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