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) E g1 E g2

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 (E f ) separates occupied states from unoccupied states at T=0K E f is halfway between highest filled state and lowest empty state

Metal/Insulator Band Structure Energy Metal Insulator EfEf EfEf

Semiconductor Band Structure Intrinsic Semiconductor (E g ≤ ~100 kT) Extrinsic Semiconductor (p-type) Extrinsic Semiconductor (n-type) EfEf EgEg EfEf EfEf electrons “holes”

Surface Energies Metal EfEf Insulator E a = electron affinity = E vac - E c Vacuum Level (E vac ) ФoФo Ф o = work function = E vac - E f EcEc EaEa

Work Function of Elements Silver (Ag)4.26 eVPotassium (K)2.30 Aluminum (Al)4.28Magnesium (Mg)3.66 Barium (Ba)2.70Nickel (Ni)5.15 Berylium (Be)4.98Antimony (Sb)4.55 Cesium (Cs)2.14Silicon (Si)4.85 Copper (Cu)4.65Sodium (Na)2.75 Iron (Fe)4.5Tungsten (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 ~10 6 through secondary electron emission

PMT Concept

Window Materials

Photocathode Quantum efficiency (η q ) – η q = (# emitted photoelectrons/# of incident photons) Photon absorbed Photoelectron created Photoelectron escapes surface Wavelength limits – hν > E g + E a –UV tubes: CsI, CsTe “solar blind” ( < nm) –IR tubes: multi-alkali materials (Sb-Na-K-Cs)

Photocathode Band Models

Photocathode Quantum Efficiency η = P A P ν P t P s P A = Probability that photon will be absorbed by material = (1-R) P ν = Probability that light absorption will excite electron above vacuum level P t = Probability that electron will reach surface P S = Probability that electron reaching surface will be released into vacuum

dx

Probability of absorption between x and x+dx =

Probability of Electron Reaching Surface

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(x 1 ) + P(x 2 ) + P(x 3 ) + …

Photocathode Quantum Efficiency P ν = Probability that light absorption will excite electron above vacuum level P S = 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 EcEc EaEa Primary Electron x E Surface Electron-Hole Pairs Secondary Electrons EgEg 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 (E a ) –Secondary emission coefficient (σ) = (# of secondaries)/ (number of primaries)

Electron-Electron Scattering Metal EfEf Insulator E a = electron affinity = E vac - E c Vacuum Level (E vac ) ФoФo Ф o = work function = E vac - E f EcEc EaEa Electrons Holes Many final states availableFew final states available

Secondary Electron Emission Coefficient

Secondary Emission Coefficients Materialδ max E max Materialδ max E max Al VNaCl V Be0.5200BeO Ni1.3550MgO Si1.1250GeCs7700 W1.4650Glasses 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