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1 Ab-initio study of work functions of element metal surface MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) MAE 715 final project, May 7 th, 2007 Instructor: Professor Zabaras Xiang Ma Materals Process Design and Control laboratory

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2 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) Outline Definition of Work function Slab model and super cell Computation Methods (Density functional theory) Change of work function due to the orientation of clean surface Change of work function due to absorption of H atom Conclusion

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3 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) From Solid to Surface In this course, most of the problems we deal with are bulk properties. In nature, crystals are not infinite but finite macroscopic three-dimensional objects terminated by surfaces. Many phenomena and processes occur at the interface between a condensed phase and the environment. Modeling surfaces is then of great theoretical and practical interest. A image of surface for fcc(111)

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4 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) From Solid to Surface The key-ingredient to surface science experiments is ultra-high vacuum (UHV). To main a low pressure to assure that a surface stays clean for a time long enough to do some experiments. With the development of density functional theory, we can also explore the surface properties through the ab-initio study. A very good surface science tutorial.surface science tutorial Atomic resolution on Pt(100)

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5 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) From Solid to Surface A lot of phenomenon associated with surface can be studied by first-principal calculation --- surface reconstruction and surface relaxation --- surface energy --- adsorption on surfaces --- interface --- work function With the adsorption of atoms or molecules, the surface electronic structure is modified and the work function can change by several eV. The measurement of the work function changes can give valuable insight in to the condition of a given surface. Nowadays, the work function can be calculated by ab-initio methods in the framework of density functional theory.

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6 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) Work function definition Work function is defined as the minimum energy necessary to extract an electron from the metal at 0K. For a crystal with electrons, if is the initial energy of the metal and that of the metal with one electron removed to a region of electrostatic potential, we define Note: The removed electron is assumed to be at rest, and therefore possesses only potential energy.

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7 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) Work function definition Schematic energy diagram of a metal At 0K, the chemical potential is by definition In the limit of large systems, all polarisation effect can be neglected after removing the electron. Then chemical potential is then shown to coincide with the Fermi energy The work function, finally, is the difference between the Fermi level and the vacuum level.

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8 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) Work function definition The calculation of work function is then divided into two parts. First to perform a self-consistent calculation to find the Fermi energy of the slab. Second, we need to find the electrostatic potential in the vacuum level. Macroscopic average

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9 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) Macroscopic average The electronic density is the basic variable calculated by DFT. Introduce the plane-averaged electronic density: where z axis is perpendicular to the slab surface The macroscopic-average electronic density is then defined from the integration over the interplanar distance d of the slab: The potential is related to the charge density via the Poisson equation. So we can get a similar relation between plane-averaged potential and macroscopic average

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10 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) Macroscopic average By plotting the macroscopic average over the z axis, the vacuum level is found. Because the curve of the average is nearly flat in the vacuum provided the vacuum is large enough. Subtracting this vacuum level from the Fermi level get the work function for the metal surface. Work Function

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11 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) Slab model and supercell approach Slab model is the most popular way to model the surface. The slab model consists of a film formed by a few atomic layers parallel to the crystalline plane of interest. Using plane waves needs to force a 3-D periodicity. The thin slabs needs to repeat in one direction. To perform a supercell calculation, one defines a unit cell oriented with one axis perpendicular to the surface of interest, containing the inequivalent atoms of a crystalline thin film and some vacuum layers. Ideally, the thickness of the vacuum layer and of the slab must be large enough for two successive metal surfaces not to interact significantly. super cell thin slabs vacuum layer

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12 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) Slab model and supercell approach o It is not trivial to construct the slab model at first. You need to visualize them. o A nice web tool Surface Explorer is used for this purpose.Surface Explorer fcc(100) fcc(110) fcc(111)

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13 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) Slab model and supercell approach XCrysDen is an application for visualizing crystalline and molecular structures.XCrysDen All of the slab models studied were viewed using XCrysDen to ensure that their geometries were described correctly. Surface primitive cell is two-dimensional, which is different from conventional bulk primitive cell.

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14 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) DFT calculations 1.As a preliminary step towards the study of surface, we have to find the equilibrium lattice constant; 2.It is well known that the equilibrium atomic positions in a crystal surface are generally different from those in the ideal bulk-terminated surface. We need to perform a relaxation calculation to find the equilibrium geometry of the surface. 3.The relaxed coordinates are put into another input file to perform a self- consistent calculation to find the Fermi energy in the slab 4.Using post-process code to extract the electrostatic potential from the output file. 5.Calculate the macroscopic average potential to determine the vacuum level 6.Put the two values into the definition of the work function to determine the final solution.

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15 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) DFT calculations Basis sets --- plane wave Cut-off energy of 16 Ry for the plane wave expansion ultrasoft pesudopotentials The Fermi level is positioned using the Methfessel-Paxton (MP) scheme, with the smearing parameter set to 0.01 Ry. 8x8x1 special Monkhorst-Pack special k-points slab models A surface unit cell with a slab of 8 atom layers and 8 equivalent vacuum layers was chosen to model the metal surface. H atom coverage is a full monolayer. Exchange-Correlation approximation LDA(Perdew-Zunger form) Software: Quantum Espresso (opEn-Source Package for Research in Electronic Structure, Simulation, and Optimization), version 3.2

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16 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) Summarize of the computation procedure Fit E Vs V curve to find the theoretical lattice constant (pw.x) Set up the appropriate thickness of slabs and vacuums relax the geometry of the slab (pw.x) self-consistent calculation to find the Fermi energy (pw.x) Extract the electrostatic potential form the self-consistent calculation (pp.x) Calculate the macroscopic average (average.x)

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17 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) Numerical examples 1.Change of work function depends on the surface orientation 2.Change of work function due to the H atom adsorption

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18 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) Lattice constant Theoretic: 7.50 bohr Experimental : 7.66 bohr LDA underestimate

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19 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) Al and Al(100) Al fcc structure a = 7.50 a.u Al(100) side viewAl(100) top view 1 st layer3 rd layer unit cell

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20 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) Al(100) Work Function Plane-averaged electronic charge density (dashed line) Macroscopic average (solid line) Plane-averaged electrostatic potential (dashed line) Macroscopic average (solid line)

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21 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) Al(110) Al(110) top viewAl(110) side view 1 st layer unit cell 3 rd layer

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22 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) Al(110) Plane-averaged electronic charge density (dashed line) Macroscopic average (solid line) Plane-averaged electrostatic potential (dashed line) Macroscopic average (solid line) Work function

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23 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) Al(111) Al(111) top view Al(111) side view A unit cell C B

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24 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) Al(111) Plane-averaged electronic charge density (dashed line) Macroscopic average (solid line) Plane-averaged electrostatic potential (dashed line) Macroscopic average (solid line) Work Function

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25 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) Result AlFermi Level (eV) Vacuum (eV)Work Function (eV) Experimental (eV) (100) 2.3646.7824.418 (110) 2.4886.7684.28 (111) 2.6346.8694.235 Calculations of Work function of Al The results are in a good agreement with the experimental values.

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26 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) Result CuFermi Level (eV) Vacuum (eV)Work Function (eV) Experimental (eV) (100) 5.55110.3914.84 (110) 2.3907.1054.715 (111) 5.58110.7805.199 Calculations of Work function of Copper The results shows a little deviation from the experimental values. It may be due to the experiment is performed at room temperature, while the calculation is at 0K. Overall, it shows good accuracy using this method since the error is within the computational range.

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27 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) Anisotropy of the work function From the Cu, we see that it shows the trend (110), (100),(111) of increasing work function. This is best explained by the Smoluchowski [1] smoothing. This smoothing leads to a dipole moment which opposes the dipole created by the spreading of electron and thus reducing the work function Surface orientations of high density experience small smoothing, inducing a small reverse dipole, and thus a high work function. [1] R Smoluchowski, Phy. Rev. 60, 1941

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28 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) Anomaly anisotropy of Al work function However, from the calculation, it is seen that the Al doesn’t obey this increasing ordering. In the paper [1], the author investigated this phenomenon and concluded that the trend of the work function Al can be explained by a charge transfer the atomic- like p orbitals of the surface ions perpendicular to the surface plane to those parallel to the surface, when compared to the bulk charge density. Thus it results from a dominant p-atomic-like character of the density of states near the Fermi energy. Overall, our methods recovered both the normal and abnormal anisotropy of then work function of the fcc metals. [1] C.J.Fall, N.Binggeli and A. Baldereschi, Phy. Rev. B, 58,1998

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29 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) Adsorption of H on the Al(111) surface There are four inequivalent adsorption sites on an fcc (111) surface. We consider a monolayer of H atom adsorpted on one Al (111) surface.

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30 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) H on the Al(111) surface (top view) bridge hcp hollow fcc hollow ontop

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31 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) H on the Al(111) surface (side view) ontopbridge hcp hollow fcc hollow H/Al(111)Fermi Level (eV) Vacuum (eV)Work Function (eV) ontop 1.0506.1065.056 bridge 0.45274.7914.338 fcc hollow 0.59224.8074.215 hcp hollow 0.63914.8034.164 Clean surface: 4.235 eV

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32 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) H on the Al(111) surface H coverageFermi Level (eV) Vacuum (eV)Work Function (eV) 0.25 1.2995.7724.473 0.50 1.1745.8874.713 1.00 1.0506.1065.056 Calculations of Work function of H/Al(111) ontop site

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33 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) H on the Al(111) surface Adsorption at the ontop and bridge site increase the work function while at the hollow sites decrease the work function. This is due to the dipole induced by H-adsorption: when the H atom at the ontop and bridge site, it pulls away the electron from the surface. However, when the induced dipole opposes the spill-out of the electrons, it reduces the work function. The work function increases with the increase of the H coverage. This is because at the low coverage, the dipole-dipole interaction will keep the atoms apart, while at high coverage, the same interaction will cause a depolarization of the dipoles and increase the work function.

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34 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) Conclusion The method can be used to calculate the accurate work function. The change of work function depends on the surface orientation, adsorption sites and the adsorption coverage. work function is the fundamental properties of the electronic structure of the surface. Its measurement can give valuable insight into the condition of a given surface. This method can also be extended to semiconductor.

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35 MAE 715 – Atomistic Modeling of Materials N. Zabaras (5/7/2007) Acknowledgement Prof. Zabaras MPDCC cluster for the computation Software: Quantum Espressor Thank you!

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