Thermionics in Topological Materials

Abstract

Thermionic emission is fundamental to many technologies and devices, including thermionic energy converters, X‐ray tubes, scanning electron microscopes, and transmission electron microscopes. The discovery of topological materials, particularly graphene, has significantly advanced thermionics research. Thermionic emission in these materials deviates from the Richardson‐Dushman equation due to their linear energy dispersion. Various models are developed to accurately describe thermionic emission. Graphene, with its dangling bond‐free surface, can be stacked either vertically or laterally with materials to form heterostructures. The Schottky barrier height at the interface of heterostructures can be tuned from a few millielectronvolts to several electronvolts by selecting appropriate materials or adjusting the Fermi level of graphene. This low and tunable barrier height gives rise to a great potential in developing thermionic energy converters and photodetectors. While free‐standing single‐layer graphene exhibits high electron mobility, its thermionic emission capability is constrained by the low density of states. This constraint can be alleviated by using 3D Dirac materials, which also possess linear energy dispersion. Thermionic emission in 3D Dirac materials is further enhanced by the emergence of nodal‐ring semimetals and Weyl semimetals that exhibit linear‐like energy dispersion. This review highlights recent progress in thermionic emission and devices in graphene structures and other topological materials.

Thermionics is one of the fundamental energy conversion mechanisms in solid state systems. Recent development in topological materials opens new avenues in developing thermionic systems and devices. Due to the linear energy dispersion and topological protection of charge transport, these new materials are promising candidates for high efficiency thermionic energy generation, cooling and other applications.

1. Introduction

The advancement of technology is often driven by the discovery of novel materials. Key milestones include the identification of high‐temperature superconductivity in copper‐oxide‐based materials,^{[ 1 ]} the fabrication of 2D materials through the mechanical exfoliation of graphene,^{[ 2 ]} and the realization of magic angle and flat bands in twisted bilayer graphene.^{[ 3} , ⁴ , ^{5 ]} Furthermore, the theoretical predictions and experimental confirmations of topological materials have significantly advanced our understanding of quantum phenomena.^{[ 6} , ^{7 ]} Topological materials represent a class of materials distinguished by their unique electronic properties, which emerge from their topological order. This category typically includes topological insulators,^{[ 6} , ^{7 ]} topological magnetic materials,^{[ 8} , ^{9 ]} topological superconductors,^{[ 10 ]} Weyl semimetals,^{[ 11} , ^{12 ]} and Dirac semimetals.^{[ 13} , ¹⁴ , ¹⁵ , ^{16 ]} Each of these materials demonstrates specific behaviors that hold significant implications for both fundamental physics and potential technological applications. Topological materials have been thoroughly reviewed across various topics, including the prediction and calculation of topological quantum materials,^{[ 17 ]} fundamental concepts of Weyl semimetals,^{[ 18 ]} topological insulators,^{[ 19} , ^{20 ]} the topology of electronic band structures,^{[ 21 ]} and topological superconductors.^{[ 19 ]} In this review, we focus on the application of topological materials in thermionics.

With the rapid advancement of novel materials, there has been a concerted and intense drive to develop high‐efficiency, low‐cost solid‐state power devices. These solid‐state power devices facilitate energy conversion between heat and electricity without relying on moving mechanical components or hazardous working fluids.^{[ 22} , ²³ , ^{24 ]} Moreover, they possess the unique ability to function in both directions, either for power generation or refrigeration purposes, and can be easily integrated with most electronic devices. Solid‐state power devices are based on two fundamental mechanisms, thermoelectrics and thermionics. The key distinction between them lies in the way electrons move. In thermoelectric devices,^{[ 25 ]} electrons move diffusively. During their transport between the hot and cold regions of the device, electrons undergo numerous collisions. In contrast, in thermionic devices,^{[ 26 ]} the barrier separating the hot and cold electrodes of the device is shorter than the mean free path for electron‐phonon scattering. As a result, electrons travel ballistically.

Thermoelectricity in bulk materials has long been known, but its applications have been limited by the lack of materials with a high figure of merit. The figure of merit, Z  =  σS ²/κ, involves the electric conductivity σ, the Seebeck coefficient S, and the thermal conductivity κ. Based on the figure of merit, semiconductors are among the best thermoelectric materials and prime candidates for solid‐state devices. However, progress in increasing the room‐temperature ZT of bulk semiconductors has been very slow. Thermionic devices operate similarly to thermoelectric devices. However, thermionic devices can achieve higher efficiency due to two mechanisms that are absent in thermoelectric devices: (i) electrons traverse the device ballistically (free of scattering), and (ii) only the most energetic electrons contribute to the heat transport process. A typical thermionic device consists of two parallel metal plates separated by a small distance. One metal plate is hot, and the other is cold. Their work functions can be equal or unequal; if unequal, the hot side can have either a small or large work function. An electron can jump between the two metal plates over the potential barrier due to thermal excitation. Since one metal plate has a higher temperature, there is a net electron flow from one side to the other. By connecting the two metal plates to an external load, one can create a thermionic power generator. One of the main challenges in thermionics is finding materials with low and tunable work functions. The emergence of topological materials creates new opportunities for developing high‐efficiency thermionic devices.

Thermionic emission is the mechanism underlying all thermionic devices. It refers to the release of electrons driven by thermal energy. A comprehensive understanding of thermionic emission is essential for developing various technologies, including electron microscopes,^{[ 27 ]} X‐ray tubes,^{[ 28} , ²⁹ , ^{30 ]} photoelectric devices,^{[ 31} , ^{32 ]} traveling wave tubes,^{[ 33} , ³⁴ , ³⁵ , ³⁶ , ³⁷ , ³⁸ , ^{39 ]} cathode ray tubes,^{[ 40 ]} thermionic energy generators,^{[ 26 ]} and thermionic cooling systems.^{[ 41 ]} Thermionic emission was first discovered by Edmond Becquerel in 1853 and later rediscovered by Thomas Edison. In thermionic emission, electrons are emitted from the surface of a heated metal when they possess sufficient thermal energy to overcome the work function (ϕ), an inherent property of the metal. By using the parabolic energy dispersion of conventional materials, Owen Richardson and his collaborator Saul Dushman formulated the Richardson‐Dushman equation to calculate thermionic emission current.^{[ 42 ]} The Richardson‐Dushman equation provides an effective method for calculating thermionic emission current based on operating temperature and material properties, which is crucial for the design of thermionic devices. Consequently, this equation serves as a foundation in the development of thermionic devices, including power generators, vacuum tubes and cathode ray tubes. However, it is important to note that this equation is not applicable to topological materials with non‐parabolic energy dispersion and with zero mass.^{[ 43 ]}

Recent studies indicate that topological materials possess unique thermionic emission properties compared to conventional materials.^{[ 42} , ⁵³ , ⁸⁸ , ^{89 ]} Additionally, advancements in topological materials offer a promising opportunity for developing thermionic heat‐to‐electricity devices. In this review, we specifically focus on the applications of topological materials in thermionics. The review is organized as follows: First, we discuss the fundamentals of thermionic emission in Section 2. Next, in Section 3, we address thermionic emission in Dirac materials, with an emphasis on graphene structures. In Section 4, thermionic emission in 3D topological materials is discussed. Finally, conclusions and outlooks for further study are presented.

2. Fundamentals of Thermionic Emission

2.1. Electron Emission

Electron emission refers to the process by which electrons are released from materials into a vacuum or the surrounding environment.^{[ 44 ]} Based on the emission mechanisms, electron emission can be categorized into several types, including photoemission, field emission, and thermionic emission, as illustrated in Figure 1a.

Figure 1.

Schematic diagrams of various electron emission mechanisms and thermionic emission with different band structures of different materials. a) Key electron emission processes, including photoemission, thermionic emission, and field emission. Reproduced with permission.^{[ 44 ]} Copyright 2017, Springer Nature. b) Linear band structure characteristic of Dirac materials. c) Parabolic band structure typical of conventional materials. d) Band structure of Nodal‐ring semimetals. e) Band structure of Weyl semimetals. Panels d and e reproduced with permission.^{[ 57 ]} Copyright 2022, John Wiley and Sons. To show the key thermionic properties with different energy dispersions, we specify the mean thermal energy per degree of freedom and the emission current density for a give energy dispersion in panels b, c, d and e. f) Full band structure of graphene. Reproduced with permission.^{[ 58 ]} Copyright 2012, John Wiley and Sons.

Photoemission occurs when electrons are emitted from a material after absorbing photons,^{[ 45 ]} which is crucial for understanding the interaction between light and matter. The photoemission process occurs when a photon strikes the surface of a material. If the energy of the photon is equal to or greater than the material's work function, the minimum energy required for an electron to escape, absorption occurs. Albert Einstein's explanation of this effect in 1905 was pivotal in the development of quantum theory, highlighting the quantized nature of light. Field emission involves the release of electrons from the surface of a material due to the influence of a strong electric field.^{[ 46 ]} When a strong electric field is applied, it distorts the potential barrier at the material's surface, allowing electrons to escape more easily than they would under normal conditions. Field emission is particularly significant in applications related to electronics and nanotechnology,^{[ 47} , ⁴⁸ , ^{49 ]} field emission displays^{[ 50 ]} and electron microscopes.^{[ 51} , ^{52 ]} Thermionic emission is the process by which electrons are emitted from a material, typically a metal or semiconductor, as a result of thermal activation.^{[ 53 ]} When the temperature of the material rises sufficiently, the thermal energy enables electrons to overcome the work function and be emitted. This mechanism is crucial for the operation of vacuum tubes^{[ 54 ]} and electron guns.^{[ 55} , ^{56 ]} In the following sections, we will focus on thermionic emission, exploring its principles, applications, and significance in modern technologies.

2.2. Mechanism of Thermionic Emission

Thermionic emission from a heated material can be understood through the following key steps. When the material is heated, the electron thermal energy increases, causing some electrons to occupy higher energy states. The distribution of these electrons follows Fermi‐Dirac statistics, and as the temperature rises, more electrons gain sufficient energy to overcome the energy barrier at the material's surface. The work function (ϕ), which is the minimum energy required for an electron to escape, plays a critical role in this process; for thermionic emission to occur, an electron must have energy greater than ϕ. Once an electron acquires enough energy through thermal excitation, it can escape from the solid into the vacuum, resulting in the emission of electrons and contributing to the overall current density.

2.3. Richardson‐Dushman Equation

The current density of thermionic emission from heated materials with parabolic energy dispersion can be accurately described by the Richardson–Dushman Law, given as

$$J=A{T}^2\exp \left(-\frac{\varphi }{k_{B}T}\right)$$ (1)

where $A=\frac{em{k}_B^2}{2{\pi }^2{\hslash }^3}\approx 120\mathrm{A}·\mathrm{c}{\mathrm{m}}^{-2}{\mathrm{K}}^{-2}$ is the Richardson constant, e is the elementary charge, m is the electron mass, k_B is the Boltzmann constant, ℏ is the reduced Plank constant T is the absolute temperature. The Richardson‐Dushman equation is fundamental for designing thermionic devices for several reasons. First, it guides material selection for thermionic emission by highlighting the importance of choosing materials with lower work functions, which can significantly enhance thermionic emission.^{[ 59} , ⁶⁰ , ⁶¹ , ^{62 ]} Second, the equation provides insights into optimizing device performance by determining the appropriate operating temperature. Third, it can be used to predict the performance of thermionic devices under various conditions. When applying the Richardson‐Dushman equation to describe thermionic emission from a metal‐semiconductor interface, the reduction in the potential barrier caused by the image force must be considered. This leads to the Schottky diode equation:$J=A{T}^2\exp (-\frac{\varphi -\mathrm{\Delta }\varphi }{k_{B}T})$, where Δϕ is the reduction in the potential barrier caused by the image force.

While the Richardson‐Dushman equation remains fundamental for designing thermionic devices, it is important to note that this equation is formulated based on parabolic energy dispersion. In recent decades, a new class of materials known as Dirac materials has been discovered. A key distinction between Dirac materials and conventional metals is that the energy dispersion of Dirac materials is linear,^{[ 63 ]} whereas that of conventional metals is parabolic. Figure 1b depicts the linear band structure characteristic of Dirac metals. In contrast, Figure 1c illustrates a typical parabolic band structure of conventional metals. Figure 1d showcases the band structure of a nodal‐ring semimetal, while Figure 1e presents the band structure of a Weyl semimetal. Notably, all these structures exhibit a non‐parabolic energy‐momentum dispersion. Consequently, thermionic emission in Dirac materials cannot be described by the Richardson‐Dushman equation. In the following sections, we will focus on recent advancements in thermionic emission in various topological materials.

3. Thermionics in graphene 

3.1. Thermionic Emission in 2D Dirac Material: Graphene

Since its discovery in 2004,^{[ 2 ]} graphene has attracted significant attention due to its distinctive properties, including ultrahigh mobility,^{[ 64} , ^{65 ]} exceptional optical characteristics,^{[ 66 ]} and the ability to confine light.^{[ 67 ]} Additionally, graphene has found numerous applications in various fields, such as optical modulators,^{[ 68 ]} transistors,^{[ 69} , ⁷⁰ , ^{71 ]} biochemical sensors,^{[ 72} , ⁷³ , ^{74 ]} and thermionic devices.^{[ 75} , ⁷⁶ , ^{77 ]}

3.1.1. Determining the Intrinsic Work Function of Graphene via Thermionic Emission

Thermionic emission in graphene was experimentally studied in 2014 to determine its intrinsic work function,^{[ 78 ]} a crucial parameter for graphene‐based electronic devices. Although the work function of graphene has been measured using various techniques including scanning Kelvin probe microscopy, scanning tunneling microscopy, angle‐resolved ultraviolet photoelectron spectroscopy, and low‐energy electron microscopy, the reported values vary significantly, ranging from 3.7 to 5.2 eV.^{[ 79} , ⁸⁰ , ⁸¹ , ⁸² , ⁸³ , ^{84 ]} This large discrepancy is primarily attributed to interactions between graphene and its substrate,^{[ 85} , ^{86 ]} as well as the influence of adsorbates.^{[ 87 ]} To accurately determine the intrinsic work function of graphene, Zhu et al.^{[ 78 ]} heated graphene to ≈1800 K to emit thermionic emission. The thermionic current was measured at temperatures ranging from about 1600 to 1750 K. The work function was extracted by fitting the emission current to temperature data using the Richardson‐Dushman equation. This study narrows the previously reported work function range of 3.7–5.2 eV^{[ 79} , ⁸⁰ , ⁸¹ , ⁸² , ⁸³ , ^{84 ]} down to a more precise 4.7–4.8 eV. One of the main advantages of measuring the graphene work function via thermionic emission, compared to other methods, is that this technique operates at very high temperatures (up to 1800 K) to minimize the influence of adsorbates on the measurements.

3.1.2. Theoretical Modelling of Thermionic Emission from Graphene

The experimental work conducted by Zhu et al.^{[ 78 ]} soon sparked numerous theoretical investigations into thermionic emission in graphene.^{[ 42} , ⁵³ , ⁸⁸ , ^{89 ]} A primary focus of these theoretical studies is whether thermionic emission in graphene can be described by the traditional Richardson‐Dushman equation. Electrons in graphene exhibit a unique linear band structure,^{[ 66 ]} expressed as E  =  pv_F (Figure 1b), where E is the electron energy, p  =  ℏk is the electron momentum, k is the wavevector, and v_F is the Fermi velocity of the electrons. This linear energy dispersion fundamentally distinguishes graphene from traditional 3D materials, such as tungsten, gold, and copper, which have a parabolic energy dispersion represented by E  = p ² /2m (Figure 1c). Since the Richardson‐Dushman equation is derived from parabolic energy dispersion, its accuracy in calculating thermionic emission in graphene is questionable. Furthermore, both theoretical^{[ 76 ]} and experimental^{[ 90} , ^{91 ]} investigations have demonstrated that the Richardson‐Dushman equation also fails to characterize thermionic and field emission from carbon nanotubes.

By employing the linear energy dispersion of graphene, Liang et al. derived an equation to describe thermionic emission in suspended graphene, where the influence of the substrate can be disregarded. The equation is expressed as,^{[ 88} , ^{89 ]}

$$J=\frac{e{k}_B^3{T}^3}{\pi {\hslash }^3{v}_F^2}\exp \left(-\frac{\varphi -E_F}{k_{B}T}\right)$$ (2)

where ϕ is the work function, and E_F is the Fermi energy of graphene. Following the convention established in previous work,^{[ 42 ]} we refer to Equation (2) as the Liang and Ang model. This equation differs significantly from the traditional Richardson‐Dushman equation (Equation 1) in several aspects. First, Equation (2) does not include a mass dependency, reflecting the fact that electrons in graphene behave like massless Dirac particles. When applying Equation (1) to thermionic emission in graphene, determining the effective mass of electrons can be challenging due to their massless nature. However, this issue is resolved in Equation (2). Second, the T ² scaling in the Richardson‐Dushman equation has been replaced by T ³ scaling, a change that arises from the linear energy dispersion. Liang et al. fitted the experimental data in^{[ 78 ]} with Equation (2) and determined the work function of intrinsic graphene to be 4.514 eV.^{[ 88 ]} This value is lower than its counterpart (4.74 eV) obtained via fitting the same data with the Richardson‐Dushman equation.^{[ 78 ]} The determined work function of 4.514 eV closely matches the experimental value of 4.50 ± 0.05 eV.^{[ 92 ]} A similar model has also been derived by Trushin using the concept of a hot electron liquid confined in a 2D plane.^{[ 53 ]}

Thermionic emission in graphene has typically been studied in a temperature range from 1600 K to 1750 K.^{[ 78 ]} However, the work function of graphene is expected to depend on temperature. To account for this influence, De and Olawole proposed a modified Richardson‐Dushman equation for thermionic emission in graphene.^{[ 93 ]} The primary modification occurs in the work function ϕ, which is now related to temperature through the following equation:

$$\begin{array}{ccc}\hfill \varphi \left(T\right)& =& {\varphi }_0+[r\alpha T+\frac{\left(1+r\alpha T\right){\pi }^2}{12}{\left(\frac{k_{B}T}{E_F}\right)}^2{E}_F\hfill \\ & & +\left(1+r\alpha T\right)\left(\frac{7{\pi }^4}{960}\right){\left(\frac{k_{B}T}{E_F}\right)}^4{E}_F]\hfill \end{array}$$ (3)

where ϕ₀ is the work function of graphene at 0 K, r is the dimensionality of material, α is the linear thermal expansion coefficient of graphene, and E_F is the Fermi energy. By inserting Equation (3) into Equation (1), they obtained a modified Richardson‐Dushman equation for thermionic emission from monolayer graphene, expressed as follows:^{[ 42} , ⁹³ , ⁹⁴ , ^{95 ]}

$$\begin{array}{ccc}\hfill J& =& A{T}^2\exp \{-[{\varphi }_0+[r\alpha T+\frac{\left(1+r\alpha T\right){\pi }^2}{12}{\left(\frac{k_{B}T}{E_F}\right)}^2{E}_F\hfill \\ & & +\left(1+r\alpha T\right)\left(\frac{7{\pi }^4}{960}\right){\left(\frac{k_{B}T}{E_F}\right)}^4{E}_F\left]\right]/k_{B}T\}\hfill \end{array}$$ (4)

where A is the Richardson constant. We refer to Equation (4) as the De and Olawole model. Using this method, the work function of graphene at 0 K was determined to be 4.592 eV^{[ 93} , ^{94 ]} by fitting the experimental data.^{[ 78 ]} This approach establishes a relationship between the work function of graphene and temperature, while assuming that thermionic emission from graphene can be described by the conventional Richardson‐Dushman equation with a temperature‐dependent work function. Khatoon et al. improved this model by simultaneously considering the linear energy dispersion of graphene and the temperature‐dependent work function,^{[ 42 ]} expressed as follows:

$$J=\frac{e{k}_B^3{T}^3}{\pi {\hslash }^3{v}_F^2}\exp \left(-\frac{{\varphi }_0+{\mu }_0\left(1-\alpha T\right)-\left({\mu }_0/2\ln 2\right)\left(T_F/T\right)}{k_{B}T}\right)$$ (5)

where the pre‐factor before the exponent is identical to that of the Liang and Ang model, μ₀​ represents the Fermi energy at 0 K, and T_F is the Fermi temperature. Additionally, Kim et al.^{[ 96 ]} and Wei et al.^{[ 97 ]} have proposed a modified Richardson‐Dushman equation for thermionic emission from monolayer graphene, expressed as follows:

$$J=\sqrt{\frac{m}{2}}{\left(\frac{k_{B}T}{\pi }\right)}^{\frac{3}{2}}\frac{e}{{\hslash }^2}\exp \left(-\frac{W}{k_{B}T}\right)$$ (6)

Olawole et al. compared the performance of the five models mentioned above in describing thermionic emission by fitting the experimental data^{[ 78 ]} with these models. The results show that the De and Olawole model provides the best fit.^{[ 42 ]} Although the five models have been proposed to describe the thermionic emission current in graphene, question regarding the theoretical modelling of this phenomenon remains. The primary issue is the lack of sufficient experimental data. Currently, the only available experimental data comes from ref. [78], which is limited to a temperature range of 1600 to 1750 K. Extending this temperature range and measuring the thermionic emission current over a broader temperature range would provide more definite information. Notably, the traditional field emission model based on the Fowler‐Nordheim law also fails to describe field emission in graphene.^{[ 98} , ^{99 ]} Table 1 shows the thermionic properties described by various models discussed above.

Table 1.

Comparison of six models used to investigate thermionic emission in graphene and 3D Dirac materials. All these models are assumed to work for all temperatures during their application in studying thermionic emission in graphene. However, the work function of graphene depends on temperature. Thus, the accuracy of the Richardson‐Dushman equation, Liang and Ang model, Kim et al. model, and Wei et al. model is reduced when they are employed to investigate thermionic emission over a wide range using a constant work function ϕ.

Mode names	Underlying assumptions	Applicable materials	Equations
Richardson‐Dushman equation	3D parabolic energy dispersion & temperature independent work function	Conventional metals	$J=\frac{em{k}_B^2}{2{\pi }^2{\hslash }^3}{T}^2\exp (-\frac{\varphi }{k_{B}T})$
Liang and Ang model	2D linear energy dispersion & temperature independent work function	Graphene	$J=\frac{e{k}_B^3}{\pi {\hslash }^3{v}_F^2}{T}^3\exp (-\frac{\varphi -E_F}{k_{B}T})$
De and Olawole model	3D parabolic energy dispersion & temperature dependent work function	Graphene	$J=\frac{em{k}_B^2}{2{\pi }^2{\hslash }^3}{T}^2\exp (-\frac{\varphi (T)}{k_{B}T})$
Khatoon et al. model	2D linear energy dispersion & temperature dependent work function	Graphene	$J=\frac{e{k}_B^3}{\pi {\hslash }^3{v}_F^2}{T}^3\exp (-\frac{\varphi (T)}{k_{B}T})$
Kim et al. and Wei et al. model	2D parabolic energy dispersion & temperature independent work function	The edge of 2D materials like graphene	$J=\sqrt{\frac{m}{2}}{(\frac{k_{B}T}{\pi })}^{\frac{3}{2}}\frac{e}{{\hslash }^2}\exp (-\frac{\varphi }{k_{B}T})$
Huang et al. model	3D linear energy dispersion & temperature independent work function	3D Dirac materials	$J(T)=\frac{q{k}_B^2}{4{\pi }^2{\hslash }^3{v}_F^2}(\varphi +E_F+2k_{B}T)T^2{\mathrm{e}}^{-\frac{\varphi }{k_{B}T}}$

The linear energy dispersion of graphene (Figure 1b) obtained from the Dirac cone approximation is only valid in the low energy regime. However, thermionic emission usually occurs at temperatures above 1000 K where energetic electrons are far away from the linear energy dispersion regime. Thus, the Liang and Ang model would break down at high operating temperatures. To address this issue, a generalized thermionic electron emission model (referred to as the full band thermionic model) was constructed for high‐energy electrons in graphene based on the full‐band model of graphene^{[ 100 ]} (Figure 1f). Results show that the Liang and Ang model (Dirac thermionic model) and the full‐band thermionic model yield similar emission current and heat current densities around room temperature. However, when the operating temperature ranges from 1000 to 1800 K, the Liang and Ang model overestimates the electrical and heat currents by about 60%.

3.1.3. Enhancing Thermionic Performance of Graphene Heterostructures via Thomson Effect

Recently, it has been shown that thermionic performance in graphene heterostructures can be improved by the Thomson effect.^{[ 101 ]} The Thomson effect is a higher‐order transport process that describes heating or cooling in a single current‐carrying conductor with a temperature gradient. It has been demonstrated that the Thomson effect improves thermionic energy conversion efficiency by up to 20%. This result indicates that while the Thomson effect is weak in conventional materials such as metals and semiconductors, it can play a significant role in devices based on topological materials. These findings offer valuable insights into the design of graphene heterostructure‐based thermionic devices.

3.2. Graphene Based Thermionic Devices

Graphene is a single layer of carbon atoms arranged in a honeycomb lattice, illustrated in Figure 2a. The potential of using graphene in thermionic energy converters is enhanced due to that the work function can be tuned over a wide range. While the intrinsic work function of graphene is ≈4.514 eV^{[ 88 ]}, it can be reduced to as low as 1 eV through a combination of electrostatic gating and a cesium/oxygen surface coating.^{[ 105 ]} Additionally, its dangling bond‐free surface allows for vertical or lateral stacking with conventional and 2D materials, facilitating the creation of heterostructures, as depicted in Figure 2b,c.^{[ 102} , ¹⁰⁶ , ¹⁰⁷ , ^{108 ]} The difference in work functions between graphene and these materials results in the formation of Schottky barriers at interfaces. These Schottky barriers are crucial for the fabrication of various electronic devices, such as diodes and transistors, where electron transport is primarily or partially dominated by thermionic emission. The Schottky barrier height can be tuned from a few millielectronvolts to several electronvolts by selecting appropriate conventional or 2D materials or by adjusting the Fermi level of graphene.^{[ 109} , ^{110 ]} The Schottky barrier height can also be reduced through atomic adsorption.^{[ 111 ]} This low barrier height, along with its tunability, makes Schottky barriers widely utilized in the development of thermionic devices.^{[ 112} , ^{113 ]}

Figure 2.

Schematic diagrams of graphene‐based materials and devices. a) Schematic diagram of graphene. b) Schematic diagram of graphene/conventional materials heterostructures. c) Schematic diagram of graphene/van der Waals heterostructures. Panel c reproduced with permission.^{[ 102 ]} Copyright 2013, Springer Nature. d) Band diagram of a Schottky barrier. When a metal comes into contact with a semiconductor, a Schottky barrier is formed. The Schottky barrier height is given by Φ _B = ϕ _m   − χ, where ϕ _m is the work function of the metal and χ is the electron affinity of the semiconductor material. Panel d reproduced with permission.^{[ 103 ]} Copyright 2017, American Physical Society. e) Schematic diagram of graphene‐based thermionic devices. f) Optical microscope image of an Au‐Graphene‐WSe₂‐Graphene‐Au thermionic device. g) Cooling curve of the Au‐Graphene‐WSe₂‐Graphene‐Au thermionic device. Panels e, f and g reproduced with permission.^{[ 104 ]} Copyright 2019, The American Association for the Advancement of Science.

In thermionic devices, the thermionic emission current is proportional to $\left(-\frac{\varphi }{k_{B}T}\right)$, indicating that it can be significantly affected by the work function of the emission materials. When a metal comes into contact with a semiconductor, a Schottky barrier is formed. The Schottky barrier height is given by Φ _B = ϕ _m   − χ (Figure 2d),^{[ 103 ]} where ϕ _m is the work function of the metal and χ is the electron affinity of the semiconductor material. For thermionic emission from metal to vacuum, electrons in metals need to overcome the work function ϕ _m . For thermionic emission across a heterostructure electrons in metal only need to overcome the Schottky barrier height Φ _B . Since the Schottky barrier height Φ _B is usually lower than the work function ϕ _m , the formation of the Schottky barrier can considerably enhance thermionic emission. Thermionic emission can be further enhanced by reducing the Schottky barrier height Φ _B via Schottky barrier modulation and band alignment. Additionally, thermionic emission can be increased by employing an energy filtering process, such as selectively blocking high‐energy electrons on the cold material side to prevent them from flowing back to the hot material side.

Recently, gold‐graphene‐WSe₂ van der Waals heterostructures have been both theoretically proposed and experimentally investigated for nanoscale thermal‐to‐electrical energy conversion and integrated electronic cooling applications (shown in Figure 2e–g). The cooling curve obtained using a thermoreflectance imaging technique at low bias voltages of up to ≈0.06 V is presented in Figure 2f. Although the estimated equivalent ZT of ≈1.5 × 10⁻³ is too small for practical applications, it represents a three‐order‐of‐magnitude enhancement compared to previous counterparts.^{[ 104 ]}

3.2.1. Graphene Based Thermionic Energy Converters

One important application of thermionic emission is the direct conversion of thermal energy (heat) into electricity, known as thermionic energy converters (TECs). TECs are a type of solid‐state power converter that facilitates energy conversion between heat and electricity. They operate effectively at high temperatures, making them suitable for applications such as waste heat recovery from industrial processes, nuclear reactors, and solar energy. Since their initial proposal in 1959,^{[ 114 ]} TECs have been the subject of intensive study.^{[ 26} , ^{115 ]} However, their practical applications have been limited by the lack of materials with sufficiently low work functions that can operate at high temperatures, as well as the severe space charge effect. Theoretical studies indicate that the efficiency of TECs decreases from 32% to 3% when the work function of the anode increases from 1 eV to 2 eV.^{[ 116 ]} The work function is a material parameter that measures the energy difference between the Fermi level and the vacuum level. For most conventional materials, the work function is above 2 eV. For example, it is ≈4.26 eV for silver (Ag), 5.10 eV for gold (Au), and 4.32 eV for tungsten (W). To achieve 50% energy efficiency, the operating temperature of a thermionic energy converter typically needs to be above 1500 K.^{[ 88 ]} This limits the application of TECs in harvesting low‐grade waste. To relieve this limitation, one needs to find materials with sufficiently low work functions to produce adequate thermionic emission at lower temperatures.

The discovery of graphene has partially alleviated the limitations posed by the scarcity of low work function materials. The work function of graphene and the Schottky barrier height of its heterostructures can be widely tuned by adjusting the Fermi level of graphene or by selecting appropriate 2D materials for the heterostructures. The Schottky barrier height of graphene heterostructures can be reduced to just a few millielectronvolts, making them an ideal platform for developing thermionic energy converters (TECs). Therefore, graphene and its heterostructures have been extensively utilized in TECs, both as cathode and anode materials.^{[ 88} , ¹¹⁶ , ¹¹⁷ , ¹¹⁸ , ¹¹⁹ , ¹²⁰ , ¹²¹ , ^{122 ]} Liang et al. theoretically proposed a thermionic energy converter utilizing graphene (work function = 4.514 eV) as the cathode material and LaB₆ (work function = 2.5 eV) as the anode material (shown in Figure 3a).^{[ 88 ]} This TEC can achieve energy efficiency as high as 45% at an operating temperature of 900 K. This efficiency can be further improved by lowering the work function of graphene or increasing the operating temperature.^{[ 88 ]} In another study, Misra and his colleagues demonstrated an energy efficiency of 56% with a graphene‐based TEC operating at 1200 K, which corresponds to ≈84% of the Carnot efficiency.^{[ 117 ]} Theoretical analyses indicates that the performance of graphene‐based TECs surpasses that of metal‐based TECs.^{[ 118 ]} Figure 3b illustrates a graphene‐based TEC in which graphene serves as the anode material. The corresponding near‐field heat transfer between the emitter and the parallel graphene planes is depicted in Figure 3c. The maximum power output density and efficiency of this graphene‐based TEC are enhanced by 2.135% and 8.824%, respectively, compared to metal‐based TECs.^{[ 119 ]}

Figure 3.

Graphene‐based thermionic energy converters (TECs). a) Schematic diagram of a TEC featuring a graphene cathode. Reproduced with permission.^{[ 88 ]} Copyright 2015, American Physical Society. b) Schematic diagram of a TEC with a graphene anode. c) Neat‐field heat transfer between the emitter and the parallel graphene planes of the TEC shown in (b). Panels b annd c reproduced with permission.^{[ 119 ]} Copyright 2022, Elsevier. d) A back‐gated graphene‐based TEC with a micron‐sized inter‐electrode gap. Reproduced with permission.^{[ 116 ]} Copyright 2017, Elsevier. e) An enhanced graphene‐based TEC utilizing a reflector for improved efficiency. Reproduced with permission.^{[ 120 ]} Copyright 2021, AIP Publishing. f) An enhanced graphene‐based TEC employing ultra‐low ionization energy caesium vapor. Reproduced with permission.^{[ 122 ]} Copyright 2024, Elsevier. g) A TEC based on graphene/transition metal dichalcogenides/graphene heterostructures, capable of harvesting low‐grade waste heat. Reproduced with permission.^{[ 123 ]} Copyright 2017, Springer Nature. h) A graphene‐based field‐assisted thermionic energy converter that demonstrates advanced capabilities for harvesting low‐grade waste heat efficiently. Reproduced with permission.^{[ 124 ]} Copyright 2021, IEEE.

While the theoretical energy efficiency of graphene‐based TECs is notably high, the practical energy efficiency is constrained by the space charge barrier and the inter‐electrode gap. By employing back‐gated graphene as the anode material and reducing the inter‐electrode gap to just 17 µm (shown in Figure 3d), an experimental energy efficiency of 9.8% has been achieved. This is the highest value reported to date.^{[ 116 ]} The advantage of using graphene as the anode material is evident, as the overall energy efficiency is 6.7 times greater than that of a TEC utilizing a tungsten anode with the same inter‐electrode gap.^{[ 116 ]} Additionally, the performance of graphene‐based TECs can be enhanced by incorporating an optical reflector behind the graphene anode (shown in Figure 3e). The theoretical maximum efficiency of 76.6% and output power densities of 95.1 W cm^{− 2} were achieved.^{[ 120 ]} Furthermore, significant improvements in energy efficiency can be achieved by further reducing the inter‐electrode gap to submicrometer sizes.^{[ 121 ]} To mitigate the constraints imposed by the space charge effect between the cathode and anode, Ming et al. introduced ultra‐low ionization energy cesium vapor into the electrode gap of a graphene‐based TEC, as illustrated in Figure 3f. The cesium pressure must be carefully optimized as both excessively high and low pressures can adversely affect the TEC's performance.^{[ 122 ]} Additionally, a TEC based on multilayer graphene has been demonstrated to achieve ≈55% energy conversion efficiency with cathode and anode temperatures set at 900 and 400 K, respectively.^{[ 125 ]}

To achieve high energy efficiency, the operating temperature of TECs is typically above 900 K. To explore applications at lower temperatures, researchers have proposed a TEC utilizing graphene/transition metal dichalcogenides/graphene heterostructures, as illustrated in Figure 3g. Theoretical calculations indicate that this TEC can effectively harvest 400 K waste heat and achieve an efficiency of ≈8%.^{[ 123 ]} Additionally, Chen et al. have theoretically attained ≈10% energy efficiency from 700 K waste heat using a graphene‐based field‐assisted TEC.^{[ 124 ]}

As discussed above, the energy efficiency of TECs can be enhanced by reducing the work function of the electrodes, minimizing the inter‐electrode gap, increasing the operating temperature, and alleviating the space charge effect. To further enhance energy efficiency, various types of hybrid TECs, such as thermionic‐thermoradiative converters, thermionic‐solid oxide fuel cells, and thermionic‐photovoltaic converters, have been proposed for effectively harvesting thermal energy, particularly low‐grade thermal energy.^{[ 126} , ¹²⁷ , ¹²⁸ , ^{129 ]} For example, Zhang et al. proposed a thermionic‐thermoradiative hybrid energy converter, as shown in Figure 4a. the converter simultaneously captures thermal energy through a graphene‐based thermionic device and a thermoradiative device.^{[ 130 ]} The thermoradiative device includes a p‐n junction capable of harvesting thermal energy from low‐grade waste heat via emissive photons.^{[ 131 ]} When this hybrid energy converter operates at 1500 K, it can achieve a maximum power output of 0.301 W cm^{− 2} and an energy efficiency of 22.5%, surpassing the performance of either the thermionic energy converter or the thermoradiative device alone.^{[ 130 ]}

Figure 4.

Hybrid thermionic devices. (a) Schematic diagram of a thermionic‐thermoradiative hybrid energy converter. Reproduced with permission.^{[ 130 ]} Copyright 2018, IEEE. b) Schematic diagram of a thermionic‐photovoltaic hybrid energy converter. Reproduced with permission.^{[ 132 ]} Copyright 2020, IOP Publishing. c) Reproduced with permission.^{[ 133 ]} Copyright 2020, Elsevier. and d) Illustrations of hybrid thermionic devices that integrate a graphene‐based thermionic energy converter (TEC) with a solid oxide fuel cell. Reproduced with permission.^{[ 134 ]} Copyright 2023, Elsevier. e) A hybrid thermionic device combining a graphene‐based TEC with molten carbonate fuel cells. Reproduced with permission.^{[ 135 ]} Copyright 2024, Elsevier. f–i) Depictions of a four‐terminal hybrid thermionic‐photovoltaic converter. Reproduced with permission.^{[ 136 ]} Copyright 2023, Elsevier.

Graphene‐based TECs can be integrated with photovoltaic cells to enhance thermal energy harvesting efficiency compared to that of single systems (shown in Figure 4b).^{[ 132 ]} To harvest waste heat from solid oxide fuel cells, hybrid systems that integrate a solid oxide fuel cell with a graphene‐based thermionic energy converter (as depicted in Figure 4c,d) have been proposed, where the top section consists of the solid oxide fuel cell and the bottom section features the graphene thermionic energy converter.^{[ 133} , ^{134 ]} Results indicate that these hybrid energy converters can significantly enhance output power density compared to that of single energy converters. Similarly, graphene‐based thermionic converters have been integrated with molten carbonate fuel cells to improve energy efficiency (shown in Figure 4e).^{[ 135 ]}

Despite the growing interest in hybrid TECs and extensive theoretical studies, more experimental investigations are needed. Recently, Qiu et al. theoretically proposed and experimentally demonstrated a four‐terminal hybrid thermionic‐photovoltaic converter featuring a dispenser cathode, a transparent indium‐tin‐oxide anode, and tandem graphene/GaAs Schottky junction photovoltaics (shown in Figure 4f) for thermal energy harvesting.^{[ 136 ]} A prototype of this four‐terminal hybrid thermionic‐photovoltaic converter is illustrated in Figure 4g–i. Experimental results indicate that this converter yields a power density of 962 W m^{− 2} at a cathode temperature of 1373 K.^{[ 136 ]}

Solar energy is a vast and inexhaustible resource, offering a sustainable energy solution that can be harnessed indefinitely. Solid‐state power converters such as TECs are promising candidates for harvesting solar energy, thereby promoting sustainable energy solutions for both terrestrial and space applications. Consequently, the potential applications of graphene‐based TECs in generating electricity from solar energy have been widely explored (shown in Figure 5 ).^{[ 137} , ^{138 ]} In a typical TEC, solar energy is absorbed by an absorber, which raises the temperature of the cathode. This increase in temperature causes electrons to be emitted from the cathode. The electrons are then collected at the anode, generating usable electrical power. To enhance overall energy efficiency, TECs are often combined with other energy converters, such as thermoradiative solar cells, as illustrated in Figure 5a. Such devices demonstrate a theoretical solar‐to‐electricity conversion efficiency of 22.5%.^{[ 139 ]}

Figure 5.

Graphene‐based solar thermionic energy converters (TECs). a) A thermionic‐thermoradiative hybrid solar energy converter. Reproduced with permission.^{[ 139 ]} Copyright 2020, Elsevier. b) A concentrated solar thermionic energy converter. Reproduced with permission.^{[ 140 ]} Copyright 2021, IOP Publishing. c) An enhanced concentrated solar TEC utilizing total photon reflection to improve energy efficiency. Reproduced with permission.^{[ 141 ]} Copyright 2021, Elsevier.

The solar‐to‐electricity conversion efficiency of TECs can be improved by concentrating solar energy onto the absorber.^{[ 115 ]} Figure 5b illustrates a typical concentrated solar thermionic energy converter. The solar energy is focused onto the solar absorber using an optical concentrator and the temperature of the cathode is raised. Electrons emitted from the cathode are subsequently collected at the anode, generating usable electrical power. The theoretical maximum efficiency of such a concentrated solar TEC is 12.8% when illuminated by 800 suns.^{[ 140 ]} Figure 5c illustrates an enhanced concentrated solar TEC where the performance is improved by incorporating total photon reflection. This design effectively reduces irreversible losses within the thermionic energy converter, thereby enhancing solar energy conversion efficiency. The maximum energy efficiency of such a TEC is 44.56%^{[ 141 ]} when harvesting solar energy under 3000 solar concentrations. Although graphene‐based TECs have shown promising applications in harvesting solar energy, their practical applications require further experimental and technological investigation.

3.2.2. Applications of Graphene Thermionic Emission in Photon Detection

Photodetectors are widely used in our daily lives.^{[ 142} , ¹⁴³ , ^{144 ]} Many of these devices are based on the photoelectric effect, where light shines on a material and causes the emission of electrons from its surface. However, traditional photodetectors are unable to detect photons whose energy is below the work function or the potential barrier. To address this limitation, photodetectors based on the photo‐thermionic effect have been proposed. Graphene has shown promising applications in photo‐thermionic based photodetectors.^{[ 109} , ¹⁴⁵ , ¹⁴⁶ , ¹⁴⁷ , ^{148 ]} Figure 6a depicts a photodetector based on graphene/p‐type silicon Schottky junctions, where electron transport across the junctions is dominated by thermionic emission. As illustrated in Figure 6b, the ratio of photocurrent to dark current for this photodetector can reach approximately five orders of magnitude at room temperature with a 5 V bias under illumination from a 633 nm wavelength laser.^{[ 145 ]}

Figure 6.

Graphene‐based photo‐thermionic detectors. a) a thermionic photodetector based on graphene/p‐type silicon Schottky junction. b) Dark current and photocurrent versus bias voltage for the graphene/p‐Si photodetector. Panels a and b reproduced with permission.^{[ 145 ]} Copyright 2013, AIP Publishing. c) Simplified band diagram of a photo‐thermionic detector constructed from graphene‐WSe₂‐graphene heterostructures. Reproduced with permission.^{[ 149 ]} Copyright 2016, Springer Nature. d) Dark current and photocurrent versus bias voltage for a photo‐thermionic detector constructed from graphene‐nanowall/silicon heterojunction. Reproduced with permission.^{[ 151 ]} Copyright 2019, American Chemical Society.

Figure 6c shows a typical photo‐thermionic detector constructed from a graphene‐WSe₂‐graphene heterostructure.^{[ 149 ]} When illuminated, this detector generates a multitude of electron‐hole pairs in the graphene layer. These pairs quickly reach an equilibrium state, resulting in a thermalized carrier distribution where the electron temperature exceeds both the lattice and environmental temperatures. In this distribution, carriers with energy surpassing the Schottky barrier height at the graphene/WSe₂ interface can be injected into the WSe₂ layer. These carriers then traverse through the WSe₂ and migrate toward the opposing graphene layer. As a result, light energy is converted to an electrical signal. Experimental results have demonstrated that the photo‐thermionic effect in a graphene‐WSe₂‐graphene heterostructure can effectively detect sub‐bandgap photons.^{[ 149 ]} Theoretical investigations into photo‐thermionic emission from graphene have shown strong agreement with these experimental findings.^{[ 150 ]} Additionally, the photo‐thermionic effect in a graphene‐nanowall/silicon heterojunction has been utilized for infrared detection. A photo‐to‐dark current ratio of the order of 10⁴ is achieved when detecting 1550 nm infrared light at room temperature (Shown in Figure 6d).^{[ 151 ]} Graphene‐based photo‐induced thermionic emission can also be employed to detect cyclotron resonance.^{[ 152 ]}

The graphene‐based photo‐thermionic detector offers significant advantages compared to other photo‐thermionic detectors due to two key factors. First, photoinduced carriers experience rapid thermalization among electrons while dissipating heat to the lattice at a considerably slower rate.^{[ 153 ]} This phenomenon arises from the substantial difference in scattering rates. The electron‐electron scattering occurs on the order of femtoseconds,^{[ 154} , ^{155 ]} whereas electron‐phonon scattering occurs on the order of tens of picoseconds.^{[ 156} , ¹⁵⁷ , ^{158 ]} The approximately three orders of magnitude difference in scattering rates allows the detector to maintain a non‐equilibrium state of carriers for an extended period. As a result, the efficiency of the photo‐thermionic process is enhanced. Second, graphene‐based devices demonstrate a high degree of compatibility with conventional solid‐state devices. This characteristic not only simplifies the fabrication of complex optoelectronic systems but also facilitates seamless integration into existing technological infrastructures. Consequently, this paves the way for a wide array of applications in optoelectronics, including high‐speed photodetectors, efficient solar cells, and advanced communication devices.^{[ 159 ]} Additionally, photo‐thermionic effects can also be observed in graphite, where strong optical absorption rapidly elevates the temperature of electrons, leading to thermionic emission.^{[ 160 ]} In a photo‐thermionic process, the electron temperature exceeds the lattice temperature. However, if the electron temperature and the lattice temperature reach equilibrium before electron emission occurs, the process is termed photo‐enhanced thermionic emission.^{[ 31} , ³² , ¹⁶¹ , ¹⁶² , ¹⁶³ , ^{164 ]}

3.2.3. Applications of Graphene Thermionic Emission in Diodes and Transistors

Graphene‐based thermionic emission also finds applications in diodes and transistors. Figure 7a illustrates a graphene/GaN Schottky diode, where the right edge of the graphene is in contact with GaN and the left edge is in contact with Au.^{[ 113 ]} This graphene/GaN diode exhibits higher thermionic emission current and reduced levels of inhomogeneities and flicker noise compared to other metal‐GaN diodes.^{[ 113 ]} Figure 7b presents a vertical transistor based on graphene‐WS₂ heterostructures where electron transport across the barrier is governed by tunneling and thermionic emission. The combination of tunneling and thermionic transport enables current modulation exceeding 1 × 10⁶ even at room temperature (shown in Figure 7c).^{[ 165 ]} This significant current modulation is facilitated by the tunability of the tunneling barrier height and shape. Both tunneling and thermionic currents are dependent on the barrier height which can be adjusted by shifting the Fermi level of the graphene.

Figure 7.

Graphene thermionic emission based diodes and transistors. a) Schematic diagram of a graphene/GaN Schottky diode. Reproduced with permission.^{[ 113 ]} Copyright 2016, American Chemical Society. b) Schematic diagram of a vertical transistor based on graphene‐WS₂ heterostructures. c) I‐V plot of the vertical transistor shown in (b). Panels b and c reproduced with permission.^{[ 165 ]} Copyright 2012, Springer Nature.

3.2.4. Applications of Graphene Thermionic Emission in Generating Free Electron Sources

Thermionic emission has been widely used to construct electron guns. The thermionic electron guns serve as the foundation for many vacuum electronic devices, including X‐ray tubes, traveling wave tubes, scanning electron microscopes, and transmission electron microscopes. Although many electron microscopes have transitioned from thermionic electron guns to field‐emission electron guns to achieve higher spatial resolution,^{[ 166 ]} thermionic electron gun‐based microscopes remain popular due to their cost‐effectiveness and the ability to generate larger emission currents compared to field‐emission electron gun‐based microscopes.

Key parameters of thermionic‐emission guns include stability, lifetime, electron emission current, vacuum quality, work function, and operating temperature. Stability of the guns is the ability to maintain consistent performance over time, which is usually affected by thermal fluctuations and material degradation. Lifetime is the operational lifespan of the cathode before significant degradation occurs, which is determined by the material properties and operating conditions. Electron emission current is the amount of current generated by the emitted electrons, ranging from nanoampere to ampere depending on the specific applications. Vacuum quality is the level of vacuum in the gun. To achieve high performance, high vacuum conditions are typically required to minimize scattering in thermionic emission guns. Lower work functions lead to higher emission currents at lower temperatures. Operating temperature is the cathode temperature which must be sufficiently high to produce enough electrons. Typically, the work temperatures of a thermionic gun range from 1270 K to 2070 K since the work function of most conventional metals is larger than 4 eV.

According to the Richardson‐Dushman equation (Equation 1), the operating temperature of a thermionic gun can be significantly reduced by lowering the work function of the cathode materials while keeping the emission current constant. The work function of a material usually can be altered via two methods, namely, electrostatic gating and surface coatings.^{[ 105 ]} In the method of surface coating, thin films of materials with different work functions are deposited onto the surface of targeted materials to reduce the surface work function. Although materials like alkali metals can lower the work function when deposited on a metal surface, graphene surface coating offers many advantages over conventional materials for thermionic emission due to the following factors. First, graphene is quite stable even at high temperatures and is capable of operating at high temperatures. Second, graphene is chemically inert, imparting resistance to molecular adsorption and oxidation.^{[ 167 ]} Third, graphene can be grown over many materials. Finally, graphene is known to lower the work function of other materials.^{[ 105} , ¹⁶⁸ , ^{169 ]} When conventional metals are coated with graphene, the work function of the metal/graphene surface is considerably smaller than the work function of either the metal or graphene, resulting in higher thermionic emission current.^{[ 170 ]} For example, the work function of Ru(0001)/graphene is ≈3.3 eV, which is smaller than the work function of Ru(0001) is 5.3 eV^{[ 171 ]} and the work function of graphene is 4.5 eV.^{[ 88 ]} As a result, the operating temperature of a thermionic gun whose cathode material is Ru(0001)/graphene is ≈1300 K. Additionally, the operating temperature of a thermionic gun can be considerably affected by the orientation of the graphene coating. For example, when the coating graphene on an Ir(111) surface is rotated by 30 degrees, the operating temperature is higher compared to that at zero rotation.

3.2.5. Applications of graphene thermionic emission in developing free‐electron‐driven light sources

Thermionic emission can be used for studying various types of free electron radiation which serves as a crucial platform for investigating light‐matter interactions and creating compact, on‐chip light sources (Figure 8a,b,c).^{[ 67} , ¹⁷² , ^{173 ]} The primary types of free electron radiation include Bremsstrahlung radiation, synchrotron radiation, Cherenkov radiation, and Smith‐Purcell radiation. Bremsstrahlung radiation is emitted when a free electron is deflected and decelerated by the electric field of an atomic nucleus or other charged particles. Synchrotron radiation is generated when charged particles, typically electrons, travel through a magnetic field. Cherenkov radiation occurs when a charged particle moves through a medium at a speed exceeding the phase velocity of light in that medium (Figure 8c). Smith‐Purcell radiation is produced when an electron beam travels parallel to or through a periodic structure (Figure 8d), resulting from the interaction between the moving electrons and the periodic potential of the grating.

Figure 8.

free‐electron‐driven light sources. a) Tunable light sources generated from graphene plasmon‐based free electron radiation. Reproduced with permission.^{[ 67 ]} Copyright 2015, Springer Nature. b) Integrated tunable all‐silicon free electron light sources. Reproduced with permission.^{[ 172 ]} Copyright 2019, Springer Nature. c) An integrated Cherenkov radiation light source. Reproduced with permission.^{[ 173 ]} Copyright 2017, Springer Nature. Panels d and e, reproduced with permission.^{[ 30 ]} Copyright 2022, John Wiley and Sons. and f) Tunable X‐rays from free electron‐driven van der Waals materials. Reproduced with permission.^{[ 176 ]} Copyright 2020, Springer Nature. g) Multicolor X‐rays from free electron‐driven van der Waals heterostructures. Reproduced with permission.^{[ 177 ]} Copyright 2023, The American Association for the Advancement of Science. h) A schematic diagram of a tabletop water‐window X‐ray imaging setup, with the inset illustrating a potential biological application that demonstrates the precise detection of dense granules in blood platelet cells using tunable water‐window X‐rays. Reproduced with permission.^{[ 178 ]} Copyright 2024, Springer Nature. i) An experimental demonstration of quantum recoil effects in free electron radiation. Reproduced with permission.^{[ 175 ]} Copyright 2024, Springer Nature.

Among various types of free electron radiation mentioned above, Smith‐Purcell radiation is used to develop tunable light sources.^{[ 174} , ^{175 ]} Smith‐Purcell effect‐based light sources are distinguished by several remarkable features, such as real‐time photon energy tunability (Figure 8e),^{[ 30 ]} continuous tunability (Figure 8f),^{[ 176 ]} multicolor X‐ray generation (Figure 8g),^{[ 177 ]} water‐window X‐ray production (Figure 8h),^{[ 178 ]} X‐ray caustics and focusing,^{[ 29} , ¹⁷⁹ , ^{180 ]} and quantum recoil (Figure 8i).^{[ 181} , ^{182 ]} Notably, free‐electron‐driven vdW crystals provide a way to address the limitations of current commercial X‐ray sources namely compactness and photon energy tunability. The Smith‐Purcell effect has been extensively studied for several decades, yet the practical applications of free electron light sources have remained severely limited due to the lack of effective electron sources. An efficient electron source is crucial for developing Smith‐Purcell effect‐based free electron light sources.

Currently, Smith‐Purcell radiation is mainly studied by using free electron sources from scanning electron microscopes (SEMs) and transmission electron microscopes (TEMs). SEMs and TEMs allow precise manipulation of electron beam current, kinetic energies, spot size, and beam focusing. Furthermore, SEMs and TEMs inherently offer a vacuum environment which is essential for generating Smith‐Purcell light sources. Due to these unique characteristics, SEMs and TEMs have become indispensable platforms for investigating Smith‐Purcell light sources. Several new phenomena have been discovered, including maximal spontaneous photon emission,^{[ 183 ]} flatband‐enhanced Smith‐Purcell radiation,^{[ 184 ]} and Smith‐Purcell radiation driven by low‐energy electrons. However, SEMs and TEMs' free electron sources have drawbacks including low electron current and relatively large size. The electron current in TEMs is typically limited to the nanoampere range, while that in field emission SEMs is limited to 100 nanoamperes. Although thermionic emission SEMs can enhance electron current by approximately tenfold, the electron current is still limited to the microampere level. Such a current is sufficient for studying phenomena related to Smith‐Purcell radiation but insufficient for practical applications which require milliampere‐level free electron beam currents. On the other hand, there is a growing belief that Smith‐Purcell radiation presents an avenue for developing on‐chip light sources with frequencies below X‐rays and for creating compact X‐ray sources. To realize free electron‐driven on‐chip and compact light sources, the size of electron sources must be either compact or integrated onto chips. Unfortunately, SEMs and TEMs' free electron sources cannot be directly utilized for this purpose.

Thermionic emission, particularly graphene‐based thermionic emission, presents a pathway for developing on‐chip Smith‐Purcell light sources and advancing Smith‐Purcell X‐ray sources for several reasons. First, graphene‐based thermionic emission electron sources can be miniaturized to nanometer scales.^{[ 185 ]} Second, these graphene thermionic emission sources are relatively easy to integrate into Smith‐Purcell light source setups since the heating mechanism can be designed to fit within the vacuum chamber where the electron‐grating interaction takes place. This simplicity of integration is a significant advantage for developing on‐chip light sources using thermionic emission. Third, graphene thermionic emission has the potential to provide milliampere‐level free electron beam currents which are essential for moving Smith‐Purcell light sources into the realm of practical applications. Finally, the beam current from thermionic emission can be controlled by adjusting the temperature of the thermionic emitter, higher temperatures lead to increased emission current. This ability to modulate beam intensity is crucial for optimizing the power of radiation generated by Smith‐Purcell processes.

Despite the advantages of using thermionic emission electron sources for developing Smith‐Purcell light sources, there are limitations. One such limitation is the substantial power required to heat the emitter to the required temperature. This can be a concern for applications demanding energy efficiency. For instance, in portable or space‐based Smith‐Purcell light source applications, the high power consumption associated with thermionic emission may render it impractical. Additionally, precise temperature control of the thermionic emitter is vital for stable electron emission. However, maintaining this control can be challenging, especially in environments prone to temperature fluctuations. Furthermore, the broad energy spread of electrons emitted via thermionic emission can be disadvantageous in applications that require a more mono‐energetic electron beam for producing a precise and narrow‐band Smith‐Purcell radiation spectrum. While techniques like post‐emission energy filtering are being explored to reduce this energy spread, they add complexity to the system.

Nevertheless, the application of thermionic emission in Smith‐Purcell‐based light sources represents a promising area of research. While thermionic emission offers a convenient and stable method for generating electron beams, improvement in efficiency, temperature management, and beam quality are required. Recent research efforts focused on advanced thermionic materials,^{[ 54} , ^{186 ]} the optimization of the electron‐grating interaction,^{[ 187} , ^{188 ]} and hybrid approaches. These approaches offer significant potential for enhancing the performance of these light sources. Continued exploration in this field could lead to more efficient, stable, and versatile Smith‐Purcell‐based light sources, applicable in spectroscopy, imaging, and telecommunications.

To conclude this section, we summarize key performance parameters of graphene‐based thermionic devices in Table 2 .

Table 2.

Key performance parameters of graphene‐based thermionic devices.

Devices	Unique properties	Underline reasons
Thermionic energy converters	1) Achieving high energy efficiencies of up to 55% at an operating temperature of 900 K; 2) generating electricity from 400 K low‐grade waste heat with an energy efficiency of 7%.	The work function of graphene can be widely tuned, and the Schottky barrier height of its heterostructures is low.
Thermionic photon detectors	Achieving high photo‐to‐dark current ratios on the order of 104.	Photoinduced carriers rapidly thermalize among electrons, but they dissipate heat to the lattice at a much slower rate.
Thermionic diodes and transistors	High current modulation exceeding 1 × 106 is achieved at room temperature.	Enabled by the tunability of the tunneling barrier height and shape.
Thermionic free electron sources	1)High emission current, 2)high stability, 3)low operating temperature, 4) long lifetime	Enabled by: 1) A tunable work function; 2) Chemically inert; 3) Stable even at high temperatures.
Thermionic free‐electron‐driven light sources	1)Compact, 2)frequency tunable, 3) high flux	Enabled by: 1) the small size of graphene‐based thermionic electron sources; 2) ease of integration with free electron light setups; 3) milliampere‐level free electron beam currents.

4. Thermionic Emission in 3D Topological Material

4.1. Theoretical modelling of Thermionic Emission in 3D Topological Material

While free‐standing single‐layer graphene exhibits high electron mobility, its thermionic emission capability is constrained by the low density of states and its performance can be influenced by the substrate. The low emission current in graphene due to the vanishing density of states can be improved in 3D Dirac materials like Cd₃As₂ ^{[ 189 ]} with increased group velocity. Additionally, the thermal energy carried by electrons in 3D Dirac materials is twice that of conventional materials. Consequently, 3D Dirac materials demonstrate superior thermal efficiency and coefficient of performance compared to traditional semiconductors and graphene.^{[ 190 ]} Cd₃As₂ possesses unexpectedly low thermal conductivity and exhibits exceptional thermoelectric performance,^{[ 191 ]} making it a promising candidate for thermionic emission applications.

Both single‐layer graphene and 3D Dirac materials have linear energy dispersion (shown in Figure 1c), described by the equation E  =  ℏv_Fk. In the case of single‐layer graphene, the wavevector k  =  (k_x ,k_y ) is a 2D vector, while for 3D Dirac materials, the wavevector k  =  (k_x ,k_y , k_z ) is a 3D vector. The linear energy dispersion of 3D Dirac materials means that the Richardson–Dushman law, designed for conventional materials, is inadequate for accurately describing thermionic emission in these materials. Although both types of materials share a linear energy dispersion, the thermionic emission behavior of 3D Dirac materials is anticipated to differ from that of single‐layer graphene due to their distinct dimensional characteristics. Based on the linear energy dispersion of 3D Dirac materials, the thermionic emission current is derived as follows:

$$J\left(T\right)=\frac{q{k}_B^2}{4{\pi }^2{\hslash }^3{v}_F^2}\left(q\varphi +E_F+2k_{B}T\right)T^2{\mathrm{e}}^{-q\varphi \beta }$$ (7)

where q is the charge of an electron, k_B is the Boltzmann constant, v_F is the Fermi velocity whose value is ≈1 × 10⁶ m/s for Cd₃As₂, ϕ is the surface potential, E_F is the Fermi energy, and β  =  1/(k_BT). It is important to note that Equation(7) differs slightly from the results presented in reference.^{[ 192 ]} This discrepancy arises from the use of θ_max in reference^{[ 193 ]} and reference,^{[ 192 ]} where cos ²θ_max = k _min /k in reference^{[ 193 ]} and cos  θ_max = k _min /k in reference,^{[ 192 ]} respectively.

Despite different energy dispersion in conventional materials, single‐layer graphene, and 3D Dirac materials, thermionic emission is isotropic in these systems. There exist anisotropic topological systems such as topological nodal ring semimetals and Weyl semimetals.^{[ 193} , ^{194 ]} Consequently, thermionic emission in these materials also exhibits anisotropic properties.

Nodal‐ring semimetals are defined as materials wherein the conduction and valence bands make contact along a closed loop within the Brillouin zone (Figure 1d). This distinct closed loop is referred to as the nodal ring. A key characteristic of nodal‐ring semimetals is their anisotropic energy dispersion. As a result, electrons in these materials exhibit markedly different behaviors and properties depending on their direction of motion. The existence of nodal‐ring semimetals has not only been theoretically predicted but also experimentally verified, as demonstrated in the case of ZrSiSe.^{[ 195} , ¹⁹⁶ , ^{197 ]} The nodal ring in these materials is topologically protected by a combination of time‐reversal symmetry, inversion symmetry, mirror reflection symmetry, and nonsymmorphic symmetries. This topological protection grants the nodal ring robustness against minor perturbations and disorders, ensuring its stability even in the presence of external influences. The typical energy dispersion of nodal‐ring semimetals can be expressed as

$$\epsilon =s\hslash v_F\sqrt{k_x^2+{\left(k_{\perp }+s^{\prime }b\right)}^2}$$ (8)

where s  =   ± and s′  =   ± are the band indexes, $k_{\perp }=\sqrt{k_y^2+k_z^2}$ and b is the radius of the nodal‐ring semimetal.

Thermionic emission in Nodal‐ring semimetals exhibits anisotropy in the x‐and y‐directions.^{[ 193 ]} This anisotropic emission becomes more pronounced as the radius of the nodal‐ring increases. When b  =  0, the nodal‐ring semimetal transforms into a Dirac semimetal, and the anisotropy in both the energy dispersion and the thermionic emission vanish. This transformation provides a clear indication of the role of  b in determining the anisotropic behavior. Specifically, the thermionic emission current density of nodal‐ring semimetals increases as = ε₀ /(ℏv_F ) increases (Figure 9a). The thermionic emission current density in nodal‐ring semimetals depends on the Fermi energy (Figure 9b), a feature they share with Dirac semimetals. This similarity can be attributed to the linear or linear‐like energy‐momentum dispersion in both nodal‐ring and Dirac semimetals. The work function dependence of the thermionic emission current density in nodal‐ring semimetals is shown in Figure 9c, indicating that a reduced work function can considerably increase the thermionic emission current. Figure 9d demonstrates that nodal‐ring semimetals exhibit anisotropic thermionic emission properties in the x and y directions, that is, J _y,1/J _x,1 ≠ 1. This anisotropic effect diminishes as b decreases. When b  =  0, the anisotropic effect disappears, which is anticipated since b  =  0 reduces nodal‐ring semimetals to Dirac semimetals, which have isotropic thermionic emission in the x and y directions.

Figure 9.

Unique thermionic emission in nodal‐ring semimetals. a) The temperature dependence of the thermionic emission current at various values of ε₀, where ε₀ =  ℏv_Fb and b is the radius of the nodal ring. b) The temperature dependence of the thermionic emission current at various values of the Fermi level E_F . c) The temperature dependence of the thermionic emission current at various work function values W. d) Anisotropic thermionic emission current in the x and y directions. Reproduced with permission.^{[ 193 ]} Copyright 2020, American Institute of Physics.

Weyl semimetals also exhibit intriguing thermionic emission properties due to their anisotropic energy dispersion (Figure 1e).^{[ 194 ]} The key topological parameter of Weyl semimetals is the Weyl point separation b. The separation b makes the energy dispersion of Weyl semimetals become anisotropic, resulting in anisotropic thermionic emission (Figure 10a). Thermionics in Weyl semimetals can be tuned with the separation b. Specifically, the response perpendicular to the direction of b increases monotonically as b increases. For large b, emission is higher along the perpendicular direction. If b is small, the directionally dependent performance varies with temperature. At low temperatures, emission along the parallel direction dominates. As temperature increases, emission along the perpendicular direction becomes dominant. The optimal cooling efficiency of a single barrier device along the perpendicular direction can reach 80% of the theoretical limit (Figure 10b). This is 5% higher than that of a conventional parabolic material. These results suggest that Weyl semimetals have potential applications in thermionic cooling and power generation. Since b can be designed or altered by doping when it exists as a child phase in symmetry‐broken Dirac materials (such as Hg_1‐x‐yCd_xMn_yTe^{[ 198 ]}) or nodal ring materials,^{[ 199 ]} or by straining the crystal (such as in SrIrO₃ ^{[ 200 ]}), materials or device engineering can optimize the thermionic response by varying b.

Figure 10.

Unique thermionic emission in Weyl semimetals. a) Anisotropic thermionic emission current of Weyl semimetals in the z and x directions. b) Performance of a thermionic refrigeration device based on Weyl semimetals at different values of cone separation b, where T_c =  250 K, E_F =  100 meV, W  =  200 meV and the unit of b is 10⁸ ℏ. Reproduced with permission.^{[ 194 ]} Copyright 2024, American Institute of Physics.

It is worth noting that non‐Richardson‐Dushman thermionic emission can also exist in Rashba spin‐orbit coupling systems, such as those found in InAs‐ and InGaAs‐based 2D semiconductors.^{[ 201 ]} The Rashba spin‐orbit coupling significantly alters thermionic behavior in two key ways. First, the mean thermal energy associated with a degree of freedom deviates from the energy equipartition of k_BT/2. Second, the divergent density of states in the low Rashba spin‐orbit band significantly enhances charge transport.^{[ 201 ]}

4.2. Topological Materials based Thermionic Devices

Since 3D Dirac materials demonstrate superior thermal efficiency and coefficient of performance compared to traditional semiconductors and graphene, their potential applications in thermionic emission have been explored in thermionic cooling,^{[ 193} , ²⁰² , ^{203 ]} thermionic energy generators,^{[ 189} , ¹⁹² , ^{204 ]} and enhanced heat transfer in X‐ray tubes.^{[ 28 ]} X‐ray tubes have become indispensable tools in medical imaging, radiation therapy, and non‐destructive inspection. However, the development of high‐power X‐ray tubes faces significant challenges due to overheating, as only about 1% of the input energy is transformed into X‐rays, while the remaining energy is dissipated as heat.^{[ 205 ]} To address the overheating issue in X‐ray tubes, various cooling methods have been proposed, including water‐cooling technology^{[ 206 ]} and rotatable target designs.^{[ 207 ]} Among these, thermionic cooling emerges as an innovative solution that offers distinct advantages over conventional cooling methods. The benefits of thermionic cooling include high thermal dissipation power, the absence of moving parts, and a simplified structural configuration. Figure 11a illustrates the diagram of a thermionic cooling‐enhanced X‐ray tube. By utilizing thermionic cooling, the target temperature of the X‐ray tube, which operates at an input power of 2000 W, can be reduced from 1206 °C (which exceeds the melting temperature of copper) to 393 °C (which is significantly below the melting point).

Figure 11.

Thermionic Devices Utilizing Topological Materials. a) Enhancement of heat transfer in X‐ray tubes through thermionic cooling enabled by topological materials. Reproduced with permission.^{[ 28 ]} Copyright 2024, AIP Publishing. b) Thermionic‐enhanced heat transfer in electronic devices employing 3D Dirac materials, with the green regions of the planes indicating Dirac semimetals. Reproduced with permission.^{[ 202 ]} Copyright 2019, AIP Publishing. c) A solar thermionic energy converter based on 3D Dirac materials, featuring tungsten as the cathode and 3D Dirac materials as the anode. Reproduced with permission.^{[ 192 ]} Copyright 2018, IOP Publishing. d) Thermionic energy conversion utilizing 3D Dirac semimetals, where 3D Dirac materials serve as the cathode and a metal plate is used as the anode. Reproduced with permission.^{[ 204 ]} Copyright 2021, Optical Society of America.

Thermionic cooling can enhance the heat transfer in high‐power vacuum electronic devices and establish a cool environment. As a result, the interior temperature of the vacuum electronic devices can be kept lower than the ambient temperature (Figure 11b).^{[ 202 ]} The applications of 3D Dirac materials in TECs have also been explored (Figure 11c). TECs based on Dirac materials demonstrate a superior performance compared to TECs based on monolayer graphene and metallic materials.^{[ 192 ]} Despite extensive research on solar TECs,^{[ 26 ]} their practical applications have been constrained by relatively low conversion efficiencies, usually below 10%.^{[ 204 ]} However, by employing 3D Dirac material as the novel anode in a concentrated solar TEC (Figure 11d), the conversion efficiency can be increased to 11.8% under a solar concentration of 500.^{[ 204 ]}

5. Conclusions and Outlooks

The discovery of topological materials has significantly advanced the development of thermionic technology and devices. Due to the non‐parabolic energy dispersion in topological materials, including graphene, Dirac semimetals, Weyl semimetals, and nodal‐ring semimetals, thermionic emission in these materials can no longer be described by the Richardson‐Dushman equation. This limitation has stimulated the development of various models to characterize thermionic emission from topological materials. Generally, these models do not have mass dependency, reflecting the behavior of electrons in these topological systems as massless Dirac particles. Furthermore, the T ² scaling in the Richardson‐Dushman equation has been replaced by T ³ scaling.

Among these topological materials, graphene has demonstrated promising applications in various types of thermionic devices, including TECs, thermionic cooling devices, thermionic photodetectors, thermionic diodes, thermionic transistors, and free electron‐driven light sources. The appeal of using graphene in thermionic devices is further enhanced by its surface which is free of dangling bonds. This surface property allows for vertical or lateral stacking with conventional or 2D materials to form heterostructures. The height of the Schottky barrier at the heterostructure boundary can be tuned from a few millielectronvolts to several electronvolts by selecting suitable materials or by adjusting the Fermi level of graphene. This low barrier height, along with its tunability, makes graphene and its heterostructures highly desirable for thermionic devices because thermionic emission is exponentially dependent on the barrier height. Enhancing the thermionic emission current is particularly crucial for many thermionic devices, including TECs, thermionic cooling devices, and vacuum thermionic devices that require high fluxes of free electrons. In TECs, lowering the barrier height not only enables the harvesting of low‐grade waste heat but also improves energy efficiency.

In fact, the dangling bond‐free surface is not unique to graphene; it is also widely present in various 2D van der Waals materials. The emergence of graphene in 2004 has led to the discovery of a large group of 2D materials, including metals, (topological) semimetals, semiconductors, and (topological) insulators. All these 2D van der Waals materials possess dangling bond‐free surfaces and can be vertically or laterally stacked to form heterostructures, resulting in the emergence of Schottky barriers. This provides additional platforms to investigate thermionic emission phenomena and develop high‐performance thermionic devices. Moreover, 2D materials can be rolled into nanotubes, which also have promising applications in thermionic devices. For example, single‐walled carbon nanotubes have been demonstrated to generate thermionic electron current densities on the order of 10⁵ A cm⁻¹, which is superior to that of graphene‐based thermionic emitters and conventional thermionic emitters.^{[ 208 ]}

The linear energy dispersion of graphene not only leads to unique properties in thermionic emission but also gives rise to distinct characteristics in hot carrier relaxation. This property is useful for developing thermionic‐based photodetectors. When graphene is illuminated by light, electrons are excited to high‐energy states, and the photoinduced electrons undergo rapid thermalization among themselves, while heat is dissipated to the lattice at a considerably slower rate. This phenomenon arises from the that the electron‐electron scattering rate is about three orders of magnitude greater than the electron‐phonon scattering rate. This difference is attributed to graphene's linear energy dispersion. The huge difference in scattering rates enables the detector to maintain a non‐equilibrium state of carriers for a relatively long duration, thereby enhancing the efficiency of the photo‐thermionic process. Additionally, graphene‐based devices demonstrate a high degree of compatibility with conventional solid‐state devices. This characteristic simplifies the fabrication process of complex optoelectronic systems and facilitates seamless incorporation into existing technological infrastructures.

Practically, thermionic emission has been widely used to generate free electron beams in vacuum electronic devices such as X‐ray tubes, traveling wave tubes, scanning electron microscopes, and transmission electron microscopes. Topological materials, particularly graphene, can enhance the performance of these devices by increasing the electron beam current through the reduction of barrier height. Additionally, the applications of graphene in thermionic photodetectors have been demonstrated both theoretically and experimentally. Although the significant progress has been made in graphene‐based TECs, further experimental studies are required. Practical applications for harvesting waste heat or solar energy need to be developed. Furthermore, there is potential to utilize graphene thermionic emission for generating compact, on‐chip free electron light sources.

Conflict of Interest

The authors declare no conflict of interest.

Author Contributions

All authors play a vital role in writing and review the article, contributing significantly through their own areas of expertise, which enriches the entire review.

Biographies

Sunchao Huang earned his Ph.D. in physics from the University of Wollongong, Australia, in 2019. Following this, he served as a research fellow at the School of Electrical and Electronic Engineering at Nanyang Technological University, Singapore. He is currently a professor at the School of Electronic Science and Engineering at the University of Electronic Science and Technology of China, China. His research interests focus on thermionic emission and tunable free electron‐driven light sources.

Yubin Gong is currently a full and chair professor at the University of Electronic Science and Technology of China (UESTC). He received his bachelor's degree in applied optics from Changchun University of Science and Technology in 1989. He received his master's degree and Ph.D. in physical electronics from UESTC in 1992 and 1998 respectively. Prof. Gong's research mainly focus on novel slow‐wave structure millimeter‐wave and terahertz TWTs, novel radiation mechanisms and principles of terahertz vacuum electron devices, as well as application of vacuum electron devices in life science. He has published over 400 peer‐reviewed academic papers.

Chao Zhang received his Ph.D. in physics in 1987 from City University of New York, USA. From 1987 to 1989, he was a postdoctoral fellow at Max‐Planck‐Institute for Solid Research in Germany, working on quantum magnetotransport in semiconductor nanostructures. From 1989 to 1992, He was a research associate at TRIUMF in Canada, working on quantum dissipation in solids. He is current an honorary professor at University of Wollongong. He has been the fellow of Australian Institute of Physics since 1998. His research interest is in areas of quantum transport of nanostructures, optical properties of semiconductors and topological insulators.

Huang S., Zhang Z., Yang Y., et al. “Thermionics in Topological Materials.” Adv. Mater. 37, no. 36 (2025): 37, 2505619. 10.1002/adma.202505619