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High field enhancement due to the surface changesCLIC workshop 2015 V. Zadin, S. Parviainen, K. Kuppart, K. Eimre, S. Vigonski, A. Aabloo, F. Djurabekova 
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Mechanisms behind field emitting tipsField emitters with aspect ratio ~100 Voids or precipitates as possible mechanisms responsible for generating the emitters Multiplication of betas Influence of surface roughness Emitter on top of emitter …. Dynamic surface changes, thermal effects? Can low aspect ratio features lead to high field enhancement? V. Zadin, University of Tartu 
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Simulated systemsCoupled electric, mechanical, thermal interactions Electric field deforms sample and causes emission currents Emission currents lead to current density distribution in the sample Material heating due to the electric currents Electric and thermal conductivity temperature and size dependent (Deformed) sample causes local field enhancement Dc El. field ramped up to 10 000 MV/m Comsol Multiphysics 4.4 (and 5) Nonlinear Structural Materials Module AC/DC module HELMOD (Combined Electrodynamics, Molecular dynamics) Simulated materials: Copper V. Zadin, University of Tartu 
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MD vsFEM in nanoscale MD – exaggerated el. fields are needed MD simulations are accurate, but time consuming FEM is computationally fast, but limited at atomistic scale Very similar protrusion shape to MD Material deformation starts in same region Maximum field enhancement is 2 times E0~ 2000 MV/m V. Zadin, University of Tartu 
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Deformation at realistic electric field strengthField enhancement factor ~2.4 Thin material layer over the void acts like a lever, decreasing the pressure needed for protrusion formation Void formation starts at fields > 400 MV/m Material is plastic only in the vicinity of the defect Thin slit may be formed by combination of voids or by a layer of fragile impurities V. Zadin, University of Tartu 
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Polycrystalline Cu in high electric fieldsCu sample obtained from an explosive welding simulation Severe plastic deformations due to the applied stress and temperature Similar treatment and conditions as during breakdown Defect reduction methods: ConjugateGradient minimization scheme to relax the lattice simulated annealing to grow the grains and remove stacking faults Final sample contains several defect free grains and a number of surface intersecting grain boundaries Opportunities to study grain boundary effects and influence of surface roughness V. Zadin, University of Tartu 
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The influence of surface roughness1. Atomistic surface detection using common neighbor analysis: 2. Surface reconstruction in FEM using splines: 3. Calculating the surface roughness enhanced el. field: V. Zadin, University of Tartu Imperfect surface leads to nonuniform stress distribution MD simu. must be coupled to el. field calculations Coordination analysis to find the surface atoms The surface is imported into COMSOL Multiphysics for Finite Element Analysis the electric field distribution mechanical stresses in the sample Deformation of the polycrystalline copper under el. field: Using already existing EDMD (HELMOD) code or Coupling the FEM simulations to LAMMPS Simulations with uniform pressure over surface already demonstrated mass transport starting from surface roughness 
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Multiplication of betasWe can see different surface modifications leading to small ? Large ? is needed Multiplication of field enhancement factors Can explain observed high beta values Incorporates surface roughness r_1/r_2<0.1 is needed to observe significant influence r_1 r_2 Max. enhancement Reference sim. V. Zadin, University of Tartu 
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Schottky conjecture – reducing the aspect ratio of emitterHow to identify the shape of the surface defect causing field enhancement? FN plot is characterized by beta and emission surface area Compared geometries: High aspect ratio emitter Low aspect ratio emitter standing on top of a protrusion Field enhancement of protrusion ?~34 h/r=10 h/r= 17 ?~17 Both emitters have similar height but different „thickness“ Shape of the top part is the same  equal emission area Beta is fitted by adjusting the geometry h/r=6 V. Zadin, University of Tartu 
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Rising tip in elfield Field emitting tip, rising from the surface is assumed Simulation starts, when the emitter is ~40o angle Simulation ends when fast increase of field enhancement factor starts Dynamic behavior of field enhancement factor Elastic deformation up to ~90MV/m Corresponding field enhancement factor ~20 Rising tip can cause significant increase of the field enhancement Elastic limit V. Zadin, University of Tartu 
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Field enhancement by „dynamic tip“Comparison of static (reference) and dynamic emitters Static emitter does not change the shape during simulation Dynamic emitter deforms elastoplastically 100 MV/m ?  slope 100 MV/m Beta decreases 23 times during dynamic deformation of emitter Instead of growing emitters, we have decreasing emitters? Evaporation of surface protrusions? V. Zadin, University of Tartu Direct calculation from simulation From FN plot Beta from static tip 18 22 ln(I/E2) Beta from dynamic tip 1833 11.5 
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General Thermal Field modelSimulations of emission currents over large surfaces Thermionic emission: high temperature, low field Field emission: low temperature, high field Combined effects : general thermal field equation: Special interest: Intermediate region where thermal contribution is significant V. Zadin, University of Tartu K. L. Jensen, J. Appl. Phys. (2007) 
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Heating and emission currentsLocal emission currents – connection to the experiment Field emitters as nanowires F(Kn) V. Zadin, University of Tartu Heat equation in steady state Fully coupled currents and temperature Emission currents concentrated to the top of the tip Fast, exponential temperature rise in the emitter Size dependence of electric and thermal conductivity Conductivity in nanoscale emitters is significantly decreased (more than 10x for subnanometer tip) Knudsen number to characterizes nanoscale size effects WiedemannFranz law for thermal conductivity 
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Current density in EDMD and FEM modelsLocal current density and el. field Different solutions methods for el. field using FEM and HELMOD Discretization in HELMOD tied to atomic structure FEM geometry represented by perfectly cylindrical and hemispherical structures Good comparison between obtained electric fields The current density dependence on local electric field for FEM and HELMOD. Apex el. fields are compared FEM and HELMOD implementations agree, validating the results V. Zadin, University of Tartu 
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Emission currents & temperature using FEM and HELMODSensitivity to numerical effects: Electric field calculations Emission current integration algorithms Difficulties at estimating material heating Both FEM and HELMOD represent surface incorrectly (smooth, continuous for FEM and discrete for HELMOD) Significant difference due to integration algorithms from fundamentally different surfaces Both approaches capture the same general behavior! V. Zadin, University of Tartu 
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Influence of temperature – FN plotSimulation of single emitter Fully coupled currents, temperature and external field Emission current is integrated over whole surface Taller emitters demonstrate smaller thermal effects high local E is reached faster Thermal effects influence lower applied fields FN equation assumes static system Thermal effects introduce a dynamic component Problem – effect remains in low current region Possible use – allows us to estimate the actual size of the emitter? V. Zadin, University of Tartu 
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Some conclusionsField enhancement due to single protrusion is not sufficient Additional mechanisms are needed Multiplication of betas Thermal effects or dynamic surface changes? Emission currents are now calculated using general thermal field model Thermal effects can have significant influence over the field enhancement Dynamic surface changes can lead to modification of measured ? V. Zadin, University of Tartu 
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Thank you for your attention 
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«High field enhancement due to the surface changes» 