phonons

Phonon Wavelengths that Carry Heat 1.0 Germanium Silicon Cumulative distribution 0.8 0.5 0.2 0.0 0 0.5 1 1.5 2 2.5 3 3.5 4 Wavelength [nm] Greater than 95% of heat conduction in Si / Ge from phonons with wavelengths between 1.2 and 3.5 nm

Phonon Enhancements Phonon scattering: Require structures below the phonon mean free path (10s nm) Phonon Bandgaps: Change the acoustic phonon dispersion > stationary phonons or bandgaps Require structures with features at the phonon wavelength (< 5 nm) Phonon group velocity de dkq Frequency (THz) 4 2 0 Γ Δ wavenumber TA X 20 10 0 Energy (ev)

ZT versus Temperature p-type n-type Nanostructures can improve Seebeck coefficient and/or decrease thermal conductivity

q z (a+ Thermoelectric Low Dimensional Structures 378 QWs Lateral superlattice heat source metal Th Vertical superlattice heat source metal Th n p n p metal heat sink metal Tc metal heat sink metal Tc 2 nm Quantum Dots heat source metal Th Nanowires heat source metal Th n p n p metal heat sink metal Tc metal heat sink metal Tc

Vertical (Cross-plane) Superlattice TEs Use of transport perpendicular to superlattice quantum wells Vertical superlattice heat source metal Th Higher α from the higher density of states Lower electron conductivity from tunnelling n metal heat sink p metal Tc Lower apple ph from phonon scattering at heterointerfaces Able to engineer lower apple ph with phononic bandgaps Overall Z and ZT should increase Figure of merit ZT = 2 T

p-type Wafer Designs SL1 to SL4: 922 x 5 nm 2.85 ± 1.5 nm p-ge QW 1.1 ± 0.6 nm p-si0.5ge0.5 Si0.175Ge0.825 SL5: 2338 x 1.1 ± 0.2 nm p-ge QW 0.5 ± 0.1 nm p-si0.5ge0.5 Si0.175Ge0.825 5 nm

Electron and Phonon Dispersion Holes (Electronic Dispersion) Phonon Dispersion Distance (nm) 0.1 0.0 0 0.5 1 1.5 2 2.5 3 3.5 4 HH1 dispersion 20 15 Rytov model Energy (ev) -0.1-0.2-0.3 LH1 dispersion HH2 dispersion HH LH Energy (mev) 10 5 SL5-0.4 SL2-0.5 0 0.2 0.4 0.6 0.8 1 k z ( /L) SO [001] 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 q k z (a+b) [001] S.V. Rytov, Sov. Phys. Acoustics 2, 67 (1956)

Thermal Parasitic Removal Isotropic structure 1/2 lateral parasitic contribution half structure Half structure allows parasitics to be measured and removed for more accurate heat flux determination

Thermal Measurements Measured 41% of heat in vertical transport

Bulk SiGe ZT Comparisons MIT, Nano Lett. 8, 4670 (2008) GREEN Si p-type SiGe J.P. Dismukes et al., J. Appl. Phys. 35, 2899 (1964)

Nanowire Fabrication on Suspended Hall Bar heater thermometer thermometer heater 100 x 45 nm wide Si nanowires with integrated heaters, thermometers and electrical probes

Si Nanowires: How many atoms wide? Pt coat for TEM silicon Si SiO2 SiO2

45 nm Wide n-silicon Nanowires @ 300 K: σ = 20,300 S/m 4 terminal κ = 7.78 W/mK α = 271 µv/k ZT = 0.057 ZT enhanced by x117 α 2 σ = 1.49 mw m 1 K 2 What enhancements with SiGe?

Micropelt Microfabrication of BiTe Alloys n-bi2te3 p-sb2te3 20 µm Bi2Te3 http://www.micropelt.com/

System Design: Power Output l c Ll hot side electrical insulator, T H metal metal metal n p n p n p A = module leg area L = module leg length N = number of modules l c metal metal metal cold side electrical insulator, T c metal apple c = thermal contact conductivity ρc = electrical contact resistivity P = 2 AN T 2 2( c +L)(1+2 applel c D.M. Rowe & M. Gao, IEE Proc. Sci. Meas. Technol. 143, 351 (1996) applecl ) System: power in BiTe alloys limited by Ohmic contacts 2 Power density (mw/cm 2 ) 10 2 10 1 10 0 10-1 300 K data BiTe Micropelt ZT = 0.6 SiGe Dismukes ZT = 0.11 Nano SiGe ZT= 0.26 Nano BiTe ZT = 0.9 ρc (Bi2Te3) 1 x 10 7 Ω-cm 2 10-2 ρc (Si1-xGex) = 1.2 x 10 8 Ω-cm 2 0 10 20 30 40 50 Δ temperature (K or C)

122 Leg Modules n-type p-type Process tested and works well SOI growths now in progress for final modules

Thermoelectric References D.M. Rowe (Ed.), Thermoelectrics Handbook: Macro to Nano CRC Taylor and Francis (2006) ISBN 0-8494-2264-2 G.S. Nolas, J. Sharp and H.J. Goldsmid Thermoelectrics: Basic Principles and New Materials Development (2001) ISBN 3-540-41245-X M.S. Dresselhaus et al. New directions for low-dimensional thermoelectric materials Adv. Mat. 19, 1043 (2007) D.J. Paul, "Thermoelectric Energy Harvesting" Intech Open Access from "ICT - Energy - Concepts Towards Zero - Power Information & Communication Technology " (2014) - DOI: 10.5772/57347

Further Information Contact: Prof Douglas Paul Douglas.Paul@glasgow.ac.uk Tel:- +44 141 330 5219 http://userweb.eng.gla.ac.uk/douglas.paul/index.html Address: School of Engineering, University of Glasgow, Rankine Building, Oakfield Avenue, Glasgow, G12 8LT, U.K. http://www.greensilicon.eu/greensilicon/index.html