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PSim.py
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PSim.py
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# -*- coding: utf-8 -*-
"""
PSim.py - The Python Semiconductor Dynamics Simulator
Created on Mon Mar 09 10:07:36 2015
@author: Matthew Rowley
"""
from __future__ import division
import numpy as np
from multiprocessing import Pool
# Some universal constants
ps = 10.0**-12
ns = 10.0**-9
sqrt_2pi = np.sqrt(2 * np.pi)
def bEqn(g, e, h, Gdecay, G2decay, G3decay, GHdecay, Gescape, G3loss, Gform,
pulse, step, stepsize):
'''
High concentration gem_pair master rate equation
'''
Gchange = (pulse[step]
- g * Gdecay
- g * g * G2decay
- g * g * g * G3decay
- g * h * GHdecay
- g * Gescape
- g * g * g *G3loss
+ e * h * Gform)
return Gchange * stepsize
def hEqn(g, e, h, f, Gescape, Gform, EHdecay, FHloss, stepsize):
"""
Hole master rate equation
"""
hchange = (g * Gescape
- h * e * EHdecay
- h * f * FHloss
- e * h * Gform)
return hchange * stepsize
def eEqn(g, e, h, f, trap, Gescape, Gform, EHdecay, Etrap, stepsize):
"""
Electron master rate equation
"""
echange = (g * Gescape
- h * e * EHdecay
- e * (trap - f) * Etrap
- e * h * Gform)
return echange * stepsize
def fEqn(e, h, f, trap, Etrap, FHloss, stepsize):
"""
Filled trap master rate equation
"""
fchange = (e * (trap - f) * Etrap
- f * h * FHloss)
return fchange * stepsize
def gsignalEqn(g, h, Gdecay, G2decay, G3decay, GHdecay):
signal = (g * Gdecay
+ g * g * G2decay
+ g * g * g * G3decay
+ g * h * GHdecay)
return signal
def ehsignalEqn(e, h, EHdecay):
"""
E-H Recombination Signal
"""
signal = (h * e * EHdecay)
return signal # Note that the scalar is not included here
def glossEqn(g, G3loss):
gloss = g * g * g * G3loss
return gloss
def tlossEqn(f, h, FHloss):
'''
Filled trap loss
'''
tloss = f * h * FHloss
return tloss
def steadyYet(newg, oldg, newe, olde, newh, oldh, newf, oldf, tolerance):
"""
Test if the simulation has reached steady state yet.
"""
steady_yet = True
if oldg == 0 or (abs(newg-oldg)/oldg > tolerance or
abs(newe-olde)/olde > tolerance or
abs(newh-oldh)/oldh > tolerance or
abs(newf-oldf)/oldf > tolerance):
steady_yet = False
return steady_yet
def qOverk(g, e, h, Keq):
q = e*h/g
return q/Keq
def powerRun(power, pulse, steps, trap, tolerance, EHdecay, Etrap, FHloss,
Gdecay, G2decay, G3decay, GHdecay, Gescape, Gform, G3loss, Keq,
trackQ, verbose):
numsteps = len(steps)
signal = np.zeros(numsteps)
gsignal = np.zeros(numsteps)
ehsignal = np.zeros(numsteps)
gloss = np.zeros(numsteps)
tloss = np.zeros(numsteps)
gem_pair = np.zeros(numsteps)
electron = np.zeros(numsteps)
hole = np.zeros(numsteps)
filled = np.zeros(numsteps)
qk = np.zeros(numsteps)
failed = False
new_g, new_e, new_h, new_f = 1, 1, 1, 1
old_g, old_e, old_h, old_f = 1, 1, 1, 1
runs = 0
steady = False
while not steady:
runs = runs + 1
for s, stepsize in enumerate(steps): # s for step
# Calculate the signal for this time step
try:
gsignal[s] = gsignalEqn(new_g, new_h, Gdecay, G2decay,
G3decay, GHdecay)
ehsignal[s] = ehsignalEqn(new_e, new_h, EHdecay)
gloss[s] = glossEqn(new_g, G3loss)
tloss[s] = tlossEqn(new_f, new_h, FHloss)
signal[s] = gsignal[s] + ehsignal[s]
if trackQ:
qk[s] = qOverk(new_g, new_e, new_h, Keq)
# calculate changes in populations for the next time step
hchange = hEqn(new_g, new_e, new_h, new_f, Gescape, Gform,
EHdecay, FHloss, stepsize)
echange = eEqn(new_g, new_e, new_h, new_f, trap, Gescape,
Gform, EHdecay, Etrap, stepsize)
fchange = fEqn(new_e, new_h, new_f, trap, Etrap, FHloss,
stepsize)
gchange = bEqn(new_g, new_e, new_h, Gdecay, G2decay,
G3decay, GHdecay, Gescape, G3loss, Gform,
pulse, s, stepsize)
except Exception as e:
print("Failed by {}".format(e))
failed = True
break
new_f = filled[s] + fchange
new_h = hole[s] + hchange
new_e = electron[s] + echange
new_g = gem_pair[s] + gchange
# Update the values for the next time step
if s + 1 < numsteps:
gem_pair[s+1] = new_g
hole[s+1] = new_h
electron[s+1] = new_e
filled[s+1] = new_f
else: # Set up initial state for next round.
old_g = gem_pair[0]
gem_pair[0] = new_g
old_h = hole[0]
hole[0] = new_h
old_e = electron[0]
electron[0] = new_e
old_f = filled[0]
filled[0] = new_f
steady = steadyYet(new_g, old_g, new_e, old_e, new_h,
old_h, new_f, old_f, tolerance)
if verbose:
print("Runs to steady state: {}".format(runs))
return gem_pair, electron, hole, filled, signal, gsignal, ehsignal, gloss, tloss, qk
class DecaySim():
"""
This class creates a simulation of semiconductor excited state transients.
Solving the master rate equations numerically allows for quickly exploring
the consequences of different decay rates or master rate equations.
"""
def __init__(self, trap=2.5*10**16, Keq=1.0*10**17,
EHdecay=1.0*10**-10, Etrap=2.0*10**-10, FHloss=8.0*10**-12,
G3decay = 0, step=200*ps, pretime=2, reprate=10000000,
verbose=False, trackQ=False, scalar=1, Gdecay=0, GHdecay=0,
tolerance=0.005, G2decay=0. ,Gescape=1., Gform=1., G3loss=0.):
"""
Initialization script sets up the parameters
"""
# Some other variables used
self.tolerance = tolerance
self.scalar = scalar
self.verbose = verbose
self.reprate = reprate
self.duration = 1.00 / reprate
self.step = step
self.steps = int(self.duration / self.step)
self.powers = []
self.pretime = pretime
# Variables which hold state densities
self.exciton = []
self.hole = []
self.electron = []
self.trap = (trap) # Total number of traps
self.filled = [] # Filled traps
self.signal = []
self.xsignal = []
self.ehsignal = []
self.xloss = []
self.tloss = []
self.pulses = []
self.qk = []
self.trackQ = trackQ
# Rate and equilibrium constants, corrected for time step size
self.Keq = Gescape/Gform # Equilibrium constant for X<-->e+h
self.EHdecay = (EHdecay * step) # e+h->ground
self.Etrap = (Etrap * step) # e+trap->filled
self.FHloss = (FHloss * step) # filled+h->ground
self.Gdecay = Gdecay * step
self.G2decay = G2decay * step
self.G3decay = G3decay * step
self.GHdecay = GHdecay * step
self.Gescape = Gescape * step
self.G3loss = G3loss * step
self.Gform = Gform * step
def runSim(self):
"""
Generate the data arrays for all powers
"""
if self.verbose:
print("Running Simulation, This may take a while")
self.makeXData(float(self.pretime))
pool = Pool(processes=len(self.powers))
jobs = []
self.gem_pair = []
self.electron = []
self.hole = []
self.filled = []
self.signal = []
self.gsignal = []
self.ehsignal = []
self.gloss = []
self.tloss = []
self.qk = []
for power, pulse in zip(self.powers, self.pulses):
inputs = [power, pulse, self.steps, self.trap, self.tolerance,
self.EHdecay, self.Etrap, self.FHloss, self.Gdecay,
self.G2decay, self.G3decay, self.GHdecay, self.Gescape,
self.Gform, self.G3loss, self.Keq, self.trackQ,
self.verbose]
jobs.append(pool.apply_async(powerRun, inputs))
for job in jobs:
gem_pair, electron, hole, filled, signal, gsignal, ehsignal, gloss, tloss, qk = job.get()
self.signal.append(signal * self.scalar / self.step)
self.gsignal.append(gsignal * self.scalar / self.step)
self.ehsignal.append(ehsignal * self.scalar / self.step)
self.gloss.append(gloss * self.scalar / self.step)
self.tloss.append(tloss * self.scalar / self.step)
self.gem_pair.append(gem_pair)
self.electron.append(electron)
self.hole.append(hole)
self.filled.append(filled)
self.qk.append(qk)
pool.close()
def makeXData(self, pretime):
"""
Generate the xdata (time) array, which is shared by all powers in
the sim
"""
xdata = []
steps = []
self.pulses = []
time = - pretime * ns # start the time
while time < 2 * ns: # around the pulse, just take minimum size steps
xdata.append(time / ns)
steps.append(1)
time = time + self.step
while time < self.duration - self.pretime * ns:
xdata.append(time / ns)
stepsize = int(np.log(time/self.step)*2)
steps.append(stepsize)
time = time + stepsize*self.step
self.xdata = np.array(xdata)
self.steps = np.array(steps)
for power in self.powers:
this_pulse = np.zeros_like(self.xdata)
for i, time in enumerate(self.xdata):
this_pulse[i] = self.excitationPulse(time, power)
self.pulses.append(this_pulse)
def addPower(self, power):
"""
Add a power to simulate. The value should be the density of carriers
generated by the pulse, in units of N/cm^3
"""
self.powers.append(float(power))
def resetSim(self):
"""
Remove all the added powers by reinitializing the powers list
"""
self.powers = []
def excitationPulse(self, time, power):
"""
A function describing the excitation pulse.
"""
t = time * ns + self.step # Should center at one step before 0
if self.step <= 200 * ps: # resolution warrants modelling the pulse
width = 200.0 * ps # self.step
if t < width * 10: # Only evaulate when the value is significant
amp = power / (width * sqrt_2pi) # normalized amplitude
value = amp * np.exp(-1.0 * (t) * (t) / (2 * width * width))
value = value
else:
value = 0.0
else: # impulsive limit, just dump all the excitons in at t=0
# if time >= 0 - self.step/2 and time < 0 + self.step/2:
if t > -0.5 * self.step and t <= 0.5 * self.step:
value = power / self.step
else:
value = 0.0
return (value*self.step)