def solve(self, E, solution_start):
self._reset_to_default_units()
E.convert_to(E.units_default)
lattice_potential = spsc_data.Potential(
self.potential[:self.well_start], self.potential.units)
flat_lattice_potential = self._flatten_potential(lattice_potential)
lattice_length = spsc_data.LengthValue(
self.length.value * (len(flat_lattice_potential) - 1) /
(len(self.potential) - 1), self.length.units)
iteration = SolutionIterationFlatPotential(flat_lattice_potential,
self.mass, lattice_length)
lattice_solution = iteration.solve(E, solution_start)
well_solution_start = (lattice_solution[0][-1],
lattice_solution[1][-1])
well_potential = spsc_data.Potential(
self.potential[self.well_start:self.well_end],
self.potential.units)
well_length = spsc_data.LengthValue(
self.length.value * len(well_potential) /
(len(self.potential) - 1), self.length.units)
iteration = SolutionIterationRungeKutt(well_potential, self.mass,
well_length)
well_solution = iteration.solve(E, well_solution_start)
N = len(self.potential)
solution = (spsc_data.WaveFunction(np.zeros(
(N, ))), spsc_data.WaveFunction(np.zeros((N, ))))
solution[0][:len(lattice_solution[0])] = lattice_solution[0]
solution[0][len(lattice_solution[0]) - 1:len(lattice_solution[0]) +
len(well_solution[0]) - 1] = well_solution[0]
solution[1][:len(lattice_solution[1])] = lattice_solution[1]
solution[1][len(lattice_solution[1]) - 1:len(lattice_solution[1]) +
len(well_solution[1]) - 1] = well_solution[1]
return solution
def solve(self):
symmetry_solver = LatticeSymmetrySolver(self.state)
symmetry_solver.solve()
# for j in xrange(5):
# self.__gamma_shrod()
# self.__x_shrod()
# self.state.density_potential = self.__solve_puass()
E_start = spsc_data.EnergyValue(0.001, "eV")
E_end = spsc_data.EnergyValue(0.3, "eV")
dE = spsc_data.EnergyValue(0.0001, "eV")
meta_info = self.state.electron_states[1].static_potential.meta_info
self.state.electron_states[1].static_potential.convert_to('eV')
self.state.density_potential.convert_to('eV')
static_potential_arr = self.state.electron_states[
1].static_potential.value[
meta_info['x_solution_start']:meta_info['x_solution_end']]
density_potential_arr = self.state.density_potential.value[
meta_info['x_solution_start']:meta_info['x_solution_end']]
potential_arr = static_potential_arr + density_potential_arr
potential = spsc_data.Potential(potential_arr, "eV")
potential_offset = spsc_data.EnergyValue(np.amin(potential_arr), 'eV')
potential = potential - spsc_data.Potential(
potential_offset.value * np.ones(
(len(potential), ), "float64"), potential_offset.units)
potential.meta_info = meta_info
mass = self.state.electron_states[1].mass
length = self.state.length
iteration_factory = spsc_shrod.SolutionIterationRungeKuttFactory()
solution_strategy = spsc_shrod.IterableSolutionStrategyNonSymmetricWell(
E_start, E_end, dE, 1, iteration_factory)
solutions = solution_strategy.solve(potential, mass, length,
(10.0**-20, 0, 10.0**-25, 0))
wave_function = solutions[0][1]
zeros = np.zeros((len(self.state.density_potential), ))
wave_function_full_arr = np.concatenate(
(zeros[:meta_info['x_solution_start']], wave_function.value,
zeros[meta_info['x_solution_end']:]))
wave_function = spsc_data.WaveFunction(wave_function_full_arr)
wave_function.mirror()
wave_function.normalize()
self.state.electron_states[1].wave_functions.append(wave_function)
energy_level = solutions[0][0]
energy_level = energy_level + potential_offset
self.state.electron_states[1].energy_levels.append(energy_level)
def superlattice_well_sloped(periods_num, well_length, lattice_well_length,
lattice_barrier_length, slope):
state = superlattice_well(periods_num, well_length, lattice_well_length,
lattice_barrier_length)
slope.convert_to(slope.units_default)
state.length.convert_to(state.length.units_default)
energy_diff = slope.value * state.length.value * constants.e
energy_diff = spsc_data.EnergyValue(energy_diff)
energy_diff.convert_to("eV")
state.electron_states[0].static_potential.convert_to("eV")
potential_arr = state.electron_states[0].static_potential.value
slope_arr = np.zeros((len(potential_arr), ))
dE = energy_diff.value / (len(slope_arr) - 1)
for i in range(len(slope_arr)):
slope_arr[i] = dE * i
potential_arr = potential_arr + slope_arr
well_min_index = potential_arr.argmin()
well_min_value = potential_arr[well_min_index]
potential_arr = potential_arr - np.full(
(len(potential_arr), ), well_min_value)
meta_info = state.electron_states[0].static_potential.meta_info
state.electron_states[0].static_potential = spsc_data.Potential(
potential_arr, "eV")
state.electron_states[0].static_potential.meta_info = meta_info
return state
def single_well(well_length):
state = spsc_core.StateSimple()
granularity = well_length.value * 10
length = well_length * 3
length.convert_to("nm")
potential = spsc_data.Potential(np.ones((granularity, ), "float64"), "eV")
potential.append(
spsc_data.Potential(np.zeros((granularity, ), "float64"), "eV"))
potential.append(
spsc_data.Potential(np.ones((granularity + 1, ), "float64"), "eV"))
electron_state = spsc_core.ElectronStateSimple()
electron_state.static_potential = potential
electron_state.mass = spsc_data.MassValue(0.068 * constants.m_e)
state.electron_states = [electron_state]
state.length = length
return state
def solve(self, E, solution_start):
iteration_factory = SolutionIterationSymmetryLatticeFactory()
iteration = iteration_factory.get_iteration(self.potential, self.mass,
self.length)
left_solution = iteration.solve(E,
(solution_start[0], solution_start[1]))
potential_turned = spsc_data.Potential(self.potential.value[::-1],
self.potential.units)
potential_turned.meta_info = {
"well_start":
len(potential_turned) - self.potential.meta_info["well_end"] - 1,
"well_end":
len(potential_turned) - self.potential.meta_info["well_start"] - 1,
"lattice_bar_width":
self.potential.meta_info["lattice_bar_width"],
"lattice_well_width":
self.potential.meta_info["lattice_well_width"]
}
iteration = iteration_factory.get_iteration(potential_turned,
self.mass, self.length)
right_solution = iteration.solve(
E, (solution_start[2], solution_start[3]))
right_solution[0].value = right_solution[0].value[::-1]
right_solution[1].value = right_solution[1].value[::-1] * -1
return left_solution[0], left_solution[1], right_solution[
0], right_solution[1]
def solve(self, E, solution_start):
self._reset_to_default_units()
E.convert_to(E.units_default)
N = len(self.potential)
solution = (spsc_data.WaveFunction(np.zeros(
(N, ))), spsc_data.WaveFunction(np.zeros((N, ))))
solution[0][0] = solution_start[0]
solution[1][0] = solution_start[1]
h = 1.0 / (N - 1)
h1 = h / 6
for i in xrange(1, N):
(k, q) = self._k_q(i, solution[0][i - 1], solution[1][i - 1], E)
solution[0][i] = solution[0][i - 1] + h1 * (k[0] + 2 * k[1] +
2 * k[2] + k[3])
solution[1][i] = solution[1][i - 1] + h1 * (q[0] + 2 * q[1] +
2 * q[2] + q[3])
if len(solution_start) == 4:
potential_turned = spsc_data.Potential(self.potential.value[::-1],
self.potential.units)
iteration_turned = self.__class__(potential_turned, self.mass,
self.length)
solution_turned = iteration_turned.solve(
E, (solution_start[2], solution_start[3]))
reverse_solution = (spsc_data.WaveFunction(
solution_turned[0].value[::-1]),
spsc_data.WaveFunction(
solution_turned[1].value[::-1]))
solution = (solution[0], solution[1], reverse_solution[0],
reverse_solution[1])
return solution
def __init__(self, potential, mass, length):
super(SolutionIterationRungeKutt,
self).__init__(potential, mass, length)
self.expanded_potential = spsc_data.Potential(
np.zeros((2 * len(self.potential) - 1, ), "float64"),
self.potential.units)
self.expanded_potential.value[0::2] = self.potential.value
self.expanded_potential.value[1::2] = (self.potential.value[0:-1:] +
self.potential.value[1::]) / 2
def solve(self, E, solution_start):
self._reset_to_default_units()
E.convert_to(E.units_default)
lattice_potential = spsc_data.Potential(
self.potential[:self.well_start], self.potential.units)
flat_lattice_potential = self._flatten_potential(lattice_potential)
lattice_length = spsc_data.LengthValue(
self.length.value * (len(flat_lattice_potential) - 1) /
(len(self.potential) - 1), self.length.units)
lattice_mass = spsc_data.MassArray(
self.mass[:len(flat_lattice_potential)])
# Need this because the last point in the lattice potential is artificial,
# and we need to keep the same mass as it was in the last point.
lattice_mass.value[-1] = lattice_mass.value[-2]
iteration = SolutionIterationFlatPotentialDiffMass(
flat_lattice_potential, lattice_mass, lattice_length)
lattice_solution = iteration.solve(E, solution_start)
well_solution_start = (lattice_solution[0][-1],
lattice_solution[1][-1])
well_potential = spsc_data.Potential(
self.potential[self.well_start:self.well_end],
self.potential.units)
well_length = spsc_data.LengthValue(
self.length.value * len(well_potential) /
(len(self.potential) - 1), self.length.units)
well_mass = spsc_data.MassValue(self.mass.value[self.well_start])
iteration = SolutionIterationRungeKutt(well_potential, well_mass,
well_length)
well_solution = iteration.solve(E, well_solution_start)
N = len(self.potential)
solution = (spsc_data.WaveFunction(np.zeros(
(N, ))), spsc_data.WaveFunction(np.zeros((N, ))))
solution[0][:len(lattice_solution[0])] = lattice_solution[0]
solution[0][len(lattice_solution[0]) - 1:len(lattice_solution[0]) +
len(well_solution[0]) - 1] = well_solution[0]
solution[1][:len(lattice_solution[1])] = lattice_solution[1]
solution[1][len(lattice_solution[1]) - 1:len(lattice_solution[1]) +
len(well_solution[1]) - 1] = well_solution[1]
return solution
def solve(self):
E_start = spsc_data.EnergyValue(0.0001, "eV")
E_end = spsc_data.EnergyValue(0.2, "eV")
dE = spsc_data.EnergyValue(0.0001, "eV")
static_potential = self.state.electron_states[0].static_potential
meta_info = static_potential.meta_info
iteration_factory = spsc_shrod.SolutionIterationSlopedLatticeFactory()
solution_strategy = spsc_shrod.IterableSolutionStrategyNonSymmetricWell(
E_start, E_end, dE, 1, iteration_factory)
density_potential = self.state.density_potential
mass = self.state.electron_states[0].mass
length = self.state.length
electron_state = self.state.electron_states[0]
for j in xrange(10):
potential = static_potential + density_potential
potential_offset = spsc_data.EnergyValue(
potential[meta_info["well_start"]], potential.units)
potential = potential - spsc_data.Potential(
potential_offset.value * np.ones(
(len(potential), ), "float64"), potential_offset.units)
potential.meta_info = meta_info
solutions = solution_strategy.solve(potential, mass, length,
(10.0**-20, 0, 10.0**-25, 0))
for i in xrange(len(solutions)):
solution = solutions[i]
if len(electron_state.wave_functions) > i:
electron_state.wave_functions[i] = solution[1]
else:
electron_state.wave_functions.append(solution[1])
energy_level = solution[0] + potential_offset
if len(electron_state.energy_levels) > i:
electron_state.energy_levels[i] = energy_level
else:
electron_state.energy_levels.append(energy_level)
h = 1.0 / (len(self.state.electron_states[0].wave_functions[0]) -
1)
electron_density = spsc_data.Density(
electron_state.sum_density.value * h *
(electron_state.wave_functions[0].value**2),
electron_state.sum_density.units)
self.state.static_density.convert_to("m^-2")
density = self.state.static_density - electron_density
puass_solution_strategy = spsc_puass.GaussSolutionStrategy()
prev_density_potential = density_potential
density_potential = puass_solution_strategy.solve(
density, 12, self.state.length)
density_potential.convert_to(prev_density_potential.units)
density_potential.value = (density_potential.value +
prev_density_potential.value) / 2
self.state.density_potential = density_potential
def solve(self, density, eps, length):
N = len(density)
h = 1.0 / (N - 1)
length.convert_to(length.units_default)
density.convert_to(density.units_default)
potential = spsc_data.Potential(np.zeros((N, ), "float64"))
k = 2.0 * np.pi * (constants.e**2) * length.value * h / eps
for i in xrange(N):
for j in xrange(N):
if i > j:
potential[i] += k * density[j] * (i - 2 * j)
else:
potential[i] += -k * density[j] * i
return potential
def _flatten_potential(self, potential):
current_index = 0
flat_potential = spsc_data.Potential([], potential.units)
# Start from bar.
is_bar = True
mean_value = 0
while current_index < len(potential):
if is_bar:
potential_piece = potential[current_index:current_index +
self.lattice_bar_width]
current_index += self.lattice_bar_width
else:
potential_piece = potential[current_index:current_index +
self.lattice_well_width]
current_index += self.lattice_well_width
mean_value = np.mean(potential_piece)
flat_potential.append(
spsc_data.Potential(mean_value *
np.ones(len(potential_piece))))
is_bar = not is_bar
# This last point is needed for clue potential and solutions and keeping length consistent.
flat_potential.append(spsc_data.Potential(mean_value * np.ones(1)))
return flat_potential
def solve(self):
# 30 nm well
E_start = spsc_data.EnergyValue(0.001, "eV")
E_end = spsc_data.EnergyValue(0.4, "eV")
# 13 nm well
# E_start = spsc_data.EnergyValue(0.01, "eV")
# E_end = spsc_data.EnergyValue(0.08, "eV")
dE = spsc_data.EnergyValue(0.0001, "eV")
static_potential = self.state.electron_states[0].static_potential
meta_info = static_potential.meta_info
mass = self.state.electron_states[0].mass
if isinstance(mass, spsc_data.APhysValueArray):
iteration_factory = spsc_shrod.SolutionIterationSymmetryLatticeDiffMassFactory(
)
else:
iteration_factory = spsc_shrod.SolutionIterationSymmetryLatticeFactory(
)
solution_strategy = spsc_shrod.IterableSolutionStrategySymmetricWell(
E_start, E_end, dE, 1, iteration_factory)
density_potential = self.state.density_potential
length = self.state.length
electron_state = self.state.electron_states[0]
for j in xrange(5):
potential = static_potential + density_potential
potential_offset = spsc_data.EnergyValue(
potential[meta_info["well_start"]], potential.units)
potential = potential - spsc_data.Potential(
potential_offset.value * np.ones(
(len(potential), ), "float64"), potential_offset.units)
potential.meta_info = meta_info
solutions = solution_strategy.solve(potential, mass, length,
(10.0**-20, 0))
for i in xrange(len(solutions)):
solution = solutions[i]
if len(electron_state.wave_functions) > i:
electron_state.wave_functions[i] = solution[1]
else:
electron_state.wave_functions.append(solution[1])
energy_level = solution[0] + potential_offset
if len(electron_state.energy_levels) > i:
electron_state.energy_levels[i] = energy_level
else:
electron_state.energy_levels.append(energy_level)
density_potential = self.__solve_puass()
# density_potential = self.__solve_puass() + density_potential
# density_potential.value = density_potential.value / 2
self.state.density_potential = density_potential
def superlattice_well(periods_num, well_length, lattice_well_length,
lattice_barrier_length):
well_length.convert_to("nm")
lattice_well_length.convert_to("nm")
lattice_barrier_length.convert_to("nm")
state = spsc_core.StateSimple()
electron_state = spsc_core.ElectronStateSimple()
length = spsc_data.LengthValue(0, "nm")
lattice_length = spsc_data.LengthValue(0, "nm")
for i in range(periods_num):
lattice_length += lattice_well_length + lattice_barrier_length
length += lattice_barrier_length * 2 + well_length + lattice_length * 2
potential = spsc_data.Potential(
np.ones((int(lattice_barrier_length.value * DOTS_PER_NM), ),
"float64"), "eV")
next_index = lattice_barrier_length.value * DOTS_PER_NM
for i in range(periods_num):
potential.append(
spsc_data.Potential(
np.zeros((int(lattice_well_length.value * DOTS_PER_NM), ),
"float64"), "eV"))
potential.append(
spsc_data.Potential(
np.ones((int(lattice_barrier_length.value * DOTS_PER_NM), ),
"float64"), "eV"))
next_index += lattice_well_length.value * DOTS_PER_NM + lattice_barrier_length.value * DOTS_PER_NM
meta_info = {
"well_start": int(next_index),
"lattice_bar_width": int(lattice_barrier_length.value * DOTS_PER_NM),
"lattice_well_width": int(lattice_well_length.value * DOTS_PER_NM)
}
potential.append(
spsc_data.Potential(
np.zeros((int(well_length.value * DOTS_PER_NM), ), "float64"),
"eV"))
next_index += well_length.value * DOTS_PER_NM
meta_info["well_end"] = int(next_index)
empty_dots = int(length.value * DOTS_PER_NM) + 1 - len(potential)
potential.append(
spsc_data.Potential(np.zeros((empty_dots, ), "float64"), "eV"))
potential.mirror()
potential.meta_info = meta_info
electron_state.static_potential = potential
electron_state.mass = spsc_data.MassValue(constants.m_e)
electron_state.sum_density = spsc_data.DensityValue(0, "m^-2")
state.electron_states = [electron_state]
state.length = length
state.static_density = spsc_data.Density(
np.zeros((len(potential, )), "float64"), "m^-2")
state.density_potential = spsc_data.Potential(
np.zeros((len(potential, )), "float64"))
return state
def single_well_sloped(well_length, slope):
state = single_well(well_length)
length = well_length * 3
slope.convert_to(slope.units_default)
length.convert_to(length.units_default)
energy_diff = slope.value * length.value * constants.e
energy_diff = spsc_data.EnergyValue(energy_diff)
energy_diff.convert_to("eV")
state.electron_states[0].static_potential.convert_to("eV")
potential_arr = state.electron_states[0].static_potential.value
slope_arr = np.zeros((len(potential_arr), ))
dE = energy_diff.value / (len(slope_arr) - 1)
for i in range(len(slope_arr)):
slope_arr[i] = dE * i
potential_arr = potential_arr + slope_arr
well_min_index = potential_arr.argmin()
well_min_value = potential_arr[well_min_index]
potential_arr = potential_arr - np.full(
(len(potential_arr), ), well_min_value)
state.electron_states[0].static_potential = spsc_data.Potential(
potential_arr, "eV")
return state
def __init__(self):
self.electron_states = []
self.static_density = spsc_data.Density([])
self.density_potential = spsc_data.Potential([])
self.length = spsc_data.LengthValue(0)
def __init__(self):
self.wave_functions = []
self.energy_levels = []
self.static_potential = spsc_data.Potential([])
self.mass = spsc_data.MassValue(0)
self.sum_density = spsc_data.DensityValue(0)