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Mr. Ignacio Yaselli ( [email protected] ) Prof. Peter Hobson
School of Engineering and Design
Simulation of the Time Response of a VPT
INTRODUCTION
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.
SIMULATION
1. Cathode
Electrons are produced where photons hit this Electrode
2. Anode
This is a fine Mesh 50% transparent, some
electrons pass through and some are
collected here.
SIGNAL FORMATION
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:
i  q  v  Eo (x)
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).
MEASUREMENTS
VPT
60 ps, 435 nm laser
Trigger
Anode
Signal
Pulse Height
3 GHz Digital Oscilloscope
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.
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.
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.
4) A good simulation (i.e. matches real data well) allows for the
development of improved configurations of VPT structure (nonplanar dynodes for example).
Therefore they are both separated and different.
Helmuth Spieler Radiation Detectors and Signal Processing - II. Signal Formation Oct. 8 – Oct. 12, 2001; Univ.
Heidelberg
4. Dynode
Those released secondary electrons
are flown against the Anode
 E0 
N SECONDARY 
EPRIMARY
40
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.
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.
1
d
qe  v
i
d
5. Anode
Most of the secondary electrons are
drawn and absorbed at this stage.
Where “qe” is the charge of the electron and is equal to
1.602 176 53  10-19 Coulombs
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.
iA (t )  n in (t )
RESULTS
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.
BASIC MODEL OF THE VPT
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:
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.
So finally, knowing v and knowing d the induced current for a
moving electrode is
1) VPT are important photodetectors which should be as fully
understood as possible.
3) We have no current data or previous simulation on the speed of
these potentially very fast devices.
•“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.”
The weighting field is obtained by grounding all the electrodes
except for the collection electrode which is allocated a unit potential.
MOTIVATION
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.
Helmuth Spieler noted that:
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.
Photoelectrons
Secondary Electrons
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.
CONCLUSION
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.
This discrepancy might be due to
•
Signal integration due to impedance and finite bandwidth
effects
•
Some as yet unknown important parameter
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.
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.
Acknowledgements: PPARC, CMS colleagues in particular the PPD Group at RAL UK and RIE, St Petersburg, Russia who supply the VPT.
www.brunel.ac.uk