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High field enhancement due to the surface changes
High field enhancement due to the surface changes
High field enhancement due to the surface changes
High field enhancement due to the surface changes
High field enhancement due to the surface changes
High field enhancement due to the surface changes
Mechanisms behind field emitting tips
Mechanisms behind field emitting tips
Mechanisms behind field emitting tips
Mechanisms behind field emitting tips
Simulated systems
Simulated systems
MD vs
MD vs
MD vs
MD vs
MD vs
MD vs
Deformation at realistic electric field strength
Deformation at realistic electric field strength
Deformation at realistic electric field strength
Deformation at realistic electric field strength
Polycrystalline Cu in high electric fields
Polycrystalline Cu in high electric fields
Polycrystalline Cu in high electric fields
Polycrystalline Cu in high electric fields
The influence of surface roughness
The influence of surface roughness
The influence of surface roughness
The influence of surface roughness
The influence of surface roughness
The influence of surface roughness
The influence of surface roughness
The influence of surface roughness
Multiplication of betas
Multiplication of betas
Multiplication of betas
Multiplication of betas
Multiplication of betas
Multiplication of betas
Multiplication of betas
Multiplication of betas
Schottky conjecture – reducing the aspect ratio of emitter
Schottky conjecture – reducing the aspect ratio of emitter
Schottky conjecture – reducing the aspect ratio of emitter
Schottky conjecture – reducing the aspect ratio of emitter
Schottky conjecture – reducing the aspect ratio of emitter
Schottky conjecture – reducing the aspect ratio of emitter
Schottky conjecture – reducing the aspect ratio of emitter
Schottky conjecture – reducing the aspect ratio of emitter
Rising tip in el
Rising tip in el
Rising tip in el
Rising tip in el
Rising tip in el
Rising tip in el
Field enhancement by „dynamic tip“
Field enhancement by „dynamic tip“
General Thermal Field model
General Thermal Field model
General Thermal Field model
General Thermal Field model
Heating and emission currents
Heating and emission currents
Heating and emission currents
Heating and emission currents
Heating and emission currents
Heating and emission currents
Current density in ED-MD and FEM models
Current density in ED-MD and FEM models
Current density in ED-MD and FEM models
Current density in ED-MD and FEM models
Emission currents & temperature using FEM and HELMOD
Emission currents & temperature using FEM and HELMOD
Emission currents & temperature using FEM and HELMOD
Emission currents & temperature using FEM and HELMOD
Emission currents & temperature using FEM and HELMOD
Emission currents & temperature using FEM and HELMOD
Influence of temperature – FN plot
Influence of temperature – FN plot
Influence of temperature – FN plot
Influence of temperature – FN plot
Influence of temperature – FN plot
Influence of temperature – FN plot
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High field enhancement due to the surface changes

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1High field enhancement due to the 9geometry. h/r=6. V. Zadin, University of
surface changes. CLIC workshop 2015. V. Tartu.
Zadin, S. Parviainen, K. Kuppart, K. 10Rising tip in el. field. Field
Eimre, S. Vigonski, A. Aabloo, F. emitting tip, rising from the surface is
Djurabekova. assumed Simulation starts, when the
2Mechanisms behind field emitting tips? emitter is ~40o angle Simulation ends when
Field emitters with aspect ratio ~100 fast increase of field enhancement factor
Voids or precipitates as possible starts. Dynamic behavior of field
mechanisms responsible for generating the enhancement factor Elastic deformation up
emitters Multiplication of betas Influence to ~90MV/m Corresponding field enhancement
of surface roughness Emitter on top of factor ~20 Rising tip can cause
emitter …. Dynamic surface changes, significant increase of the field
thermal effects? Can low aspect ratio enhancement. Elastic limit. V. Zadin,
features lead to high field enhancement? University of Tartu.
V. Zadin, University of Tartu. 11Field enhancement by „dynamic tip“.
3Simulated systems. Coupled electric, Comparison of static (reference) and
mechanical, thermal interactions Electric dynamic emitters Static emitter does not
field deforms sample and causes emission change the shape during simulation Dynamic
currents Emission currents lead to current emitter deforms elastoplastically. 100
density distribution in the sample MV/m. ? - slope. 100 MV/m. Beta decreases
Material heating due to the electric 2-3 times during dynamic deformation of
currents Electric and thermal conductivity emitter Instead of growing emitters, we
temperature and size dependent (Deformed) have decreasing emitters? Evaporation of
sample causes local field enhancement. Dc surface protrusions? V. Zadin, University
El. field ramped up to 10 000 MV/m Comsol of Tartu. Direct calculation from
Multiphysics 4.4 (and 5) Nonlinear simulation. From FN plot. Beta from static
Structural Materials Module AC/DC module tip. 18. 22. ln(I/E2). Beta from dynamic
HELMOD (Combined Electrodynamics, tip. 18-33. 11.5.
Molecular dynamics) Simulated materials: 12General Thermal Field model.
Copper. V. Zadin, University of Tartu. Simulations of emission currents over
4MD vs. FEM in nanoscale. MD – large surfaces. Thermionic emission: high
exaggerated el. fields are needed MD temperature, low field Field emission: low
simulations are accurate, but time temperature, high field Combined effects :
consuming FEM is computationally fast, but general thermal field equation: Special
limited at atomistic scale Very similar interest: Intermediate region where
protrusion shape to MD Material thermal contribution is significant. V.
deformation starts in same region Maximum Zadin, University of Tartu. K. L. Jensen,
field enhancement is 2 times. E0~ 2000 J. Appl. Phys. (2007).
MV/m. V. Zadin, University of Tartu. 13Heating and emission currents. Local
5Deformation at realistic electric emission currents – connection to the
field strength. Field enhancement factor experiment. Field emitters as nanowires.
~2.4 Thin material layer over the void F(Kn). V. Zadin, University of Tartu. Heat
acts like a lever, decreasing the pressure equation in steady state Fully coupled
needed for protrusion formation. Void currents and temperature Emission currents
formation starts at fields > 400 MV/m concentrated to the top of the tip Fast,
Material is plastic only in the vicinity exponential temperature rise in the
of the defect Thin slit may be formed by emitter. Size dependence of electric and
combination of voids or by a layer of thermal conductivity Conductivity in
fragile impurities. V. Zadin, University nanoscale emitters is significantly
of Tartu. decreased (more than 10x for sub-nanometer
6Polycrystalline Cu in high electric tip) Knudsen number to characterizes
fields. Cu sample obtained from an nanoscale size effects Wiedemann-Franz law
explosive welding simulation Severe for thermal conductivity.
plastic deformations due to the applied 14Current density in ED-MD and FEM
stress and temperature Similar treatment models. Local current density and el.
and conditions as during breakdown Defect field. Different solutions methods for el.
reduction methods: Conjugate-Gradient field using FEM and HELMOD Discretization
minimization scheme to relax the lattice in HELMOD tied to atomic structure FEM
simulated annealing to grow the grains and geometry represented by perfectly
remove stacking faults Final sample cylindrical and hemispherical structures
contains several defect free grains and a Good comparison between obtained electric
number of surface intersecting grain fields. The current density dependence on
boundaries Opportunities to study grain local electric field for FEM and HELMOD.
boundary effects and influence of surface Apex el. fields are compared FEM and
roughness. V. Zadin, University of Tartu. HELMOD implementations agree, validating
7The influence of surface roughness. 1. the results. V. Zadin, University of
Atomistic surface detection using common Tartu.
neighbor analysis: 2. Surface 15Emission currents & temperature
reconstruction in FEM using splines: 3. using FEM and HELMOD. Sensitivity to
Calculating the surface roughness enhanced numerical effects: Electric field
el. field: V. Zadin, University of Tartu. calculations Emission current integration
Imperfect surface leads to nonuniform algorithms. Difficulties at estimating
stress distribution MD simu. must be material heating Both FEM and HELMOD
coupled to el. field calculations represent surface incorrectly (smooth,
Coordination analysis to find the surface continuous for FEM and discrete for
atoms The surface is imported into COMSOL HELMOD) Significant difference due to
Multiphysics for Finite Element Analysis integration algorithms from fundamentally
the electric field distribution mechanical different surfaces Both approaches capture
stresses in the sample Deformation of the the same general behavior! V. Zadin,
polycrystalline copper under el. field: University of Tartu.
Using already existing ED-MD (HELMOD) code 16Influence of temperature – FN plot.
or Coupling the FEM simulations to LAMMPS Simulation of single emitter Fully coupled
Simulations with uniform pressure over currents, temperature and external field
surface already demonstrated mass Emission current is integrated over whole
transport starting from surface roughness. surface Taller emitters demonstrate
8Multiplication of betas. We can see smaller thermal effects high local E is
different surface modifications leading to reached faster Thermal effects influence
small ? Large ? is needed Multiplication lower applied fields FN equation assumes
of field enhancement factors Can explain static system Thermal effects introduce a
observed high beta values Incorporates dynamic component Problem – effect remains
surface roughness r_1/r_2<0.1 is needed in low current region Possible use –
to observe significant influence. r_1. allows us to estimate the actual size of
r_2. Max. enhancement. Reference sim. V. the emitter? V. Zadin, University of
Zadin, University of Tartu. Tartu.
9Schottky conjecture – reducing the 17Some conclusions. Field enhancement
aspect ratio of emitter. How to identify due to single protrusion is not sufficient
the shape of the surface defect causing Additional mechanisms are needed
field enhancement? FN plot is Multiplication of betas Thermal effects or
characterized by beta and emission surface dynamic surface changes? Emission currents
area. Compared geometries: High aspect are now calculated using general thermal
ratio emitter Low aspect ratio emitter field model Thermal effects can have
standing on top of a protrusion Field significant influence over the field
enhancement of protrusion ?~3-4. h/r=10. enhancement Dynamic surface changes can
h/r= 17 ?~17. Both emitters have similar lead to modification of measured ? V.
height but different „thickness“ Shape of Zadin, University of Tartu.
the top part is the same - equal emission 18Thank you for your attention!
area Beta is fitted by adjusting the 19
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