def transient_3D():
n_pixel_x, n_pixel_y = 3, 3
width_x = 250.
width_y = 50.
radius = 6.
nD = 2 # Number of columns per pixel
n_eff = 1e12
T = 300
V_bias = -20.
V_readout = 0.
pot_w_descr, pot_descr, geom_descr = sensor.sensor_3D(n_eff=n_eff,
V_bias=V_bias,
V_readout=V_readout,
temperature=T,
n_pixel_x=n_pixel_x,
n_pixel_y=n_pixel_y,
width_x=width_x,
width_y=width_y,
radius=radius,
nD=nD,
resolution=80,
smoothing=0.1)
# Start parameters of e-h pairs
# 10 pairs per position
xx, yy = np.meshgrid(
np.linspace(-width_x / 2., width_x / 2., 25), # x
np.repeat(np.linspace(-width_y / 2., width_y / 2., 5), 10), # y
sparse=False) # All combinations of x / y
p0 = np.array([xx.ravel(), yy.ravel()])
# Initial charge
q0 = np.ones(p0.shape[1])
# Time steps
dt = 0.001 # [ns]
n_steps = 10000
t = np.arange(n_steps) * dt
dd = solver.DriftDiffusionSolver(pot_descr,
pot_w_descr,
geom_descr=geom_descr,
T=T,
diffusion=True)
traj_e, traj_h, I_ind_e, I_ind_h, T, I_ind_tot, Q_ind_e_tot, Q_ind_h_tot = dd.solve(
p0, q0, dt, n_steps)
I_ind_e[np.isnan(I_ind_e)] = 0.
I_ind_h[np.isnan(I_ind_h)] = 0.
Q_ind_e = integrate.cumtrapz(I_ind_e, T, axis=0, initial=0)
Q_ind_h = integrate.cumtrapz(I_ind_h, T, axis=0, initial=0)
for i in (5, 13):
plt.plot(T[:, i], Q_ind_e[:, i], color='blue', label='Electrons')
plt.plot(T[:, i], Q_ind_h[:, i], color='red', label='Holes')
plt.plot(T[:, i], (Q_ind_e + Q_ind_h)[:, i],
color='magenta',
label='Sum')
plt.plot(plt.xlim(), [(Q_ind_e_tot + Q_ind_h_tot)[i]] * 2,
'-',
color='magenta')
plt.legend(loc=0)
plt.xlabel('Time [ns]')
plt.ylabel('Charge normalized to 1')
plt.grid()
plt.title('Induced charge of drifting e-h pairs, start pos. %d/%d um' %
(p0[0, i], p0[1, i]))
plt.show()
# Plot numerical result in 2D with particle animation
fig = plt.figure()
plot.get_3D_sensor_plot(fig, width_x, width_y,
radius, nD,
n_pixel_x, n_pixel_y,
V_bias=V_bias, V_readout=V_readout,
pot_func=pot_descr.get_potential_smooth,
field_func=pot_descr.get_field,
# Comment in if you want to see the mesh
mesh=None, # potential.mesh,
title='Potential and field of a 3D sensor, '\
'%dx%d pixel matrix, numerical solution' % \
(n_pixel_x, n_pixel_y))
# Create animation
frames = 50
init, animate = plot.animate_drift_diffusion(fig,
T=T,
pe=traj_e,
ph=traj_h,
dt=t.max() / frames,
n_steps=frames)
ani = animation.FuncAnimation(fig=fig,
func=animate,
blit=True,
init_func=init,
frames=frames,
interval=5000 / frames)
# ani.save('Example_3D_drift.gif', dpi=80, writer='imagemagick')
plt.show()
def get_charge_planar(width,
thickness,
pot_descr,
pot_w_descr,
t_e_trapping=0.,
t_h_trapping=0.,
t_e_t1=0.,
t_h_t1=0.,
t_r=0.,
grid_x=5,
grid_y=5,
n_pairs=10,
dt=0.001,
n_steps=25000,
temperature=300,
multicore=True):
''' Calculate the collected charge in one planar pixel
Charge is given as a 2d map depending on the start postitions of the e-h pairs.
Parameters
----------
width: number
Pixel width in um
thickness: number
Pixel thickness in um
pot_descr, pot_w_descr: scarce.fields.Description
Solution for the drift/weightning potential.
grid_x, grid_y: number
Grid spacing in um
n_pairs: number
of pseudo e-h pairs per grid point
dt: float
Time step in simulation in ns. Should be 1 ps to give reasonable diffusion
n_steps: int
Time steps to simulate
'''
# Number of x/y bins
x_bins = int(width / grid_x)
y_bins = int(thickness / grid_y)
# Bin positions
range_x = (-width / 2., width / 2.)
range_y = (0, thickness)
# Create e-h pairs in the pixel, avoid charge carriers on boundaries
# e.g. x = -width / 2 or y = 0
xx, yy = np.meshgrid(
np.linspace(range_x[0] + grid_x / 2., range_x[1] - grid_x / 2.,
x_bins),
np.repeat(
np.linspace(range_y[0] + grid_y / 2., range_y[1] - grid_y / 2.,
y_bins), n_pairs), # 10 e-h per position
sparse=False) # All combinations of x / y
# Start positions
p0 = np.array([xx.ravel(), yy.ravel()]) # Position [um]
# Initial charge set to 1
q_start = 1.
q0 = np.ones(p0.shape[1]) * q_start
# Needed for histograming, numerical accuracy demands > 1
q_max = q_start * 1.05
dd = solver.DriftDiffusionSolver(pot_descr,
pot_w_descr,
T=temperature,
diffusion=True,
t_e_trapping=t_e_trapping,
t_h_trapping=t_h_trapping,
t_e_t1=t_e_t1,
t_h_t1=t_h_t1,
t_r=t_r,
save_frac=50)
traj_e, traj_h, I_ind_e, I_ind_h, T, _, Q_ind_e_tot, Q_ind_h_tot = dd.solve(
p0, q0, dt, n_steps, multicore=multicore)
# Trajectory at t=0 is start position
pos_0 = traj_e[0]
# Interpolate data to fixed time points for easier plotting
# I_ind_e = tools.time_data_interpolate(T, I_ind_e, t, axis=0, fill_value=0.)
# I_ind_h = tools.time_data_interpolate(T, I_ind_h, t, axis=0, fill_value=0.)
# I_ind_e[np.isnan(I_ind_e)] = 0.
# I_ind_h[np.isnan(I_ind_h)] = 0.
# Q_ind_e = integrate.cumtrapz(I_ind_e, T, axis=0, initial=0)
# Q_ind_h = integrate.cumtrapz(I_ind_h, T, axis=0, initial=0)
q_ind = Q_ind_e_tot + Q_ind_h_tot
# Histogram charge per start position
data = np.vstack((pos_0[0], pos_0[1], q_ind)).T
n_bins_c = 200 # Number of charge bins
H, edges = np.histogramdd(sample=data,
bins=(x_bins, y_bins, n_bins_c),
range=((range_x[0], range_x[1]),
(range_y[0], range_y[1]), (0., q_max)))
# Result hist
charge_pos = np.zeros(shape=(x_bins, y_bins))
sel = (np.sum(H, axis=2) != 0)
weights = (edges[2][:-1] + edges[2][1:]) / 2.
charge_pos[sel] = np.average(
H, axis=2, weights=weights)[sel] * weights.sum() / np.sum(H,
axis=2)[sel]
# edges_x = (edges[0][:-1] + edges[0][1:]) / 2.
# edges_y = (edges[1][:-1] + edges[1][1:]) / 2.
# for xi, yi in zip(*np.where(np.logical_and(charge_pos > 0.1,
# charge_pos < 0.9))
# ):
# print edges_x[xi], edges_y[yi], charge_pos[xi, yi]
# plt.clf()
# plt.bar(weights, H[xi, yi], width=np.diff(weights)[0])
# plt.show()
# plt.clf()
# sel = np.logical_and(pos_0[0] == edges_x[xi],
# pos_0[1] == edges_y[yi])
# plt.plot(T[:, sel], Q_ind_e[:, sel] + Q_ind_h[:, sel])
# for c in weights[H[xi, yi].astype(np.bool)]:
# plt.plot(plt.xlim(), [c, c])
# plt.show()
# plt.clf()
# plt.plot(
# T[:, sel], traj_e[:, 0, sel], '-.', linewidth=1, label='e_x')
# plt.plot(
# T[:, sel], traj_e[:, 1, sel], '--', linewidth=1, label='e_y')
# plt.plot(
# T[:, sel], traj_h[:, 0, sel], '-.', linewidth=1, label='h_x')
# plt.plot(
# T[:, sel], traj_h[:, 1, sel], '--', linewidth=1, label='h_y')
# plt.legend(loc=2)
# plt.show()
# break
del dd
return edges[0], edges[1], charge_pos.T
def transient_irrad():
# For CCE important parameters
fluence = 5e15 # Neq/cm2
V_bias = -1000.
n_eff_0 = 1.7e12
# Calculate effective doping concentration after irradiation
n_eff = silicon.get_eff_acceptor_concentration(fluence=fluence,
n_eff_0=n_eff_0,
is_ntype=True,
is_oxygenated=True)
# Planar sensor parameters
width = 50.
thickness = 200.
temperature = 300.
pitch = 45.
n_pixel = 9
V_readout = 0.
resolution = 200
# Create sensor
pot_w_descr, pot_descr = sensor.planar_sensor(
n_eff=n_eff,
V_bias=V_bias,
V_readout=V_readout,
temperature=temperature,
n_pixel=n_pixel,
width=width,
pitch=pitch,
thickness=thickness,
resolution=resolution,
# Might have to be adjusted
# when changing the
# geometry
smoothing=0.01)
# Start parameters of e-h pairs
# Create 10 e-h pairs every 5 um in y
xx, yy = np.meshgrid(
np.linspace(0, width, 1), # x
np.repeat(np.linspace(0., thickness, thickness / 5.), 10),
sparse=False) # All combinations of x / y
p0 = np.array([xx.ravel(), yy.ravel()]) # Position [um]
# Initial charge set to 1
q0 = np.ones(p0.shape[1])
# Time steps
dt = 0.001 # [ns]
n_steps = 3000
t = np.arange(n_steps) * dt
t_e_trapping = silicon.get_trapping(fluence=fluence,
is_electron=True,
paper=1)
t_h_trapping = silicon.get_trapping(fluence=fluence,
is_electron=False,
paper=1)
dd = solver.DriftDiffusionSolver(pot_descr,
pot_w_descr,
T=temperature,
diffusion=True)
dd_irr = solver.DriftDiffusionSolver(pot_descr,
pot_w_descr,
T=temperature,
diffusion=True,
t_e_trapping=t_e_trapping,
t_h_trapping=t_h_trapping)
_, _, I_ind_e, I_ind_h, T, _ = dd.solve(p0, q0, dt, n_steps)
_, _, I_ind_e_irr, I_ind_h_irr, T_irr, _ = dd_irr.solve(
p0, q0, dt, n_steps)
# Interpolate data to fixed time points for easier plotting
I_ind_e = tools.time_data_interpolate(T, I_ind_e, t, axis=0, fill_value=0.)
I_ind_h = tools.time_data_interpolate(T, I_ind_h, t, axis=0, fill_value=0.)
I_ind_e[np.isnan(I_ind_e)] = 0.
I_ind_h[np.isnan(I_ind_h)] = 0.
I_ind_e_irr = tools.time_data_interpolate(T_irr,
I_ind_e_irr,
t,
axis=0,
fill_value=0.)
I_ind_h_irr = tools.time_data_interpolate(T_irr,
I_ind_h_irr,
t,
axis=0,
fill_value=0.)
I_ind_e_irr[np.isnan(I_ind_e_irr)] = 0.
I_ind_h_irr[np.isnan(I_ind_h_irr)] = 0.
Q_ind_e = integrate.cumtrapz(I_ind_e, t, axis=0, initial=0)
Q_ind_h = integrate.cumtrapz(I_ind_h, t, axis=0, initial=0)
Q_ind_e_irr = integrate.cumtrapz(I_ind_e_irr, t, axis=0, initial=0)
Q_ind_h_irr = integrate.cumtrapz(I_ind_h_irr, t, axis=0, initial=0)
plt.plot(t,
Q_ind_e.sum(axis=1) / xx.shape[0],
color='blue',
label='Electrons, depl.')
plt.plot(t,
Q_ind_h.sum(axis=1) / xx.shape[0],
color='red',
label='Holes, depl.')
plt.plot(t, (Q_ind_e.sum(axis=1) + Q_ind_h.sum(axis=1)) / xx.shape[0],
color='magenta',
label='Sum, depl.')
plt.plot(t,
Q_ind_e_irr.sum(axis=1) / xx.shape[0],
'--',
color='blue',
label='Electrons, depl. + trap.')
plt.plot(t,
Q_ind_h_irr.sum(axis=1) / xx.shape[0],
'--',
color='red',
label='Holes, depl. + trap.')
plt.plot(t,
(Q_ind_e_irr.sum(axis=1) + Q_ind_h_irr.sum(axis=1)) / xx.shape[0],
'--',
color='magenta',
label='Sum, depl. + trap.')
plt.legend(loc=0)
plt.xlabel('Time [ns]')
plt.ylabel('Total induced charge [a.u.]')
plt.grid()
plt.title('Induced charge of MIP in planar sensor, readout pixel')
plt.show()
def transient_planar():
# Sensor parameters
n_eff = 1.45e12
n_pixel = 9
width = 50.
pitch = 30.
thickness = 200.
smoothing = 0.05
resolution = 251
temperature = 300.
V_bias = -80.
V_readout = 0.
# Create sensor
pot_w_descr, pot_descr = sensor.planar_sensor(
n_eff=n_eff,
V_bias=V_bias,
V_readout=V_readout,
temperature=temperature,
n_pixel=n_pixel,
width=width,
pitch=pitch,
thickness=thickness,
resolution=resolution,
# Might have to be adjusted
# when changing the geometry
smoothing=smoothing)
# Start parameters of e-h pairs
# Create 10 e-h pairs every 5 um in y
xx, yy = np.meshgrid(
np.linspace(0, width, 1), # x
np.repeat(np.linspace(0., thickness - 10, 10), 1),
sparse=False) # All combinations of x / y
p0 = np.array([xx.ravel(), yy.ravel()]) # Position [um]
# Initial charge set to 1
q0 = np.ones(p0.shape[1])
# Time steps
dt = 0.001 # [ns]
n_steps = 20000
t = np.arange(n_steps) * dt
dd = solver.DriftDiffusionSolver(pot_descr,
pot_w_descr,
T=temperature,
diffusion=True,
t_r=0.,
save_frac=1)
traj_e, traj_h, I_ind_e, I_ind_h, T, I_ind_tot, Q_ind_e_tot, Q_ind_h_tot = dd.solve(
p0, q0, dt, n_steps, multicore=True)
# Interpolate data to fixed time points for easier plotting
# I_ind_e = tools.time_data_interpolate(T, I_ind_e, t, axis=0, fill_value=0.)
# I_ind_h = tools.time_data_interpolate(T, I_ind_h, t, axis=0, fill_value=0.)
I_ind_e[np.isnan(I_ind_e)] = 0.
I_ind_h[np.isnan(I_ind_h)] = 0.
Q_ind_e = integrate.cumtrapz(I_ind_e, T, axis=0, initial=0)
Q_ind_h = integrate.cumtrapz(I_ind_h, T, axis=0, initial=0)
Q_ind_t = integrate.cumtrapz(I_ind_tot, t, axis=0, initial=0)
# Induced current of one e-h pair
# plt.plot(T[:, 0], I_ind_e[:, 0],
# '.-', color='blue', label='e', linewidth=2)
# plt.plot(T[:, 0], I_ind_h[:, 0],
# '.-', color='red', label='h', linewidth=2)
# plt.plot(T[:, 0], I_ind_e[:, 0] + I_ind_h[:, 0], '.-', color='magenta',
# label='e+h', linewidth=2)
# plt.plot(t, I_ind_tot, '.-', color='black',
# label='e+h', linewidth=2)
# plt.ylabel('Induced current [a.u.]')
# plt.grid()
# plt.title('Signal of one drifting e-h pair, readout pixel')
# plt.show()
# plt.plot(t, I_ind_tot,
# color='black', label='Current all charges', linewidth=2)
# plt.plot(t, np.cumsum(I_ind_tot) * dt, '--', linewidth=2,
# color='black', label='all e+h')
# Induced charge of one e-h pair
# plt.plot(T[:, 0], Q_ind_e[:, 0], '.-',
# color='blue', linewidth=2, label='e')
# plt.plot(T[:, 0], Q_ind_h[:, 0], '.-',
# color='red', linewidth=2, label='h')
Q_ind_tot = Q_ind_e_tot + Q_ind_h_tot
for i in range(10):
plt.plot(T[:, i],
Q_ind_e[:, i] + Q_ind_h[:, i],
'-',
linewidth=1,
label='e+h')
plt.plot(plt.xlim(), [Q_ind_tot[i], Q_ind_tot[i]])
print Q_ind_tot[i]
# plt.plot(t, Q_ind_t, '.-', color='black',
# label='e+h', linewidth=1)
plt.legend(loc=0)
plt.title('Induced charge of e-h pair, readout pixel')
plt.xlabel('Time [ns]')
plt.ylabel('Total induced charge [a.u.]')
print Q_ind_e_tot, Q_ind_h_tot
plt.show()
# # Total induced charge of e-h pairs in readout pixel
# plt.plot(t, Q_ind_e[:, ::2].sum(axis=1) / xx.shape[0], color='blue',
# linewidth=2, label='e')
# plt.plot(t, Q_ind_h[:, ::2].sum(axis=1) / xx.shape[0], color='red',
# linewidth=2, label='h')
# plt.plot(t, (Q_ind_e[:, ::2] + Q_ind_h[:, ::2]).sum(axis=1) / xx.shape[0],
# color='magenta', linewidth=2, label='e+h')
# plt.legend(loc=0)
# plt.xlabel('Time [ns]')
# plt.ylabel('Total induced charge [a.u.]')
# plt.grid()
# plt.title('Induced charge of MIP, readout pixel')
# plt.show()
#
# # Mean induced charge of e-h pairs in readout pixel
# plt.plot(t, Q_ind_e[:, 1::2].sum(axis=1) / xx.shape[0], color='blue',
# linewidth=2, label='e')
# plt.plot(t, Q_ind_h[:, 1::2].sum(axis=1) / xx.shape[0], color='red',
# linewidth=2, label='h')
# plt.plot(t, (Q_ind_e[:, 1::2] + Q_ind_h[:, 1::2]).sum(axis=1) / xx.shape[0],
# color='magenta', linewidth=2, label='e+h')
# plt.legend(loc=0)
# plt.xlabel('Time [ns]')
# plt.ylabel('Total induced charge [a.u.]')
# plt.grid()
# plt.title('Induced charge of MIP, neighbouring pixel')
# plt.show()
# Plot numerical result in 2D with particle animation
fig = plt.figure()
plot.get_planar_sensor_plot(fig=fig,
width=width,
pitch=pitch,
thickness=thickness,
n_pixel=n_pixel,
V_backplane=V_bias,
V_readout=V_readout,
pot_func=pot_descr.get_potential,
field_func=pot_descr.get_field,
depl_func=pot_descr.get_depletion,
title='Planar sensor potential')
# Create animation
frames = 50
init, animate = plot.animate_drift_diffusion(fig,
T=T,
pe=traj_e,
ph=traj_h,
dt=t.max() / frames,
n_steps=frames)
ani = animation.FuncAnimation(fig=fig,
func=animate,
blit=True,
init_func=init,
frames=frames,
interval=5000 / frames)
# ani.save('Example_planar_drift.gif', dpi=80, writer='imagemagick')
plt.show()