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Using First-Principles Simulations to Discover Materials with Ultra-low Work Functions for Energy Conversion Applications

Global Climate and Energy Project Annual Report

April 26, 2013 Investigators Roger T. Howe, Professor, Electrical Engineering Jens K. Nørskov, Professor, Chemical Engineering/SLAC Piero A. Pianetta, Professor, Electrical Engineering/SLAC Igor Bargatin* (research associate, Electrical Engineering), Frank Abild-Pedersen (staff scientist, SLAC), Johannes Voss (postdoctoral scholar, Chemical Engineering), Aleksandra Vojvodic (postdoctoral scholar, Chemical Engineering) Sharon Chou (PhD student, Electrical Engineering), Hongyuan Yuan (PhD student, Physics) *Currently Professor of Mechanical Engineering at University of Pennsylvania Abstract

Our objective is to discover new nanostructured materials with ultra-low work functions for achieving high-efficiency thermionic energy conversion. Since the start of the project in October 2011, we have made progress on all three thrusts: (1) density functional theory (DFT) calculations of the work functions of multi-layer surfaces, (2) fabrication of multilayer surfaces with low work functions, and (3) measurements of surface properties of multi-layer surfaces.

The DFT calculations we have performed thus far offered new insights into the

atomistic processes that control the work functions of various surfaces. In particular, we have studied and visualized the formation of dipoles on the surfaces of materials with low-work-function coatings, such as cesium, barium, calcium, and strontium oxides. The density of surface dipoles created by adsorbates is directly proportional to the changes in the work function induced by the coating. We have calculated the charge distributions and the corresponding changes in the work function for a variety of cesiated transition metals and observed general trends in the behavior of such binary systems (one substrate + one coating). In addition, we have developed a new model that particularly well-captures the work function minimum with respect to the surface coverage of cesiated transition metals. The model builds on the classical point-dipole equation by characterizing the degree of orbital overlap between the 6s states of neighboring cesium adsorbates and its effect on the strength and orientation of electric dipoles along the adsorbate–substrate interface. The physical foundation of this model enables it to be generally applied to systems with similar surface dipole behavior. We also present a DFT-based method for calculating thermionic emission currents using a non-equilibrium Green’s function (NEGF) approach. It does not require semi-classical approximations or simplifications of the electronic structure used in previous methods. Thus, it provides

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quantitative predictions of thermionic emission for adsorbate-coated surfaces. This new model is a breakthrough for predicting thermionic emission from composite or multi-layer electrodes, which can often yield higher current densities than do elemental surfaces. The model results match well with experimental measurements of temperature-dependent current densities.

Additionally, we have launched experiments involving the second and third thrusts of

the project. In particular, we have fabricated multilayer structures by growing graphene via chemical vapor deposition (CVD), depositing thin alumina films on silicon via atomic-layer deposition (ALD), and measuring work functions at various bias voltages. We have performed these measurements in the upgraded vacuum chamber at the Stanford Synchrotron Radiation Light Source (SSRL), which allowed increased flexibility in handling and characterizing samples using XPS.

Introduction

The work function is the interfacial parameter of the surface of a material that determines how easily electrons can escape into a vacuum or gas environment, with lower work functions generally facilitating electron emission. By employing theoretical DFT methods and nanofabrication techniques, this interdisciplinary project will undertake a systematic approach to gain such understanding and apply it to discover new nanostructured multilayer materials with ultra-low work functions. As a result, many promising material-coating combinations will be efficiently investigated for the first time. Successful completion of this project will result in new stable surfaces with record-low work functions and prototypes of efficient thermionic energy converters that utilize such surfaces. The research team has the combined expertise in the critical areas of DFT calculations, surface characterization, and nano/micro-fabrication.

Figure 1: Left: Schematic of a traditional thermionic energy converter. The incoming heat makes the emitter (cathode) hot enough to evaporate electrons off its surface (thermionic effect). The electrons then traverse the vacuum gap, are absorbed by the collector (anode), and drive the electric current through the external load [DTRA2001]. Right: Calculated efficiency limit for a thermionic energy converter as a function of the cathode temperature for three values of the collector (anode) work function: 1.5, 1.0, and 0.5 eV (based on [Hatsopoulos1973]). For comparison, the dashed curves show the Carnot efficiency limit and the efficiency limits for a thermoelectric converter with a figure of merit of ZT = 2, which roughly corresponds to the best existing thermoelectric materials, and ZT = 10, which is much better than the current state of the art. The heat sink is assumed to be at room temperature (300 K) in all cases.

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We are interested in the discovery of new materials with low work functions because

such materials could dramatically improve the efficiency of thermionic energy converters (TECs) — a type of heat engine that directly convert heat into electricity (Fig. 1). The efficiency limit of thermionic energy converters depends very strongly on the work function of the collector (anode), as shown in Fig. 1. For a given anode temperature, the optimal work function of the anode is approximately Tanode/(700 K), expressed in eV [Hatsopoulos1973]. For example, for anodes rejecting heat near room temperature, the optimal anode work function would be approximately 0.5 eV. Materials with such low work functions have not been discovered yet and therefore, thermionic converters typically use the anodes with the lowest work functions available. In practice, most thermionic converters have used cesiated tungsten anodes with work functions on the order of 1.5 eV, which means that traditional thermionic converters could have competitive efficiencies only at heat source temperatures above 1500 K (Fig. 1). The lack of materials with lower work functions and the associated high operating temperatures were the main challenges for thermionic converters in the past, explaining both their high cost and limited applicability.

Note that there is no known fundamental limit on how low a work function of a

specially engineered surface can be. Experimentation over the last few decades has produced steady albeit small improvements in lowest-work-function surfaces and their stability. The lowest work functions reported in the literature are currently on the order of 1 eV, but most of these surfaces require an ultra-high-vacuum (UHV) environment and are therefore not suitable for high-temperature energy conversion applications. By combining theoretical simulation, experimental characterization, and device demonstration in this proposal, we plan to dramatically speed-up the search for new stable materials with work functions on the order of 1 eV and less. Discovery of new materials that have work functions in the 0.5 – 1.0 eV range and are stable at elevated temperatures in low-vacuum environments will dramatically increase the efficiency of all thermionic energy converters, making them competitive with both thermoelectric converters and mechanical heat engines (Fig. 1). It would also open up new applications for thermionic converters, such as heat harvesting at moderately high temperatures (~ 500° C) in residential combined heat and power systems (micro-CHP). Because thermionic converters have no mechanical moving parts, they produce low noise and need very low maintenance, providing inherent advantages over the mechanical heat engines currently used for CHP systems.

Background The work function is one of the most fundamental properties of a metallic surface, important in determining the material’s applicability as a contact electrode [Lindell2006, Zhou2012] or electron emitter [Yamamoto2006]. Surfaces with ultra-low work functions could therefore improve technologies requiring precise control of contact barriers such as organic and printed electronics [Zhou2012] or a variety of devices based on electron emission, ranging from fluorescent light bulbs [Wada2009, Watanabe2011] to THz sources [Snapp2012], thermionic energy converters (TECs) [Lee2009], and the photon-enhanced thermionic emission converters (PETEC) [Schwede2010]. For TEC and

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PETEC, in particular, discovery of thermally stable materials with work functions of less than 1 eV would allow thermionic conversion of high-temperature (> 500° C) heat or solar radiation directly to electricity with efficiencies exceeding 50%.

The work function is the minimum energy needed to remove an electron from the bulk of a material through a surface to a point outside the material, and is defined as: Φ = Vvac – Ef, where Ef, is the Fermi level and Vvac is the vacuum level, i.e., the potential energy of electrons immediately outside the material (Fig. 2). Among elemental materials, alkali metals are known to have the lowest work functions. However, in practical applications, a number of alloys and compounds, such as thoriated tungsten and lanthanum hexaboride, are used because they offer relatively low work functions (~2.5 eV) in combination with much better chemical and thermal stability. It has also been known since the pioneering works of Taylor and Langmuir in 1930s [Taylor1933, Langmuir1933] that it is possible to create surfaces with work functions lower than those of any elemental materials by using coatings with thicknesses on the order of a monolayer. For the W/Cs system, the lowest work function is observed in experiments when the cesium layer has an average thickness on the order of three quarters of a monolayer—a condition described as a coverage ratio of 0.75. This observation is in accordance with our DFT results as shown in the right panel of Figure 2.

Figure 2: Left: the electrostatic potential of cesium covered tungsten (110) at a coverage of ~0.75 monolayer (ML). The step in the potential at z ≈ 1 is due to the dipole correction, which is done for computational convenience and does not represent a real change in the potential. The “hump” in the potential near z ≈ 18 is the additional barrier caused by the adsorbed cesium atom. The width and height of this barrier determine the Richardson-Dushman constant of the surface. Right: work function of cesiated tungsten plotted against the coverage of cesium. Vertical dotted lines indicate the regimes of low coverage, medium coverage (where the work function is a minimum), and high coverage (where the work function approaches that of cesium).

Initially, the work function decreases approximately linearly with increasing

coverage, as the dipoles associated with individual adsorbate atoms practically do not interact with each other. However, as the coverage increases and the average distance between the adsorbate cesium atoms decreases, the dipoles begin to interact, at first electrostatically as point-dipoles and then covalently via the extended electron clouds of

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cesium [Wimmer1982]. As a result of these interactions, the dipole associated with each individual adsorbate atom decreases (i.e., depolarization occurs), causing the work function to reach a minimum and then increase again, eventually saturating at the value corresponding to the work function of bulk cesium.

We can qualitatively characterize the three regimes of the adsorbate-induced work

function reduction in Figure 2 (right) as follows: at low coverage (Figure 3(a)), the distance between neighboring adsorbate atoms is so large that they can be treated as point-dipoles, and simple electrostatic interactions between the point-dipoles provide an adequate description. Conversely, at high coverage (Figure 3(c)), strong covalent interactions dominate and the dipole can only be adequately modeled quantum mechanically. However, there is an intermediate regime of crossover between these classical and quantum-mechanical contributions. It is in this intermediate region of relatively weak covalent bonds (Figure 3(b)) that the work function typically reaches a minimum. Therefore, it is particularly important to have a model that adequately describes the dependence of the work function on the adsorbate coverage in this intermediate regime.

Figure 3: X–Z spatial profiles of net valence electron charge density showing Cs adsorbed on the W(100) surface at (a) low, (b) near optimal, and (c) high coverage. The profiles show isocontours of the change in electron charge density between a bare and cesiated tungsten surface. Cyan blue (light) = electron-rich, red (dark) = electron-poor. The centers of the Cs atoms and the top layer of the W atoms are marked by arrows.

The charge transfer at the interface between the surface and the coating plays a

crucial role in determining the emissive properties of the surface. It influences not only the work function by shifting the vacuum potential level relative to the Fermi energy of the metal, but also the Richardson-Dushman constant of the surface, by affecting the width and the height of the barrier due by the adsorbate atoms. For optimal electron emission, both a low work function and a low barrier (high Richardson-Dushman constant) are required.

To characterize the interfacial behavior of surfaces and their coatings, we study them

using density functional theory (DFT) – a well-established method for first-principles calculations that has been remarkably successful when modeling various properties of solid-state systems [Marzari2006, Hafner2006]. Our primary goal is to harness the predictive power of DFT to guide the discovery of new surfaces with the lowest possible

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work functions. First-principles calculations solve the quantum mechanical Schrödinger equation; DFT is the most widely used computational method because of its accuracy and reliability at a reasonable computational cost. The use of such quantum-mechanical computations for studying materials has today reached a sufficient level of accuracy where it can not only explain experiments, but also predict properties of yet unmeasured systems. This success is owing to significant advances in available computational power and efficient simulation software development. As a result, it is now possible to screen dozens of material candidates without the need for synthesizing and then characterizing them.

The best candidate material combinations from the DFT calculations will be tested

experimentally by measuring work functions using both thermionic emission and photoemission. Benchmarking against experiment will test the theoretical predictions and provide guidance to further experiments. In this manner, the experimental and theoretical efforts will interact, hence allowing us to screen and test a larger number of promising material combinations than was possible before. We will study surfaces involving new nano-scale materials, such as graphene, as well as various substrates with nano-scale coatings consisting of, for example, alkali metals or oxides. These coatings can be created using physical vapor deposition and advanced nanofabrication techniques, such as atomic layer deposition (ALD). Layered coatings allow for many more combinations of materials and may therefore lead to lower work functions. For example, it was discovered that oxygen-cesium covered silicon has much lower work function silicon covered with pure cesium [Levine1973]. However, the quantum-level fundamental understanding of this effect is still lacking. The proposed DFT calculations of such multi-component coatings can both address the existing gaps in our fundamental understanding of such materials and lead to the discovery of new stable surfaces with record-low work functions.

DFT can model surfaces of arbitrary complexity, subject only to the available

computational power. So far, the work functions of many solid surfaces have been successfully calculated using DFT, including pure metal surfaces [Fall1999, Fall2001, Singh-Miller2009] as well as metal surfaces with some organic [Natan2006, Rusu2006, Zhou2012] and inorganic coatings (overlayers) [Giordano2005, Lina2008, Magkoe2001, Neugebauer1992, Prada2008, Steckel2008, Todorova2004, Vlahos2010]. These prior studies have explained some of the experimental observations and demonstrated that the work function of a surface can be affected by a coating in a variety of ways. We aim to use DFT to both explain and discover new stable combinations of substrates and coatings that would achieve work functions below 1 eV.

To that end, we are currently investigating emissive materials in dispenser cathodes,

which are electron emitters with applications such as microwave tubes, X-ray guns, or high-RF power terahertz devices [Barik2011]. Commercial dispenser cathodes often contain oxide mixtures in various proportions of barium, scandium, aluminum, strontium, and calcium [Wang2009, Cronin1981, Brodie1956, Brodie1957, Wooten1955]. These materials are generally more stable than cesium-based coatings. Vlahos et al have simulated various orientations of barium oxide dimers to find the most

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thermodynamically stable orientation, which turned out to be tilted. The most stable phase was identified to be one part barium and four parts oxygen, and the addition of scandium yielded new stable compounds with even lower work function [Vlahos2010]. This demonstrated that multicomponent alloying can produce stable surface structures with lower work function than that of its individual components. We aim to extend this study by investigating mixtures of barium, calcium, and strontium oxides with addition of scandium on a tungsten substrate. Results A: Orbital-overlap model

As aforementioned, the work function of cesiated tungsten has a characteristic dependence on surface coverage (Fig. 2). In order to predict the work function minimum in the coverage regime where the classical dipole model is no longer adequate, we introduce the orbital-overlap model [Chou2012]:

∆Φ = !!!!!!!!!/! !!!!!!/! !!!!!!!/!

, (1)

where ΔΦ is the reduction in the work function and N is the number of surface-coating adsorbates per unit area. 𝑐! is proportional to the surface-normal dipole moment associated with each adsorbate in the limit of very low surface coverage (i.e., without depolarization). 𝑐! is related to the linear polarizability of the surface dipoles and the spatial arrangement of the dipoles on the surface. Due to the large extent of the outermost cesium 6s orbital, overlap becomes important at coverages as low as ≈ 2×1014 atoms cm-2 (≈0.5 ML) (monolayers). On one hand, the large extent of the 6s states renders the assumption of electrostatically interacting point-dipoles in the classical dipole model invalid. On the other hand, the formation of Cs–Cs bonds introduces further depolarization as charge transfer to these covalent bonds weakens the dipoles normal to the surface. The exponential terms exp(-c3/N) describe the orbital overlap between neighboring Cs adsorbates, c3 is inversely proportional to the areal spread of the 6s orbitals, and c4 describes the strength of depolarization due to orbital overlap.

The orbital-overlap model equation (1) demonstrates dramatically better agreement with the DFT data (Fig. 4(a)) than either the classical dipole model (Fig. 4(b)) or the modified Gyftopoulos–Levine (GL) model [Gyftopoulos1962, Jensen2006] (Fig. 4(c)). The classical dipole model exhibits reasonable fit at the low coverage regime but tends to overestimate the curve minimum and underestimate the work function in the high coverage regime. A modified GL model was devised [Jensen2006] to incorporate empirical parameters such as covalent radii, although the fit tends to overestimate the work function (Fig. 4(c)). The modified GL model also requires reconciliation of different experimental values such as atomic surface densities [Taylor1933, Wang1977, Haas1983, Longo1984]. In addition, the nature of the polynomial fit in the modified GL model results in nonphysical deviations at coverages above 1 ML (Fig. 4(c)).

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Figure 4: Work function versus coverage fit comparison for Cs adsorbed close-packed Ag, W, and Pt surfaces. (a) Orbital-overlap model, (b) classical dipole, and (c) modified Gyftopoulos–Levine model (Eq. (43) in [Jensen2006]). The cesiated Ag(111), W(110), and Pt(111) surfaces have work function minima at a normalized coverage of approximately 0.5, 0.7, and 0.75 monolayer (ML), respectively.

We examine the close-packed surfaces HCP(0001), FCC(111), and BCC(110), as well as the more open surfaces FCC(110) and BCC(100) of 3d-, 4d-, and 5d-transition metals (except for Tc and Mn). We consider these open surfaces since the work functions of the technologically important polycrystalline substrates correspond to an average over surfaces of different orientations. Empirically, the work functions measured for FCC(110) and BCC(100) substrates provide the best estimates for the observed values of polycrystalline samples [Fomenko1966, Kawano2008].

Figure 5: Minimum work functions (MWF) and their corresponding optimal coverages as calculated by the orbital-overlap model for (a) close-packed body-centered, face-centered, and hexagonal transition metal surfaces, and (b) open, or loose-packed body-centered and face-centered metal surfaces. The elliptical outlines are 1-σ confidence intervals while the tilting illustrates the correlation of optimal coverage and MWF based on finite-difference calculations of the fitting parameters in equation (1).

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An important design rule for new low-work function materials follows from this

crossover in behavior: Since the high-coverage regime dominated by adsorbate overlap is generally only weakly affected by a non-polar substrate, the cesium-substrate dipoles must be strong enough so that a low work function is reached before the crossover to the high-coverage regime occurs. This constraint can be lifted by considering compound substrates with layered, polar structure in the future. B: DFT modeling of thermionic emission

In addition to low-work functions, we are also interested in the emissivity of a surface, which is directly related to its Richardson-Dushman constant. First-principles modeling of electron transport which governs thermionic emission has proven elusive in the past; we present a method for calculating the electron tunneling rates from first principles that can treat structurally complex surfaces. Hence, we can predict thermionic emission from composite or multi-layer electrodes, which can often yield higher current densities than relatively simple elemental surfaces. Our new method does not involve semi-classical approximations or simplification of the electronic structure, and is thus able to predict thermionic current densities purely from first principles even for complex surface structures with adsorbates. The method uses a non-equilibrium Green’s function (NEGF) approach based on DFT calculations where thermodynamic reservoirs are accounted for via self-energies [Datta1995], thus overcoming the limitations of existing approaches in the literature [Modinos1982, Musho2013].

The NEGF approach allows for the calculation of steady currents which are driven by

chemical potential differences between source and drain, or as is studied here, by temperature differences. The current density (obtained from a supercell with surface area A) is obtained within the Landauer-Buettiker formalism [Landauer1957, Buettiker1986]:

𝐽 𝑇 = !!ℏ!

𝑑𝐸  𝑓 𝐸 − 𝜇 𝑇 ,𝑇 𝒯 𝐸 . (2)

𝑓 𝐸 − 𝜇 𝑇 ,𝑇  is the Fermi-Dirac distribution for the metallic lead. 𝒯 𝐸 is the transmission function of the emitting surface, calculated using maximally localized Wannier functions [Marzari1997, Thygesen2005].

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Figure 6: Thermionic emission current densities from W(110) as provided in form of a Richardson-Dushman fit to experimental data from [Nichols1940] and calculated using our NEGF approach.

We present the thermionic emission currents from W(110) as a benchmark system.

The agreement between our ab-initio results and experiments [Nichols1940] is good. We are currently using the approach to find cathode materials with higher emission currents, where we look not only at the work function but also at the tunneling properties of the emitter surface.

C: Emissive coatings consisting of alkaline-earth oxides and scandium

We are currently examining tungsten surfaces coated with alkaline-earth oxides as well as scandium oxides. The alloyed surfaces are set up with Quantum Espresso, a DFT-based simulator [Giannozzi2009]. As many commercial dispenser cathodes operate with an emissive mixture of barium, calcium, and strontium oxides, we are surveying the full range of mixing ratios for their work functions and thermodynamic stability (Fig. 7). By visualizing the optimal regions with both low work function and high stability, we can motivate further experimentation with the coating compositional mixtures located in those regions.

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Figure 7: The work function distribution (left) and relative formation energy (right) of adsorbated Ba/Ca/Sr oxide with scandium on W(100). The blue areas indicate the range of compositions with the lowest work functions (left) and highest thermodynamic stability (right). D: Measuring thermionic emission of electrostatically-doped graphene

On the experimental front, we were able to shift the work function of graphene via electrostatic doping by changing its bias voltage. This technique for adjusting the work function could allow us greater flexibility for more efficient PETEC device design. Electrostatic doping has been achieved through the following steps: 1) fabrication of alumina, an electrically reliable ultrathin gate dielectric material, 2) growth and transfer of high-quality graphene by chemical vapor deposition (CVD), and 3) measuring thermionic emission by X-ray photoemission spectroscopy by our setup (Fig. 8) at the Stanford Synchrotron Radiation Light Source (SSRL). The initial results indicate the change of graphene’s work function to be around 0.8 eV, which almost triple what has been reported previously [Yu2009] on a centimeter-scale device.

Figure 8: (Left) The experimental setup in a mini-vacuum chamber with a glowing suspended tungsten cathode and the graphene/alumina/Si anode below it. (Right) The ultra-high vacuum (UHV) chamber at SSRL. The two bias voltages (one on graphene and one on the Si substrate) are applied through the sample holder and a manual “wobble” stick.

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We have fabricated 15nm-thick alumina as the gate dielectric by atomic layer deposition (ALD) at the Stanford Nanofabrication Facility (SNF). Fig. 9 shows different annealing conditions for post-growth treatment. Rapid thermal annealing at 500 °C for one minute yields a breakdown voltage of 19.4V with less than 3μA leakage current before breakdown, which demonstrates good film quality.

Figure 9: Different rapid thermal annealing I-V curves for 15nm ALD alumina. Higher annealing temperature and longer annealing time degrade the quality of alumina.

We have prepared our graphene sample by CVD, which is a well-developed process to grow thin films with large areas. However, the pin holes in our graphene sample (Fig. 10) indicate that we should further optimize the growth parameters during CVD and transferring in order to minimize thermal and mechanical stresses.

Figure 10: SEM image of the CVD graphene sample (left). Raman spectroscopy of the graphene sample (right).

The x-ray photo-emission experiments have shown that the work function of graphene can be tuned by applying a negative bias through the alumina gate (Fig. 11 left). However, due to the existence of pin holes in the graphene, the bare alumina region has a different electrostatic potential compared to the region covered by graphene, which leads to the “double peak” formation in the emission spectra for graphene/alumina/Si. By comparing with the spectra of the bare alumina sample (Fig. 11 right), we can deduce that the change in graphene’s work function is around 0.8 eV when a -4 V bias is applied.

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Figure 11: Low energy cutoff XPS data. (Left) graphene/alumina/Si sample. (Right) alumina/Si sample. Note: low energy cutoff equals the negative of the sample’s work function.

To provide further evidence of the work function change in our graphene sample, we have measured its thermionic current emission. We can extract the change in work function from the shift of the log-linear region in the I-V plot (Fig. 12), which is around 0.8 eV with only a -3 V bias. The difference between the results from photo-emission and thermionic emission experiments is most likely due to the existence of pin-hole defects in the graphene, since thermionic emission is determined by the average work function of the entire surface.

Figure 12: Thermionic emission current vs. bias voltage through alumina. The shift of the emission current’s log-linear region indicates the change in work function of the emissive material.

We plan to use double-transferred graphene (with two layers of graphene on alumina) to minimize the pin hole density. We have also set up deep-ultraviolet (DUV) optical lines for photo-emission studies instead of X-ray to eliminate the signals from alumina. Moreover, we will activate the graphene samples with cesium and oxygen to find the optimal degree of cesiation, with the goal of reducing the work function to less than 1.0 eV, which is predicted by our simulations on p-doped graphene.

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Progress • Developed a new model that captures and predicts the minimum of a work

function vs. coverage plot for cesiated metals that can be generally applied to systems with similar surface dipole behavior.

• Generated a new DFT-based model that for the first time, calculates the emission current of arbitrary surfaces based on first-principles NEGF.

• Fabricated alumina and graphene experimental samples • Demonstrated electrostatic control of work function in graphene in an upgraded

XPS measurement setup at SSRL. Future plans

We will study the formation energies and work functions for surfaces with promising adsorbates other than scandium. The region of interest includes surfaces with low work functions and high formation energies, which is correlated with stability at the high operating temperatures needed for PETEC. We also plan to explore materials such as intercalated graphite compounds to predict their work functions and stabilities. On the experimental side, we will next perform measurements of cesiated alumina and graphene surfaces. Further out, we will attempt to synthesize and characterize the new compound systems identified by our modeling effort.

Publications and Patents

1. S.H. Chou, J. Voss, I. Bargatin, A. Vojvodic, R.T. Howe, F, Abild-Pedersen, An orbital-overlap model for minimal work functions of cesiated metal surfaces, J. Phys.: Condens. Matter 24, 445007 (2012)

2. (Submitted, in revision) J. Voss, A. Vojvodic, S.H. Chou, R.T. Howe, I. Bargatin, F, Abild-Pedersen, Thermionic Current Densities from First Principles

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