SLIDE 1 Realization of an efficient quantum-dot heat engine
HEINER LINKE NanoLund and Solid State Physics, Lund University, Sweden Energy Conversion in the Quantum Regime, 27 August 2019, ICTP,Trieste
SLIDE 2 Hot T2 Cold T1
Thermoelectrics
Q (Heat) Current I R
- Low parasitic heat conduction by electrons (κel) and phonons (κph).
- High Seebeck coefficient S = ∆V/∆T
- Little Joule heating (high conductivity σ)
Figure of merit:
Z = S2σ κe + κ ph
Power factor
SLIDE 3
Classic, cyclic Carnot engine: Working gas (WG) in contact with only one heat reservoir at a time. Fundamental efficiency limit of thermoelectrics?
HOT COLD e-
Thermoelectric: In contact with both reservoirs at all times.
Z = S2σ κe + κ ph
SLIDE 4 Outline
- Energy-filtering and energy-specific equilibrium in
thermoelectrics
- Realizing “the best thermoelectric”: quantum-dot heat
engines
- Experiments: QD heat engine with > 70% of Carnot
efficiency at finite power
- Single-molecule “quantum dots”
- Application of energy filtering to hot-carrier solar cells
SLIDE 5
Fundamental elements of thermoelectrics
?
A cold electron reservoir A bias voltage to do work against. A warm electron reservoir
SLIDE 6 TL TR µL µR
eV Transfer of one electron at energy ε from L to R:
- T. E. Humphrey and H. Linke, PRL 89, 116801 (2002)
“Energy-specific equilibrium”
Reversible electron transfer
TR TL
- T. E. Humphrey, H Linke, PRL 94, 096601 (2005)
SLIDE 7 1 1 2 3
Normalized Efficiency
Generator Refrigerator Increasing resonance width
Resonance position η/ηCarnot E0
Power generation or Refrigeration with tuneable efficiency and power
E0
- T. E. Humphrey and H. Linke, PRL 89, 116801 (2002)
SLIDE 8
The “best thermoelectric”
Z = S2σ κe + κ ph
Figure of merit
SLIDE 9 Efficiency at maximum power: Curzon-Ahlborn efficiency
Carnot efficiency requires reversible operation, which is equivalent to zero power output. Curzon-Ahlborn efficiency describes the efficiency of an ideal Carnot engine operated at maximum power (neglecting dissipation in reservoirs)
II Novikov, J Nuclear Energy 7, 125 (1954)︎.
- F. Curzon and B. Ahlborn, Am. J. Phys. 43, 22 ︎1975︎.
SLIDE 10 Esposito, Lindenberg, van den Broeck, PRL 102, 130602 (2009)
SLIDE 11 Outline
- Energy-filtering and energy-specific equilibrium in
thermoelectrics
- Realizing “the best thermoelectric”: quantum-dot heat
engines
- Experiments: QD heat engine with > 70% of Carnot
efficiency at finite power
- Single-molecule “quantum dots”
- Application of energy filtering to hot-carrier solar cells
SLIDE 12 InP InAs
Epitaxially grown nanowires, e.g. InAs/InP
TBAs (group-V) TMIn (group-III) Substrate surface InAs (111)B
Ann Persson, Linus Fröberg
CBE
Conduction band edge
SLIDE 13 Applying a temperature gradient along a nanowire
Traditional side-heater
Substantial global device heating limits use for low-temperature experiments
Local top-heater
Local, direct heating of the warm contact without electrical interference.
n-Si backgate SiO2
SLIDE 14 Top-heaters to enable high ∆T with minimal heating
Nanotechnology 25, 385704 (2014)
SLIDE 15 Quantum-dot heat engine: device
Artis Svilans
SLIDE 16 Quantum-dot heat engine: characterisation
Martin Josefsson Artis Svilans
SLIDE 17
Quantum-dot heat engine: performance
Pmax
SLIDE 18 Quantum-dot heat engine: 70% of Carnot efficiency demonstrated
- M. Josefsson, A. Svilans, et al. Nature Nanotechnology 13, 920 (2018)
Quantum-dot heat engine achieves Curzon-Ahlborn efficiency at maximum power and about 70 % of Carnot efficiency with finite power output
SLIDE 19 Outline
- Energy-filtering and energy-specific equilibrium in
thermoelectrics
- Realizing “the best thermoelectric”: quantum-dot heat
engines
- Experiments: QD heat engine with > 70% of Carnot
efficiency at finite power
- Single-molecule “quantum dots”
- Application of energy filtering to hot-carrier solar cells
SLIDE 20
Higher maximum power by using interference
SLIDE 21
Higher maximum power by using interference
SLIDE 22
First step: interference effects yield measurable difference in thermopower
August 2018
SLIDE 23
First step: interference effects yield measurable difference in thermopower
Higher thermopower S predicted in presence of destructive interference
SLIDE 24 Outline
- Energy-filtering and energy-specific equilibrium in
thermoelectrics
- Realizing “the best thermoelectric”: quantum-dot heat
engines
- Experiments: QD heat engine with > 70% of Carnot
efficiency at finite power
- Application of energy filtering to hot-carrier solar cells
SLIDE 25
- L. C. Hirst and N. J. Ekins-Daukes,
“Fundamental losses in solar cells,”
- Progr. in Photovolt.: Res. Appl., 19 286–293 (2011)
- Carrier cooling decreases the energy
each carrier can provide to an external circuit.
- pn-junction solar cells of small
bandgap materials are rarely made due to the magnitude of thermalisation losses.
Eg
SLIDE 26
- M. A. Green, Third Generation Photovoltaics. Heidelberg: Springer, 2006.
Time scale of pn- junction solar cell carrier collection. Targeted time scale for carrier collection in this work
SLIDE 27 Basic idea of a hot-carrier cell: photothermoelectrics
Thermoelectric system for electrons Thermoelectric system for holes
SLIDE 28
Can a hot-carrier photovoltaic system be run reversibly?
SLIDE 29
∆S = 0 when (equivalent to energy-specific equilibrium across both junctions)
SLIDE 30 Open-circuit voltage
Explicit term describing the reduction of voltage due to irreversibility Heat engine Solar cell
- S. Limpert, S. Bremner, H. Linke,
New J. Phys. (2015)
Steven Limpert
SLIDE 31
Basic idea for hot-carrier experiments
Heterostructure nanowire with small band gap and high electron-hole mass asymmetry (e.g. InAs/InP)
Local light absorption (photonic hot spot) Energy filter (or thermionic barrier) for hot electrons Block for holes (high mass -> small kinetic energy)
SLIDE 32
Device
CBE grown InAs/InP/InAs nanowire
SLIDE 33 Wavelength-sensitivity (Double-barrier device)
- S. Limpert et al, Nano Lett. 17, 4055 (2017)
Model Experiment
SLIDE 34 Photovoltaic power production (without pn-junction!)
Eg of WZ InAs ≈ 0.39 eV
- S. Limpert et al, Nano Lett. 17, 4055 (2017)
- S. Limpert et al., Nanotechnology 28, 43 (2017)
Single-barrier (thermionic) device Voc > 90% of the bandgap
SLIDE 35 Photovoltaic power production (without pn-junction!)
- S. Limpert et al, Nano Lett. 17, 4055 (2017)
- S. Limpert et al., Nanotechnology 28, 43 (2017)
Single-barrier (thermionic) device Voc > 90% of the bandgap
Eg of WZ InAs ≈ 0.39 eV
SLIDE 36 Thermionic interpretation
Thermionic interpretation: Voc = (k/e) (2+ Ebarrier/kT) ∆Tcarrier Voc ≈ 0.35 V is consistent with ∆Tcarrier ≈ 170 K Since ∆T in this interpretation is the carrier temperature, phonon-mediated heat flow is irrelevant to the efficiency analysis.
Ebarrier
- S. Limpert et al, Nano Lett. 17, 4055 (2017)
SLIDE 37 Controlling the light-absorption hot spot
I-Ju Chen et al. in preparation
I-Ju Chen
SLIDE 38 Evidence of quasi-ballistic extraction of hot carriers
|E|2
d
0.0 0.1 0.2 0.3 0.0 0.1 0.2 0.3
Power (mW)
0.0 0.2 0.4 0.6 5 10 15
ISC (pA) Power (mW)
I-Ju Chen et al. in preparation
I-Ju Chen
SLIDE 39 Acknowledgments
Experiment: Steven Limpert, A. Svilans, I-Ju Chen, Jonatan Fast, A. Burke, M.E. Pistol, S. Fahlvik,
- C. Thelander, S. Lehmann, K. Dick
Theory: Steven Limpert, N. Anttu, M. Josefsson, M. Leijnse Collaboration: Stephen Bremner, UNSW, Sydney
Steven Limpert Martin Josefsson Artis Svilans I-Ju Chen Jonatan Fast
SLIDE 40
