WO2013035100A1 - Dispositifs thermoélectriques à rendement amélioré - Google Patents

Dispositifs thermoélectriques à rendement amélioré Download PDF

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WO2013035100A1
WO2013035100A1 PCT/IL2012/050355 IL2012050355W WO2013035100A1 WO 2013035100 A1 WO2013035100 A1 WO 2013035100A1 IL 2012050355 W IL2012050355 W IL 2012050355W WO 2013035100 A1 WO2013035100 A1 WO 2013035100A1
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electrical
terminal
region
thermoelectric
heat
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PCT/IL2012/050355
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English (en)
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Yoseph IMRY
Ora ENTIN-WOHLMAN
Jianhua Jiang
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Yeda Research And Development Co. Ltd. At The Weizmann Institute Of Science
Ben Gurion University Of The Negev Research And Development Authority
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Application filed by Yeda Research And Development Co. Ltd. At The Weizmann Institute Of Science, Ben Gurion University Of The Negev Research And Development Authority filed Critical Yeda Research And Development Co. Ltd. At The Weizmann Institute Of Science
Priority to US14/343,168 priority Critical patent/US10777727B2/en
Priority to CN201280054693.1A priority patent/CN103918095B/zh
Priority to EP12790685.7A priority patent/EP2754187B1/fr
Publication of WO2013035100A1 publication Critical patent/WO2013035100A1/fr
Priority to IL231325A priority patent/IL231325A0/en

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    • H—ELECTRICITY
    • H10—SEMICONDUCTOR DEVICES; ELECTRIC SOLID-STATE DEVICES NOT OTHERWISE PROVIDED FOR
    • H10N—ELECTRIC SOLID-STATE DEVICES NOT OTHERWISE PROVIDED FOR
    • H10N10/00—Thermoelectric devices comprising a junction of dissimilar materials, i.e. devices exhibiting Seebeck or Peltier effects
    • H10N10/10—Thermoelectric devices comprising a junction of dissimilar materials, i.e. devices exhibiting Seebeck or Peltier effects operating with only the Peltier or Seebeck effects
    • H10N10/17—Thermoelectric devices comprising a junction of dissimilar materials, i.e. devices exhibiting Seebeck or Peltier effects operating with only the Peltier or Seebeck effects characterised by the structure or configuration of the cell or thermocouple forming the device
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01L—SEMICONDUCTOR DEVICES NOT COVERED BY CLASS H10
    • H01L29/00—Semiconductor devices specially adapted for rectifying, amplifying, oscillating or switching and having potential barriers; Capacitors or resistors having potential barriers, e.g. a PN-junction depletion layer or carrier concentration layer; Details of semiconductor bodies or of electrodes thereof ; Multistep manufacturing processes therefor
    • H01L29/66—Types of semiconductor device ; Multistep manufacturing processes therefor
    • H01L29/68—Types of semiconductor device ; Multistep manufacturing processes therefor controllable by only the electric current supplied, or only the electric potential applied, to an electrode which does not carry the current to be rectified, amplified or switched
    • H01L29/70—Bipolar devices
    • H01L29/72—Transistor-type devices, i.e. able to continuously respond to applied control signals
    • H01L29/739—Transistor-type devices, i.e. able to continuously respond to applied control signals controlled by field-effect, e.g. bipolar static induction transistors [BSIT]
    • H01L29/7391—Gated diode structures

Definitions

  • the present invention relates to thermoelectric devices, and particularly, relates to efficiency-enhancing schemes.
  • thermoelectric effects include devices which rely on physical effects including the Seebeck effect (electrical currents generated by temperature differences in junctions of dissimilar materials), the Peltier effect (emitting and absorbing of heat caused by electrical current flowing through junctions of dissimilar materials), and the Thomson effect (emitting or absorbing of heat by a current-carrying electrical conductor with a temperature gradient).
  • Seebeck effect electrical currents generated by temperature differences in junctions of dissimilar materials
  • Peltier effect emitting and absorbing of heat caused by electrical current flowing through junctions of dissimilar materials
  • the Thomson effect emitting or absorbing of heat by a current-carrying electrical conductor with a temperature gradient.
  • the coefficients of these effects are related. Physically, these effects involve energy interchange between charge carriers and thermal phonons in the materials.
  • thermoelectric properties of materials is a Peltier refrigerator, which uses the Peltier effect to create a heat pump at the junction of two dissimilar materials.
  • the Peltier refrigerator offers the benefits of small size, flexible shape, and lack of circulating fluids. Except for specialized uses which require such advantages, however, current Peltier refrigerators suffer from poor efficiency when compared against conventional vapor- compression fluid (reverse Rankine cycle) refrigerators. Fluid refrigerators typically exhibit effective efficiencies in the order of 50%, whereas the thermoelectric junctions of Peltier refrigerators typically achieve effective efficiencies in the order of 10%.
  • thermoelectric properties of materials include heaters and thermoelectric power generators, and battery chargers. Such devices are typically based on variations in the configuration of the dissimilar materials and the polarity of the electrical current.
  • a Peltier refrigerator being essentially a thermoelectric energy converter, can be configured to serve as a heater by reversing the current flow.
  • present thermoelectric devices typically exhibit poor conversion efficiencies. Nevertheless they are being used in several special situations and many more are envisaged should the efficiency increase significantly.
  • thermoelectric device having a thermoelectric gate interposed between two electric regions. Each electric region is connected to an electrical terminal and a heat conducting, thermal terminal is connected to the thermoelectric gate so as to enable heat transfer between the terminal and the thermoelectric gate, according to embodiments. It should be appreciated that the thermoelectric device is reversible; transfer of heat between the thermal terminal and the thermoelectric gate can cause current flow between the terminals.
  • the advantage afforded by the invention over present thermoelectric devices can be analyzed using the (matrix) equation characterizing thermoelectric linear transport for devices according to embodiments of the invention is:
  • I Q is the heat current exchanged between electrons and phonons in the thermoelectric gate
  • L 2 and L3 are additional thermoelectric transport coefficients of the material of the thermoelectric gate
  • K is the heat conductance between the phonons and electrons in the thermoelectric gate
  • AT /T is the normalized temperature differential between the thermal terminal and the electrical terminals.
  • embodiments of the invention offer the possibility of also adjusting parameters L 2 , L 3 , and K to further optimize device performance.
  • the inclusion of the thermal terminal connected to the thermoelectric gate affords additional opportunities for improving device operation. An example being the use of both temperature difference and voltage across the electrical terminals to cool the thermal one.
  • Fig. 1 is an energy-level model diagram of a thermoelectric device according to various embodiments of the invention.
  • Fig. 2 shows a configuration of a thermoelectric device according to an embodiment of the invention
  • FIG. 3 shows a configuration of a thermoelectric device according to another embodiment of the invention.
  • FIGS. 4 A and 4B show thermoelectric devices according to further embodiments of the present invention employing semiconductors having the same type of doping; but, widely varying in the degree of doping;
  • Fig. 5 is a flow diagram depicting operational steps of the present invention, according to embodiments; and [0014] Fig. 6 shows figure-of-merit curves for thermoelectric device configurations according to embodiments of the invention in comparison with a figure-of-merit curve for a corresponding conventional thermoelectric device.
  • Fig. 7a shows a two localized-state ( and j, points) system coupled to two leads, of temperatures T L and T R , and chemical potentials ⁇ and ⁇ ⁇ (with the choice ⁇ > ⁇ ⁇ and T L > T R ).
  • the phonon bath temperature is7 ⁇ , 3 ⁇ 4 .
  • the localized states are coupled (dotted lines) to the continuum of states in the leads, and are also coupled to the phonon bath (the wavy line).
  • Fig. 7b shows the effective resistors representing the system:
  • the straight arrows indicate the net electronic currents and the wavy one the phonon heat current, with G , G2 R , and an being the conductances of the tunneling and the hopping resistors, respectively.
  • Fig. 8a shows the conductance, ln(G/Go), and thermopower, S; the abscisa gives the number of computations, Ncom.
  • Ncom the number of computations
  • a new random resistor network is generated, and at the subsequent computation, only the central part of the network (within » ⁇ ⁇ ⁇ ⁇ ⁇ , ⁇ / *,3 ⁇ 4*,M. j ji i s replaced by another random configuration.
  • the thermopower is unchanged, while the conductance is more significantly modified.
  • Fig. 9 shows the suggested device: a long (d >> characteristic tunneling length) and low (u» W » K57)barrier separating two electron gases.
  • the transferred electron gets an energy W r f from the LHS thermal bath and deposits it in the RHS one.
  • Fig. 10a shows a schematic illustration of the three-terminal p-i-n junction thermoelectric device. The arrows denote the direction of the electric current.
  • Fig. 10b shows the band structure of the p-i-n junction.
  • the dotted line is the chemical potential at equilibrium.
  • Fig. 10c shows a schematic illustration of the two-terminal ⁇ (heavily s ⁇ -doped) -P- (lightly -doped) junction thermoelectric device.
  • the ?H- junction is similar except that the electric current direction is reversed.
  • Fig. 11a shows the ratio ZT/ZT + as a function of « at different i and 3 ⁇ 4 .
  • ⁇ ⁇ ( 1 , 1 ) (solid curve), (0.2,0.2) (dashed curve), (1.5,0.2) (dotted curve), and (0.2,1.5) (dot-dashed curve).
  • Fig. 1 lb shows the maximum of the ratio of ZT/ZT + .
  • Fig. 11c shows 3 ⁇ 4 TM the value at which such a maximum is reached, as functions of °- and if.
  • thermoelectric cooling device configuration such as a refrigerator
  • thermoelectric energy conversion devices including, but not limited to: heating devices; and thermoelectric energy conversion devices.
  • Devices applying semiconductor junctions play an important role, but are not the only possibility. For example, normal metal-superconductor junctions play important roles in low- temperature (cryogenic) cooling.
  • thermoelectric performance of a material In an effort to improve efficiencies of thermoelectric devices, this invention provides modifying the thermoelectric properties of materials in thermoelectric devices.
  • a "figure of merit" Z is commonl to assess the thermoelectric performance of a material. , (Equation 1)
  • thermoelectric performance increases as the Seebeck coefficient and the electrical conductance increase and as the thermal conductance decreases.
  • a material that is a good conductor of electricity, a good insulator of heat and has a good Seebeck coefficient will have a high figure of merit.
  • electrical conductance and heat conductance are not independent, so that Z cannot be arbitrarily adjusted.
  • the figure of merit is also expressed as a dimensionless constant ZT when multiplied by the average temperature T of the two electrical terminals of the thermoelectric device.
  • the efficiency is defined as the ratio of the delivered power to the consumed one, and it is a simple, monotonically increasing, function of ZT.
  • thermoelectric linear transport for current thermoelectric devices
  • I e is the electrical charge current
  • V Q is the electrical charge contribution to the heat current
  • L j is a thermoelectric coefficient of the material
  • K e ° is the material's electrical charge contribution to the thermal conductance
  • ⁇ is the voltage drop across the two terminals
  • ⁇ IT is the normalized temperature differential across the two terminals.
  • the present invention is directed at enhancing the efficiency of thermoelectric devices.
  • the efficiency may be enhanced by either contacting a thermal terminal configured to supply heat with a thermoelectric device so as to form a three- terminal device or doping the two electrical terminals of a P + - P_ or N + - N_ junction to different degrees.
  • one of two electrical terminal is heavily doped (P + or N + ) while the remaining terminal is lightly doped (N- or P-).
  • light doping one usually means doping concentrations in the range of 10 15 — 10 16 dopants (donors or acceptors) /cc.
  • Heavy doping usually means such concentrations in the range of 10 18 — 10 19 /cc.
  • Fig. 1 is an energy-level model diagram of a thermoelectric device 101 according to various embodiments of the invention.
  • a first electrical terminal 103 i.e., an electrically-conducting connective element
  • a thermal terminal 105 is operative to input heat Q into thermoelectric gate 107.
  • thermal terminal 105 is configured to input Q units of heat for each transferred electron. Typical values of Q are in the range of 3-7 kT (i. e. 0.1 to 0.25 electron volts for room temperature operation).
  • a second electrical terminal 111 is operative to remove charge carriers from thermoelectric gate 107 at an energy E2.
  • W E2 - El.
  • a bath of thermal phonons at a temperature T interact with charge carriers in the thermoelectric gate 107 and transfer energy W to each charge carrier, in order to transverse the thermoelectric gate 107.
  • heat energy of Q Wis transferred to each charge carrier in the thermoelectric gate 107 to establish a charge flow 113.
  • thermoelectric device 101 functions as a cooling device by removing heat Q from an external heat source through thermoelectric gate 107 via the thermal terminal 105, according to embodiments.
  • the thermal terminal 105 is integrally connected with the thermoelectric gate 107.
  • this configuration is non-limiting, and other thermoelectric configurations according to further embodiments of the invention are possible.
  • the semiconducting materials include II-VI family semiconductors, such as BiTe (the work-horse of present thermoelectric devices) or Hgl-xCdxTe (mentioned below for special advantages).
  • materials of the III-V family e.g. GaAs
  • metallic elements and metal-semiconductor interfaces may play a role as well. All this is to be regarded as non-limiting.
  • Fig. 2 shows a configuration of a thermoelectric device 201 according to another embodiment of the invention.
  • a first electrical terminal 203 is in electrical contact with a first electrical localized state 203a within a thermoelectric gate 207, which is connected to a thermal terminal 205.
  • a second electrical terminal 211 is in electrical contact with a second electrical localized state 211a within thermoelectric gate 207.
  • localized states are provided by quantum dots; in another related embodiment of the invention, localized states are provided by diatomic molecules.
  • Fig. 3 shows a configuration of a thermoelectric device 301 according to another embodiment of the three-terminal thermoelectric device.
  • a first electrical terminal 303 is in electrical contact with a first electrical region 303a, which is a positive region in a P-I-N junction 309.
  • a thermal terminal 305 is in thermal contact with a thermoelectric gate 307, which is an intrinsic region in P-I-N junction 309.
  • a second electrical terminal 311 is in electrical contact with a second electrical region 311a, which is a negative region in P-I-N junction 309.
  • Thermoelectric gate 307 provides an effective energy barrier between first electrical region 303a and second electrical region 311a.
  • a semiconductor material is selected whose optical phonon frequency v is close to the electronic band gap W (that is, a material for which hv ⁇ W), This happens in extremely narrow-gap semiconductors like Hgi_ x Cd x Te in which the band-gap varies from 0 to 1.5 eV when "x" is changed.
  • metal-semiconductor- metal junctions may also be formed from metal-semiconductor-metal junctions providing the functionality associated with junctions constructed of Au - p-type Si -Au, or a superlattice separating the two metallic electrodes, where the Fermi level is inside the gap is between the "valence" and “conduction” bands of the superlattice.
  • thermoelectric gate 307 of Fig. 3 An aspect of some embodiments of the invention is that the thermal terminal (e.g., thermal terminal 305 of Fig. 3) is in direct thermal contact with the thermoelectric gate (e.g., thermoelectric gate 307 of Fig. 3). That is, there is no other component, structure, thermal conductor, or other material between the thermal terminal and the thermoelectric gate. In other embodiments of the invention, the thermal terminal is not in direct thermal contact with any electrical region connected to an electrical terminal (e.g., electrical region 303a or electrical region 311a). Furthermore, in some embodiments, the electrical terminals are thermally isolated from the thermal one. It should be appreciated that the energy differential W is substantially greater than kT, wherein k is Boltzmann's constant
  • Figures 4 A and 4B depict alternative embodiments of an efficiency-enhanced thermoelectric device based on differing degrees of "P" or "N" doping.
  • device 370 shown in Fig. 4A has a junction of heavily p-doped semiconductor 350 and lightly p-doped semiconductor 352 in contact with electrical terminals 303 and 311, respectively.
  • device 372 shown in Fig. 4B has a junction of heavily n-doped semiconductor 360 and lightly p- doped semiconductor 362 in contact with electrical terminals 303 and 311, respectively.
  • Non- limiting embodiments have a doping differential of roughly the higher doping level (10 18 19 dopants/cc), the doping differential for n-doped embodiments is similar.
  • FIG. 5 is a flow chart depicting the steps of operation for three-terminal embodiments of thermoelectric devices. After the device is provided in step 540, a voltage is applied collectively across both of the electrically active regions in step 550. Furthermore, in some embodiments the first and the second electrical regions are set at different temperatures by way of a temperature control configuration. For example, such temperature differences may be achieved by contacting each of the electrical regions with a separate heat source, each source having a different temperature.
  • thermoelectric gate configured to produce a temperature between either one of the electrical regions and the thermoelectric gate are also included in the scope of the present invention.
  • step 560 heat is transferred between the thermoelectric gate and the thermal terminal and the direction of the heat transfer is a function of the direction of the current flow between the terminals, according to embodiments.
  • heat transfer causes a corresponding flow of current between the electrical terminals, and analogously, the direction of the resulting current flow is a function of the heat transfer.
  • step 570 charge carriers traverse the thermoelectric gate causing heat transfer between the thermoelectric gate and the thermal terminal.
  • thermoelectric devices Potential advantages offered by the 3-terminal thermoelectric devices, according to embodiments of the present invention are quantitatively illustrated in Fig. 6 as a graph 401 of figure-of-merit curves, for three-terminal ("3-T") thermoelectric device configurations according to embodiments of the present invention in comparison with a figure-of-merit curve 407 for a corresponding conventional two-terminal ("2-T") thermoelectric device.
  • Figure of merit is normalized and dimensionless as ZT in Fig. 6.
  • FIG. 6 the figure of merit for cooling one of the electric terminals is plotted logarithmically on a vertical axis 403 against the parasitic phonon heat conductance Kp on a horizontal axis 405, K p is very often the crucial limiting factor for such devices.
  • Figure-of-merit curve 409 is for a three-terminal device having only a voltage difference across the electrical terminals.
  • Figure-of-merit curve 411 is for a three-terminal device having only a temperature difference between the thermal terminal and the electrical terminals.
  • Figure-of-merit curve 413 is for a three-terminal device having both a temperature difference between the thermal terminal and the electrical terminals and a voltage difference across the electrical terminals.
  • the first example of an embodiment relates to "Thermoelectric Three-Terminal Hopping
  • thermoelectric transport temperature differences can be converted to (or generated by) electric voltages. Such phenomena have already found several useful applications.
  • the need for higher performance thermoelectrics as well as the pursuit of understanding of various relevant processes (especially the inelastic ones) motivated a significant research effort.
  • Theory predicts that high values of the thermopower follow when the conductivity of the carriers depends strongly on their energy. Indeed, in bulk systems, the thermoelectric effects come from the electron-hole asymmetry which is often rather small. However, in nanosystems, due to intrinsic fluctuations, such asymmetry can arise in individual samples in ensembles with electron-hole symmetry on average.
  • the inelastic processes and interference/dissipation effects may play nontrivial roles in thermoelectric transport in nanosystems. It is known that the thermoelectric performance is governed by the dimensionless figure of merit ZT, where T is the 7 — rr ' t n 4- r - 3 ⁇ 4
  • K g and K p h the electronic and the phononic heat conductivities, respectively.
  • K g and Kp ⁇ can be smaller in nanosystems than in bulk ones, opening a route for better thermoelectrics.
  • thermoelectric transport in small one-dimensional (ID) nanosystems accomplished via inelastic phonon-assisted hopping is considered, and that such interactions lead to several nontrivial properties.
  • Conclusions are drawn for the simple, but important, two localized-state junction in which hopping is nearest-neighbor.
  • i labels the localized states, of energies Z3 ⁇ 4, and ⁇ ( ⁇ ) marks the extended states in the left (right) lead, of energies ' *" ⁇ ' (energies are measured from the common chemical potential, taken as zero).
  • the matrix element (in units of energy) coupling the localized states to each other is Ji +i, and those coupling them to the lead states are Ji ; k(p> . Both are exponentially decaying, with a localization length ⁇ , e.g.
  • ⁇ is a dimensionless e-ph coupling constant.
  • the transport through the system is governed by hopping when the temperature is above a crossover temperature, ⁇ , estimated below for the most important two-site case. At lower temperatures the dominant transport is via tunneling.
  • Fig. 7a The two-site example of the system is depicted in Fig. 7a.
  • the tunneling conduction from, say, site i to the left lead can be accomplished by elastic processes with a transition rate where Jij are the Fermi distribution and the density of states of the left lead.
  • the corresponding linear interface conductance is then "
  • site 1 (2) is in a good contact with left (right) lead, we may assume that the local chemical potential and temperature there are and The transport is dominated by the hopping from 1 to 2 when the temperature is higher than ⁇ . This temperature is estimated from the requirement that the thermal-equilibrium (elastic) tunneling conductance across the former is given by the transmission where the tunneling rates are
  • thermoelectric linear transport Three-terminal thermoelectric linear transport.
  • the electronic particle current through the system is
  • L2, L3, and Kpe are related to AE, because Q vanishes with Z3 ⁇ 47.
  • the transport coefficients L 2 (L 3 ) correspond to, e.g., generating electronic current (energy current) via the temperature difference AT.
  • this process performs as a refrigerator: Electric current pumps heat current away from the phononic system and cools it down. The efficiency of such a process will be discussed below.
  • thermopower S here we use the three-terminal thermopower of this process.
  • thermoelectric application Three-terminal figure of merit.
  • the three-terminal geometry suggests novel possibilities for thermoelectric applications. For example, when ⁇ ⁇ 0 and ⁇ > 0, the setup is a refrigerator of the local phonon system, whose efficiency is given by the rate of the heat pumped from the phonon system to the work done by the electrical component,
  • Eq. (11) of this example is generalized by adding the elastic transmission, the tunneling conductance G e i, to the hopping conductance G, and the elastic component, Lj e , to Lj.
  • the elastic transmission does not contribute to L2, L3, and Kpe, which are related to the heat transfer between the r*. f electronic and phononic systems.
  • the phonon heat conductance Kp, replacing ⁇ ' Q " the total heat current from the left to the right lead ( ⁇ is now also the temperature difference for the phononic systems in the left and right leads).
  • the wasted work is due to the elastic conductance and the unwanted heat diffusion, and Z ' i ' is limited by the ratio of the waste to the useful powers.
  • K PP can be limited by the contact between the system and the leads. Hence the ratios can be made small and i can still be large.
  • the three-terminal device can also serve as a heater and as a thermoelectric battery, where the same figure of merit describes the efficiency .
  • thermopower coefficients S and S p are completely determined at the left and right boundaries, despite the fact that all the transport coefficients are determined by both boundaries and "bulk".
  • FIG. 8a depicts results for the thermopower S and the conductance G, which demonstrate the sensitivity of G to changes of the sample's configuration, to which S is practically immune. As can be further seen in Fig. 8b, sites located away from the boundaries have an exponentially minute effect on the latter.
  • a second non-limiting example of an embodiment relates generally to "High-ZT Thermoelectric Activated Transport Above An Effective Barrier” and specifically relates electron transport through a barrier bridging two conducting leads is considered as a model system.
  • the barrier is low (but higher than the thermal energy ⁇ B T ) and wide so that transport is dominated by thermal activation.
  • the leads have slightly different temperatures and chemical potentials.
  • the linear transport (“Onsager") matrix is evaluated and found to be very favorable for thermoelectric energy conversion. This is due to the fact that each transferred electron carries an energy roughly equal (within ⁇ ⁇ ⁇ « W) to the barrier height W.
  • the purely electronic figure of merit is given by * "' ⁇ ; 3 ⁇ 4»r s ⁇ .
  • thermoelectric transport temperature differences can be converted to (or generated by) electric voltages. Such phenomena have already found several useful applications.
  • the need for higher performance thermoelectrics as well as the pursuit of understanding of various relevant processes (especially the inelastic ones) motivated a significant research effort.
  • Theory predicts that high values of the thermopower follow when the conductivity of the carriers depends strongly on their energy near the Fermi level, EF.
  • the thermoelectric effects come from the electron-hole asymmetry which is often, unfortunately, rather small.
  • thermoelectric performance is governed by the dimensionless figure of merit ZT, where T is the common, average, temperature of the system and ⁇ ⁇ r * ; tiii T 3 ⁇ 4 ⁇ ⁇ ⁇ , with G being the electrical conductance, S the Seebeck coefficient, and Ke and Kph the electronic and the phononic heat conductances, respectively. Both Ke and Kph can be smaller in nanosystems than opening a route for better thermo-electrics.
  • junction model Here we consider a very simple system where the electronic transport is effectively funneled to a narrow band. It is contemplated, an ordinary tunnel junction in one dimension (ID, generalized later), depicted in Fig. 9.
  • ID an ordinary tunnel junction in one dimension
  • the barrier is chosen so that its height W (measured from the averaged chemical potential ⁇ ) and thickness, d, satisfy » 3 ⁇ 4 » i ⁇ d > > l/v3 ⁇ 4 , ⁇ /A . ( i s
  • the dominant transport is via thermal activation above the barrier and not by quantum-mechanical tunneling. It is assumed that the barrier is tapered (see Fig. 9) so that the transmission through it changes rather quickly from 0 to 1 when the electron energy E increases through W. This is certainly the case in the ID clean tunnel junction of the type discussed here, or in the quantum point contact. Its validity in a high dimensional system will be confirmed later on. When some disorder exists, rendering the electron motion diffusive, it makes sense that the transmission still changes from 0 to 1 when the electron energy increases through W. This increase may become slower than in clean systems, but that should not change the qualitative behavior.
  • Ke/G is proportional to the variance of that energy.
  • the latter obviously vanishes for a very narrow transmission band. In this case the transmission band is the range of a few ⁇ above W.
  • Ke is of the order of (KBT/W)2.
  • thermoelectric linear transport problem Formulation of transport and calculation of coefficients in one dimension (ID).
  • ID thermoelectric linear transport problem
  • a vacuum junction has too high a barrier for most applications.
  • the ballistic quantum point contact is a very effective realization of the model, when biased in the pinch-off regime and in the region where activated conduction is dominant. It requires however rather high technology and can handle only small powers.
  • embodiments as follows: [0073] A metal-semiconductor-metal junction, with a properly chosen difference between work function and electron affinity (an example might be Au - p-type Si -A u). A large area will increase the power of the device.
  • thermoelectricity For semiconducting systems, in an embodiment, first an intrinsic small-gap semiconductor, such as BiTe, the current work-horse of applied thermoelectricity.
  • BiTe intrinsic small-gap semiconductor
  • the model is via such a semiconductor, e.g., n-doped such that the Fermi level is, say, (5-10) ⁇ below the conduction band and much further from the valence band.
  • the conduction band should then play the role of our activation barrier.
  • a third non-limiting example of an embodiment relates to "Semiconductor Junction Thermoelectric Devices: Avoiding Electron-Hole Cancelations and Improving Performance".
  • thermoelectric devices Two schemes of thermoelectric devices based on p-i-n and p + -p- (or n + -n.) junctions we examined.
  • the unifying key feature is the avoidance of the cancelation of the electron and hole contributions to the relevant thermopower. This is achieved in a three-terminal geometry or with a homopolar two-terminal one.
  • the three-terminal thermoelectric device is based on a p-i-n junction where the intrinsic region is contacted with a hot reservoir whereas the p and n regions are at lower temperatures.
  • electrons or holes experience step-like barrier transport.
  • the figure of merit and the power factor in both schemes is estimated and find that they can be enhanced in certain parameter regimes.
  • the figure of merit of the junction can be higher than that of the uniformly-doped phase of the same material.
  • Thermoelectric energy conversion has stimulated much research on fundamentals and applications for decades. For a long time, people strove to find good thermoelectric materials where the figure of merit ZT is high.
  • fvS*; + is actually limited by several competing transport properties, the conductivity ⁇ , the Seebeck coefficient 5, and the electronic (phononic) thermal conductivity ⁇ ⁇ ( ⁇ ⁇ ), which makes high ZT hard to achieve.
  • M-S Mahan and Sofo
  • the three- terminal figure of merit benefits from a "selection" of the energy change ⁇ ⁇ . ⁇ > either via the electronic structure or via the bosonic spectrum so that the variance of can be small. The latter can be achieved also by a small bandwidth of the "selected" bosons.
  • the merits of the three- terminal configuration are several, (i) There is no restriction on the electronic bandwidth [or other parameters prerequisites for a small variance of ⁇ (£)] as the electronic thermal conductivity K e does not appear in the three-terminal figure of merit; (ii) Smaller effective boson bandwidths can only make the bosonic thermal conductance K pp smaller, which improves 2r, (iii) In general, if, e.g., due to momentum or energy conservation (a "selection"), only the bosons in a small energy range are involved in the transitions, the effective bandwidth can also be small. As a possible candidate, optical phonons have small band-widths (see Table I) and their coupling with carriers is strong.
  • thermoelectric configuration Exploiting the three-terminal thermoelectric configuration as well as the normal two- terminal one, two schemes of embodiments of devices based on p-n and related junctions are provided.
  • the intrinsic region of a p-i-n junction is contacted with a thermal terminal forming a three -terminal device.
  • a thermal terminal forming a three -terminal device.
  • thermopower (or n + -n.) junctions are provided.
  • the device is in the two-terminal geometry where p + (heavily p doped) and p. (lightly p doped) (or n + and n.) regions are coupled to reservoirs with different temperatures. We find there are parameter regions where, by tuning the height of the barrier, such junctions can have higher figure of merit and power factor than the same uniformly-doped phase.
  • the unifying feature of the two schemes is the absence of electron-hole cancelations in the relevant thermopower. In the first scheme, the reason is that the three-terminal thermopower is proportional to the energy difference between the final and initial states which is positive definite for both charge carriers. In the second scheme, it is because there is only a single type of carriers.
  • a p-i-n junction made of "extremely narrow-gap semiconductors".
  • the structure is depicted in Fig. 10. It can be viewed as an analog of the p-i-n photo-diode, where photons are replaced by phonons i.e., the phonon-assisted inter-band transitions lead to current generation in the junction.
  • the band gap is then required to be a bit smaller than the phonon en- ergy.
  • the optical phonon energy is in acoustic phonons as well as optical ones. For simplicity, here we consider a direct band semiconductor system and assume that the contribution from the optical phonons is the dominant one.
  • thermoelectric trans ort equations are written as
  • / and IQ are the electronic charge and heat currents flowing between the two electric terminals, e > 0 is the absolute value of the electronic charge, IQ is the heat current from the thermal terminal to the two electric ones, G M is the conductance in the inelastic channel, K° is related to the electronic heat conductance between the electric terminals, and K PE is that between the thermal terminal and the electric ones.
  • the transport coefficients L L 2 , and L 3 are related to the currents induced by the temperature differences (thermopower effect) and the current- induced temperature differences (refrigerator and heater effects).
  • S/z (ST) is the chemical potential (temperature) difference between the two electric terminals
  • AT is the difference between the temperature of the thermal terminal and the average temperature of the two electric
  • A is the phonon branch index and M qA is the coupling matrix element
  • V is the volume of the system
  • C (eft) is the operator creating an electron (hole) in the conduction (valence) band. Due to momentum or energy conservations, phonons involved in such processes can be in a small energy range. For indirect band semiconductors, those phonons can be acoustic phonons as well as optical ones. For simplicity, here we consider a direct band semiconductor system and assume that the contribution from the optical phonons is the dominant one.
  • the equilibrium distribution functions at the appropriate reservoirs In the linear-response regime, one may use the equilibrium distribution functions at the appropriate reservoirs.
  • T p temperature of thermal terminal
  • n ⁇ is the number of relevant branches (assumed to be coupled similarly to the electrons in the intrinsic region) of the optical phonons
  • D p is the effective density of states for the phonons that are involved in the inter-band transition processes. It depends on whether the momentum is conserved and possibly on the width of the phonon band.
  • the transport coefficients are determined by studying the currents at a given bias and/or a temperature difference.
  • the key relation is the continuity equation
  • Ia are the charge currents
  • q a are the charges of the electron and the hole
  • T a are the carrier lifetimes
  • g p is the carrier generation rate given in Eq. (6) of this example.
  • E — aE ⁇ (eL) is the built-in electric field in the intrinsic region.
  • n a n a>g + n a>n
  • Equation (11) of this example is a generalized example, which has a single microscopic channel. When many inelastic processes coexist, the contribution of each process is weighed by its conductance. From Eqs. (4) and (11) of this example, we find that the ideal three- terminal figure of merit is
  • the ideal figure of merit for the photon-assisted transport under the same conditions i.e., the photonic temperature is equal to the phononic one
  • thermoelectric transport equations are written as
  • the three-terminal figure of merit can be obtained by optimizing the efficiency of, say, a refrigerator working at 1 ' - ! (but with finite & and : ⁇ ).
  • the optimized efficiency is determined by the "three-terminal figure of merit" which leads to Eq. (2) of this example.
  • the diode conductance is f - ⁇ f ⁇ ' t ' A ⁇ * ⁇ « ' « «.
  • thermoelectric figure of merit of a ? , ;! junction has been discussed in the literature. It was found that, due to the bipolar thermal current, the figure of merit of a junction cannot exceed unity. This is consistent with the physical picture: the coexistence of electrons and holes not only spoils the Seebeck coefficient (the Seebeck coefficients of electrons and holes have opposite signs, as they carry opposite charges) but also introduces additional bipolar thermal current channels. Hence, it is crucial to increase the electron-hole asymmetry, or even to use junctions with a single type of doping.
  • the absolute value of the Seebeck coefficient of the junction is iSi > 4-H 1 ⁇ 2r ⁇ (43 ⁇ 4-/ «r).
  • the conductivity and the electronic thermal conductivity scale almost linearly with the carrier density. Since only a fraction, ⁇ the carriers is transmitted through the junction, the electric conductivity and thermal conductivity are approximately - « ? «tj?r- ; 3 ⁇ 4 * ? l and >3 ⁇ 4 ⁇ 5 ⁇ tl71 ⁇ 2r;,respectively.
  • the figure of merit of the junction is
  • Fig. 11a The figure indicates that the proposed scheme can indeed enhance ZT significantly when a+ is small, i.e., for small absolute values of the Seebeck coefficient. Plots of the maximum of the ratio of 2r.m as well as the value at which such a maximum is reached, as functions of a+ and ⁇ + are presented in Figs, l ib and 1 lc, respectively. The figure of merit of the junction ZT is plotted in Fig. l id, from which we can see that small ⁇ + and large a+ are favorable for high ZT. It is proposed and studied two schemes of thermoelectric devices using f ⁇ « anc i related junctions.
  • the first scheme is based on the "three-terminal" geometry of thermoelectric applications, where inelastic processes play a crucial role. It has been shown that a high thermoelectric figure of merit can be achieved in this geometry in several nanosystems, where only one microscopic channel in which the relevant electronic energy is fixed, is available. In this paper we derived the figure of merit for the multi-channel case. We find that, when only the inelastic processes are considered, the figure of merit is the ratio of the square of the mean value of energy difference between final and initial states to its variance with the average weighed by the conductance of each microscopic process. A small variance in the energy exchange is then favorable for a high figure of merit. The realistic figure of merit including other processes, Eq. (2) of this example, is also derived.
  • the second proposal is to enhance the thermoelectric efficiency by exploiting i' (or "'' -) junctions in the two-terminal geometry.
  • i' or "'' -) junctions in the two-terminal geometry.
  • the junctions can have a better thermoelectric performance than the uniformly-doped phase of the same material.
  • the cancelation of the Seebeck coefficient of electrons and holes in junction is eliminated in such junctions -P -or » +- « -) with only a single type of carriers in the two-terminal geometry. It is also noted that there is no such cancelation in three-terminal thermoelectric device which exploits the three-terminal Seebeck coefficient.
  • M-S suggested a narrow electronic band for elastic two-terminal transport to achieve high ZT.
  • the latter can be achieved via the narrow bandwidth of optical phonons or by controlling the initial and final electronic states by a barrier higher enough than T.
  • a small ideal figure of merit often entails a reduced realistic figure of merit, unless the coupling between the carriers and the photons is strong.
  • a narrow distribution of spectra can be obtained by confinement, such as in a cavity with only a single mode that is preferentially occupied. In that case we expect the cooling efficiency to be largely enhanced.
  • the working temperature range is 50 ⁇ 90 K.
  • the working temperature can be as high as 200 ⁇ 300 K thanks to the high frequency of the optical phonons there.
  • the power factor of the three- terminal device, P ⁇ Gm (Wji) 2 — Gj n u 2 can be larger than that of the uniformly-doped phase of the same material, i.e., ⁇ G e i(k B T) 2 exp[E g /k B T], at the same conditions discussed above.
  • the thermalization rate of the optical phonons physically governed by their collisions with other excitations such as carriers and acoustic phonons in the thermal terminal, should be large enough for high power output.

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  • Cooling Or The Like Of Semiconductors Or Solid State Devices (AREA)

Abstract

La présente invention a trait à un dispositif thermoélectrique à deux jonctions, à trois bornes et à rendement amélioré qui est commandé par des paramètres de température et de tension réglables de façon indépendante.
PCT/IL2012/050355 2011-09-08 2012-09-09 Dispositifs thermoélectriques à rendement amélioré WO2013035100A1 (fr)

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CN201280054693.1A CN103918095B (zh) 2011-09-08 2012-09-09 效率增强的热电装置
EP12790685.7A EP2754187B1 (fr) 2011-09-08 2012-09-09 Methode d'utilisation de dispositifs thermoélectriques à rendement amélioré
IL231325A IL231325A0 (en) 2011-09-08 2014-03-05 Thermoelectric devices with increased efficiency

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Cited By (3)

* Cited by examiner, † Cited by third party
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WO2014120841A1 (fr) * 2013-01-29 2014-08-07 University Of Rochester Moteur thermique et procédé pour collecter une énergie thermique
WO2018061001A3 (fr) * 2016-09-28 2018-05-11 Yeda Research And Development Co. Ltd. Dispositif thermoélectrique
CN113330590A (zh) * 2019-03-26 2021-08-31 绿色能源未来有限责任公司 半导体热电发生器

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EP0526897A2 (fr) * 1991-08-06 1993-02-10 Nec Corporation Dispositif à effet tunnel à trois électrodes
US20030218209A1 (en) * 2002-05-25 2003-11-27 Xemod, Inc. Microwave field effect transistor structure
US20080108227A1 (en) * 2006-02-06 2008-05-08 Matsushita Electric Industrial Co., Ltd. Method for producing single electron semiconductor element
DE102007050741A1 (de) * 2007-10-22 2009-04-23 O-Flexx Technologies Gmbh Thermoelektrischer Generator

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EP0526897A2 (fr) * 1991-08-06 1993-02-10 Nec Corporation Dispositif à effet tunnel à trois électrodes
US20030218209A1 (en) * 2002-05-25 2003-11-27 Xemod, Inc. Microwave field effect transistor structure
US20080108227A1 (en) * 2006-02-06 2008-05-08 Matsushita Electric Industrial Co., Ltd. Method for producing single electron semiconductor element
DE102007050741A1 (de) * 2007-10-22 2009-04-23 O-Flexx Technologies Gmbh Thermoelektrischer Generator

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2014120841A1 (fr) * 2013-01-29 2014-08-07 University Of Rochester Moteur thermique et procédé pour collecter une énergie thermique
WO2018061001A3 (fr) * 2016-09-28 2018-05-11 Yeda Research And Development Co. Ltd. Dispositif thermoélectrique
CN113330590A (zh) * 2019-03-26 2021-08-31 绿色能源未来有限责任公司 半导体热电发生器

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