Physics-Driven probability distribution function of
energy loss and corresponding pixel TOT counter
Value for high energy particles in thin silicon layers
Mathieu Benoit
Outline
• Dead time in high-rate pixel ASIC
• The VEPIX Framework (RD53) and LHC-Style
ASIC architecture
• Calculation of a PDF for Laudau distributed
energy deposition in System Verilog
Dead time in high-rate pixel ASIC
Pixel that crossed threshold are insensitive to further incoming particles and ToT
Value of the first particle is increased
In HL-LHC, worst case scenario hitrate is 1GHz/cm2 -> 2.5kHz/pixel (50x50um2)
~ 40 us in average between hits, average ToT << 4000 @ 100MHz
To preserve high efficiency O(99.5%) -> permil effect need to be understood
ToT
Threshold
Time
clock
Hit distribution in Vertex layers
Monster events
Low ToT
Delta rays
Large number of
hit per chip
90 deg hits :
MiP
High TOT value
Localized
Shallow hits:
MiP
Low TOT value
Spread hits ->
Buffer occupancy
Loopers :
Intermediate energies
High TOT value
Localized
Pixel energy distribution varies in the vertex layer
• Various absorber thickness
• Various particles,energies
The VEPIX Framework (RD53) and LHCStyle ASIC architecture
Calculation of a PDF for Laudau distributed
energy deposition in System Verilog
• Constraint :
– SystemVerilog only provides a function
to generate bitcode for a given
Probability Distribution Function
– Keep system standalone as much
possible
– Provide Physically sound Counter values
Calculation of a PDF for Laudau distributed
energy deposition in System Verilog
/afs/cern.ch/work/m/mbenoit/public/Landau_Unitless_24bits.txt
Calculation of a PDF for Laudau distributed
energy deposition in System Verilog
B= ((-1 + Power(2.,NbitFinal))*(-0.423 - Threshold + (178.944*(-5. + (505.*bitcode)/(-1 + Power(2,NbitIni)))*Power(Ep,2)*x)/(Power(Ep,2) Power(mass,2)) +
(178.944*Power(Ep,2)*x*((-17860.5*Power(Ep,2)*log*(1 - (Power(Ep,2) - Power(mass,2))/Power(Ep,2)))/(mass*(Power(Ep,2) - Power(mass,2))) +
(178.944*Power(Ep,2)*log*x)/(Power(Ep,2) - Power(mass,2))))/
(Power(Ep,2) - Power(mass,2))))/(Overflow - Threshold)
Calculation of a PDF for Laudau distributed
energy deposition in System Verilog
Calculation of a PDF for Laudau distributed
energy deposition in System Verilog
Conclusion
• A Standalone method to generate counter value
distribution for particle crossing siliconhas been
developed
– Agreement within ~keV of measurements for thin
layers
– Noise and other effects not included
• A first implementation will be made in VEPIX in
order to obtain dead-time distribution for their
current pixel architecture