WO2013173922A1

WO2013173922A1 - Thermionic generation of free electrons

Info

Publication number: WO2013173922A1
Application number: PCT/CA2013/050394
Authority: WO
Inventors: Parham Yaghoobi; Mehran VAHDANI MOGHADDAM; Alireza NOJEH
Original assignee: The University Of British Columbia
Priority date: 2012-05-23
Filing date: 2013-05-23
Publication date: 2013-11-28

Abstract

A method and apparatus is provided for generating free electrons thermionically that includes providing a substantially one-dimensional, electrically conductive material having a restricted, anisotropic thermal conductivity, and irradiating a region of the substantially one-dimensional material with electromagnetic energy having a power density above a threshold to heat the region and generate a temperature gradient having a magnitude of at least 0.1 K/μm between the irradiated region and the remainder of the substantially one-dimensional material to thermionically generate free electrons at the region.

Description

THERMIONIC GENERATION OF FREE ELECTRONS

Cross-Reference to Related Applications

[0001 ] This application claims priority from U.S. Provisional Patent Application No. 61/650,932 filed May 23, 2012 and U.S. Provisional Patent Application No.

61/652,296 filed on May 28, 2012, both of which are entitled THERMIONIC

GENERATION OF FREE ELECTRONS. For purposes of the United States of America, this application claims the benefit under 35 U.S.C. §1 19 of U.S. Provisional Patent Application Nos. 61/650,932 filed May 23, 2012 and 61/652,296 filed May 28, 2012, both of which are hereby incorporated herein by reference for all purposes.

Technical Field

[0002] The present disclosure relates to thermionic generation of free electrons. Background

[0003] Present methods for converting electromagnetic energy, such as sunlight, into electricity include using photovoltaic devices, using indirect methods such as boiling water for a steam turbine, and generating free electrons thermionically.

[0004] In photovoltaic devices, the electrons of a semi-conducting material transition across a band gap from a valence band into a conduction band by absorbing photons with energy greater than the band gap energy. A disadvantage of photovoltaic systems is that nearly all of the photons of an electromagnetic energy source having a broad spectrum, such as sunlight, have, either, insufficient energy to excite electrons into the conduction band, or energy excessive of the band gap energy, which is converted to heat, raising the temperature of the material and decreasing the efficiency of conversion. A more detailed discussion of electron-hole separation (typically happening at the junction of two semiconductors) and movement of electrons through the circuit and a load may be found in: David L. Pulfrey, Understanding Modern

Transistors and Diodes, Cambridge University Press (2010).

[0005] Generating free electrons thermionically involves heating an electrically conductive material to a temperature at which the kinetic energy of the electrons is increased such that electrons overcome the work function of the material and are emitted as free electrons. The thermionic emission current increases exponentially with increased cathode temperature, which provides the potential for greater conversion efficiencies than photovoltaic devices. However, because electrically conductive materials are generally also good conductors of heat, absorbed heat quickly dissipates throughout the material, as well as to the surrounding environment, making heating the conventional materials to thermionic temperatures challenging. For this reason, heating conventional electrically conductive materials, such as metals, with a low intensity electromagnetic energy source, such as sunlight, requires a large collection apparatus to direct an amount of energy to the material that is sufficient to achieve thermionic temperatures. A more detailed discussion of electron movement through a gap and collection at an anode of a thermionic device, which are part of the overall conversion process, may be found in: Yue-Guang Deng and Jing Liu, "Recent advances in direct solar thermal power generation," Journal of Renewable and Sustainable Energy, volume 1 , page 052701 (2009); doi: 10.1063/1 .3212675.

[0006] Improvements to thermionic electrical conversion means are desirable to address the above limitations. Summary

[0007] According to an aspect of the present invention, there is provided a method of generating free electrons that includes providing a substantially one- dimensional, electrically conductive material having a restricted, anisotropic thermal conductivity, and irradiating a region of the substantially one-dimensionally material with electromagnetic energy having a power density above a threshold to heat the region and generate a temperature gradient having a magnitude of at least 0.1 Κ/μιη between the irradiated region and the remainder of the substantially one-dimensional material to thermionically generate free electrons at the region.

[0008] According to another aspect of the invention, there is provided a thermionic converter that includes an anode, a cathode separated from the anode by a gap, the cathode comprising a substantially one-dimensional, electrically conductive material having a restricted, anisotropic thermal conductivity, wherein electromagnetic energy having a power density above a threshold, irradiated on a region of the substantially one-dimensional, electrically conductive material, heats the region and generates a temperature gradient of at least 0.1 Κ/μιη between the irradiated region and the remainder of the substantially one-dimensional material to thermionically generate free electrons at the region.

[0009] According to another aspect of the present invention, there is provided an electron beam emitter that includes a cathode comprising a substantially one- dimensional, electrically conductive material having a restricted, anisotropic thermal conductivity, wherein electromagnetic energy having a power density above a threshold, irradiated on a region of the substantially one-dimensional, electrically conductive material, heats the region and generates a temperature gradient of at least 0.1 Κ/μιη between the irradiated region and the non-irradiated region of the substantially one- dimensional material to thermionically generate free electrons at the region, and an electrode to generate an electric field to accelerate the thermionically generated free electrons away from the cathode, to produce an electron beam deliverable to a target.

[0010] According to another aspect of the present invention, the electromagnetic energy utilized in one or more of the above method, thermionic converter, and electron beam emitter is non-coherent.

[0011 ] Other aspects of the present invention will be apparent from the following detailed description of the embodiments and the accompanying drawings.

Drawings

[0012] The following figures set forth embodiments in which like reference numerals denote like parts. Embodiments are illustrated by way of example and not by way of limitation in the accompanying figures.

[0013] FIG. 1 is a block diagram illustrating a thermionic electrical generation system according to an embodiment of the invention;

[0014] FIG. 2 is a perspective view of a portion of the thermionic electrical generation system shown in FIG. 1 ;

[0015] FIG. 3 is a graph showing simulated data of the threshold power density of electromagnetic energy required for rapidly heating multi-walled carbon nanotubes versus the radius of the region of incidence of the electromagnetic energy;

[0016] FIG. 4 is a block diagram illustrating a thermionic electron emitter according to another embodiment of the invention;

[0017] FIG. 5 is a flowchart illustrating a method of generating free electrons thermionically;

[0018] FIG. 6 is a perspective view of a thermionic electron generation system for generating multiple, shaped electron beams;

[0019] FIG. 7 is a two-dimensional thermal map obtained from irradiating a region having a radius of 50 μιη on the side surface of a carbon nanotube forest with a laser having power of 150 mW; and [0020] FIG. 8 is a graph showing emission current versus laser power for experimental data obtained using three different lasers having wavelengths of 488 nm, 514 nm, and 532 nm focused to a region 208 having a radius of approximately 250 μιη. Detailed Description

[0021 ] The following describes apparatuses and methods for generating free electrons thermionically using substantially one-dimensional, electrically conductive materials exhibiting restricted thermal conductivity heated by low intensity non-coherent electromagnetic energy source such as, for example, sunlight. Other embodiments may use other electromagnetic energy sources, such as, for example readily available low- power lasers.

[0022] For simplicity and clarity of illustration, reference numerals may be repeated among the figures to indicate corresponding or analogous elements.

Numerous details are set forth to provide an understanding of the examples described herein. The examples may be practiced without these details. In other instances, well- known methods, procedures, and components are not described in detail to avoid obscuring the examples described. The description is not to be considered as limited to the scope of the examples described herein.

[0023] Referring to FIG. 1 , a block diagram of a thermionic electrical generation system 100 is illustrated. The thermionic electrical generation system 100 includes a cathode 102, an electromagnetic (EM) energy source 104, a focusing element 106 for focusing EM energy 108 onto the cathode 102, and an anode 1 10 separated from the cathode 102 by a gap 1 14 and connected to the cathode 102 through a load 1 12.

[0024] The focusing element 106 focuses EM energy 108 from the EM energy source 104 to increase the power density of the EM energy 108 that is incident on the cathode 102 by a sufficient amount to heat the cathode 102 to temperatures at which electrons in the cathode 102 have sufficient kinetic energy to overcome the work function of the cathode 102 and are emitted into the gap 1 14 as free electrons.

[0025] The anode 1 10 is separated from the cathode 102 by the gap 1 14 such that free electrons that are emitted by the heated cathode 102 with sufficient kinetic energy to cross the gap 1 14 are collected at the anode 1 10. The electrons emitted from the cathode 102 and accumulated at the anode 1 10 result in a voltage differential between the cathode 102 and the anode 1 10 that creates a flow of electrical current through the load 1 12. [0026] The gap 1 14 may be a reduced pressure environment relative to atmospheric pressure. For example, the gap 1 14 may be a low vacuum environment, a high vacuum environment (pressure less than 10^"3 Torr), or an ultra-high vacuum environment (pressure less than 10^"9 Torr). Alternatively, the gap 1 14 may be at atmospheric or higher pressure. In some embodiments, the gap 1 14 may contain a gas of neutral or ionized species that, for example, reduces the work function at the interface between the cathode 102 and the gap 1 14, facilitating thermionic emission at lower temperatures. In some embodiments, the gap 1 14 may contain a gas of neutral or ionized species that, for example, reduces the work function at the interface between the anode 1 10 and the gap 1 14, facilitating increased collection of electrons emitted from the cathode 102. In some embodiments, the gap 1 14 may contain a gas of neutral or ionized species that, for example, reduces space-charge effects arising from the Coulomb repulsion between electrons emitted from the cathode 102, facilitating the emission of further electrons from the cathode 102. In some embodiments, the gas or ionized species may be, for example, hydrogen, cesium, potassium, or lithium.

Alternatively or additionally, electrodes or magnets may be provided within the gap 1 14 to create an electric or magnetic field within the gap 1 14 to reduce space-charge effects. Alternatively, the gap 1 14 between the cathode 102 and the anode 1 10 may be substantially zero by placing the cathode 102 and anode 1 10 in close proximity or contact.

[0027] In some embodiments, the load 1 12 may be not present, in which case the thermionic electrical generation system 100 operates as a thermionic battery. Electrons emitted from the heated cathode 102 are collected at and accumulated on the anode 1 10, generating a potential differential between the anode 1 10 and cathode 102.

Because there is no return path between the anode 1 10 and cathode 102, the electrons are stored at the anode 1 10, deliverable at a later time when the anode 1 10 and cathode 102 are coupled together by the load 1 12, or another element.

[0028] Referring to FIG. 2, a perspective view of the cathode 102 and anode 1 10 of the thermionic electrical generation system 100 of FIG. 1 is shown having incident EM energy 108 incident on the cathode at a region 208.

[0029] The cathode 102 may be a forest of strands 202 of an electrically conductive, substantially one-dimensional material on a substrate 204. A "substantially one dimensional" material, or "quasi-one-dimensional" material, is a material in which the electrical and thermal behaviour differs from the bulk material and can be

approximated by considering the material as being constrained to a single dimension. For the purpose of the present disclosure, substantially one-dimensional materials are materials having lengths in two dimensions that are on the order of the wavelength of a phonon, being typically tens of nanometers, and are at least a factor of 5 shorter than the length of the third dimension. Non-limiting examples of substantially one- dimensional materials include nanotubes, nanowires, and nanofibers having a diameter less than 100 nm, and a length to diameter ratio of at least 5. For example,

substantially one-dimensional materials include, but are not limited to, carbon nanotubes, boron-nitride nanotubes, tungsten nanowires, platinum nanowires, zinc oxide nanowires, yttrium nanowires, gallium nitride nanowires, silicon nanowires, molybdenum nanowires, chromium nanowires, titanium nanowires, nickel nanowires, tantalum nanowires, rhenium nanowires, niobium nanowires, nanowires made of oxides such as, for example, silicon oxide, magnesium oxide, aluminum oxide. As discussed in greater detail below, experiments have shown that carbon nanotubes are suitable for utilization as the strands 202 in a cathode 102 of a thermionic electrical generating system 100.

[0030] The strands 202 shown in FIG. 2 are generally aligned such that the strands 202 extend away from the surface of the substrate 204 in generally the same direction. In some embodiments, the strands 202 are not generally aligned as shown in FIG. 2, but may be, for example, oriented randomly or laying on their sides.

[0031 ] The substantially one-dimensional strands 202 of the cathode 102 have restricted thermal conduction compared to bulk materials. The restricted thermal conduction in the strands 202 facilitates efficient localized heating at the region 208 because heat lost to surrounding regions is reduced compared with bulk electrically conductive materials in which heat readily flows in all dimensions. The restricted thermal conduction is provided, at least, by the anisotropic heat conduction in the substantially one-dimensional strands 202. Anisotropic heat conduction constrains the flow of the heat through the strands 202 generally along the substantially single dimension of each strand 202, with heat conduction between strands 202 being much less than conduction within each strand 202. For example, heat conduction between the strands 202 may be at least a factor of 10 less than the heat conduction within one strand 202.

[0032] In an example, the restricted heat conduction in the strands 202 may be enhanced by selection of a material for the strands 202 that has a thermal conductivity that decreases with increased temperature such that the more the material is heated, the more restricted the heat flow through the material becomes. This temperature dependent thermal conductivity provides a heat trap effect that increases the efficiency of the localized heating compared to materials with substantially temperature

independent thermal conductivity. Materials that are suitable for providing a heat trap in this way include , for example, materials having a thermal conductivity that is

approximately proportional to 1/Tⁿ, where T is the temperature of the material and n is any (not necessarily integer) number greater than or equal to 1 . A non-limiting example of a material having thermal conductivity that decreases with increased temperature is carbon nanotubes, which are discussed in more detail below. Without wishing to be bound by theory, further discussion of this heat trap effect may be found in P. Yaghoobi, M. Vahdani Moghaddam, and A. Nojeh, "Heat trap: Unusual light-induced-heat localization in carbon nanotube arrays," Solid State Communications, volume 151 , pages 1 105-1 108 (201 1 ), which, along with the published Supplementary Information to the article, is hereby incorporated by reference herein.

[0033] In another example, the restricted heat conduction in the cathode 102 is enhanced by engineering an interface 206 between the strands 202 and the substrate 204 that restricts thermal conduction between the strands 202 and the substrate 204. For example, it has been shown that heat flow across the interface between a carbon nanotube forest and a silicon substrate is insignificant when the carbon nanotubes are heated directly. Without wishing to be bound by theory, further discussion of restricted thermal conduction across an interface may be found in P. Yaghoobi, M. Vahdani Moghaddam, M. Michan, and A. Nojeh, "Visible-light induced electron emission from carbon nanotube forests," Journal of Vacuum Science and Technology B:

Microelectronics and Nanometer Structures, volume 29, pages 02B104-1 - 02B104-4 (201 1 ), which is hereby incorporated by reference herein.

[0034] In an example, defects on the order of tens of nanometers in the interface 206 cause phonons from the strands 202 to be scattered at the interface 206, restricting heat conduction from the strands 202 to the substrate 204 and facilitating localized heating of the strands 202 by reducing heat loss to the surrounding environment.

Because the defects at the interface 206 on the order of tens of nanometers may be much larger than the wavelength of electrons (typically on the order of Angstroms) the interface 206 may not significantly inhibit electrical conduction between the strands 202 and the substrate 204. In a non-limiting example, such defects at the interface 206 are produced by catalyst nanoparticles on the substrate 204 surface prior to deposition of the strands 202 on the substrate 204. [0035] In some embodiments, restricted, anisotropic heat conduction may be enhanced by one or both of the selection of materials having temperature dependent thermal conductivity and engineering of the interface 206 between the strands 202 and the substrate 204.

[0036] The focused EM energy 108 that exits the focusing element 106 is incident on the cathode 102 at a region 208 as shown in FIG.2, heating the region 208. The region 208 is heated locally due to the restricted thermal conduction of the strands 202, creating a temperature gradient between the hotter region 208 and the cooler surrounding areas of the cathode 102 that are not irradiated by the EM energy 108. The temperature gradient from the centre of the region outwards and/or between the region 208 and the surrounding regions may be, for example, at least about 0.1 Κ/μιη. In some embodiments, the temperature gradient may be 1 Κ/μιη or greater.

[0037] The localized heating of the substantially one-dimensional, electrically conductive strands 202 of the cathode 102 facilitates heating the cathode 102 to sufficiently high temperature using EM energy 108 having a much lower power density than the power density of EM energy 108 that would be required to heat a non-one- dimensional material in which thermal conduction is not constrained, such as a bulk metal, to thermionic temperatures. Without wishing to be bound by theory, the threshold power density of the EM energy 108 required to rapidly heat a substantially one-dimensional, thermally anisotropic material has been predicted to be inversely proportional to the square root of the area of the region 208 because thermal anisotropy of the strands 202 constrains the thermal conduction within the region 208 linearly along the length of the strands 202. This is more fully described in the thesis by P. Yaghoobi, "Laser-Induced Electron Emission from Arrays of Carbon Nanotubes" (see, for example, section 5.3.3), which may be found at http://hdl.handle.net/2429/42076, the entirety of which is hereby incorporated by reference herein.

[0038] The EM energy input into the substantially one-dimensional material dissipates in the system through the thermionic emission of electrons, blackbody radiation of photons and heat transfer to the surroundings, which can be expressed as the following conservation of energy equation:

[0039] P_EM = (Φ + 21ίΤ)Α_ΰΑΤ²βϊ + ΑεσΤ* + k(T)(T - T_room) (1 )

[0040] where A is the area of the region 208, σ is the Stefan-Boltzmann constant, e is the emissivity of the material (which is close to 1 for dark materials such as carbon nanotubes), T_room is the room temperature, A_heat is the cross-sectional area of the region 208 perpendicular to the strands 202 (i.e. the diameter of the region 208 times the depth), L is the distance between the hot area (where electron emission occurs) and the room-temperature area, and k(T) is the temperature dependent thermal conductivity of the strands 202, which is assumed to be— with a = 3.7 x 10^"7 and β = 9.7 x αΤ+βΤ²

10^"10 for carbon nanotubes. For simplicity, the temperature is assumed to be constant across the entire region 208 (area A) and then decay linearly to the rest of the nanotube forest over the length L. Although these assumptions are somewhat simplistic, the goal here is not the accurate, quantitative prediction of the temperature.

[0041 ] The relationship between temperature vs. EM energy power is expected to change as a function of size of the region 208 over which the EM energy is incident because the ratio of area of heat dissipation to the size of the region 208 (i.e. for different region sizes will change as a function of ^ (or -= for non-circular regions 208), where r is the radius of the region 208, for an anisotropic material. This can be demonstrated by dividing both sides of equation (1 ) by the heated area (A), which can be assumed to be size of the region 208, to calculate the EM intensity (power per unit area or power density) as a function of temperature. All area (A) terms will disappear from the first two terms on the right side of equation (1 ) and will remain in the third, thermal conduction, term. For the case of substantially one-dimensional materials, A-heat = 2 x radius x depth; therefore ^ - = ^2x^^th given A = π x r² , and is therefore proportional to - (or for non-circular regions 208).

r A

[0042] Utilizing approximations for the constants in equation (1 ) and solving it numerically to determine the threshold power density for heating the material, the relationship between the threshold power density and the area of the region 208 can be approximated as / = where / is the threshold intensity (i.e. power density) in W/m² and A is area in m². For example, for an illuminated region 208 having an area of approximately 0.2 mm², the threshold intensity is approximately 0.45 W/mm². For an illuminated region 208 having an area of 0.03 cm², the threshold intensity is

approximately 10 W/cm². For an illuminated region 208 having an area of

approximately 3 cm², the threshold intensity is approximately 1 W/cm². These approximations are based on both empirical data and simulations.

[0043] Typically, the temperature within the irradiated region 208 is not uniform. For example, if the illuminating beam of light has a circular cross-section, the temperature will be highest at the center of the illuminated area, and will gradually drop to the ambient temperature with distance from this central region. This transition region over which the temperature drops to the ambient temperature is much smaller than in a regular metal due to the localized heating effect of the substantially one-dimensional material. Referring to FIG. 7, a two-dimensional thermal map 702 obtained from irradiating a region having a radius of approximately 50 μιη (the approximate location of the irradiated region is by the circle 704) on the side surface of a carbon nanotube forest with a laser having power of 150 mW, which is above the threshold power density required for thermal emission, is shown. The nanotubes are substantially aligned along the axis labeled "Longitudinal". The thermal map 702 shows a temperature peak 706, approximately centered on the irradiated region 704. The peak 706 may be truncated depending on the measuring apparatus utilized to generate the thermal map 702. The thermal map 702 includes a pair of shoulders 708 that are generally aligned with the temperature peak 706 along the longitudinal axis direction indicating that the heat flow in the nanotube forest is greater along the nanotube strands than transversely between nanotube strands. The thermal map 702 shows regions having thermal gradients of approximately 0.1 Κ/μιη, 0.3 Κ/μιη, 0.5 Κ/μιη, 1 Κ/μιη, and greater with the temperature gradient increasing closer to the temperature peak 706.

[0044] As a non-limiting example, FIG. 3 shows simulated data (the points 302) for the threshold intensity (i.e. power density) of EM energy 108 as a function of the radius of the region 208 of incidence. The dotted line 304 is a 1 /r function that has been fit to the simulated data points 302, demonstrating the 1/r relationship between threshold power density and size of the region 208. The simulated data shown in FIG. 3 was generated by numerically solving a conservation of energy equation (1 ) for a forest of multi-walled carbon nanotubes heated with EM energy 108 having a wavelength of 532 nm. By extrapolating the 1 /r function shown in FIG. 3, rapid heating of the carbon nanotubes is predicted to be achievable with a power density of, for example, approximately 10 W/cm² incident on a region 208 having a radius of approximately 0.1 cm, or, for example, approximately 1 W/cm² incident over a region 208 having a radius of approximately 1 cm.

[0045] Although a laser was assumed to be the EM energy source 104 used to obtain the simulated data shown in FIG. 3, the EM energy source 104 could be, for example, a non-coherent light source. A non-coherent light source is a light source in which the photons are not in a fixed phase relationship. Non-coherent light sources generally comprise a broad spectrum of wavelengths. Examples of non-coherent light sources include sunlight and incandescent lamps. [0046] In all the cases discussed, the incident EM energy could be continuous or varying in time such as, for example, a pulsed EM energy beam. Time-varying EM energy may be utilized to, for example, generate a time-varying electron beam.

[0047] For example, sunlight has an average power density on the surface of the Earth of approximately 0.1 W/cm². A focusing element 106 having a demagnification factor of, for example, 10 times and generating a region 208 of incidence having a radius of at least 1 cm would be sufficient to heat the carbon nanotube strands 202 to thermionic temperatures utilizing sunlight as a EM energy source. A demagnification factor of 10 times is attainable by readily available and relatively inexpensive lenses. Experiments conducted using sunlight as the EM energy source, a lens having a diameter of approximately 50 mm as the focusing element 106, which focused the light to a region 208 of approximately 700 μιη (focusing ratio of approximately 5, 100) produced an incandescent hotspot localized at the region 208 of incidence of the EM energy 108.

[0048] Alternatively, the power density threshold could be attained by low power laser as the EM energy source 104 without the need a focusing element 106. Those skilled in the art will understand that if the power density of the EM energy source 104 is, for example, 1 W/cm² and the region 208 has a radius of at least 1 cm, or the power density is 10 W/cm² and the region 208 has a radius of at least 0.1 cm, then the focusing element 106 may be omitted.

[0049] The anode 1 10 of the electrical generation system 100 shown in FIG.2 may be, for example, copper. The anode 1 10 may be any electrically conductive material that has a work function lower than the work function of the strands 202 to facilitate collecting the electrons emitted from the strands 202 of the cathode 102. The anode 1 10 is spaced away from a top surface 212 of the cathode 102 by the gap 1 14 having a length between the anode 1 10 and the cathode 102 of approximately 1 mm in some embodiments. In other embodiments, the gap 1 14 may be more or less than 1 mm. For example, the gap 1 14 may be on the order of 1 micrometer, or less. The anode 1 10 shown in FIG. 2 has a surface area that is larger than the surface area of the top surface 212 of the cathode 102 to facilitate collection of the electrons emitted from the cathode 102. In other embodiments, the anode 1 10 may be sized differently than shown in FIG. 2 and may, for example, have a size equal to or less than the surface area than the top surface 212 of the cathode 102.

[0050] In some embodiments, the anode 1 10, the top surface 212, the side surface 210, or any combination thereof, may be non-planar to facilitate the collection of electrons. For example, the anode 1 10, the top surface 212, or the side surface 210 may be patterned with microscale or nanoscale features to mitigate space-charge effects, facilitating improved emission of electrons from the cathode 102 and collection at the anode 1 10.

[0051 ] FIG. 2 shows an example embodiment wherein the EM energy 108 is incident on the side surface 210 of the aligned, one-dimensional strands 202, from a direction generally perpendicular to longitudinal axis of the strands 202. In other embodiments, the EM energy 108 may be incident on the strands 202 of the cathode 102 from other directions, and may be incident onto any of the surfaces of the strands 202 or within the volume of the nanotube forest. For example, in one embodiment (not shown), the anode 1 10 is a transparent conductive material such as, for example, indium titanium oxide (ITO), or another transparent conducting film. In this

arrangement, the EM energy 108 can pass through the transparent anode 1 10, irradiating the top surface 212 formed by the ends of the strands 202 opposite the end at the substrate 204. Alternatively, the EM energy 108 may irradiate the side surface 210 of the strands 202. Alternatively, if the strands 202 are grown on a substrate 204 transparent to EM radiation, the EM energy 108 may irradiate the interface 206 between the strands and the substrate, through the substrate 204.

[0052] An advantage of heating the strands 202 at or near the side surface 210 is that the side surface 210 of the strands 202 are more resilient to the EM energy 108 than the tips of the strands 202, providing a more durable electrical generation system 100 when the side surface 210 is heated. For carbon nanotubes, it has been observed that when linearly polarized EM energy 108 is incident on the side surface 210, electron emission is greatest when the polarization axis of the EM energy 108 is parallel to the longitudinal axis of the nanotubes, and emission is lowest when the polarization axis of the EM energy 108 is perpendicular to the longitudinal axis of the nanotubes. Further details may be found in: M. Vahdani Moghaddam, P. Yaghoobi, and A. Nojeh,

"Polarization-dependent light-induced thermionic electron emission from carbon nanotube arrays using a wide range of wavelengths", Appl. Phys. Lett. 101 , 2531 10 (2012); doi: 10.1063/1 .4772504, which is hereby incorporated by reference herein.

[0053] An advantage of heating the strands 202 at or near the top surface 212 is that heating the tips of the stands 202 may generate higher current densities and efficiencies compared with heating at other surfaces such as, for example, the side surface 210. [0054] In a non-limiting embodiment, the strands 202 of the substantially one- dimensional material of the cathode 102 are electrically conductive carbon nanotubes. The carbon nanotubes may be either single-walled or multi-walled nanotubes.

[0055] As seen in FIG. 7, carbon nanotubes have anisotropic thermal

conductivity. Thermal conductivity of carbon nanotubes along the longitudinal axis has been reported as a factor of 150 times greater than thermal conductivity in the lateral directions (i.e. between adjacent nanotubes). Additionally, the thermal conductivity of carbon nanotubes has an inverse dependence on the carbon nanotube temperature, with a behaviour of approximately (αΤ + βΤ²)^"1 being reported for single-walled carbon nanotubes, where T is the temperature of the carbon nanotube, and a and β are constants having values of 3.7 x 10^"7 m/W and 9.7 x 10^"10 mK/W, respectively. The inverse relationship between thermal conductivity and temperature in carbon nanotubes provides a heat trap effect wherein the thermal conductivity of the carbon nanotube drops as the temperature increases, resulting in a localized hot spot at the region 208 where the EM energy 108 is incident. The combined effects of the anisotropic and temperature dependent thermal conductivity facilitates efficient localized heating of the carbon nanotube forest by EM energy 108 having, for example, a power density as low as 1 W/cm² over a region 208 of incidence having a radius of at least 1 cm. As discussed above, these power densities are readily achievable using low intensity EM energy sources 104 such as, for example, focused sunlight or low power laser light.

[0056] Also, as discussed above, forests of carbon nanotubes on a silicon substrate show restricted heat flow across the interface from the nanotubes to the substrate compared to heat conduction within the carbon nanotubes when the nanotubes are heated directly.

[0057] Carbon nanotubes readily absorb photons over a broad spectral range of EM energy 108, facilitating efficient heating of the carbon nanotube emitter using readily available EM energy sources such as, for example, off-the-shelf lasers or non-coherent sources such as sunlight or incandescent lamps. Carbon nanotubes have been shown to have good absorptivity of EM energy over the spectrum from, at least, X-ray to infrared frequencies, and potentially as high as microwave frequencies.

[0058] In a non-limiting example experiment, a cathode 102 comprising a forest of aligned, multi-walled carbon nanotubes approximately 5mm wide and 2 mm high, and an Indium Tin Oxide (ITO) anode 1 10 approximately 2 cm by 2cm and spaced approximately 1 mm from the cathode 102, are used. The anode 1 10 was placed parallel with the side surface 210 of the cathode 102 and EM energy 108 was incident on the side wall 210 after passing through the ITO anode 1 10. EM energy 108 comprising focused sunlight having an approximate power density of 780 W/cm² (corresponding to focusing ratio of approximately 27,800) irradiated a region 208 having a diameter of approximately 300 μιη, and an area of approximately 0.07 mm², on the side surface 210. No external electric field was applied during the experiment. When the anode 1 10 and the cathode 102 were connected by a 10 ΜΩ load, a voltage of approximately 1 .3 V between the anode 1 10 and cathode 102 was measured, providing a current through the 10 ΜΩ of approximately 130 nA. When the anode 1 10 and the cathode 102 were connected by 38 kQ load, approximately 45 mV between the anode 1 10 and the cathode 102 was measured, providing a current of approximately 1 .2 μΑ through the 38 kQ load. When no load connected the anode 1 10 and the cathode 102, an open circuit voltage of 3.5 V between the anode 1 10 and the cathode 102 was measured.

[0059] Further discussion regarding experiments using sunlight may be found in: P. Yaghoobi, M. Vahdani, and A. Nojeh, "Solar electron source and thermionic solar cell", AIP Advances 2, 042139 (2012); doi: 10.1063/1 .4766942, which is hereby incorporated by reference herein.

[0060] In a non-limiting example experiment, a cathode 102 comprising a forest of aligned, multi-walled carbon nanotubes having lateral dimensions of approximately 5mm and having a height of approximately 1 mm, and an copper anode 1 10

approximately 1 cm by 1 cm and spaced approximately 1 mm from the cathode 102, were used. The anode 1 10 was parallel with the top surface 212 of the cathode 102. The anode 1 10 extended approximately 2-3 mm past the side surfaces 102 of the cathode 102 to improve the collection of electrons emitted from the cathode 102. A collection voltage of 50V was applied, which is below the voltage required for field emission. EM energy 108 was incident on the side wall 210 of the carbon nanotubes. The EM energy 108 comprised three different lasers having wavelengths of 488 nm, 514 nm, and 532 nm focused to a region 208 having a radius of approximately 250 μιη and an area of approximately 0.2 mm². A Keithly 6517A electrometer was used to apply the collection voltage to the anode 1 10 and measure the emission current collected at the anode 1 10. The measured emission currents for the different power densities of each of the wavelengths of EM radiation are shown in FIG. 8. For example, a current of approximately 18 μΑ was measured when a power of 300 mW

(corresponding to a power density of approximately 150 W/cm²) from the 488 nm laser was focused onto the region 208 having a radius of approximately 250 μιη. [0061 ] Referring now to FIG. 4, a schematic for a thermionic electron emitter 400 is shown. The thermionic electron emitter 400 includes a cathode 402, an EM energy source 404, a focusing element 406 that focuses EM energy 408 from the EM energy source 404 onto the cathode 402 to heat the cathode to thermionic temperatures, and an anode 410 separated from the cathode by a gap 414. The cathode 402, EM energy source 404, focusing element 406, and anode 410 are substantially similar to corresponding elements described previously for the electric generator 100 shown in FIGs. 1 and 2.

[0062] The electron emitter 400 includes a biasing element 412 that couples to the cathode 402 and anode 410. The biasing element 412 provides a positive voltage at the anode 410, relative to the cathode 402, to produce an electric field in the gap 414 between the cathode 402 and the anode 410. The electric field accelerates

thermionically generated electrons emitted from the cathode toward the anode 410.

[0063] In some embodiments, the electric field in the gap 414 between the cathode 402 and anode 410 may be provided by a means other than the biasing element 412 that connects the cathode 402 and the anode 410 in FIG. 4. The electric field may be provided, for example, externally to the environment surrounding the thermionic electron emitter 400.

[0064] In some embodiments, the electric field is provided in the gap 414 between the cathode 402 and the anode 410 to facilitate more efficient collection of the emitted electrons at the anode 410 than would be achieved in the absence of an applied field. The electric field may be, for example, below the field emission threshold for the substantially one-dimensional material of the cathode 402 at room temperature (e.g. less than approximately 1 V/nm at the surface of the cathode 402). In this

arrangement, the cathode 402 and the anode 410 may be connected by a load (not shown) to facilitate the electron emitter 400 operating as a more efficient electrical generation system compared to the electrical generation system 100 described previously. The thermionically generated free electrons emitted with kinetic energy that is insufficient to traverse the gap 414 will be accelerated across the gap 414 by the electric field and are collected at the anode 410, increasing the electric current through the load compared to the current delivered in the absence of an applied electrical field. Further, electrons emitted at the cathode 402 with momentum directed away from the anode 410 may be directed toward the anode 410 by the electric field, increasing the electric current through a load compared to the current delivered in the absence of an applied electrical field. [0065] In substantially one-dimensional materials, field emission may be enhanced in a material having a sharp end or high aspect ratio, such as a substantially one-dimensional material, because the shape of the material will substantially enhance an applied electric field compared with a flat material. For example, in the case of carbon nanotubes, typically an applied electric field on the order of V/μιη will be sufficient to field-emit electrons because the enhancement by the nanotube's shape will result in the V/nm fields required at the surface. For example, for a distance between a nanotube emitter material and an "extractor" gate (which could be the anode or another, intermediate electrode) of the order of 1 mm, an applied voltage on the order of 1000 V will be required to produce significant field-emission. By contrast, in a thermionic device a voltage of, for example, 10-100 V may be applied across a gap of 1 mm separating the anode 1 10 and the cathode 102, which is much lower than the electric field on the order of 1000 V that would be required for field-emission.

[0066] Alternatively, a large bias may be applied to produce a large electric field in the gap 414 between the cathode 402 and the anode 410 such as, for example, to facilitate accelerating the free electrons generated at the cathode 402 to energies greater than the energy required to merely traverse the gap 414. In this arrangement, the thermionic electron emitter is operable as an electron beam emitter wherein the electrons are accelerated toward a target for utilization in processes such as, for example, lithography, microscopy, welding, machining, flue gas treatment, vacuum electronics applications, or display screens. Note that in this arrangement, the material of the anode 410 need not have a work function below the work function of the cathode 402 because electrons are not necessarily being collected by the anode 410.

[0067] Referring now to FIG. 5, a flowchart illustrating a method for generating free electrons thermionically is shown.

[0068] A substantially one-dimensional, electrically conductive material having a restricted, anisotropic thermal conductivity is provided at 502.

[0069] The substantially one-dimensional, electrically conductive material may be as described above. The restricted, anisotropic thermal conductivity may be enhanced by one or both of a thermal conductivity that decreases as the temperature of the substantially one-dimensional material increases, and an interface between the substantially one-dimensional material and a substrate that restricts heat flow between the substantially one-dimensional material and the substrate. The substantially one- dimensional material may be formed of aligned strands. The substantially one- dimensional material may be, for example, a forest of electrically conductive carbon nanotubes on a substrate. The carbon nanotubes may be provided on a silicon substrate having an interface between the nanotubes and the substrate that restricts the flow of heat across the interface.

[0070] The substantially one-dimensional, electrically conductive material is heated by irradiating the substantially one-dimensional material with EM energy having a power density above a threshold to generate free electrons at 504. The EM energy is non-coherent in some embodiments, and may comprise, for example, focused sunlight as described above. In other embodiments, the EM energy may be a low powered laser or other EM energy source. As described above, the threshold may, for example, be determined based on the size of the irradiated region.

[0071 ] The substantially one-dimensional, electrically conductive material may be heated to create a heat gradient of at least 0.1 Κ/μιη between the heated region and non-heated regions of the substantially one-dimensional material. The EM energy may be incident on the substantially one-dimensional material on a surface formed by the ends of aligned strands of the substantially one-dimensional material by shining the EM energy through a transparent anode.

[0072] The free electrons generated may be collected by an anode and used to provide an electrical current to a load. Alternatively, the free electrons may be accelerated by an applied electric field to deliver an electron beam to a target.

[0073] Referring now to FIG. 6, an embodiment in which the above described method is used to produce multiple, shaped electron beams is illustrated.

[0074] Multiple, shaped electron beams 602a-602d are produced by irradiating multiple, separate regions 208a-208d by respective separate, multiple EM energy beams 108a-108d that locally heat the separate regions 208a-208d to thermionically generate free electrons, as discussed above. The thermionically generated free electrons are accelerated by an external field, producing multiple, separate electron beams 602a-602d associated with respective regions 208a-208d. The cross-sectional shape of each of the electron beams 602a-602d is determined by the shape of the associated region 208a-208d. The shapes at regions 208a-208d may be controlled by selection of the cross-sectional shape of the EM energy beam 108a-108d that irradiates the region 208a-208d.

[0075] For example, in FIG. 6, the respective cross-sections of the multiple EM energy beams 208a-208d are shaped to form regions 208a-208d, each having a shape determined by the cross-section of the associated EM energy beam 208a-208d. For example, as shown in FIG. 6, EM energy beam 108a has a circular cross-sectional shape that forms a region 208a having a circular shape, EM beam 108b has a diamond cross-sectional shape that forms a region 208b having a diamond shape, EM beam 208c has a pentagonal cross-sectional shape that forms a region 208c that has a pentagonal shape, and EM energy beam 208d has an elongated cross-sectional shape that forms a region 208d has an elongated shape.

[0076] Localized heating at the regions 208a-208d cause thermionic emission of free electrons at the regions 208a-208d. When the thermionic electrons are accelerated away from the cathode 202 by an applied electrical field, the resulting multiple electron beams 602a-602d will have respective cross-sectional shapes determined by the shape of the associated region 208a-208d. In the example illustrated in FIG. 6, electron beam 602a has a circular cross-sectional shape, electron beam 602b has a diamond cross- sectional shape, electron beam 602c has a pentagonal cross-sectional shape, and electron beam 602d has an elongated cross-sectional shape.

[0077] Although FIG. 6 shows four separate EM energy beams 108a-108d forming four separate regions 208a-208d, in other embodiments more or less than four EM beams my irradiate the cathode 202. Also, although FIG. 6 shows each EM energy beam 108a-108d having a different cross-sectional shape, in other embodiments, all or some of the EM energy beams may have the same cross-sectional shapes, and the cross-sectional shapes may be different than the four shapes illustrated in FIG. 6.

Although the regions 208a-208d are shown in FIG. 6 as isolated regions, in other embodiments the regions 208a-208d may be connected or partially overlap.

[0078] In a non-limiting example experiment, two laser beams having

wavelengths of 532 nm and 1064 nm, spot radii of 250 micrometers and 525

micrometers, and powers of 23 mW and 18 mW, respectively, were used to generate two electron beams simultaneously from a single cathode made of carbon nanotubes. The resulting electron beams were accelerated by an applied electric field of 2000 V and projected onto a phosphor screen (without the use of any focusing element). The resulting beam spot sizes and shapes on the phosphor screen were similar to the spot sizes and shapes of the laser beams used for excitation. In another non-limiting example experiment, a cylindrical lens was used to create a line-shaped laser spot on the carbon nanotube cathode. The laser wavelength was 532 nm and the power was 256 mW. The resulting electron beam was accelerated by an applied electric field of 2000 V and projected onto a phosphor screen (without the use of any focusing element). The resulting line-shaped image on the phosphor screen was similar in size to that of the laser beam used for excitation. [0079] In some embodiments, multiple shaped regions 208a-208d may be formed by pre-patterning the substantially one-dimensional material of the cathode 202 into multiple regions 208a-208d of desired shapes. A single flood beam of EM energy 108 incident on the cathode will irradiate only pre-patterned regions 208a-208d, producing multiple, shaped electron beams. For example, in the case of nanotube forests, a growth catalyst must be deposited as a thin layer on a substrate before nanotube deposition. Various shapes could be patterned on the catalyst layer using standard lithography techniques to remove portions of the catalyst such that, during nanotube growth, the nanotubes will be deposited only in the regions of the substrate in which the catalyst remains. For example the cathode may include an array of cylindrical columns of nanotubes, each column being a nanotube forest comprising many individual nanotubes. In other embodiments, the surface of the nanotubes could be shaped by forming angled surfaces and variable heights in different regions of the cathode surface.

[0080] The multiple, shaped regions 208a-208b may be provided by a

combination of multiple EM energy beams 108a-108d and pre-patterning of the substantially one-dimensional material of the cathode 202. For example, one of the cylindrical columns described above may be irradiated with multiple EM beams such that multiple beams are generated from a single column of nanotubes. Alternatively, multiple beams may be used to selectively irradiate some of the pre-patterned regions to control the number or shape of the electron beams that are generated.

[0081 ] There are many applications for multiple electron beams, or beams with different cross-sectional geometries. For example, multiple electron beams, and shaped electron beams, are useful in applications such as electron beam microscopy, inspection, and lithography. In lithography a focused beam of electrons in vacuum is used to create patterns or images with extremely high resolutions, such as the nanometer or even sub-nanometer scale. Shaped or multiple beams are also utilized in other applications. For example, in electron beam flue-gas treatment, a moving flow of gases is exposed to electron beams and coverage of the electron beam over a wide portion of the gas flow path is advantageous. In applications such as materials treatment (curing shrink wrap and tires, for example) or electron beam welding and machining, the usage of a plurality of beams or shaped beams may significantly enhance throughput.

[0082] High resolution lithographic patterning is enabled by the fact that electron beams can be focused to extremely small spots. The usual approach to such image formation or pattern generation is one of scanning the beam across the area to be imaged or in the pattern to be generated (a "direct write" approach). As such, the throughput of these systems is low, in contrast to systems that use the projection of an entire image/pattern in one shot (typically the case in optical systems). Therefore, despite superior resolution, electron-beam lithography has not been able to capture a significant portion of the mainstream micro/nanolithography market in the

semiconductor/electronics industry. By providing multiple, shaped electron beams produced by the methods and systems disclosed herein, throughput of electron beam lithography may be increased. For example, multiple shaped electron beams may be produced to facilitate the projection of an entire image/pattern in one shot using electron-beam lithography.

[0083] Utilizing the method above, substantially one-dimensional, electrically conductive material having a restricted, anisotropic thermal conductivity facilitates heating the material to thermionic temperatures using EM energy having power densities lower than would be required for bulk electrically conductive materials in which heat conduction is substantially unrestricted. The described method also facilitates thermionically generating free electrons using readily available sources of EM energy such as, for example, sunlight or low power lasers focused with readily available focusing elements. The method facilitates generating electricity in, for example, a thermionic solar cell, or delivering an electron beam in a thermionic solar electron beam emitter.

[0084] The present disclosure may be embodied in other specific forms without departing from its spirit or essential characteristics. The described embodiments are to be considered in all respects only as illustrative and not restrictive.

Claims

1 . A method of generating free electrons comprising: providing a substantially one-dimensional, electrically conductive material having a restricted, anisotropic thermal conductivity; and irradiating a region of the substantially one-dimensionally material with non-coherent electromagnetic energy having a power density above a threshold to heat the region and generate a temperature gradient having a magnitude of at least 0.1 Κ/μιη between the irradiated region and the remainder of the substantially one-dimensional material to thermionically generate free electrons at the region.

2. The method of claim 1 , wherein the threshold power density is determined based on an area of the region irradiated with electromagnetic energy, wherein power density threshold is inversely proportional to the square root of the area of the region.

3. The method of claim 2, wherein the relationship between the threshold power density and area is approximately / = where / is the threshold power density in W/m² and A is the area of the region in m².

4. The method of claim 2, wherein the threshold power density is approximately 0.45 W/mm² when the region has an area of at least 0.2 mm².

5. The method of any one of claims 1 to 4, wherein the non-coherent electromagnetic energy is focused sunlight.

6. The method of claim 5, wherein providing the substantially one-dimensional material comprises providing a forest of multi-walled carbon nanotubes approximately 5mm by 5mm and 2 mm high on a substrate, wherein irradiating the region comprises irradiating an area of approximately 0.07 mm²located on a side surface of the forest of multi-walled carbon nanotubes with sunlight having a power density of at least approximately 780 W/cm² to generate a current of at least 1 .2 μΑ at an ITO anode approximately 2cm by 2cm in size and spaced approximately 1 mm from the region and coupled to the substrate by a 38 kQ load.

7. The method of any one of claims 1 to 6, wherein the substantially one-dimensional, electrically conductive material is carbon nanotubes.

8. The method of any one of claims 1 to 7, wherein providing the substantially one- dimensional material comprises providing a substantially one-dimensional material having a thermal conductivity that decreases as the temperature of the material increases, to facilitate localized heating at the region.

9. The method of any one of claims 1 to 8, wherein the substantially one-dimensional material is coupled to a substrate at an interface, the interface having defects to restrict the thermal conductivity from the material to the substrate.

10. The method of any one of claims 1 to 9, wherein irradiating the region with noncoherent electromagnetic energy comprises irradiating a region of a side surface of the substantially one-dimensional material.

1 1 . The method of claim 10, further comprising linearly polarizing the electromagnetic energy in a direction substantially parallel to a longitudinal axis of the substantially one- dimensional material.

12. The method of any one of claims 1 to 1 1 , wherein the region comprises a plurality of separate regions of the substantially one-dimensional material, and irradiating the region comprises irradiating each of the plurality of separate regions with

electromagnetic energy having a power density above a threshold to heat each of the plurality of regions and generate temperature gradients of at least 0.1 Κ/μιη between each of the plurality of regions and the remainder of the substantially one-dimensional material to thermionically generate free electrons at each of the plurality of regions.

13. The method of claim 12, wherein the plurality of separate regions are formed by patterning the substantially one-dimensional material such that electromagnetic energy incident on the substantially one-dimensional material irradiates the substantially one- dimensional material at the plurality of regions.

14. The method of claim 12, wherein irradiating a plurality of regions comprises irradiating the substantially one-dimensional material with a plurality of beams of electromagnetic energy, each of the plurality of beams having a power density above the threshold.

15. The method of any one of claims 1 to 14, further comprising applying an electric field to accelerate the thermionically generated electrons away from the substantially one-dimensional material to generate an electron beam deliverable to a target or an anode.

16. The method of any one of claims 1 to 15, further comprising shaping the cross- section of a beam of the non-coherent electromagnetic energy irradiating the region to generate an electron beam having a shape determined by at least the cross-section of the beam of the electromagnetic energy.

17. The method of any one of claims 1 to 16, further comprising collecting the thermonically generated free electrons at an anode.

18. The method of claim 17, wherein the anode is substantially transparent, further comprising directing the non-coherent electromagnetic energy through the anode to irradiate the region of the substantially one-dimensional material.

19. The method of claim 17, further comprising providing a gas in a gap between the anode and the substantially one dimensional material, wherein the gas provides at least one of reduced space-charge effects at a surface of the irradiated region, reduced space-charge effects in the gap, and reduce a work-function at an interface between the anode the gap.

20. The method of any one of claims 1 to 19, wherein a surface of the irradiated region is patterned to include features that reduce space-charge effects.

21 . The method of any one of claims 1 to 20, wherein the temperature gradient between the irradiated region and the remainder of the substantially one-dimensional material has a magnitude of at least 0.3 Κ/μιη.

22. The method of any one of claims 1 to 20, wherein the temperature gradient between the irradiated region and the remainder of the substantially one-dimensional material has a magnitude of at least 0.5 Κ/μιη.

23. The method of any one of claims 1 to 20, wherein the temperature gradient between the irradiated region and the remainder of the substantially one-dimensional material has a magnitude of at least 1 .0 Κ/μιη.

24. The method of any one of claims 1 to 23, wherein the EM energy is time-varying.

25. A thermionic converter comprising: an anode; and a cathode separated from the anode by a gap, the cathode comprising a substantially one-dimensional, electrically conductive material having a restricted, anisotropic thermal conductivity; wherein non-coherent electromagnetic energy having a power density above a threshold, irradiated on a region of the substantially one-dimensional, electrically conductive material, heats the region and generates a temperature gradient of at least 0.1 Κ/μιη between the irradiated region and the remainder of the substantially one- dimensional material to thermionically generate free electrons at the region.

26. The thermionic converter of claim 25, wherein the threshold power density is determined based on an area of the region irradiated with electromagnetic energy, wherein power density threshold is inversely proportional to the square root of the area of the region.

27. The thermionic converter of claim 26, wherein the relationship between the threshold power density and area is approximately / = where / is the threshold power density in W/m² and A is the area of the region in m².

28. The thermionic converter of claim 26, wherein the threshold power density is approximately 0.45 W/mm² when the region has an area of at least 0.2 mm².

29. The thermionic converter of any one of claims 25 to 28, wherein the non-coherent electromagnetic energy is focused sunlight.

30. The thermionic converter of claim 29, wherein when the cathode comprises a forest of multi-walled carbon nanotubes approximately 5mm by 5mm and 2 mm high, the region has an area of approximately 0.07 mm² located on a side surface of the forest of multi-walled carbon nanotubes, the sunlight has a power density of at least

approximately 780 W/cm², and the anode is ITO and is approximately 2cm by 2cm in size and spaced approximately 1 mm from the region and coupled to the cathode by a 38 kQ load, a current of approximately 1 .2 μΑ is generated through the load.

31 . The thermionic converter of any one of claims 25 to 30, wherein the substantially one-dimensional, electrically conductive material is carbon nanotubes.

32. The thermionic converter of any one of claims 25 to 31 , wherein the substantially one-dimensional material has a thermal conductivity that decreases as the temperature of the material increases, to facilitate localized heating at the region.

33. The thermionic converter of any one of claims 25 to 32, wherein the substantially one-dimensional material is coupled to a substrate at an interface, the interface having defects to restrict the thermal conductivity from the material to the substrate.

34. The thermionic converter of any one of claims 25 to 33, wherein irradiating the region with the electromagnetic energy comprises irradiating a region of a side surface of the substantially one-dimensional material.

35. The thermionic converter of claim 34, wherein the electromagnetic energy is linearly polarized in a direction substantially parallel to a longitudinal axis of the substantially one-dimensional material.

36. The thermionic converter of any one of claims 25 to 35, wherein the region comprises a plurality of separate regions of the substantially one-dimensional material, and irradiating the region comprises irradiating each of the plurality of separate regions with non-coherent electromagnetic energy having a power density above a threshold to heat each of the plurality of regions and generate temperature gradients of at least 0.1 Κ/μιη between each of the plurality of regions and the remainder of the substantially one-dimensional material to thermionically generate free electrons at each of the plurality of regions.

37. The thermionic converter of claim 36, wherein the plurality of separate regions are formed by patterning the substantially one-dimensional material such that the noncoherent electromagnetic energy incident on the substantially one-dimensional material irradiates the substantially one-dimensional material at the plurality of regions.

38. The thermionic converter of claim 36, wherein the plurality of regions are formed by irradiating the substantially one-dimensional material with a plurality of beams of noncoherent electromagnetic energy, each of the plurality of beams having a power density above the threshold.

39. The thermionic converter of any one of claims 25 to 38, further comprising an electric field to accelerate the thermionically generated electrons away from the cathode and toward the anode.

40. The thermionic converter of any one of claims 25 to 39, wherein the anode is substantially transparent to facilitate directing the non-coherent electromagnetic energy through the anode to irradiate the region of the substantially one-dimensional material.

41 . The thermionic converter of any one of claims 25 to 40, further comprising providing a gas in a gap between the anode and the substantially one dimensional material, wherein the gas provides at least one of reduced space-charge effects at a surface of the irradiated region, reduced space-charge effects in the gap, and reduce a work- function at an interface between the anode the gap.

42. The thermionic converter of any one of claims 25 to 41 , wherein a surface of the irradiated region is patterned to include features that reduce space-charge effects.

43. The thermionic converter of any one of claims 25 to 41 , wherein the temperature gradient between the irradiated region and the remainder of the substantially one- dimensional material has a magnitude of at least 0.3 Κ/μιη.

44. The thermionic converter of any one of claims 25 to 41 , wherein the temperature gradient between the irradiated region and the remainder of the substantially one- dimensional material has a magnitude of at least 0.5 Κ/μιη.

45. The thermionic converter of any one of claims 25 to 41 , wherein the temperature gradient between the irradiated region and the remainder of the substantially one- dimensional material has a magnitude of at least 1 .0 Κ/μιη.

46. The thermionic converter of any one of claims 25 to 45, wherein the EM energy is time-varying.

47. An electron beam emitter comprising: a cathode comprising a substantially one-dimensional, electrically conductive material having a restricted, anisotropic thermal conductivity; wherein non-coherent electromagnetic energy having a power density above a threshold, irradiated on a region of the substantially one-dimensional, electrically conductive material, heats the region and generates a temperature gradient of at least 0.1 Κ/μιη between the irradiated region and the non-irradiated region of the substantially one-dimensional material to thermionically generate free electrons at the region; and an electrode to generate an electric field to accelerate the thermionically generated free electrons away from the cathode, to produce an electron beam deliverable to a target.

48. The electron beam emitter of claim 47, wherein the threshold power density is determined based on an area of the region irradiated with electromagnetic energy, wherein power density threshold is inversely proportional to the square root of the area of the region.

49. The electron beam emitter of claim 48, wherein the relationship between the threshold power density and area is approximately / = where / is the threshold power density in W/m² and A is the area of the region in m².

50. The electron beam emitter of claim 48, wherein the threshold power density is approximately 0.45 W/mm² when the region has an area of at least 0.2 mm².

51 . The electron beam emitter of any one of claims 47 to 50, wherein the non-coherent electromagnetic energy is focused sunlight.

52. The electron beam emitter of claim 51 , wherein when the cathode comprises a forest of multi-walled carbon nanotubes approximately 5mm by 5mm and 2 mm high, the region has an area of approximately 0.07 mm² located on a side surface of the forest of multi-walled carbon nanotubes, the sunlight has a power density of at least approximately 780 W/cm², and the anode is ITO and is approximately 2cm by 2cm in size and spaced approximately 1 mm from the region and coupled to the cathode by a 38 kQ load, a current of approximately 1 .2 μΑ is generated through the load.

53. The electron beam emitter of any one of claims 47 to 52, wherein the substantially one-dimensional, electrically conductive material is carbon nanotubes.

54. The electron beam emitter of any one of claims 47 to 53, wherein the substantially one-dimensional material has a thermal conductivity that decreases as the temperature of the material increases, to facilitate localized heating at the region.

55. The electron beam emitter of any one of claims 47 to 54, wherein the substantially one-dimensional material is coupled to a substrate at an interface, the interface having defects to restrict the thermal conductivity from the material to the substrate.

56. The electron beam emitter of any one of claims 47 to 55, wherein irradiating the region with the electromagnetic energy comprises irradiating a region of a side surface of the substantially one-dimensional material.

57. The electron beam emitter of claim 56, wherein the electromagnetic energy is linearly polarized in a direction substantially parallel to a longitudinal axis of the substantially one-dimensional material.

58. The electron beam emitter of any one of claims 47 to 57, wherein the region comprises a plurality of separate regions of the substantially one-dimensional material, and irradiating the region comprises irradiating each of the plurality of separate regions with electromagnetic energy having a power density above a threshold to heat each of the plurality of regions and generate temperature gradients of at least 0.1 Κ/μιη between each of the plurality of regions and the remainder of the substantially one- dimensional material to thermionically generate free electrons at each of the plurality of regions.

59. The electron beam emitter of claim 58, wherein the plurality of separate regions are formed by patterning the substantially one-dimensional material such that

electromagnetic energy incident on the substantially one-dimensional material irradiates the substantially one-dimensional material at the plurality of regions.

60. The electron beam emitter of claim 58, wherein the plurality of regions are formed by irradiating the substantially one-dimensional material with a plurality of beams of electromagnetic energy, each of the plurality of beams having a power density above the threshold.

61 . The electron beam emitter of any one of claims 47 to 60, wherein the electrode is substantially transparent to facilitate directing the electromagnetic energy through the anode to irradiate the region of the substantially one-dimensional material.

62. The electron beam emitter of any one of claims 47 to 61 , further comprising a gas between the electrode and the substantially one dimensional material, wherein the gas provides reduced space-charge effects at a surface of the irradiated region.

63. The electron beam emitter of any one of claims 47 to 62, wherein a surface of the irradiated region is patterned to include features that reduce space-charge effects.

64. The electron beam emitter of any one of claims 47 to 63, wherein the temperature gradient between the irradiated region and the remainder of the substantially one- dimensional material has a magnitude of at least 0.3 Κ/μιη.

65. The electron beam emitter of any one of claims 47 to 63, wherein the temperature gradient between the irradiated region and the remainder of the substantially one- dimensional material has a magnitude of at least 0.5 Κ/μιη.

66. The electron beam emitter of any one of claims 47 to 63, wherein the temperature gradient between the irradiated region and the remainder of the substantially one- dimensional material has a magnitude of at least 1 .0 Κ/μιη.

67. The electron beam emitter of any one of claims 47 to 63, wherein the EM energy is time-varying.

68. A method of generating free electrons comprising: providing a substantially one-dimensional, electrically conductive material having a restricted, anisotropic thermal conductivity; and irradiating a region of the substantially one-dimensionally material with electromagnetic energy having a power density above a threshold to heat the region and generate a temperature gradient having a magnitude of at least 0.1 Κ/μιη between the irradiated region and the remainder of the substantially one-dimensional material to thermionically generate free electrons at the region.

69. The method of claim 68, wherein the threshold power density is determined based on an area of the region irradiated with electromagnetic energy, wherein power density threshold is inversely proportional to the square root of the area of the region.

70. The method of claim 69, wherein the relationship between the threshold power density and area is approximately / = where / is the threshold power density in

W/m² and A is the area of the region in m².

71 . The method of claim 69, wherein the threshold power density is approximately 1 W/cm² when the region has an area of at least 0.2 mm².

72. The method of claim 68, wherein the electromagnetic energy is non-coherent.

73. The method of claim 72, wherein the non-coherent electromagnetic energy is focused sunlight.

74. The method of claim 73, wherein providing the substantially one-dimensional material comprises providing a forest of multi-walled carbon nanotubes approximately 5mm by 5mm and 2 mm high on a substrate, wherein irradiating the region comprises irradiating an area of approximately 0.07 mm² located on a side surface of the forest of multi-walled carbon nanotubes with sunlight having a power density of at least approximately 780 W/cm² to generate a current of at least 1 .2 μΑ at an ITO anode approximately 2cm by 2cm in size and spaced approximately 1 mm from the region and coupled to the substrate by a 38 kQ load.

75. The method of claim 68, wherein the substantially one-dimensional, electrically conductive material is carbon nanotubes.

76. The method of claim 68, wherein providing the substantially one-dimensional material comprises providing a forest of multi-walled carbon nanotubes approximately 5mm by 5mm and 2 mm high on a substrate, wherein irradiating the region comprises irradiating an area of approximately 0.2 mm² located on a side surface of the forest of multi-walled carbon nanotubes with laser light having a wavelength of 488 nm having a power density of at least approximately 150 W/cm² to generate a current of at least 18 μΑ at a copper anode approximately 1 cm by 1 cm in size and spaced approximately 1 mm from the region and biased with a collection voltage of 50V.

77. The method of claim 68, wherein providing the substantially one-dimensional material comprises providing a substantially one-dimensional material having a thermal conductivity that decreases as the temperature of the material increases, to facilitate localized heating at the region.

78. The method of claim 68, wherein the substantially one-dimensional material is coupled to a substrate at an interface, the interface having defects to restrict the thermal conductivity from the material to the substrate.

79. The method of claim 68, wherein irradiating the region with electromagnetic energy comprises irradiating a region of a side surface of the substantially one-dimensional material.

80. The method of claim 79, further comprising linearly polarizing the electromagnetic energy in a direction substantially parallel to a longitudinal axis of the substantially one- dimensional material.

81 . The method of claim 68, wherein the region comprises a plurality of separate regions of the substantially one-dimensional material, and irradiating the region comprises irradiating each of the plurality of separate regions with electromagnetic energy having a power density above a threshold to heat each of the plurality of regions and generate temperature gradients of at least 0.1 Κ/μιη between each of the plurality of regions and the remainder of the substantially one-dimensional material to thermionically generate free electrons at each of the plurality of regions.

82. The method of claim 81 , wherein the plurality of separate regions are formed by patterning the substantially one-dimensional material such that electromagnetic energy incident on the substantially one-dimensional material irradiates the substantially one- dimensional material at the plurality of regions.

83. The method of claim 81 , wherein irradiating a plurality of regions comprises irradiating the substantially one-dimensional material with a plurality of beams of electromagnetic energy, each of the plurality of beams having a power density above the threshold.

84. The method of claim 68, further comprising applying an electric field to accelerate the thermionically generated electrons away from the substantially one-dimensional material to generate an electron beam deliverable to a target or an anode.

85. The method of claim 68, further comprising shaping the cross-section of a beam of the electromagnetic energy irradiating the region to generate an electron beam having a shape determined by at least the cross-section of the beam of the electromagnetic energy.

86. The method of claim 68, further comprising collecting the thermonically generated free electrons at an anode.

87. The method of claim 86, wherein the anode is substantially transparent, further comprising directing the electromagnetic energy through the anode to irradiate the region of the substantially one-dimensional material.

88. The method of claim 86, further comprising providing a gas in a gap between the anode and the substantially one dimensional material, wherein the gas provides at least one of reduced space-charge effects at a surface of the irradiated region, reduced space-charge effects in the gap, and reduce a work-function at an interface between the anode the gap.

89. The method of claim 68, wherein a surface of the irradiated region is patterned to include features that reduce space-charge effects.

90. The method of claim 68, wherein the temperature gradient between the irradiated region and the remainder of the substantially one-dimensional material has a magnitude of at least 0.3 Κ/μιη.

91 . The method of claim 68, wherein the temperature gradient between the irradiated region and the remainder of the substantially one-dimensional material has a magnitude of at least 0.5 Κ/μιη.

92. The method of claim 68, wherein the temperature gradient between the irradiated region and the remainder of the substantially one-dimensional material has a magnitude of at least 1 .0 Κ/μιη.

93. The method of claim 68, wherein the EM energy is time-varying.

94. A thermionic converter comprising: an anode; and a cathode separated from the anode by a gap, the cathode comprising a substantially one-dimensional, electrically conductive material having a restricted, anisotropic thermal conductivity; wherein electromagnetic energy having a power density above a threshold, irradiated on a region of the substantially one-dimensional, electrically conductive material, heats the region and generates a temperature gradient of at least 0.1 Κ/μιη between the irradiated region and the remainder of the substantially one-dimensional material to thermionically generate free electrons at the region.

95. The thermionic converter of claim 94, wherein the threshold power density is determined based on an area of the region irradiated with electromagnetic energy, wherein power density threshold is inversely proportional to the square root of the area of the region.

96. The thermionic converter of claim 95, wherein the relationship between the threshold power density and area is approximately / = where / is the threshold power density in W/m² and A is the area of the region in m².

97. The thermionic converter of claim 95, wherein the threshold power density is approximately 0.45 W/mcm² when the region has an area of at least 0.2 mm².

98. The thermionic converter of claim 94, wherein the electromagnetic energy is non- coherent.

99. The thermionic converter of claim 98, wherein the non-coherent electromagnetic energy is focused sunlight.

100. The thermionic converter of claim 99, wherein when the cathode comprises a forest of multi-walled carbon nanotubes approximately 5mm by 5mm and 2 mm high, the region has an area of approximately 0.07 mm² located on a side surface of the forest of multi-walled carbon nanotubes, the sunlight has a power density of at least approximately 780 W/cm², and the anode is ITO and is approximately 2cm by 2cm in size and spaced approximately 1 mm from the region and coupled to the cathode by a 38 kQ load, a current of approximately 1 .2 μΑ is generated through the load.

101 . The thermionic converter of claim 94, wherein the substantially one-dimensional, electrically conductive material is carbon nanotubes.

102. The thermionic converter of claim 94, wherein when the cathode comprises a forest of multi-walled carbon nanotubes approximately 5mm by 5mm and 2 mm high, the region has an area of approximately 0.2 mm² located on a side surface of the forest of multi-walled carbon nanotubes, the electromagnetic energy energy is laser light having a wavelength of 488 nm having a power density of at least approximately 150 W/cm², the anode is copper and is approximately 1 cm by 1 cm in size and spaced approximately 1 mm from the region and biased with a collection voltage of 50V, a current of at least 18 μΑ is measured.

103. The thermionic converter of claim 94, wherein the substantially one-dimensional material has a thermal conductivity that decreases as the temperature of the material increases, to facilitate localized heating at the region.

104. The thermionic converter of claim 94, wherein the substantially one-dimensional material is coupled to a substrate at an interface, the interface having defects to restrict the thermal conductivity from the material to the substrate.

105. The thermionic converter of claim 94, wherein irradiating the region with the electromagnetic energy comprises irradiating a region of a side surface of the substantially one-dimensional material.

106. The thermionic converter of claim 105, wherein the electromagnetic energy is linearly polarized in a direction substantially parallel to a longitudinal axis of the substantially one-dimensional material.

107. The thermionic converter of claim 94, wherein the region comprises a plurality of separate regions of the substantially one-dimensional material, and irradiating the region comprises irradiating each of the plurality of separate regions with

108. The thermionic converter of claim 107, wherein the plurality of separate regions are formed by patterning the substantially one-dimensional material such that the electromagnetic energy incident on the substantially one-dimensional material irradiates the substantially one-dimensional material at the plurality of regions.

109. The thermionic converter of claim 107, wherein the plurality of regions are formed by irradiating the substantially one-dimensional material with a plurality of beams of electromagnetic energy, each of the plurality of beams having a power density above the threshold.

1 10. The thermionic converter of claim 94, further comprising an electric field to accelerate the thermionically generated electrons away from the cathode and toward the anode.

1 1 1 . The thermionic converter of claim 94, wherein the anode is substantially transparent to facilitate directing the electromagnetic energy through the anode to irradiate the region of the substantially one-dimensional material.

1 12. The thermionic converter of claim 94, further comprising providing a gas in a gap between the anode and the substantially one dimensional material, wherein the gas provides at least one of reduced space-charge effects at a surface of the irradiated region, reduced space-charge effects in the gap, and reduce a work-function at an interface between the anode the gap.

1 13. The thermionic converter of claim 94, wherein a surface of the irradiated region is patterned to include features that reduce space-charge effects.

1 14. The thermionic converter of claim 94, wherein the temperature gradient between the irradiated region and the remainder of the substantially one-dimensional material has a magnitude of at least 0.3 Κ/μιη.

1 15. The thermionic converter of claim 94, wherein the temperature gradient between the irradiated region and the remainder of the substantially one-dimensional material has a magnitude of at least 0.5 Κ/μιη.

1 16. The thermionic converter of claim 94, wherein the temperature gradient between the irradiated region and the remainder of the substantially one-dimensional material has a magnitude of at least 1 .0 Κ/μιη.

1 17. The thermionic converter of claim 94, wherein the EM energy is time-varying.

1 18. An electron beam emitter comprising: a cathode comprising a substantially one-dimensional, electrically conductive material having a restricted, anisotropic thermal conductivity; wherein electromagnetic energy having a power density above a threshold, irradiated on a region of the substantially one-dimensional, electrically conductive material, heats the region and generates a temperature gradient of at least 0.1 Κ/μιη between the irradiated region and the non-irradiated region of the substantially one-dimensional material to thermionically generate free electrons at the region; and an electrode to generate an electric field to accelerate the thermionically generated free electrons away from the cathode, to produce an electron beam deliverable to a target.

1 19. The electron beam emitter of claim 1 18, wherein the threshold power density is determined based on an area of the region irradiated with electromagnetic energy, wherein power density threshold is inversely proportional to the square root of the area of the region.

120. The electron beam emitter of claim 1 19, wherein the relationship between the threshold power density and area is approximately / = where / is the threshold power density in W/m² and A is the area of the region in m².

121 . The electron beam emitter of claim 1 19, wherein the threshold power density is approximately 0.45 W/mm² when the region has an area of at least 0.2 mm².

122. The electron beam emitter of claim 1 18, wherein the electromagnetic energy is non-coherent.

123. The electron beam emitter of claim 122, wherein the non-coherent electromagnetic energy is focused sunlight.

124. The electron beam emitter of claim 122, wherein when the cathode comprises a forest of multi-walled carbon nanotubes approximately 5mm by 5mm and 2 mm high, the region has an area of approximately 0.07 mm²located on a side surface of the forest of multi-walled carbon nanotubes, the sunlight has a power density of at least approximately 780 W/cm², and the anode is ITO and is approximately 2cm by 2cm in size and spaced approximately 1 mm from the region and coupled to the cathode by a 38 kQ load, a current of approximately 1 .2 μΑ is generated through the load.

125. The electron beam emitter of claim 1 18, wherein the substantially one- dimensional, electrically conductive material is carbon nanotubes.

126. The electron beam emitter of claim 1 18, wherein when the cathode comprises a forest of multi-walled carbon nanotubes approximately 5mm by 5mm and 2 mm high, the region has an area of approximately 0.2 mm² located on a side surface of the forest of multi-walled carbon nanotubes, the electromagnetic energy energy is laser light having a wavelength of 488 nm having a power density of at least approximately 150 W/cm², a current of at least 18 μΑ is measured at a copper anode that is approximately 1 cm by 1 cm in size and spaced approximately 1 mm from the region and biased with a collection voltage of 50V.

127. The electron beam emitter of claim 1 18, wherein the substantially one-dimensional material has a thermal conductivity that decreases as the temperature of the material increases, to facilitate localized heating at the region.

128. The electron beam emitter of claim 1 18, wherein the substantially one-dimensional material is coupled to a substrate at an interface, the interface having defects to restrict the thermal conductivity from the material to the substrate.

129. The electron beam emitter of claim 1 18, wherein irradiating the region with the electromagnetic energy comprises irradiating a region of a side surface of the

substantially one-dimensional material.

130. The electron beam emitter of claim 129, wherein the electromagnetic energy is linearly polarized in a direction substantially parallel to a longitudinal axis of the substantially one-dimensional material.

131 . The electron beam emitter of claim 1 18, wherein the electromagnetic energy is sunlight focused to a power density above the threshold.

132. The electron beam emitter of claim 1 18, wherein the region comprises a plurality of separate regions of the substantially one-dimensional material, and irradiating the region comprises irradiating each of the plurality of separate regions with

133. The electron beam emitter of claim 132, wherein the plurality of separate regions are formed by patterning the substantially one-dimensional material such that electromagnetic energy incident on the substantially one-dimensional material irradiates the substantially one-dimensional material at the plurality of regions.

134. The electron beam emitter of claim 132, wherein the plurality of regions are formed by irradiating the substantially one-dimensional material with a plurality of beams of electromagnetic energy, each of the plurality of beams having a power density above the threshold.

135. The electron beam emitter of claim 1 18, wherein the electrode is substantially transparent to facilitate directing the electromagnetic energy through the anode to irradiate the region of the substantially one-dimensional material.

136. The electron beam emitter of claim 1 18, further comprising a gas between the electrode and the substantially one dimensional material, wherein the gas provides reduced space-charge effects at a surface of the irradiated region.

137. The electron beam emitter of claim 1 18, wherein a surface of the irradiated region is patterned to include features that reduce space-charge effects.

138. The electron beam emitter of claim 1 18, wherein the temperature gradient between the irradiated region and the remainder of the substantially one-dimensional material has a magnitude of at least 0.3 Κ/μιη.

139. The electron beam emitter of claim 1 18, wherein the temperature gradient between the irradiated region and the remainder of the substantially one-dimensional material has a magnitude of at least 0.5 Κ/μιη.

140. The electron beam emitter of claim 1 18, wherein the temperature gradient between the irradiated region and the remainder of the substantially one-dimensional material has a magnitude of at least 1 .0 Κ/μιη.

The electron beam emitter of claim 1 18, wherein the EM energy is time-varying.