Electron Emission and Near

Cathode Effects

Lecture 3

J.B. Rosenzweig

UCLA Dept. of Physics and Astronomy

USPAS, 6/28/04

Emission processes

• Thermionic emission

• Field emission

• Photoemission

• Spin polarization

• “Bulk” effects limiting emission

• Look at microscopic mechanisms…

Microscopic models: Metals

• In a metallic crystal latticethe outer electrons, valenceelectrons, orbits overlap andare shared by all the atomsin the solid.

• These electrons are notbound and are free toconduct current, typicallythe free electron density ina metal is 1023 cm-3. Theyform a plasma gas.

Nucleus

Core electrons

ConductionElectrons

DRUDE'S MODEL OF AN ELECTRON "GAS"

Microscopic Models: Semiconductors

• In a semiconductor such asGaAs the valence electronsare bound in covalent bonds.

• At low temperatures theelectrons are all bound but athigher temperatures or withdoping they are liberated tocontribute to currentconduction.

• A semiconductor acts like aninsulator at low temperaturesand a conductor at hightemperatures.

k

E

a a

First Band

Second Band

Forbidden Band

Valence Band

Conduction Band

Energy Gap

Band structure diagrams

• A material’sinternal structuredictates itselectroniccharacteristics

• This is displayedby Brillouindiagrams (U-k)

• Three distinctpossibilities

Metal Because

of electron

Concetration

Metal or semi-metal

because of band

overlap

Insulator for Egap~8eV

Semiconductor for

Egap~1eV

Density of states and Fermi energy

• In solid, one has at low temperature, a “sea” of electrons

forming a sphere in k-space. This surface is at the Fermi

energy,

• Density of states is obtained by differentiating N by E

• In Fermi-Dirac statistics, the energy levels are populated as

• To calculate emission one must sum relevant electrons as

E f =h2

2mk f2

=h2

2m3 2 N

V

2 / 3

D E( )dN

dE=

V

2 2

2m

h2

3 / 2

E =4 (2m)3 / 2

h3E

f (E) =1

e(E Ef ) / KT +1

dN = D(E) f (E)dE

Thermionic emission

• The work function W is defined as the distancefrom the Fermi energy to the potential of themetal m

• To calculate the thermionic current, one mustsum only the electrons going in the rightdirection (x). Flux:

• Integrate to obtain the Richardson-Dushman eqn.

I = A qvxdN =4A q 2m( )

h3

3 / 2

vx EE f +q m

eE E f( ) KT

dE

I AT 2 exp(q m

KT)

Enhanced emission from heating

• At room temperature,there is no thermioniccurrent for metals

• At high temperature(>1000 K) there isnotable current

• Metalloids (LaB6, etc)have much betterperformance

• Applications of strongfields helps!

0 500 1000 1500

4.05839e-06

8.28654e-63

JN

TN

Current Density A/cm^2

Electron Temperature (K)

Thermionic Current Density

Calculation for Cu

The Schottky Effect

• Application of external fields lowers work

function (barrier suppression)

• Schottky enhancement factor

exp(q m

KT) exp(

q m Vexternal[ ]KT

)

IS AT 2 exp(q m Vexternal[ ]

KT)

IS = I0 expqVexternalKT

Field (cold) emission

• The Schottky effect isaccompanied by quantumtunneling, because of the finitewidth of the barrier

• These effects are summarizedin the Fowler-Nordheimrelation (E is the electric field):

• This is a very fast function ofE!

• One also introduces ad hocfield enhancement factor

External Field

W

µ

IF = 6.2 106µ( )

1/ 2

2 + µ( )E 2 exp( 6.8 107 3 / 2

E)

Measurement of

• Fit electron emissioncurrent to electric field(Fowler-Nordheimplot)

• Fit radiation from RFcavities to Fowler-Nordheim

• Enhancement alwaysvery large (>40)

-55.5

-55.0

-54.5

-54.0

-53.5

-750 -700 -650 -600

y = -46.053 + 0.012626x R= 0.99543

- c20 .956 3 / 2/ E

ln(D/E

4)

.

Do

J( Ep )Ep2 Ep

4 exp c23 2 0.956

Ep

1.06c32

2

Data from UCLA RF gun

Photoemission in metals

• Photoemission occurs for metals when the photon energyexcedes the work function

• For very high photon intensity, multiphoton effects mayoccur, emission with

• Field enhancement from Schottky barrier lowering is

• Useful in high field RF photoinjectors!

• Quantum efficiency (QE)

is low (<10-3) because of electron-electron scattering inconduction band

– Electrons lose 1/2 of their energy on average in collision

– Low QE gives risk of laser-surface damage for desired charge.

I = I0 exp( h W( )2) h W( )

2

h >W = 4.5 eV in Cu.

nh >W

= Ne /Nph = Ne h /Ulaser

Photoemission in semiconductors

• Cesiated surfaces good

– Negative electron affinity (NEA)

– CsKSb (high QE at 500 nm illumination!)

– Cs2Te

• Very high QE possible because scattering is

electron-phonon in semiconductor

• High spin polarization from strained lattices

Polarized electron emission from strained

GaAs cathode

>80% polarization obtained; beats NLC requirmentsLow photon energy! (<1.5 eV)

Charge limit observed from

SLAC polarized electron source

Internal space-charge effect

Enhanced doping of GaAs

allows fast recovery from charge limit

DC electron source with Pierce

electrode geometry

DC-field cathodes

• Switching options

– Thermionic heating, gated voltage (klystron)

– Photoemission

• Gated voltage problems

– Laminar flow of current with space-charge

– Child-Langmuir limit on current density

– Capture of beam into RF buckets (emittancegrowth)