Download Humphrey, Tammy - Quantum Electronics Group

Thermoelectrics: Reversibility and
Efficiency at Maximum power
Tammy Humphrey
Department of Theoretical Physics, University of Geneva
*Email: [email protected] Web: www.humphrey.id.au
Outline
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Background
The Physics of Thermoelectrics
The Thermodynamics of Thermoelectrics
Comparison to other solid state energy
converters and to Carnot cycle
• Efficiency at Maximum power
Brief history of thermoelectrics
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1823 – Seebeck and Carnot
1835 – Peltier effect
1850’s – Kelvin relations and entropy
1931 – Onsager relations
1950’s – Development of Bi2Te3 thermoelectric coolers
1993 – Beginning of investigation of low-dimensional
thermoelectrics
• 2001 to Present – Experimental development of
nanostructured thermoelectrics with significantly higher
efficiency than Bi2Te3
Physics underlying thermoelectrics
Closed Circuit
I
Open Circuit
V0
Underlying thermodynamics…
Open circuit
Finite thermal conductivity at open circuit means that
heat is consumed but no work is done.
Zero efficiency at the crossover from power generation to
refrigeration is the hallmark of an irreversible HE.
What is the limiting ‘electronic’
efficiency of a thermoelectric
power generator/refrigerator?
First: Heat transfer in Carnot cycle
Feynman on reversible heat engines…
The Feynman lectures on Physics, Chapter 44-3
“We need to find an analog of frictionless motion: heat
transfer whose direction we can reverse with only a tiny
change. If the difference in temperature is finite, that is
impossible…”
Heat transfer in thermoelectrics
Carnot Efficiency requires
reversible electron transport
Reversible electron transport
requires equilibrium
“No thermoelectric device can ever reach Carnot efficiency”
H. Littman and B. Davidson, J. Appl. Phys., 32 (2) 217 (1961).
Physics of reversible thermoelectrics
One energy where the effect of the temperature gradient
cancels with that of the electrochemical potential gradient
Physics of reversible thermoelectrics
One energy at which current reverses:
(Carnot limit)
Constant occupation of states = Equilibrium
(despite temperature and electrochemical potential gradients)
“Reversible thermoelectric nanomaterials”, T. E. Humphrey and H. Linke, Phys.
Rev. Lett. 94, 096601 (2005)
Interestingly,
Other heat engines achieve
reversibility in the same way…
Carnot efficiency in thermionic devices
(Carnot limit)
T. E. Humphrey, R. Newbury, R. P. Taylor and H. Linke “A Reversible quantum Brownian
heat engine for electrons” Phys. Rev. Lett. 89, 116801 (2002)
Solar Cells and LEDs
Loss Mechanisms in solar cells
1) Non-absorption of below band-gap photons
2) Lattice thermalisation losses
3) & 4) Junction and contact resistance losses
5) Recombination losses
Finite thermal conductivity
between the sun and the cell
at open circuit means that
heat is consumed but no
work is done.
 Irreversible heat engine
Reversible thermophotovoltaics
Reversibility achieved at open circuit voltage eVOC, when a filter is
used to limit photons exchanged to those with energy equal to the
bandgap, EG. Then:
Efficiency of energy conversion
is:
(Carnot limit)
P. T. Landsburg and G. Tongue, J. Appl. Phys., 51, R1 (1980)
Thermally pumped laser
Efficiency at
population inversion:
H. E. D. Scovil and E. O. Schulz-DuBois, Phys. Rev. Lett., 2, 262 (1959)
Summary of the talk so far:
• Thermoelectric energy conversion can occur
reversibly if particle transport is energy selective (i.e.
heat transfer can be non-isothermal but still isentropic)
• This is fundamentally different from the situation
in cyclic heat engines such as the Carnot cycle
(where isothermal heat transfer is essential for reversibility)
• A range of electronic and photonic heat engines
share with thermoelectric devices the same
mechanism for reversible operation
What about Maximum power?
Finite time thermodynamics
Points out that:
1) In practice, it is never desirable to operate a heat engine
reversibly, as in this limit power output must be zero
2) The difference between the Carnot limit and the actual
efficiency of a practical heat engine does not therefore
represent a ‘true’ measure of the efficiency gain which might
be achieved with further optimization
FFT asks:
1) What is the efficiency of a heat engine which is optimized to
produce maximum power rather than maximum efficiency?
2) How general is this result? Is it applicable to a wide range of
different heat engines?
Finite power production in the ‘Carnot’ cycle
- The Curzon Ahlborn ‘endoreversible’ model
•For Carnot cycle and Fourier law heat transfer [1]:
[1] F.L. Curzon and B. Ahlborn, Am. J. Phys. 43, 22 (1975) “Efficiency of a Carnot engine at maximum power output”
Maximum power in thermoelectrics
“number of
electrons”
E0
Energy
Efficiency at maximum power
1
Ratio of efficiency at MP to Carnot efficiency
0.9
-function
hMP / hC
0.8
CA effic
0.7
0.6
‘thermionic’
0.5
0.4
1D
2D
0.3
3D
0.2
0
0.2
0.4
0.6
1- t
1-t
0.8
1
Acknowledgements
Collaboration partners:
- Ali Shakouri (UCSC)
- Mark O’Dwyer (University of Wollongong, Australia)
- Heiner Linke (University of Oregon)
Support has been provided by:
- ONR
- The Australian research council
- A Marie Curie Incoming International Fellowship
from the European Commission