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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
Simulated systems
Simulated systems
MD vs
MD vs
Deformation at realistic electric field strength
Deformation at realistic electric field strength
Polycrystalline Cu in high electric fields
Polycrystalline Cu in high electric fields
The influence of surface roughness
The influence of surface roughness
Multiplication of betas
Multiplication of betas
Schottky conjecture – reducing the aspect ratio of emitter
Schottky conjecture – reducing the aspect ratio of emitter
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
Heating and emission currents
Heating and emission currents
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
Influence of temperature – FN plot
Influence of temperature – FN plot
Some conclusions
Some conclusions
Thank you for your attention
Thank you for your attention
High field enhancement due to the surface changes
High field enhancement due to the surface changes

Презентация: «High field enhancement due to the surface changes». Автор: UT user. Файл: «High field enhancement due to the surface changes.pptx». Размер zip-архива: 6347 КБ.

High field enhancement due to the surface changes

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1 High field enhancement due to the surface changes

High field enhancement due to the surface changes

CLIC workshop 2015

V. Zadin, S. Parviainen, K. Kuppart, K. Eimre, S. Vigonski, A. Aabloo, F. Djurabekova

2 Mechanisms behind field emitting tips

Mechanisms behind field emitting tips

Field 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

3 Simulated systems

Simulated systems

Coupled 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

4 MD vs

MD vs

FEM 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

5 Deformation at realistic electric field strength

Deformation at realistic electric field strength

Field 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

6 Polycrystalline Cu in high electric fields

Polycrystalline Cu in high electric fields

Cu 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: Conjugate-Gradient 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

7 The influence of surface roughness

The influence of surface roughness

1. 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 ED-MD (HELMOD) code or Coupling the FEM simulations to LAMMPS Simulations with uniform pressure over surface already demonstrated mass transport starting from surface roughness

8 Multiplication of betas

Multiplication of betas

We 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

9 Schottky conjecture – reducing the aspect ratio of emitter

Schottky conjecture – reducing the aspect ratio of emitter

How 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 ?~3-4

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

10 Rising tip in el

Rising tip in el

field

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

11 Field enhancement by „dynamic tip“

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 2-3 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

18-33

11.5

12 General Thermal Field model

General Thermal Field model

Simulations 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)

13 Heating and emission currents

Heating and emission currents

Local 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 sub-nanometer tip) Knudsen number to characterizes nanoscale size effects Wiedemann-Franz law for thermal conductivity

14 Current density in ED-MD and FEM models

Current density in ED-MD and FEM models

Local 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

15 Emission currents & temperature using FEM and HELMOD

Emission currents & temperature using FEM and HELMOD

Sensitivity 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

16 Influence of temperature – FN plot

Influence of temperature – FN plot

Simulation 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

17 Some conclusions

Some conclusions

Field 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

18 Thank you for your attention

Thank you for your attention

19 High field enhancement due to the surface changes
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