Transcript Lecture Notes 4 - Materials Considertations in Photoemissive Detectors

Materials Considerations in
Photoemission Detectors
S W McKnight
C A DiMarzio
Energy Bands in Solids
Energy
Eg2
Forbidden electron
energies (Energy Gap)
Allowed electron energies
(Energy Band)
Eg1
Energy Bands and Gaps
• Metals, insulators, and semiconductors all
have energy bands and gaps
• Difference is due to electron filling of
bands
– Metals: highest band with electrons in it is
part-filled.
– Insulators: highest band with electron in it is
completely filled. (Filled band carries no net
current.)
Electron Fermi Energy
• Pauli Exclusion Principle (“fermions”):
each electron state can be occupied by no
more than one electron per spin state
• Fermi Energy (Ef) separates occupied
states from unoccupied states at T=0K
• Ef is halfway between highest filled state
and lowest empty state
Metal/Insulator Band Structure
Energy
Ef
Ef
Metal
Insulator
Semiconductor Band Structure
Ef
Eg
Ef
Ef
electrons
“holes”
Intrinsic Semiconductor
(Eg ≤ ~100 kT)
Extrinsic
Semiconductor
Extrinsic
Semiconductor
(n-type)
(p-type)
Surface Energies
Vacuum Level (Evac)
Ea
Ec
Vacuum Level (Evac)
Фo
Ef
Фo= work
function
Ea = electron
affinity
= Evac - Ec
= Evac - Ef
Metal
Insulator
Work Function of Elements
Silver (Ag)
4.26 eV
Potassium (K)
2.30
Aluminum (Al)
4.28
Magnesium (Mg)
3.66
Barium (Ba)
2.70
Nickel (Ni)
5.15
Berylium (Be)
4.98
Antimony (Sb)
4.55
Cesium (Cs)
2.14
Silicon (Si)
4.85
Copper (Cu)
4.65
Sodium (Na)
2.75
Iron (Fe)
4.5
Tungsten (W)
4.55
Photomultiplier Tubes
• Vacuum photoemissive device
• Window
– End-on, side-looking
• Photocathode
– Insulator/semiconductor materials (better η than
metals)
– Spectral response from UV to Near IR
– Moderate quantum efficiency (< 0.3)
• Dynode chain
– Gain ~106 through secondary electron emission
PMT Concept
Window Materials
Photocathode
• Quantum efficiency (ηq)
– ηq= (# emitted photoelectrons/# of incident
photons)
• Photon absorbed
• Photoelectron created
• Photoelectron escapes surface
• Wavelength limits
– hν > Eg + Ea
– UV tubes: CsI, CsTe “solar blind” (<300-200
nm)
– IR tubes: multi-alkali materials (Sb-Na-K-Cs)
Photocathode Band Models
Photocathode Quantum Efficiency
η = PA Pν Pt Ps
PA = Probability that photon will be
absorbed by material = (1-R)
Pν = Probability that light absorption will
excite electron above vacuum level
Pt = Probability that electron will reach
surface
PS = Probability that electron reaching
surface will be released into vacuum
Photon Absorption vs. Depth
In = In(0) e-k x
In(x)
k=Absorption coefficient
dx
0
0.5
1
1.5
2
x/ k
2.5
3
3.5

Probability of absorption between x and x+dx =
x  dx
x


0
 kx
In (0)e dx
In (0)e  kx dx
Probablility of Reaching Surface
Probability of Electron Reaching Surface
Pe = C e-x/L
L=Mean Escape Depth
0
0.5
1
1.5
2
x/ L
2.5
3
3.5
Probability of absorption between x and x+dx and
electron escaping to surface = P(x) = k e-kx dx e-x/L
P(x) = k e –(kx + x/L) dx
Total probability of absorption and electron escaping to
surface = P(x1) + P(x2) + P(x3) + …

 e
( x / L  kx )
0
k dx
k
(1/ L  k ) x 

e
(
|
0
 (1 / L  k )
k

( k  1 / L)
Photocathode Quantum Efficiency
k
  (1  R) P
Ps
k 1/ L
Pν = Probability that light absorption will
excite electron above vacuum level
PS = Probability that electron reaching
surface will be released into vacuum
R = Surface reflectivity
k = photon absorption coefficient
L = mean escape length of electrons
Photocathode Materials
•
•
•
•
•
•
Cs-Te: UV “solar blind”
Sb-Cs: UV-Vis
Bialkali (Sb-Rb-Cs, Sb-K-Cs): UV-Vis
Multialkali (Sb-Na-K-Cs): UV-IR
Ag-O-Cs: Vis-IR
GaAs(Cs), InGaAs(Cs): UV-IR
Bialkali
Cs-Te
Sb-Cs
Dynode Chain
• Amplification of photoelectrons by
secondary electron emission
• δ = (# of secondary electrons) / (# of
primary electrons)
• Gain: G~(δ)n (for n-stage dynode chain)
Secondary Electron Emission
E
Primary Electron
Collision Process
x
Secondary Electrons
Ea
Ec
Electron-Hole Pairs
Eg
Valence Band
Surface
Insulator/Semiconductor
Vacuum Level
Secondary Electron Emission
• Primary electron loses energy to electrons in solid
– Metals: electron-electron interactions
– Insulators: electron-hole creation
– Penetration depth proportional to primary electron energy
• Secondary electrons travel to surface
– Electron-electron or electron-phonon collisions reduce
energy and facilitate recombination
– Greater chance of collision if created deeper
– More electron-electron collisions in metals than insulators
• Secondary electrons emitted into vacuum
– Requires kinetic energy > electron affinity (Ea)
– Secondary emission coefficient (σ) = (# of secondaries)/
(number of primaries)
Electron-Electron Scattering
Vacuum Level (Evac)
Vacuum Level (Evac)
Ea
Ec
Фo
Ef
Electrons
Фo= work
function
Holes
Ea = electron
affinity
= Evac - Ec
= Evac - Ef
Metal
Insulator
Many final states available
Few final states available
Secondary Electron Emission Coefficient
Secondary Emission Coefficients
Material δmax
Emax
δmax
Emax
Al
1.0
300 V NaCl
14
1200 V
Be
0.5
200
BeO
3.4
2000
Ni
1.3
550
MgO
20-25
1500
Si
1.1
250
GeCs
7
700
W
1.4
650
Glasses
2-3
300-450
Material
From Handbook of
Physics and Chemistry
Secondary Emission Ratios
Types of Electron Multipliers
Characteristics of Dynode Types
PMT Timing Measurements
Timing Data for PMT Dynode Types
Microchannel-Plate PMT
MCP-PMT Construction
MCP-PMT
•
•
•
•
•
High gain/compact size
2D detection with high spatial resolution
Fast time response
Stable in high magnetic fields
Low power consumption and light weight
MCP-PMT Gain
Photomultiplier Limitations
•
•
•
•
•
Dark current
Drift
Response time
Saturation: space charge limit
Tube damage at high illumination (anode
current limit)
Dark Current vs. Temperature
Anode/Cathode Sensitivity
• Radiant Sensitivity: photocurrent per
incident radiant flux at given wavelength
(A/W)
• Luminous Sensitivity: photocurrent per
incident luminous flux from tungsten lamp
at 2856K (A/lm)
Luminous Sensitivity