Thermoelectric material with large power factor

Abstract

A structure for use in a thermoelectric generator, comprising a matrix comprising an arrangement of cavities, wherein the matrix is a semi-conductor. A dopant substance is disposed within the cavities and configured to modify the potential energy band profile of the matrix, such that, the potential energy band profile becomes non-uniform along a transport direction of the structure. The transport direction is the direction which, in use, current is configured to flow through the structure. The spacing between cavities along the transport direction is substantially consistent throughout the matrix.

Description

[0001] THERMOELECTRIC MATERIAL WITH LARGE POWER FACTOR

[0002] The invention relates generally to a thermoelectric material. More particularly, but not exclusively, the invention relates to a thermoelectric material comprising a plurality of cavities filled with a dopant substance.

[0003] Background

[0004] Thermoelectric generators (TEGs) convert temperature gradients across a material directly into electricity, and vice versa. They can play a major role in the search for sustainable paths for energy harvesting and cooling in a variety of applications.

[0005] However, large scale exploitation of TEGs has been limited by the high prices, toxicity, scarcity, and the low efficiencies of the prominent thermoelectric (TE) materials. Thermoelectric performance is quantified by the figure of merit ZT = r>S2T (KeKi,). where a is the electrical conductivity, S is the Seebeck coefficient, T is the absolute temperature, and Keand KL are the electronic and lattice parts of the thermal conductivity, respectively. The product aS2is called the power factor (PF). Over the last two decades, progress on thermoelectric materials has been rapidly expanding with the synthesis of a myriad of new materials and their alloys, while ZTs increased by more than two-fold reaching values close to ZT ~ 3 in some cases. Most of this increase is a result of thermal conductivity reduction through nano structuring and defect engineering, which increases phonon scattering. However, progress relating to reductions to thermal conductivity via nano structuring is slowing down.

[0006] It is becoming increasingly clear that any further benefits to ZT must now come from power factor ( .S'2) improvements, which has not experienced similar progress thus far. The lack of progress in the power factor is attributed to the adverse interdependence of the electrical conductivity ( ) and Seebeck coefficient (.S') via charge carrier density, which proves very difficult to overcome. Nano structuring techniques have been proposed to target improvements in o without strong reductions in S, and vice versa, to improve the power factor.

[0007] For improvements in . material designs that take advantage of modulation doping and gating have been proposed. These designs attempt to create dopant-free material channels with high mobility and conductivity. Modulation doping refers to the addition of a donor material to a base material which donates charge carriers to the base material such that the charge carriers are spatially separated from the donor material. Having the charge carriers move away from the donor reduces carrier-donor scattering, so modulation-doped semiconductors have very high charge carrier mobilities.

[0008] For the improvements in S, energy filtering of charge carriers is implemented by introducing potential barriers along the transport path of the charge carriers. The addition of a potential barrier favours the transport of hot, high energy charge carriers over cold, low energy charge carriers, thereby leading to increasing the energy of the current flow, and therefore the Seebeck coefficient and Seebeck voltage. Energy filtering has been attempted in nanocomposites and superlattices, where the grain / grain- boundary system in a variety of materials can allow for energy filtering.

[0009] The approaches described above have been used to achieve marginal increases in power factors. However, the aforementioned interdependence of the electrical conductivity ( ) and Seebeck coefficient (.S') via the carrier density prevents either of these approaches from providing higher power factors.

[0010] The present invention was devised with the foregoing in mind.

[0011] Summary of Invention

[0012] According to a first aspect of the invention, there is provided a structure for use in a thermoelectric generator.

[0013] The structure may comprise a matrix formed of, or comprising, a semi-conductor material, wherein the matrix comprises an arrangement of cavities. The matrix being formed of a semi-conductor may refer to the matrix itself being a semi-conductor.

[0014] The matrix may be a crystalline semi-conductor. The matrix be a semi-conductor which is at least partly crystalline (e.g., semi-crystalline). The presence of cavities may enable the insertion of dopant substances at regular intervals without substantially increasing the number of impurities in the structure of the matrix.

[0015] The semi-conductor material may comprise dopant atoms. The semi-conductor material may be positively doped. The semi-conductor material may be negatively doped. The semi-conductor material may be undoped.

[0016] The cavities may be a plurality of holes extending at least partially through the matrix. The cavities may be a plurality of holes extending at least partially through the matrix substantially perpendicular to the transport direction. The cavities may be a plurality of holes extending through the matrix between an upper and lower surface of the matrix. The cavities may be cylindrical, or substantially cylindrical, holes. The cavities may be holes which are cylindrical but with non-circular cross-sections.

[0017] The structure may comprise a dopant substance disposed within the cavities and configured to modify the potential energy band profile of the matrix, such that, the potential energy band profile becomes non-uniform along a transport direction of the structure .

[0018] The dopant substance may be an electrolyte. The dopant substance may be an electrolyte with redox couple species, wherein the redox level of the electrolyte differs from the Fermi energy of the semi-conductor material.

[0019] The dopant substance may be a conductor, wherein the workfunction of the conductor differs from the Fermi energy of the semi-conductor material.

[0020] The dopant substance may be a semiconductor, wherein the Fermi energy of the semiconductor differs from the Fermi energy of the semi-conductor material.

[0021] The transport direction may be the direction which, in use, current is configured to flow through the structure.

[0022] The spacing between adjacent cavities along the transport direction may be consistent throughout the matrix. The spacing between adjacent cavities along the transport direction may be substantially consistent throughout the matrix. The spacing between adjacent cavities along the transport direction may fall within a predetermined range.

[0023] The average distance between adjacent cavities along the transport direction may be less than three times the energy relaxation mean-free-path of charge carriers in the semiconductor material. The average distance between adjacent cavities along the transport direction may be less than two times the energy relaxation mean-free-path of charge carriers in the semi-conductor material. The average distance between adjacent cavities along the transport direction may be less than one and a half times the energy relaxation mean-free-path of carriers in the semi-conductor material.

[0024] Having the distance between adjacent cavities on the order of the mean-free-path may help to prevent a significant portion of charge carriers from losing too much energy after overcoming the potential barriers introduced by the dopant substances.

[0025] The average distance between adjacent cavities along the transport direction may be between 5-200nm. The average distance between adjacent cavities along the transport direction may be between 5-150nm.

[0026] The average distance between adjacent cavities along the transport direction may be between 10-200nm. The average distance between adjacent cavities along the transport direction may be between 10-150nm.

[0027] The average distance between adjacent cavities along the transport direction may be between 20-200nm. The average distance between adjacent cavities along the transport direction may be between 20-150nm.

[0028] The average distance between adjacent cavities along the transport direction may be between 50-200nm. The average distance between adjacent cavities along the transport direction may be between 50-150nm.

[0029] Having the distance between adjacent cavities within these ranges may ensure that the doping substances provide potential energy barriers which allow for energy filtering without being too large. The porosity of the matrix due to the cavities may be between 10-60% by volume. The porosity of the matrix due to the cavities may be between 20-50% by volume. The porosity of the matrix due to the cavities may be between 20-40% by volume.

[0030] Having a porosity within these ranges may help to prevent the scattering effects from being too large whilst providing sufficient space for dopant substances as required to provide the energy filtering.

[0031] The average cavity diameter may be between 0-150nm. The average cavity diameter may be between 10-150nm. The average cavity diameter may be between 15-150nm.

[0032] The average cavity diameter may be between 0-100nm. The average cavity diameter may be between 10-100nm. The average cavity diameter may be between 15-100nm.

[0033] The average cavity diameter may be between 0-50nm. The average cavity diameter may be between 10-50nm. The average cavity diameter may be between 15-50nm.

[0034] The average cavity diameter may be between 0-20nm. The average cavity diameter may be between 10-20nm. The average cavity diameter may be between 15-20nm.

[0035] In the case of electron transport, the dopant substance may be configured to modify the shape of the conduction band potential energy profile of the matrix by lowering the conduction band potential energy profile proximate the cavities.

[0036] In the case of electron transport, the dopant substance may be configured to modify the shape of the conduction band potential energy profile of the matrix by: lowering the conduction band potential energy profile proximate the cavities below the Fermi energy of the matrix; and keeping the conduction band potential energy profile energy within 0-5kflT of the Fermi energy of the matrix in regions distal from the cavities.

[0037] In the case of hole transport, the dopant substance may be configured to modify the shape of the valence band potential energy profile of the matrix by increasing the valence band potential energy profile proximate the cavities. In the case of hole transport, the dopant substance may be configured to modify the shape of the valence band potential energy profile of the matrix by: increasing the valence band potential energy profile proximate the cavities above the Fermi energy of the matrix; and keeping the valence band potential energy within 0-5kflT of the Fermi energy of the matrix in regions distal from the cavities.

[0038] According to a second aspect of the invention, there is provided a thermoelectric generator comprising the thermoelectric structure of the first aspect.

[0039] Brief description of the drawings

[0040] The invention will now be described, by way of example only, with reference to the accompanying drawings, in which:

[0041] Figures la and 1c show schematic plan views of a thermoelectric structure of the present invention; Figure lb shows a schematic cross-sectional view of the structure of Figure la;

[0042] Figure 2 shows a schematic plan view of a thermoelectric generator comprising the thermoelectric structure of Figure la;

[0043] Figure 3 shows a simplified schematic of a band structure obtained via traditional modulation doping;

[0044] Figure 4a shows simulated power factors as a function of charge density, Figure 4b shows how the conduction band varies with charge density and how this corresponds to the different power factor regions, and Figure 4c shows how the Seebeck coefficient, conductivity, and power factor vary as the Fermi level moves relative to the conduction band potential energy profile;

[0045] Figures 5a, b, and d, show the conduction band potential profile for a semi-conductor before and after an electrolyte is brought into contact; and Figures 5c and 5e show the simulated charge density in the semi-conductor after it is brought into contact with the electrolyte; Figures 6a and 6c show the simulated conduction band potential energy profile for structures of the present invention; and Figures 6b and 6d show the simulated charge density for structures of the present invention;

[0046] Figure 7a shows schematics for matrix geometries with different degrees of porosity, ranging from 10% up to 60%; Figure 7b shows the simulated power factors for each of the matrix geometries of Figure 7a;

[0047] Figure 8a shows simulated conduction band potential energy profiles for structures of the present invention; Figures 8b and 8c show simulated transport distribution functions for structures of the present invention;

[0048] Figures 9a-c respectively show simulated conductivities, simulated Seebeck coefficients, and simulated power factors, as a function of charge density for structures of the present invention;

[0049] Figures lOa-f respectively show simulated power factors as a function of charge density for thermoelectric structures of the present invention having different porosities;

[0050] Figures lla-d respectively show simulated conduction band potential energy profiles, simulated transports distribution functions, and simulated power factors as a function of charge density, for structures of the present invention wherein the matrix material is doped; and

[0051] Figures 12a-d respectively show simulated power factors as a function of charge density for thermoelectric structures of the present invention having different porosities, with and without conducting cavities.

[0052] Detailed description

[0053] Figure la shows a schematic plan view of a structure 100. Figure lb shows a schematic sectional side view of the structure 100. The structure 100 is a thermoelectric structure. The structure 100 is for use in a thermoelectric generator. The structure 100 can also be for use in a thermoelectric cooler. The structure 100 comprises a matrix 101 formed of, or comprising, a semi-conductor material. The matrix 101 can be a semi-conductor. The matrix 101 can be a crystalline semi-conductor. As is customary, the term “semi-conductor material” herein refers to materials comprising an energy band-gap separating valence and conduction bands. For example, the matrix 101 can be formed of, or comprise, doped or undoped Silicon, Germanium, Indium arsenide, Gallium arsenide, Indium antimonide, or half-Heuslers.

[0054] The matrix 101 comprises an arrangement of cavities 102. The cavities 102 are openings within the matrix 101 into which dopant substances can be disposed. The dopant substances in the cavities are configured to provide charge carriers in the matrix 101. The semi-conductor material can be n-type doped, p-type doped, or undoped, prior to the addition of charge carriers from the dopant substances.

[0055] In the example of Figures la and lb, each cavity 102 is a cylindrical hole extending between an upper and lower surface of the matrix 101. In other examples, the cavities 102 have a non-circular cross-section, and can form square, rectangular, or other shaped cavities. In other examples, the cavities 102 do not extend fully between upper and lower surfaces of the matrix 101, and instead only extend partially through the matrix 101.

[0056] The cavities 102 are arranged regularly throughout the matrix 101. In the example, of Figure 1, the cavities 102 are arranged is a simple square grid but, in other examples, the cavities can be arranged in a rectangular grid, triangular grid, or any other repeating grid pattern. In some examples, the cavities 102 can be staggered, as in Figure 1c.

[0057] As is explained below with reference to Figure 2, the thermoelectric structure 100 is configured for use in a thermoelectric generator, or thermoelectric cooling device. The direction in which current flows through the matrix 101 when the structure 100 is in use as part of a thermoelectric generator is referred to as the “transport” direction.

[0058] In some examples, the average distance between adjacent cavities 102 is consistent throughout the matrix along the transport direction. In some examples, the average distance between adjacent cavities 102 is consistent throughout the matrix along the transport direction whilst the spacing is irregular in directions perpendicular to the transport direction.

[0059] In some examples, the distance between adjacent cavities 102 throughout the matrix along the transport direction is substantially regular such that the distance between each pair of adjacent cavities falls within a predetermined range of distances.

[0060] In other examples, the cavities 102 are pores. The pores can be spherical or approximately spherical, and can be arranged in a repeating lattice such as a simple cubic lattice. In examples using pores, the spacing along the transport direction should be regular, or substantially regular, throughout the matrix 101, but can be irregular in directions perpendicular to the transport direction.

[0061] In some examples, the cavities 102 are arranged without a repeating pattern.

[0062] The size and arrangement of cavities 102 within the matrix 101 is discussed in greater detail later on in the description.

[0063] The structure 100 comprises a dopant substance 103. The dopant substance 103 is disposed within the cavities 102. The dopant substance 103 is configured to modify the potential energy band profile of the matrix 101.

[0064] The dopant substance 103 can be configured to transfer charge carriers (i.e ., electrons or holes) to the matrix 101. The dopant substance 103 can be configured to induce transfer of charge carriers (i.e., electrons or holes) into the matrix 101. When the structure 100 forms part of a thermoelectric generator, the dopant substance 103 can induce transfer of charge carriers from electrical contacts into the matrix 101.

[0065] In some examples, the dopant substance 103 is a semiconductor. In some such examples, the dopant substance 103 can be a semiconductor having a Fermi energy greater than the Fermi energy of the matrix 101 for negative doping. In other such examples, the dopant substance 103 can be a semiconductor having a Fermi energy less than the Fermi energy of the matrix 101 for positive doping. In some examples, the dopant substance is an electrolyte with redox couple species. In some such examples, the redox level of the electrolyte can be greater than the Fermi energy of the matrix 101 for negative doping. In other such examples, the redox level of the electrolyte can be less than the Fermi energy of the matrix 101 for positive doping.

[0066] In some examples, the dopant substance 103 is a conductor, such as a metal. In some such examples, the workfunction of the conductor can be greater than the Fermi energy of the matrix 101 for negative doping. In other such examples, the workfunction of the conductor can be less than the Fermi energy of the matrix 101 for positive doping.

[0067] Figure 2 shows an example of a thermoelectric generator 1000 comprising a negatively doped thermoelectric structure 100-1 and a positively-doped thermoelectric structure 100-2. The thermoelectric structures 100-1,2 are substantially identical to the thermoelectric structure 100 of Figures 1(a) and 1(b).

[0068] The thermoelectric generator 1000 comprises a high temperature plate 1010 and a low temperature plate 1020 disposed on opposing sides of the thermoelectric structures 100- 1,2. The high and low temperature plates 1010, 1020 create temperature gradients across the thermoelectric structures 100-1,2.

[0069] As a result of the temperature gradients across the thermoelectric structures 100-1,2, an electrostatic potential difference (i.e., a voltage) is induced across each of the thermoelectric structures 100-1,2 due to the Seebeck effect. As the thermoelectric structures 100-1,2 are doped with opposing charges, the induced voltages oppose each other and current can flow in the direction of the arrows via electrical contacts 1030 and a load 1035.

[0070] The current flows through the thermoelectric structures 100-1,2 perpendicular to the axes of the cavities 102.

[0071] Doping is a technique used to add charge carriers (i.e., electrons or holes) into the bands of a semiconductor structure. For modulation doping, rather than including dopant atoms within the semiconductor material itself, doped regions are formed outside of the semiconductor structure and charge carriers are transferred from the doped regions to the semiconductor structure. Figure 3 shows a simplified schematic of the band structure for traditional modulation doping. Ancillary semiconductors A are positioned either side of semiconductor B. For example, semiconductor A could be n-doped AlGaAs and semiconductor B could be undoped GaAs.

[0072] In this example, Semiconductors A are doped such that charge carriers are present in their conduction bands 20. Semiconductor B is not doped. As the conduction band 25 of semiconductor B is at a lower potential energy than the conductions bands 20 of semiconductor A, the charge carriers move into the Semiconductor B and become “trapped” by the potential well formed by the conduction bands 20, 25.

[0073] Using modulation doping enables charge carriers to be donated to the conduction band of semiconductor B, without having to interfere with the structure of B itself (i.e., it doesn’t require B to include dopant atoms). In this simplified example, semiconductor B is “modulation doped”.

[0074] For simplicity, Figure 3 shows uniform potential profiles for conduction bands 20, 25 and neglects the shape of the conduction bands 20, 25 proximate the interfaces between semiconductors A and B.

[0075] When implementing traditional doping to create thermoelectric materials for use in thermoelectric generators, there is an optimal charge carrier density above which the power factor decreases. Care needs to be taken such that the optimal density of charge carriers is reached, but not surpassed, in order to maximize the power factor of the thermoelectric material. This is shown in Figure 4a, which shows the simulated power factor, as a function of charge carrier density, for a pristine (i.e., non-porous) semiconductor (line 10) which is limited by phonon scattering, and for a pristine doped semiconductor (line 12) which is limited by phonon scattering and ionized impurity scattering. In both simulations, there is a charge carrier density for which the power factor peaks.

[0076] The dependence of the power factor on the charge carrier density for traditional modulation doping can be explained with reference to Figures 4b and 4c. As the charge carrier density increases, the Fermi energy increases. Figure 4b shows the relative levels of the Fermi energy and conduction band for: (1) low charge carrier density; (2) optimal charger carrier density; and (3) excessive charge carrier density. The corresponding positions for each of ( l)-(3) are also shown in Figure 4a.

[0077] As explained earlier, the power factor is given by the product of the square of the Seebeck coefficient, S, with the conductivity, .

[0078] Conductivity, . requires the presence of charge carriers. Thus, a increases with charge carrier density. By contrast, the Seebeck coefficient decreases with charge carrier density, as explained below.

[0079] As is known to the skilled person, the density of states for charge carriers in a semiconductor material g(E) (which represents the number of occupied states with energy

[0080] E, per unit volume) is proportional to E , where E is the energy relative to the lower edge of the conduction band. Therefore, at higher energies, more occupied states exist.

[0081] The number of charge carriers with energy E, per unit volume, is given by the product of the density of states g E) with the Fermi-Dirac distribution, f(E~).

[0082] When a section of the semiconductor is heated to a higher temperature, the Fermi- Dirac distribution broadens, and the probability for any given charge carrier to be in a state with energy greater than the Fermi energy increases. Thus, the higher energy states become filled, and those high energy charge carriers diffuse towards a lower temperature region of the semiconductor. Similarly, there is diffusion from the lower temperature region of the semiconductor towards the higher temperature region.

[0083] However, the flux of charge carriers away from the low temperature regions is smaller because there are less low energy states (due the dependence of g E) on E2 - following the common knowledge that the Seebeck coefficient is proportional to the gradient of g E) at the Fermi level).

[0084] Therefore, there is an imbalance between the fluxes which creates a charge build-up at the low temperature region of the semiconductor, thereby creating an electrostatic potential difference known as the Seebeck voltage. The Seebeck coefficient, S, measures the ability of a material to have a difference between the opposing charge carrier fluxes. Now, given that g(E) is proportional to E as energy increases, g(E) ‘bends’, meaning the rate at which g(E) increases, decreases with E, such that g E) tends to flatten out. As a result of this, the difference between the density of states g(E) just above and just below the Fermi energy decreases as the Fermi energy increases, and vice versa. Therefore, the Seebeck coefficient decreases as the Fermi energy increases.

[0085] At position (1), .S' is high, but a is very low, resulting in a low overall power factor. Around position (2), .S' and a are both quite high, resulting in a peak overall power factor. At position (3), a is high, but S is very low, resulting in a low overall power factor. Typically, the optimal power factor is achieved when the Fermi energy aligns (or is in close vicinity) with the band edge, as shown in Figure 4b. The relationship between . S, and aS2as a function of charge density is shown in Figure 4c.

[0086] For the present invention, the limitations imposed by the adverse interdependence of a and S with charge carrier density differ. This is demonstrated through simulations that were performed in relation to the band profile of structures of the present invention 100. The simulations and findings are discussed herein.

[0087] To simulate electronic and thermoelectric transport in the structure 100, Monte Carlo methods were used to compute thermoelectric transport properties based on a conduction band potential energy profile. The conduction band potential energy profiles were obtained by finding self-consistent solutions of the Poisson equation in the matrix 101 with equilibrium charge carrier statistics.

[0088] In these simulations, charged elements are located at the cavities 102 of the matrix 101 and the electrostatic potential throughout the matrix 101 is determined. Laws of electrostatics dictate that the electrostatic potential, and by extension the band profile of structure 100, will shift down to lower energies in the case of electron charging and shift upwards in the case of “hole” charging. The shifted band profile influences the spatial and energy distribution of charge carriers, which in turn further influences the potential and band profile. Thus, because the potential depends on the charge, and the charge on the potential, a self-consistent solution is required until the potential and charge distribution agree on a mutual solution. For the structure of Figures la and lb, the simulator used to solve the Poisson equation used is a self-consistent 2D Poisson solver. The simulator self-consistently solves the Poisson equation in the matrix 101.

[0089] To simulate the band profiles within the matrix 101, the Poisson equation is used to find a solution for the potential V which satisfies the charge density for the charge in the matrix 101. At the cavities 102 a boundary condition is imposed that dictates the difference between the Fermi energy of the matrix material 101 and the cavity dopant material 103 (which mathematically is equivalent to imposing a fixed charge on cavities 102). The semi-conductor material 101 can be undoped but, in other examples, the semiconductor material can be doped, and its significance will be explained below. The change to the band profile caused by the potential V, and subsequent redistribution of charge carriers into the matrix 101, is then determined. The redistribution of charge carriers will influence the electrostatic potential V, so the solution for V is recalculated using the new charge distribution. This process repeats until the solutions converge to an electrostatic potential V which is representative for when charge carriers reach equilibrium.

[0090] Once the electrostatic potential V is obtained, the band potential profile (conduction or valence) can also be obtained, and that is entered as an input to a Monte Carlo simulator. Simulations performed using the Monte Carlo simulator involve injecting a large number of charge carriers into the domain matrix 101 and tracing them to their exit, while recording their time of flight, which will then determine their flux. Once the flux is known, the transport distribution function of the Boltzmann Transport Equation is formed, and from there the thermoelectric coefficients are computed. The Monte Carlo simulators and associated calculations were performed in accordance with the methods and teachings described in the paper by Pankaj Priyadarshi and Neophytos Neophytou, titled “Computationally efficient Monte Carlo electron transport algorithm for nanostructured thermoelectric material configurations,” Journal of Applied Physics 133, 054301 (2023).

[0091] Alternative methods may be used to determine the band profile of structure 100 and / or the thermoelectric coefficients, but the method outlined above was used to provide the results described herein. Figures 5(a)-(e) are discussed below to explain how the band profile changes at an interface between materials.

[0092] Figure 5 a shows the initial conditions for the conduction band potential profile of a semiconductor, as well as the redox level of an electrolyte dopant, in a simple onedimensional example.

[0093] In the example of Figure 5a, the dopant material is considered as an electrolyte having a redox level greater than the Fermi energy of the matrix material. The matrix material in this example is also doped. Alternatively, in other examples, the dopant material 103 can be a semiconductor material with a Fermi energy equal to the given redox level, a conductor with a workfunction equal to the given redox level, or any material which can supply charge carrier to the matrix 101.

[0094] For ease of calculation and understanding, the Fermi energy E of the semiconductor material has been set to 0. The semiconductor and electrolyte regions are assumed to be of large length either side of an interface therebetween, to illustrate the interface effects more vividly.

[0095] When the two regions (semiconductor and electrolyte) are connected at the interface, the conduction band profile of the semiconductor material changes, as shown in Figure 5b.

[0096] Figure 5b shows the self-consistently simulated potential profile of the conduction band of the semiconductor, accounting for the presence of the electrolyte and equilibrium charge carrier statistics. The conduction band potential profile is lowered nearer to the location of the interface with the electrolyte but remains relatively unchanged away from the electrolyte region. In Figure 5b, the interface between the semiconductor and electrolyte is at 80nm.

[0097] This shift in the band potential profile provides a charging effect, as illustrated in Figure 5c. As a result of the lowered band profile, charge carriers have transferred from the electrolyte to the semiconductor. The density of charge carriers becomes non-uniform and is greatest in the vicinity of the interface, where the band profile is lowest. For the simulations in Figures 5b and 5c, the dielectric constant in the semi-conductor material is assumed to be 11.7ao (corresponding to Si), where 8o is the permittivity of free space. Since the potential profile also depends on the material dielectric constant, Figures 5d and 5e show simulation results for different values of dielectric constants. As the dielectric constant of the semi-conductor material increases, the conduction band and charge profiles need slightly more distance to reach flat conditions, meaning the effects from the electrolyte permeate further into the semi-conductor.

[0098] Further simulations were performed to determine the band profile and charge density for a matrix 101 of the present invention comprising cavities 102. Simulation results are shown in Figures 6a and 6b for a 2D matrix 101, having 30% porosity and with charged elements positioned in the cavities. For clarity, 30% porosity refers to a structure wherein 30% of the volume (or area in the case of the 2D simulations) of the matrix is formed by the cavities. In the simulations of Figures 6a and 6b, the cavity size is 18 nm in diameter, the pore spacing in the transport direction is 15.5 nm and in the perpendicular direction is 7.5 nm. The semi-conductor material is assumed to be Si with dielectric constant of 11.7ao. The redox level of the electrolyte within the pores is assumed is Eredox = 0.5 eV.

[0099] Figures 6a and 6b respectively show the simulated values for the simulated conduction band potential profile and the charge density. In this example the charge density increases from 1023cm-3between cavities, to greater than 1025cm-3proximate the cavities. Figures 6c and 6d show the corresponding results for a structure with 40% porosity. In the simulations of Figures 6c and 6d, the cavity size is 19 nm in diameter, the pore spacing in the transport direction is 9.5 nm and in the perpendicular direction is 6 nm. The semi-conductor material is assumed to be Si with dielectric constant of 11.78o. The redox level assumed is Eredox = 0.5 eV.

[0100] In traditional modulation doping, the desired outcome is for the band profile and charge density to be uniform throughout the acceptor material away from the interface. Further, in traditional doping, to optimize the power factor, the conduction band profile is lowered closer to EF across the acceptor material such that, on average, the optimal carrier density is obtained. In present invention, however, the cavities are sufficiently close to prevent the band profile from becoming substantially uniform along the transport direction, and the bandbending effect from the interface effect is present throughout the matrix material along the transport direction between the cavities. Regions in the vicinity of the cavities (i.e., near to the interface between the matrix material 101 and the cavities 103) acquire very high charge carrier densities, even far beyond the typical optimal level, while the regions between the cavities (around the middle distance between cavities) acquire fewer charge carriers.

[0101] For the structures of the present invention, in the case of donor (i.e., electron) doping, the conduction band profile Ec is lowered significantly in the vicinity of the cavities, even below EF. The conduction band is lowered less significantly in the matrix material away from the cavities and can remain in the vicinity of EF (as shown in Figure 6a, where we set EF = OeV). This effect is shown, for example, in Figure 5b, wherein the effect of the electrolyte on the conduction band decreases as it moves further from the interface.

[0102] In the middle of the regions between the cavities, the conduction band potential profile forms a finite potential barrier, which introduces energy filtering for the charge carriers. This happens for structures of the present invention, but not for structures formed using traditional doping or traditional modulation doping methods, because the cavities are sufficiently close to prevent the conduction band potential profile from becoming uniform (i.e., flattening out) along the transport direction. The only charge carriers that overcome the potential barriers are of high energy, thus increasing the Seebeck coefficient. The carriers are injected from the potential wells in the vicinity of the cavities, and have high velocity, and high mobility, thus compensating for the conductivity reduction that the potential barriers introduce. Details relating to the pore distances are discussed in further detail later on.

[0103] The structures 100 of the present invention have band potential profiles which allow for both high Seebeck coefficients (due to the energy filtering from energy barriers in the middle regions between the cavities) and high conductivities (due to the large band bending near the cavities, resulting in high charge carrier density, but also higher carrier velocities and mobility at higher energies). Thus, the power factors achievable using the structures 100 of the present invention are higher than in traditional doped, or modulation doped structures.

[0104] The achievable power factors using structures 100 of the present invention depend on the height (i.e., greatest energy) of the potential barrier (barrier height).

[0105] Optimal power factors are reached when the barrier height is in the vicinity of the Fermi energy EF. Optimal power factors are typically reached when the barrier height is within O- I OLCBT of EF. More specifically, optimal power factors are typically reached when the barrier height is within 0-51<BT of EF. Barrier height considerations are discussed in greater detail below.

[0106] The skilled person will recognise that the same principles can be applied for acceptor (i.e., hole) doping. In such cases, the valence band potential profile is raised significantly in the vicinity of the cavities and decreases to levels which can be in the vicinity of EF in the matrix material away from the cavities. In the middle of the regions between the cavities, the valence band potential profile forms a potential well (which acts as a barrier to holes), which can be in the vicinity of EF, and which introduces energy filtering to increase the Seebeck coefficient.

[0107] Although the arrangement of cavities of the present invention can provide improved power factors, as described above, the presence of cavities and cavity surfaces introduces scattering for charge carriers, which is detrimental to the power factor. Thus, it is important to consider the level of porosity that would allow for high conductivity. There will be an optimum porosity which balances the negative impact of scattering on the power factor with the positive effects provided by the unique band profiles that enable the filtering effects described above.

[0108] Figure 7(a) shows schematics for matrix geometry examples with different degrees of porosity, ranging from 10% up to 60%, together with relevant geometrical distances noted. In Figure 7(a), the transport direction is horizontal (i.e., left to right, or right to left). Figure 7(b) shows the simulated power factors for each of these matrix geometries.

[0109] The power factors in Figure 7(b) were simulated without the charging effect coming from the cavities. That is to say, in the simulations there are no charges placed in the cavities and the Fermi energy within the matrix 101 is varied arbitrarily, resembling a larger, uniform charge carrier density. The simulations assume a uniform conduction band potential profile when determining the power factor, so there is no energy filtering, and the results focus solely on the influence of the scattering by the cavities on the power factor. These simulations were performed and are shown as they provide relevant details in relation to effects of porosity.

[0110] Simulations where ionized impurity scattering (IIS) is not included are performed, and this provides a reference for comparison to another simulation discussed later on which considers charging effects but also do not contain ionized dopants.

[0111] Line 20 shows the simulated power factor as a function of charge density for a pristine (i.e., non-porous) material at phonon-limited conditions (no ionized impurity scattering). Line 21 (dashed-dot line) shows the ‘physically achievable’ power factor when ionized impurity scattering is in addition considered. Lines 20 and 21 are the same lines as shown in Figure 2(a) and are provided for reference purposes.

[0112] The simulations of the power factor as a function of charge carrier density are shown for porosities of 10%, 20%, 30%, 40%, 50%, and 60% via lines 22-27, respectively. It can be observed that for up to porosities of 30%-40% the power factor remains above or around the level that would be achievable in practice (line 21), while for larger porosities it is reduced significantly. Thus, high porosities would degrade the power factor and the benefits of energy filtering by manipulating the band potential profiles, as in structures of the present invention, would be mitigated. However, large porosities will reduce the thermal conductivity, and so the ZT figure of merit may still increase. These simulations, and all simulation herein, assume that charge carriers cannot enter or propagate within the cavities. This is the worst-case scenario for the electronic conductivity and power factor. In other situations, for example if the cavity is filled with a conductor which can allow charge propagation through it, the conductivity will degrade less and the degradation in the power factor will be less.

[0113] Further simulations which demonstrate the operating principle of the present invention for achieving high power factors are now described with reference Figures 8a-c and 9ac. Figure 8a shows simulated conduction band potential profiles Ec of a matrix 101, in a cross-section through the 2D profile along the transport direction of the matrix 101. This profile is taken in a middle line between lines of cavities. In these simulations the cavity size is 18 nm in diameter, the pore spacing in the transport direction is 15.5 nm and in the perpendicular direction is 7.5 nm. The semi-conductor material is assumed to be Si with dielectric constant of 11.7ao, with a single m.f.p. of 40 nm, such that the pristine material is calibrated to the mobility of n-type Si (approx. 1500 cm2 / Vs).

[0114] For these simulations, an electrolyte 103 is positioned in the cavities 102 with redox levels of Eredox = 0.2 eV, 0.5 eV, leV, and 2 eV, respectively. The conduction bands for each simulation (i.e., for each redox level) are represented in Figure 8a via lines 41-44, respectively.

[0115] As explained above, the electrostatic effect of the electrolyte 103 lowers the conduction band potential profile Ec in the matrix 101. Importantly, as described earlier, the conduction band potential profile Ec is lowered most significantly in the vicinity of the cavities and remains at higher levels away from the cavities, thereby forming potential barriers between the cavities. The potential barriers are visible as peaks in the simulated conduction bands. In the simulations of Figure 8(a), the conduction band potential remains greater than EF ( F = 0 eV) in the matrix material 101 away from the cavities 102. In other examples, the conduction band potential can drop below, or remain at, EF in the matrix material 101 away from the cavities 102. In other examples, the conduction band profile in the semi-conductor away from the cavities can also be lowered and controlled by a degree of uniform doping, and this will be discussed further below. Importantly, the conduction band profile is substantially non-uniform along the transport direction so as to form energy filtering barriers.

[0116] Monte Carlo simulations were performed to calculate the transport distribution function (TDF) for various structures 100, each having a porosity of 30%. Simulations were performed starting from a structure without any electrolyte charging (i.e., with no charge at the cavity locations in the simulation), and gradually increasing the electrolyte redox level Eredox (introducing more and more charging at the cavity locations). Simulations were performed with Eredox values of: 0.2eV, 0.5eV, l .OeV, and 2.0eV. The TDFs for each simulation are shown as a function of energy in Figure 8b via lines 46- 49, in order or increasing charging. The dash-dot line 45 also shows the TDF of the uniform pristine doped material for the case which provides its peak PF (the one realistically achievable), for comparison. In this case the lines are plotted at the same EF for comparison.

[0117] The TDF is a measure of the charge carrier flux for different energies. It is the basic kernel of the Boltzmann transport equation (BTE). The TDF is essentially a measure of the ability of charge carriers (i.e., electrons) at various energies to move across the matrix 101.

[0118] The gradient of the TDF provides an indication of the Seebeck coefficient (i.e. it allows for higher energy “hot” carriers to conduct more than lower energy “cold” carriers).

[0119] The integral of the TDF over the energy derivative of the Fermi distribution determines the electrical conductivity of the various structures. Thus, the magnitude of the TDF determines the conductivity.

[0120] The simulation results in Figure 8(b) show that the TDF changes with increasing charging (i.e., increasing redox level for an electrolyte, increasing Fermi level for a semiconductor dopant, etc) as follows: i) The minimum energy for which the TDFs are non-zero is lowered as charging increases, indicating the lowering of the bands by the electrostatic effect of charging the matrix material from the dopant material in the cavities. As charging increases, the start energies for non-zero TDF decrease even further (move to the left in the Figure) because the peaks of the Ec profile (i.e. the highest potential energy regions - barrier heights, which are formed in the space between the cavities), are lowered in energy, relative to the Fermi level and so more lower energy electrons can overcome the barriers. The magnitude is also larger, indicating an increase in the electrical conductivity, at least for the cases with the larger Eredox level. ii) The gradient of the TDF increases at the low energies (around E = OeV), indicating the increase in the Seebeck coefficient, which is proportional to the slope of the TDF. Compared to the pristine doped material (blue dashed- dot line), the slope of the TDFs near the Fermi level position (as indicated) of the material with doped cavities is larger. This indicates an increase in the Seebeck coefficient compared to the realistically achieved material case.

[0121] An illustration about why the device of the present invention can offer larger power factor performance even compared to the pristine undoped material, is described in Figure 8(c), where the TDFs from Figure 8(b) are all shifted to the same origin at E = OeV, together with the TDF from the pristine phonon-limited material (line 50 - representing the ultimate performance of the material). Lines 46-49 are shifted to become lines 51-54.

[0122] At the low energy region, near E = 0 eV, which is relevant for transport, as the charging from higher Eredox levels increases, the TDFs increase in amplitude compared to the pristine case. This indicates the presence of highly conducting carriers at those relevant energies and retained conductivity. As Eredox increases, the TDF also increases in magnitude across all electron energies. The slope is also higher, indicating higher Seebeck coefficients.

[0123] The effects of conduction / valence band potential profiles on the thermoelectric coefficients are shown further in Figures 9a-c, which plot the electronic conductivity, Seebeck coefficient, and PF, respectively, as functions of the charge carrier density (which is achieved by, and is essentially a measure of, increasing Eredox). The simulation results for the thermoelectric material of the present invention are compared with simulation results of the pristine uniform material under phonon-limited transport conditions, in which case the EF value is arbitrarily changed to charge the material (shown via solid lines), and under uniform doping such that the material is under phonon plus ionized impurity scattering, IIS, limited transport (shown via dashed-dot lines). The comparative simulations for the power factor are shown via lines 20-21, as in Figure 7. Compared to the latter, realistically achievable case, the thermoelectric materials of the present invention provide larger conductivity and larger Seebeck coefficients as Eredox increases, as indicated also by the insets in Figures 9(a) and (b) for clarity.

[0124] The change in power factor as Eredox increases is shown in Figure 9(c). In this particular example, the PF increases even to values above the phonon-limited pristine uniform material. For Eredox = 2. OeV, the simulated power factor is greater than the optimal power factor of line 20, and more than twice the experimentally accessible PF of line 21. As explained earlier, under optimal conditions, the barrier height (i.e., the peak of the conduction band potential profile which will appear in the regions between the dopant cavity regions, or the minimum of the valence band potential energy) should be at, or near to, the Fermi energy.

[0125] In some embodiments, the barrier height should reside within a O-lOksT of the Fermi energy. In some embodiments, the barrier height should reside within a O-5A / / 7’ of the Fermi energy. Under optimal conditions, the barrier height should reside within Q- ksT from the Fermi energy.

[0126] The barrier height is controlled partly by the geometry of the matrix 101. As such, the geometrical features (i.e., cavity 102 size and placement) of the matrix 101 are discussed below.

[0127] The distance between adjacent cavities 102 along the transport direction should be determined taking the following factors discussed below into consideration.

[0128] An upper limit for the distance between adjacent cavities is determined by the electron energy relaxation distance (i.e., the energy relaxation mean-free-path (m.f.p)) within the matrix material 101. The maximum distance between adjacent cavities 102 along the transport direction should be on the order magnitude of the m.f.p for electrons in the material, such that the electron energy does not relax significantly into the potential wells after overcoming a potential barrier. This will allow the electrons to flow at higher energies, which will retain high Seebeck coefficients. The distance between adjacent cavities along the transport direction should be less than 3 times the m.f.p. of the matrix material 101. Preferably, the distance between adjacent cavities along the transport direction should be less than 2 times, or less than 1.5 times, the m.f.p. of the matrix material 101. The energy relaxation mean-free-path can be computed for different materials using modern ab initio methods or extracted from experiments. The distance between successive barrier peaks should be on the order of the energy relaxation distance. For example, in Silicon, the electron energy relaxation path is around 50nm at 300K, and so the maximum separation between adjacent cavities along the transport direction should be of the order of this distance, or at most a few multiples of this distance, i.e. below approximately 150nm. Of course, in alternative semiconductor materials and operating temperatures, the electron m.f.p will differ, and so the geometry should be adjusted accordingly. The m.f.p may refer to the m.f.p of the matrix material at, or around, 300K. When structure of the present invention are designed for use at temperatures away from 300K, the m.f.p at the relevant temperature can be considered instead.

[0129] The distance between cavities is also determined by the desired shape of the potential barriers and wells. If cavities 102 are placed too far away from each other, the potential barrier peaks will increase, resembling an elevated uniform flat-band structure away from the cavities as in conventional doping, resulting in reduced conductivity. If the cavities 102 are too close to each other, then the potential barrier peaks will be reduced and too many low energy charge carriers will be able to cross the barrier, resulting in a reduced Seebeck coefficient. This distance between adjacent cavities when enables the barrier peaks to be in the vicinity of EF is determined by the Poisson solution and depends on the dielectric constants of the materials.

[0130] The distance between adjacent cavities along the transport direction 102 should also be determined based on the desired porosity of the matrix material. If the cavities are closer together then the overall porosity increases. The larger the porosity, the larger the interface density in the material, the larger the interface scattering, and the lower the conductivity. This will reduce the power factor, but can increase the ZT since phonons are also scattered on the interfaces. The effect on conductivity and reduction in the power factor may be mitigated in the case where the cavity is filled with a conductor which allows transport of charge through it, thereby enabling greater porosities. Porosity considerations are discussed earlier in the application and are discussed further below.

[0131] The distance in which the dopant cavity region asserts control over the shape of the potential barrier is typically a few 10s of nanometres for a typical material. In the example of Figure 5, this distance, i.e. from the cavity to the region where the band profile becomes flat is approximately 30 nm, as shown in Figure 5d-e. If the distance between a cavity interface to another cavity interface is more than approximately 50nm, then the barrier can be large enough to allow for significant power factor improvements. When the distance becomes less than approximately 10 nm, then the barrier reduces more than needed, and interface density becomes large enough to reduce power factor performance. However, as we show below, structures with periodicity even down to a few nanometers can provide power factor improvements compared to the realistic uniformly doped pristine material. Thus, the periodicity of the cavities should be below 150 nm, and more than 5nm in a typical material. The beneficial effects may be more significant for cavity distances of more than 10 nm.

[0132] As well as the distance along the transport direction between cavities being taken into consideration, the size of the cavities should also be considered. Cavities shown herein have diameters within the range of 15-20nm, as such cavities are big enough to be able to be filled with the dopant substance in practice and allow for a significant portion of the dopant material to have control over the matrix potential profile. In simulations, the same power factor improvements are observed when the cavities are made as small as possible, i.e. a few nanometers. However, such cavities cannot be easily formed and filled in practice using current technology. The skilled person will recognise that, as technology develops, smaller cavities can be used as part of the present invention.

[0133] Figures 10(a)-(f) show simulated power factors as a function of charge density (i.e., as Eredox increases), similarly to Figure 9, but for all porosities investigated. Figures 10(a)- (f) show results for porosities of 10%, 20%, 30%, 40%, 50%, and 60% respectively. The pore sizes in the simulations are between 14-19 nm in diameter as shown in Figure 7a. Redox levels of Eredox = 0.2 eV, 0.5 eV, leV, and 2 eV are used for the simulations, and these are represented respectively using triangular, circular, square, and diamond markers. For comparison, lines 20-21 (Figure 7) are also displayed together with lines 22-27, which respectively show: the simulated power factor (20) for a non-porous doped pristine material under phonon-limited conditions, i.e. without ionized impurity scattering (for comparison against the highest intrinsic performance the material can provide - although is not experimentally accessible since such densities cannot be achieved without doping); the simulated power factor (21) for a non-porous doped pristine material taking ionized impurity scattering into account (for comparison again with the experimentally accessible case); and the simulated power factors (lines 22-27) for a structure with the corresponding porosity under phonon-limited conditions but with EF adjusted arbitrarily and the band profile remaining uniform (for comparison against the performance when the energy filtering of this invention is absent). In these simulations, the distance between adjacent cavities along the transport direction ranges from approximately 50 nm for porosity = 10%, down to 10 nm for porosity = 60%. For the smaller porosity structure (p=10%), the distances between cavities are too large for these examples, and only small improvements are achieved with increased Eredox. As the porosity increases, the distance between cavities becomes more optimal and large improvements are realized in the power factor. For the largest porosity structure (p=60%) the distance between cavities becomes too small to realise significant improvements, and the interface density becomes very large, such that the barrier height is less that optimal and scattering increases substantially, and again very small improvements are realized.

[0134] Figures 12(a)-(f) show simulated power factors as a function of charge density (i.e ., as Eredox increases), similarly to Figure 10, for all porosities investigated. Figures 10(a)- (f) show results for porosities of 10%, 20%, 30%, 40%, 50%, and 60% respectively. The pore sizes in the simulations are between 14-19 nm in diameter as shown in Figure 7a. Redox levels of Eredox = 0.2 eV, 0.5 eV, leV, 2 eV and 3 eV are used for the simulations, and these are represented respectively using triangular, circular, square, diamond, and star markers. For comparison, lines 20-21 (Figure 7) are also displayed together with lines 22-27, which respectively show: the simulated power factor (20) for a non-porous doped pristine material under phonon-limited conditions, i.e. without ionized impurity scattering (for comparison against the highest intrinsic performance the material can provide - although is not experimentally accessible since such densities cannot be achieved without doping); the simulated power factor (21) for a non-porous doped pristine material taking ionized impurity scattering into account (for comparison again with the experimentally accessible case); and the simulated power factors (lines 22-27) for a structure with the corresponding porosity under phonon-limited conditions but with EF adjusted arbitrarily and the band profile remaining uniform (for comparison against the performance when the energy filtering of this invention is absent). In these simulations, the distance between adjacent cavities along the transport direction ranges from approximately 50 nm for porosity = 10%, down to 10 nm for porosity = 60%. For the smaller porosity structure (p= 10%), the distances between cavities are too large for these examples, and only small improvements are achieved with increased Eredox. Figures 12(a)-(f) differ from those in Figures 10(a)-(f) in that simulated power factors also include calculations for the cases where cavities which taken to be conducting as well as non-conducting. In each of Figures 12(a)-(f), the triangular, circular, square, diamond, and star markers are shown with a filled interior to represent simulations wherein the cavities are conductive, and they are shown with a clear interior for simulations (similar to those in Figures 10(a)-(f)) in which the cavities are nonconducting. These simulations for conducting cavities (where electronic transport is allowed uninterrupted through the cavities) show that larger power factors can be achieved, as in reality the cavities will be at least partially conducting, and surface boundary scattering may be reduced compared to non-conducting cavities.

[0135] In all the simulations presented thus far, the matrix material was undoped (i.e., all carrier density comes from the dopant substances in the cavities, rather than dopant atoms directly within the matrix material 101). However, doping of the matrix material directly can also retain and even increase the performance in some cases, especially in the low porosity materials. Doping of the matrix material 101 can even allow for the use of a reduced Eredox (or EF, or work function) of the dopant substance for the same performance, which can be easier to be achieved in practice.

[0136] Figure I la shows simulations for the conduction band profile of a structure 100 with 20% porosity for Eredox=l eV. Figure I la shows the conduction band profile for the undoped material (line 60), the material in which the matrix is doped at 1024 / cm3(line 61), and the case where the matrix material is doped at 1025 / cm3(line 62). As the matrix doping increases, the conduction band profile is lowered relative to the Fermi level, and the barrier moves towards the optimal height, in the proximity of the Fermi level. However, the conduction band in the vicinity of the cavities remains lower, which allows for the high energy, high mobility carriers that lead to high conductivity in the material.

[0137] The simulated TDFs are shown in Figure 1 lb (via lines 63-65), and are compared to the pristine, uniform potential, undoped case (line 66 which begins at E = 200 meV). For the lower doping materials, the sharper slope at the left side indicates increased Seebeck coefficients. For the highest doping case we consider, the slope is reduced, indicating that the potential barrier is reduced and the Seebeck coefficient is reduced to the levels of the pristine undoped case, non-porous case. However, the TDF amplitude is high, indicating high conductivity. Figure 11c shows the simulated power factors for each of the three doping levels. The continuous lines 20, 21 are shown as in the previous figures above. The square symbols denote the simulated power factors for the undoped and doped matrix materials. The highest power factor was achieved for the matrix with the greatest doping (corresponding to band 62) and the lowest power factor was achieved for the undoped matrix (corresponding to band 60). This demonstrates that at the same Eredox, a much higher performance can be reached if the matrix is doped as the Ec is brought closer to the optimal value in the region between the cavities (up to 48% higher in this simulation).

[0138] The doping of the matrix brings the Ec towards the optimal level, and the conductivity is high because the charge carriers of energies above that level coming from the regions around the cavities are highly mobile and conducting. Thus, for a certain performance, doping the matrix can reduce the level of Eredox required to bring the Ec to the optimal level, and can allow for larger distances between pores, both which can be practically more feasible. However, as shown in Fig. l id, which corresponds to Figure 11c but with Eredox = 2 eV, the performance increases again by up to 50%. For larger porosities the increase in power factor due to matrix doping may be reduced because the bands are already brought closer to the optimal level by the dopants in the cavity regions.

[0139] From reading the present disclosure, other variations and modifications will be apparent to the skilled person. Such variations and modifications may involve equivalent and other features which are already known in the art of thermoelectric materials, and which may be used instead of, or in addition to, features already described herein.

[0140] Although the appended claims are directed to particular combinations of features, it should be understood that the scope of the disclosure of the present invention also includes any novel feature or any novel combination of features disclosed herein either explicitly or implicitly or any generalisation thereof, whether or not it relates to the same invention as presently claimed in any claim and whether or not it mitigates any or all of the same technical problems as does the present invention.

[0141] Features which are described in the context of separate examples may also be provided in combination in a single example. Conversely, various features which are, for brevity, described in the context of a single example, may also be provided separately or in any suitable sub-combination. The applicant hereby gives notice that new claims may be formulated to such features and / or combinations of such features during the prosecution of the present application or of any further application derived therefrom. For the sake of completeness, it is also stated that the term "comprising" does not exclude other elements or steps, the term “a” or “an” does not exclude a plurality, and a single processor or other unit may fulfil the functions of several means recited in the claims and any reference signs in the claims shall not be construed as limiting the scope of the claims.

Claims

Claims1. A structure for use in a thermoelectric generator, comprising: a matrix formed of, or comprising, a semi-conductor material, wherein the matrix comprises an arrangement of cavities; and a dopant substance disposed within the cavities and configured to modify the potential energy band profile of the matrix, such that, the potential energy band profile becomes non-uniform along a transport direction of the structure; wherein the transport direction is the direction which, in use, current is configured to flow through the structure; and wherein the spacing between cavities along the transport direction is substantially consistent throughout the matrix.

2. The structure of claim 1, wherein the cavities extend through the matrix in a direction substantially perpendicular to the transport direction.

3. The structure of claim 1 or claim 2, wherein the dopant substance is configured to modify the shape of the conduction band energy profile of the matrix by lowering the conduction band energy profile proximate the cavities.

4. The structure of claim 3, wherein the dopant substance is configured to modify the shape of the conduction band energy profile of the matrix by: lowering the conduction band energy profile proximate the cavities below the Fermi energy of the matrix; and keeping the conduction band energy profile energy within 0-5kflT of the Fermi energy of the matrix in regions distal from the cavities.

5. The structure of claim 1 or claim 2, wherein the dopant substance is configured to modify the shape of the valence band energy profile of the matrix by increasing the valence band energy profile proximate the cavities.

6. The structure of claim 5, wherein the dopant substance is configured to modify the shape of the valence band energy profile of the matrix by: increasing the valence band energy profile proximate the cavities above the Fermi energy of the matrix; andkeeping the valence band energy profile within 0-5kflT of the Fermi energy of the matrix in regions distal from the cavities.

7. The structure of any preceding claim, wherein the average distance between adjacent cavities along the transport direction is less than three times the energy relaxation mean-free-path of the semi-conductor material.

8. The structure of any preceding claim, wherein the average distance between adjacent cavities along the transport direction is less than 2 times the energy relaxation mean-free-path of the semi-conductor material.

9. The structure of any preceding claim, wherein the average distance between adjacent cavities along the transport direction is between 5-200nm.

10. The structure of any preceding claim, wherein the average distance between adjacent cavities along the transport direction is between 5-150nm.

11. The structure of any preceding claim, wherein the average distance between adjacent cavities along the transport direction is between 50-150nm.

12. The structure of any preceding claim, wherein the dopant substance is:(i) an electrolyte, wherein the redox level of the electrolyte differs from the Fermi energy of the semi-conductor material;(ii) a conductor, wherein the workfunction of the conductor differs from the Fermi energy of the semi-conductor material; or(iii) a semiconductor, wherein the Fermi energy of the semiconductor differs from the Fermi energy of the semi-conductor material.

13. The structure of any preceding claim, wherein the porosity of the matrix is between 10-60% by volume.

14. The structure of claim 11, wherein the porosity of the matrix is between 20-50% by volume; and, optionally or preferably, wherein the porosity of the matrix is between 20-40% by volume.

15. The structure of any preceding claim, wherein the matrix is a crystalline, or semi-crystalline, semi-conductor.

16. A thermoelectric generator comprising the thermoelectric structure of any preceding claim.

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