Techniques for Nuclear and Particle Physics Experiments By W.R. Leo Chapter Eight:

1. Photocathode 2. Electron Optical Input System 3. Electron Multiplier 4. Anode

Photocathode converts incident photons to photoelectrons Emitted electron energy given by Einstein’s photoelectric affect: Must reach minimum frequency for equation to be applicable

1. Quantum Efficiency: 2.Radiant Cathode Sensitivity:

Or: For Units in Amperes/Watts Or: Luminous Cathode Sensitivity (Not Recommended)

 Energy Loss given by Escape Depth  Most materials η(λ): 0.1%  Semiconductors η(λ): 10%-30%  Negative Electron Affinity Metals η(λ): ≤80%

 Two electrodes guide electrons to first dynode using an electric field  Focusing electrode on the sides of the PMT  Accelerating electrode by first dynode  Two requirements: 1) As efficient as possible 2) Uniform time from cathode to dynode

 Secondary emission electrodes (dynodes)  Each has secondary emission factor δ  Like photocathode, but with incident electrons and E-field  Dynode material requirements: 1) High δ 2) Stability of emission even with current 3) Low thermionic emission  Use stages with total Gain ≈ 10^7  Use negative electron affinity metals

 Dynode Configurations: a) Venetian Blind b) Box and Grid c) Linear focused d) Side-On Configuration

e) Microchannel Plate

 Fluctuations created by variable nature of secondary emissions, variations in δ, different electron transit times  Plotting many multiplier responses to single electron give total gain fluctuations  Linear focused have lower fluctuations  Venetian blind have higher fluctuations

 Gain of dynode determined by voltage:  Assuming voltage divided equally: Gives Min voltage

 By minimizing the function for minimum V: We find: Although minimum voltage is ideal for minimal noise, this is not typical due to need for a smaller transit time  Gain vs Supply Voltage:

 Series of resistors regulate each voltage  Variable resistors used for fine adjustment  Bleeder current must be much greater than anode current:  Bleeder current maintained 100 times anode current for 1% linearity  In pulse mode, decoupling capacitors or Zener diodes are used

 Dynodes high voltage must be negative relative to photocathode  If positive, photocathode should be grounded, minimizing noise but also complicating anode setup  If negative, anode can be grounded and coupled with other detector electronics, but cathode must then be well insulated

 Current must be transferred entirely from each dynode for proportionality  Total current saturation depends on voltage  Initial formation of space charge at electrodes is swept away at increased voltage  High resistance of photocathode can allow large currents of photoelectrons to change potential; important to use sufficient voltage

 PMT can be considered current generator in parallel with a resistor and capacitor  Assuming input is exponentially decaying light:

 Then gives equation of form:  Which, solved for V(t), gives solution:  For τ<< scintillator decay constant, decay time is accurately produced: Current mode  For τ>>scintillator decay constant, amp and decay time both heightened: Voltage mode

 Two main factors affect time resolution : 1) Fluctuations in electron transit time 2) Fluctuations due to statistical noise  The electron optical input system accelerates central electrons much faster. Cathode or field can be fixed.  Transit time spread: if we have

 Dark current arises from: 1) Thermionic emission 2) Leakage currents 3) Radioactive contamination 4) Ionization phenomena 5) Light Phenomena  Thermionic dark current noise given by: lowering temperature lowers thermal noise

 Leakage currents lowered by a reduced atmosphere  Only small current from radioactive materials  Gas ions can be accelerated toward dynodes, also small amount of current (Afterpulsing)  Dark currents create no more than a few nanoamperes

 Number of photoelectrons and secondary electrons fluctuate with time: shot noise or Schottky Effect  Physical limit of photocathode determines fluctuations in emitted photoelectrons  For PMT under constant illumination, rms deviation emitted photoelectrons given by:  Extent of total deviation best measured by single electron spectrum

 Ambient light, even without high voltage, increases dark current over time  Magnetic fields interfere with Anode current and path of electrons in electron optical input section  Have least influence when oriented parallel to axis of PMT, and PMT is shielded with mu-metal and iron screen

 Small contribution to dark current  Cathode sensitivity: variation of 0.5%/degree between 25 and 50 degrees  Surface materials of dynodes can be affected and can vary gain by a few tenths of a percent per degree Kelvin, although varies between PMTs

 Two types of gain change: 1) Drift- Variation over time under constant illumination level 2) Shift- Sudden current shift drastically changes gain  Several methods of measuring PM output peaks from the same source at different time frequencies can be used to find drift and shift