1. Simulation of the Time Response of a VPT
INTRODUCTION
SIMULATION
SIGNAL FORMATION
MEASUREMENTS
When a charge “q” moves, it induces a current “i” to flow on an electrode at a distance “d” from the charge. This current can be calculated using the Shockley–Ramo theorem, where it is stated that:
2. Anode
This is a fine Mesh 50% transparent, some electrons pass through and some are collected here.
3. Dynode
Depending on the amount of energy in which the electrons hit the Dynode, some electrons may be released from this electrode. These secondary emissions follow a Poisson distribution with a mean value of 20 for a 1000eV electron.
1. Cathode
Electrons are produced where photons hit this Electrode
VPT
60 ps, 435 nm laser
Vacuum Photo Triodes (VPT) are low gain photo detectors that can operate in strong magnetic fields. These are of particular importance in High Energy Particle detectors such as the CMS Endcap Electromagnetic Calorimeter.
Trigger
Anode
Signal
Where “v” is the instantaneous velocity of the charge “q”; the weighting field E0, is the field that would exist due to “q” at a distance “d” on the x axis (the axis of the electric field).
Pulse Height
3 GHz Digital Oscilloscope
Helmuth Spieler noted that:
“The electric field determines the charge trajectory and velocity”
“The weighting field depends only on geometry and determines how charge motion couples to a specific electrode.”
“Only in 2-electrode configurations are the electric field and the weighting field of the same form.”
Therefore they are both separated and different.
Helmuth Spieler Radiation Detectors and Signal Processing - II. Signal Formation Oct. 8 – Oct. 12, 2001; Univ. Heidelberg
An experimental test has been set up, where a VPT is lit by a delta function light pulse. The resulting signal is compared to the signal generated by the model so as to evaluate at what degree they match.
Analysis of the measurements con throw clues of what type of modifications and parameters should the model consider so as to increase the match between the measured data and the observed signal.
We have created a simulation system that allows us the use of the SIMION software to model the time response of VPT’s from a delta-function light pulse.
The weighting field is obtained by grounding all the electrodes except for the collection electrode which is allocated a unit potential.
4. Dynode
Those released secondary electrons are flown against the Anode
5. Anode
Most of the secondary electrons are drawn and absorbed at this stage.
One of the challenges in simulating realistically current VPT devices is that extremely fine anode meshes (of order 10 µm hole spacing) are used. These are simulated by having an enormous potential array and then scale it down to approximate realistic dimensions.
So finally, knowing v and knowing d the induced current for a moving electrode is
MOTIVATION
Where “qe” is the charge of the electron and is equal to
1) VPT are important photodetectors which should be as fully understood as possible.
2) In CMS we can test, in the UK, their response at 1.8T at any angle to the field, but at 4T we cannot measure their response beyond 15 degrees. However they will be used at angles up to 26 degrees. A reliable simulation would give us confidence that we can predict their behavior at 4T and at any angle.
3) We have no current data or previous simulation on the speed of these potentially very fast devices.
4) A good simulation (i.e. matches real data well) allows for the development of improved configurations of VPT structure (non-planar dynodes for example).
This chart is the signal observed from the scope. Note that this signal is in Volts (current into 50 ohms) and that the total signal duration is 4 ns instead of the simulated 1.4 ns.
And using the principle of superposition, the total current at the electrode “A” is the sum of all the currents due to each electron at the time “t” from
6. Dynode
Some other electrons find their way back to the Dynode, but as they do not have enough energy they do not produce more electrons. However, on some occasions, the Dynode is hit by secondary electrons which do have sufficient energy to produce third generations. And they will be flown.
7. SIMION Output
The output from the Simion simulation is a set of data containing information about each electron. This information includes time of birth, (x,y,z) coordinates, kinetic energy, trajectory elevation, trajectory azimuth, time of flight between others. This data is used for generating secondary emission, as well as calculate the signal contribution for each of the electrons.
8. Signal Contribution
The data obtained is fed into a solution to generate the speed of approach to the anode, and the distance to the anode. This data is then used to calculate the signal contribution at each time step using Shockley–Ramo theorem; As it will be described below.
CONCLUSION
RESULTS
The simulation and measured signal are qualitatively similar, but the overall duration of the measured signal is a factor of 3 longer than the simulation predicts.
Using the model described, the simulation was run, and a signal was generated. This graph shows the induced current by the primary photoelectrons and then clearly a larger signal generated by the greater number of secondary electrons.
This discrepancy might be due to
Signal integration due to impedance and finite bandwidth effects
Some as yet unknown important parameter
BASIC MODEL OF THE VPT
Future work includes:
Simulation of 60 picoseconds pulses (Instead of instantaneous pulses) and generation of high statistics.
Study of inductive and capacitive effects on the signal.
Bandwidth analysis to explain differences in shape between the generated signal (form the simulation) and the observed signal (from the scope).
Simulation of the laser pulse, for timing compensation.
Study of relation between signal amplitude and initial number of photoelectrons.
The Gain of the dynode was set to generate N secondary electrons following a linear proportion to the incident electron’s kinetic energy given by:
Photoelectrons
Secondary Electrons
The effect of the depth at which secondary electrons are generated has not jet been implemented
A 100 lines/mm mesh was implemented so as to reproduced in Simeon the realistic geometric dimensions of the RIE VPT.