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)