def test_state():
array1 = np.array([1, 2, 3])
array2 = np.array([2, 3, 4])
state1 = State()
state1.a = 1
state1.b = True
state1.c = array1
assert state1.__len__() == 3
assert state1.a == 1
assert state1.b == True
assert all([input == output for input, output in zip(array1, state1.c)])
state2 = State()
state2.b = False
state2.d = array2
state1.update(state2)
assert state1.__len__() == 4
assert state1.a == 1
assert state2.b == False
assert all([input == output for input, output in zip(array1, state1.c)])
assert all([input == output for input, output in zip(array2, state1.d)])
def strain_calculation_parameters(substrate_material,
layer_material,
should_print=False,
SO=False):
"""Will extract materials parameters and perform a bit of conditioning to the values.
Returns a solcore State object with the following keys:
-- ac, the conduction band deformation potential
-- av, the valence band deformation potential
-- b, the valence band splitting deformation potential
-- C11, element of the elastic stiffness tensor
-- C12, element of the elastic stiffness tensor
-- a0, the unstrained substrate lattice constant
-- a, the unstrained layer lattice constant
-- epsilon, in-plain strain
-- epsilon_perp, out-plain strain
-- e_xx, in-plain strain (e_xx = epsilon)
-- e_yy, in-plain strain (e_yy = epsilon)
-- e_zz, out-plain strain (e_zz = epsilon_perp)
-- Tre, element of come matrix (Tre = e_xx + e_yy + e_zz)
-- Pe, parameter use by Chuang
-- Qe, parameter use by Chuang
-- cb_hydrostatic_shift, CB moved by this amount
-- vb_hydrostatic_shift, VB moved by this amount
-- vb_shear_splitting, VB split by this amount (i.e. HH/LH separation)
-- delta_Ec, final conduction band shift
-- delta_Elh, final light hole band shift
-- delta_Ehh, final heavy hole band shift
Care has to be taken when calculating the energy shifts because different
sign conversion are used by different authors. Here we use the approach of
S. L. Chuang, 'Physics of optoelectronic devices'.
Note that this requires that the 'a_v' deformation potential to be
positive, where as Vurgaftman defines this a negative!
"""
sub = substrate_material
mat = layer_material
k = State()
# deformation potentials
k.av = abs(mat.a_v) # make sure that av is positive for this calculation
k.ac = mat.a_c # Vurgaftman uses the convention that this is negative
k.b = mat.b
# Matrix elements from elastic stiffness tensor
k.C11 = mat.c11
k.C12 = mat.c12
if should_print: print(sub, mat)
# Strain fractions
k.a0 = sub.lattice_constant
k.a = mat.lattice_constant
k.epsilon = (k.a0 - k.a) / k.a # in-plain strain
k.epsilon_perp = -2 * k.C12 / k.C11 * k.epsilon # out-plain
k.e_xx = k.epsilon
k.e_yy = k.epsilon
k.e_zz = k.epsilon_perp
k.Tre = (k.e_xx + k.e_yy + k.e_zz)
k.Pe = -k.av * k.Tre
k.Qe = -k.b / 2 * (k.e_xx + k.e_yy - 2 * k.e_zz)
k.cb_hydrostatic_shift = k.ac * k.Tre
k.vb_hydrostatic_shift = k.av * k.Tre
k.vb_shear_splitting = 2 * k.b * (1 + 2 * k.C12 / k.C11) * k.epsilon
# Shifts and splittings
k.delta_Ec = k.ac * k.Tre
if should_print: print(k.ac, k.Tre)
k.delta_Ehh = -k.Pe - k.Qe
k.delta_Elh = -k.Pe + k.Qe
k.delta_Eso = 0.0
if SO:
k.delta = mat.spin_orbit_splitting
shift = k.delta**2 + 2 * k.delta * k.Qe + 9 * k.Qe**2
k.delta_Elh = -k.Pe + 0.5 * (k.Qe - k.delta + np.sqrt(shift))
k.delta_Eso = -k.Pe + 0.5 * (k.Qe - k.delta - np.sqrt(shift))
strain_calculation_asserts(k, should_print=should_print)
if should_print:
print()
print("Lattice:")
print("a0", k.a0)
print("a", k.a)
print()
print("Deformation potentials:")
print("ac = ", solcore.asUnit(k.ac, 'eV'))
print("av = ", solcore.asUnit(k.av, 'eV'))
print("ac - av = ", solcore.asUnit(k.ac - k.av, 'eV'))
print("b = ", solcore.asUnit(k.b, 'eV'))
print()
print("Matrix elements from elastic stiffness tensor:")
print("C_11 = ", solcore.asUnit(k.C11, "GPa"))
print("C_12 = ", solcore.asUnit(k.C12, "GPa"))
print()
print("Strain fractions:")
print("e_xx = e_yy = epsilon = ", k.epsilon)
print("e_zz = epsilon_perp = ", k.epsilon_perp)
print("e_xx + e_yy + e_zz = Tre = ", k.Tre)
print()
print("Shifts and splittings:")
print("Pe = -av * Tre = ", solcore.asUnit(k.Pe, 'eV'))
print("Qe = -b/2*(e_xx + e_yy - 2*e_zz) = ",
solcore.asUnit(k.Qe, 'eV'))
print("dEc = ac * Tre = ", solcore.asUnit(k.delta_Ec, 'eV'))
print("dEhh = av * Tre + b[1 + 2*C_11/C_12]*epsilon = -Pe - Qe = ",
solcore.asUnit(k.delta_Ehh, 'eV'))
print("dElh = av * Tre - b[1 + 2*C_11/C_12]*epsilon = -Pe + Qe = ",
solcore.asUnit(k.delta_Elh, 'eV'))
print()
return k
