In [207]:

import math,numpy,pylab; import array
 import math,numpy,pylab; import array%pylab inline

Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].
For more information, type 'help(pylab)'.

Define some parameters:

$m o d u l e t h i c k n e s s = 300 E - 06 m$ $modulethickness=300E{-06}m$
$c h a r g e m o b i l i t y = 310 c m 2 V . s$ $chargemobility=310 \frac{cm^2}{V.s}$
$c h a r g e D i s t r i b u t i o n R M S = 6.5 E - 10$ $chargeDistributionRMS=6.5E{-10}$
$V D e p l = 170 V$ $V_{Depl}=170V$
$V A p p l = 300 V$ $V_{Appl}=300V$
$C b o l t z o v e r E = 1.38 E - 23 / 1.6 E - 19$ $C_boltz_over_E=1.38E-23/1.6E{-19}$
$T e m p e r a t u r e = 273 K$ $Temperature=273K$
$n o D i f f u s i o n = 1.0 E - 03$ $noDiffusion=1.0E{-03}$

In [208]:

modulethickness=300E-6 if toPlots!="modulethickness" else numpy.asarray([300E-6,500E-6]); 
 modulethickness; chargemobility;Vdep;Vappl;Temperature;toPlots="Temperature";toPlot=Temperature;modulethickness=300E-6 if toPlots!="modulethickness" else numpy.asarray([300E-6,500E-6]); chargemobility=310    if toPlots!="chargemobility" else  numpy.asarray([310,350]);Vdep=170              if toPlots!="Vdep" else numpy.asarray(numpy.arange(120,250,10));Vappl=300             if toPlots!="Vappl" else numpy.asarray(numpy.arange(250,350,10));Temperature= 273.0   if toPlots!="Temperature" else numpy.asarray([200,273,293]);chargeDistributionRMS=6.5e-10;C_boltz_over_E=1.38E-23/1.6E-19; noDiffusion=1.0e-03;

energyDeposit_z is z position of hit, depend on the hit, typical value ~

In [209]:

energyDeposit_z=30E-6;
 energyDeposit_z=30E-6;

compute normalization time

t N o r m = m o d u l e t h i c k n e s s 2 ( 2 * V D e p l * c h a r g e m o b i l i t y )

$t_{Norm}=\frac{modulethickness^2}{(2*V_{Depl}*chargemobility)}$

In [210]:

tnorm=modulethickness**2/(2*Vdep*chargemobility)
 tnorm=modulethickness**2/(2*Vdep*chargemobility)print tnorm;

8.53889943074e-13

compute drift time and spread

d e p t h = m o d u l e t h i c k n e s s 2 - e n e r g y D e p o s i t z

$depth=\frac{modulethickness}{2}-energyDeposit_z$

t h i c k n e s s F r a c t i o n = d e p t h m o d u l e T h i c k n e s s

$thicknessFraction=\frac{depth}{moduleThickness}$

In [211]:

print "thicknessFraction=",thicknessFraction
 depth=modulethickness/2-energyDeposit_z;thicknessFraction=depth/modulethickness;print "depth=",depthprint "thicknessFraction=",thicknessFraction

depth= 0.00012
thicknessFraction= 0.4

compute drift Time
$d r i f t T i m e = - t N o r m * log (1 - 2 V D e p l V D e p l + V A p p l t h i c k n e s s F r a c t i o n) + c h a r g e D i s t r i b u t i o n R M S$ $driftTime= -t_{Norm}*\log\left({1-\frac{2V_{Depl}}{V_{Depl}+V_{Appl}}thicknessFraction}\right)+chargeDistributionRMS$

In [212]:

driftTime= -tnorm*math.log(1-(2.0*Vdep)/(Vdep+Vappl)*thicknessFraction)+chargeDistributionRMS
 print "log input value=",(1-(2.0*Vdep)/(Vdep+Vappl)*thicknessFraction)driftTime= -tnorm*math.log(1-(2.0*Vdep)/(Vdep+Vappl)*thicknessFraction)+chargeDistributionRMSprint "drift Time=",driftTime

log input value= 0.710638297872
drift Time= 6.50291681719e-10

In [213]:

diffusionConstant=C_boltz_over_E*chargemobility*Temperature*noDiffusion
 diffusionConstant=C_boltz_over_E*chargemobility*Temperature*noDiffusionprint "diffusionConstant=", diffusionConstant

diffusionConstant= [ 0.0053475   0.00729934  0.00783409]

In [214]:

spread=[math.sqrt(2.0*diffusionConstant[i]*driftTime) for i in range(len(diffusionConstant))]
 spread=[math.sqrt(2.0*diffusionConstant[i]*driftTime) for i in range(len(diffusionConstant))]print "spread=", spread

spread= [2.637208663716611e-06, 3.081135653718506e-06, 3.192003112500607e-06]

In [215]:

plt.xlabel(toPlots);plt.ylabel('charge spread')
 #pylab.axis([300,380,3.05e-06,3.30e-06]);plt.xlabel(toPlots);plt.ylabel('charge spread')pylab.plot(toPlot,spread,"ro")

Out[215]:

[<matplotlib.lines.Line2D at 0x6390750>]