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Materials Considerations in Photoemission Detectors
S W McKnight
C A DiMarzio
Energy Bands in Solids
Energy
Allowed electron energies (Energy Band)
Forbidden electron energies (Energy Gap)
Eg1
Eg2
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
Metal Insulator
Ef
Ef
Semiconductor Band Structure
Intrinsic Semiconductor
(Eg ≤ ~100 kT)
Extrinsic Semiconductor
(p-type)
Extrinsic Semiconductor
(n-type)
Ef Eg
Ef Ef
electrons“holes”
Surface Energies
Metal
Ef
Insulator
Ea = electron affinity
= Evac - Ec
Vacuum Level (Evac)
Фo
Vacuum Level (Evac)
Фo= work function
= Evac - Ef
Ec
Ea
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
0 0.5 1 1.5 2 2.5 3 3.5
x/ k
In
(x)
k=Absorption coefficient
In = In(0) e-k x
Photon Absorption vs. Depth
dx
0)0(
)0(
dxeIn
dxeIn
kx
dxx
x
kx
Probability of absorption between x and x+dx =
Probability of Electron Reaching Surface
0 0.5 1 1.5 2 2.5 3 3.5
x/ L
Pro
ba
blil
ity o
f R
ea
ch
ing
Su
rfa
ce
L=Mean Escape Depth
Pe = C e-x/L
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) + …
0
)/( dxke kxLx
|(0
)/1(
)/1(
xkLe
kL
k
)/1( Lk
k
Photocathode Quantum Efficiency
sPLk
kPR
/1)1(
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
Cs-Te
Bialkali
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
Insulator/Semiconductor
EcEa
Primary Electron
x
E
Surface
Electron-Hole Pairs
Secondary Electrons
Eg
Valence Band
Vacuum Level
Collision Process
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
Metal
Ef
Insulator
Ea = electron affinity
= Evac - Ec
Vacuum Level (Evac)
Фo
Vacuum Level (Evac)
Фo= work function
= Evac - Ef
Ec
Ea
Electrons
Holes
Many final states available Few final states available
Secondary Electron Emission Coefficient
Secondary Emission Coefficients
Material δmax Emax Material 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
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