2.5.11. strain{ }¶
- Calling sequence
strain{ }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: \(\mathrm{maximum\;1}\)
- Functionality
—
Note
In order to calculate the strain, one has to provide a substrate with respect to which the layers are strained. This can be done with the keyword global{ } ==> substrate{…}.
Nested keywords
debuglevel¶
- Calling sequence
strain{ debuglevel }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{integer}\)
values: \(\{-1,0,1,2,\ldots\}\)
unit: \(\mathrm{-}\)
default: \(2\)
- Functionality
The higher this integer number, the more information on the numerical solver is printed to the screen output
no_strain{ }¶
- Calling sequence
strain{ no_strain{ } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: \(\mathrm{maximum\;1}\)
- Functionality
Strain is not taken into account.
pseudomorphic_strain{ }¶
- Calling sequence
strain{ pseudomorphic_strain{ } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: \(\mathrm{maximum\;1}\)
- Functionality
Homogeneous strain for 1D layer structures (analytical calculation). This feature also works in 2D or 3D but the user must be sure that the model makes sense from a physical point of view, i.e., the 2D/3D structure should consist of different layers along the growth direction whereas the layers must be homogenous along the two perpendicular directions.
minimized_strain{ }¶
- Calling sequence
strain{ minimized_strain{ } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: \(\mathrm{maximum\;1}\)
- Functionality
Minimization of the elastic energy for 2D and 3D geometries (numerical calculation). It can also be used for 1D simulations. In this case, the results will be equivalent to the analytical model pseudomorphic_strain{ }.
growth_direction¶
- Calling sequence
strain{ growth_direction }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{vector\;of\;3\;integers}\)
values: \(\mathrm{no\;constraints}\)
default: \([1.0,\;0.0,\;0.0]\)
unit: \(\mathrm{-}\)
- Functionality
(for pseudomorphic strain model)
Vector in crystal coordinate system
Can be specified in a 2D or 3D simulation but not in a 1D simulation (x axis is taken by default in 1D)
If not set, x axis of simulation coordinate system is taken by default.
- example:
growth_direction = [1, 0, 0]
residual_strain¶
- Calling sequence
strain{ residual_strain }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{real\;number}\)
values: \([-1.0, 1.0]\)
unit: \(\mathrm{-}\)
- Functionality
Residuals strain in the substrate \(\eta\) scales lattice parameter of the substrate (only for the purpose of strain computation) according to the formula \(a_{\eta,s}=(1+\eta)\cdot a_{0,s}\), where \(a_{0,s}\) is the (unstrained) lattice parameter of the substrate and \(a_{\eta,s}\) the modified (strained) lattice parameter of the substrate. The latter one represents the substrate during evaluation of the strain tensor.
linear_solver{ }¶
- Calling sequence
strain{ linear_solver{ } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: \(\mathrm{maximum\;1}\)
- Functionality
—
linear_solver{ iterations }¶
- Calling sequence
strain{ linear_solver{ iterations } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{integer}\)
values: \(\{1,2,3,4,\ldots\}\)
default: \(10000\)
unit: \(\mathrm{-}\)
- Functionality
Number of iterations for linear equation solver in strain algorithm
linear_solver{ abs_accuracy }¶
- Calling sequence
strain{ linear_solver{ abs_accuracy } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{real\;number}\)
values: \([0.0, \ldots)\)
default: \(10^{-8}\)
unit: \(\mathrm{GP\,}\) (1D) / \(\mathrm{GP\,nm\,}\) (2D) / \(\mathrm{GP\,nm^{2}\,}\) (3D)
- Functionality
—
linear_solver{ rel_accuracy }¶
- Calling sequence
strain{ linear_solver{ rel_accuracy } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{real\;number}\)
values: \([0.0, 10^{-2}]\)
default: \(10^{-12}\)
unit: \(\mathrm{-}\)
- Functionality
—
linear_solver{ use_cscg }¶
- Calling sequence
strain{ linear_solver{ use_cscg } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{no}\)
- Functionality
Composite step conjugate gradient solver (try this one if standard solver fails to converge)
linear_solver{ force_diagonal_preconditioner }¶
- Calling sequence
strain{ linear_solver{ force_diagonal_preconditioner } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{no}\)
- Functionality
—
import_strain{ }¶
- Calling sequence
strain{ import_strain{ } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: \(\mathrm{maximum\;1}\)
- Functionality
—
import_strain{ import_from }¶
- Calling sequence
strain{ import_strain{ import_from } }- Properties
using: \(\mathrm{\textcolor{WildStrawberry}{required}}\)
type: \(\mathrm{character\;string}\)
- Functionality
Reference to imported data in import{ }.
The data being imported must have exactly 6 components. The expected order of strain tensor components is: \(\varepsilon_{xx}\ \varepsilon_{yy}\ \varepsilon_{zz}\ \varepsilon_{xy}\ \varepsilon_{xz}\ \varepsilon_{yz}\)
import_strain{ coordinate_system }¶
- Calling sequence
strain{ import_strain{ coordinate_system } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{crystal\;/\;simulation}\)
default: \(\mathrm{simulation}\)
- Functionality
The imported strain tensor is with respect to the simulation or crystal coordinate system (optional parameter).
piezo_density¶
- Calling sequence
strain{ piezo_density }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{yes}\)
- Functionality
Calculate piezoelectric charge density and take it into account while solving the Poisson equation.
If no strain is solved, this flag is ignored.
second_order_piezo¶
- Calling sequence
strain{ second_order_piezo }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{no}\)
- Functionality
Include 2nd order piezoelectric coefficients in the calculation
Note
Not fully implemented for wurtzite, only “standard growth directions” supported for wurtzite as the most general formula was not known to us at the time of implementation.
pyro_density¶
- Calling sequence
strain{ pyro_density }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{yes}\)
- Functionality
Calculate pyroelectric charge density and take it into account while solving the Poisson equation.
If material system is not wurtzite, this flag is ignored. The pyroelectric charge density due to spontaneous polarization applies to wurtzite only. In order to obtain pyroelectric charges, it is not necessary to calculate strain. Pyroelectric charges are only present in wurtzite materials but not in zincblende .
output_hydrostatic_strain{ }¶
- Calling sequence
strain{ output_hydrostatic_strain{ } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: \(\mathrm{maximum\;1}\)
- Functionality
prints out the hydrostatic strain, i.e. the trace of the strain tensor \(\mathrm{Tr}[\varepsilon_{ij}] = \varepsilon_{xx} + \varepsilon_{yy} + \varepsilon_{zz}\) [dimensionless]
output_hydrostatic_strain{ boxes }¶
- Calling sequence
strain{ output_hydrostatic_strain{ boxes } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{no}\)
- Functionality
—
Note
The hydrostatic strain output is in percent (This is different compared to nextnano³.)
output_strain_tensor{ }¶
- Calling sequence
strain{ output_strain_tensor{ } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: \(\mathrm{maximum\;1}\)
- Functionality
output (symmetric) strain tensor : \(\varepsilon_{ij} = (u_{ij} + u_{ji})/2\) [dimensionless]
output_strain_tensor{ crystal_system }¶
- Calling sequence
strain{ output_strain_tensor{ crystal_system } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{no}\)
- Functionality
output strain tensor in crystal coordinate system
output_strain_tensor{ simulation_system }¶
- Calling sequence
strain{ output_strain_tensor{ simulation_system } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{yes}\)
- Functionality
output strain tensor in simulation coordinate system (useful if simulation coordinate system differs from crystal coordinate system)
Note
The ordering of the strain tensor components is: \(\varepsilon_{xx},\ \varepsilon_{yy},\ \varepsilon_{zz},\ \varepsilon_{xy},\ \varepsilon_{xz},\ \varepsilon_{yz}\)
output_strain_tensor{ boxes }¶
- Calling sequence
strain{ output_strain_tensor{ boxes } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{no}\)
- Functionality
For each grid point, in 1D two points are printed out to mimic abrupt discontinuities at interfaces (in 2D four points, in 3D eight points)
output_distortion_tensor{ }¶
- Calling sequence
strain{ output_distortion_tensor{ } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: \(\mathrm{maximum\;1}\)
- Functionality
output distortion tensor \(u_{ij}\) (which can be nonsymmetric for certain growth directions) \(u_{xx}\ u_{yy}\ u_{zz}\ u_{xy}\ u_{yx}\ u_{xz}\ u_{zx}\ u_{yz}\ u_{zy}\) [dimensionless]
output_distortion_tensor{ crystal_system }¶
- Calling sequence
strain{ output_distortion_tensor{ crystal_system } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{no}\)
- Functionality
output distortion tensor in crystal coordinate system
output_distortion_tensor{ simulation_system }¶
- Calling sequence
strain{ output_distortion_tensor{ simulation_system } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{yes}\)
- Functionality
output distortion tensor in crystal coordinate system
output_distortion_tensor{ boxes }¶
- Calling sequence
strain{ output_distortion_tensor{ boxes } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{no}\)
- Functionality
—
output_stress_tensor{ }¶
- Calling sequence
strain{ output_stress_tensor{ } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: \(\mathrm{maximum\;1}\)
- Functionality
output (symmetric) stress tensor : \(\ \sigma_{ij} = C_{ijkl}\ \varepsilon_{kl}\) [GPa]
output_stress_tensor{ crystal_system }¶
- Calling sequence
strain{ output_stress_tensor{ crystal_system } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{no}\)
- Functionality
output stress tensor in crystal coordinate system
output_stress_tensor{ simulation_system }¶
- Calling sequence
strain{ output_stress_tensor{ simulation_system } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{yes}\)
- Functionality
output stress tensor in simulation coordinate system (useful if simulation coordinate system differs from crystal coordinate system)
Note
The ordering of the stress tensor components is: \(\sigma_{xx},\ \sigma_{yy},\ \sigma_{zz},\ \sigma_{xy},\ \sigma_{xz},\ \sigma_{yz}\)
output_stress_tensor{ boxes }¶
- Calling sequence
strain{ output_stress_tensor{ boxes } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{no}\)
- Functionality
—
output_displacement{ }¶
- Calling sequence
strain{ output_displacement{ } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: \(\mathrm{maximum\;1}\)
- Functionality
output displacement vector [nm]
output_displacement{ crystal_system }¶
- Calling sequence
strain{ output_displacement{ crystal_system } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{no}\)
- Functionality
output displacement vector in crystal coordinate system
output_displacement{ simulation_system }¶
- Calling sequence
strain{ output_displacement{ simulation_system } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{yes}\)
- Functionality
output displacement vector in simulation coordinate system
output_force_density{ }¶
- Calling sequence
strain{ output_force_density{ } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: \(\mathrm{maximum\;1}\)
- Functionality
output force density vector field \(f_i\) [nN/nm3] (at moment output may be not fully correct; not tested sufficiently)
output_force_density{ crystal_system }¶
- Calling sequence
strain{ output_force_density{ crystal_system } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{no}\)
- Functionality
output force density vector field in crystal coordinate system
output_force_density{ simulation_system }¶
- Calling sequence
strain{ output_force_density{ simulation_system } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{yes}\)
- Functionality
output force density vector field in simulation coordinate system
output_elastic_energy_density{ }¶
- Calling sequence
strain{ output_elastic_energy_density{ } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: \(\mathrm{maximum\;1}\)
- Functionality
output elastic energy density (\(\frac{1}{2}\ C_{ijkl}\ \varepsilon_{ij}\ \varepsilon_{kl}\)) [eV/nm3] The integrated elastic energy is printed out in log file.
output_elastic_energy_density{ boxes }¶
- Calling sequence
strain{ output_elastic_energy_density{ boxes } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{no}\)
- Functionality
—
output_polarization_charges{ }¶
- Calling sequence
strain{ output_polarization_charges{ } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: \(\mathrm{maximum\;1}\)
- Functionality
prints out piezo and pyroelectric charge densities [1018/cm3] in case they were calculated. Pyroelectric charges due to spontaneous polarization apply to wurtzite only. Piezoelectric charges can be calculated for both zinc blende and wurtzite in case the strain was calculated. The piezo charge density is written to: density_piezoelectric_charge.dat (\(\rho_\mathrm{pz}\)) For diamond like crystal structures that have an inversion center such a Si or Ge, piezoelectric charges do not exist.
The pyro charge density is written to: density_pyroelectric_charge.dat (\(\rho_\mathrm{py}\)) It applies to wurtzite only and is independent of strain and is due to spontaneous polarization. If both, piezo and pyroelectric charge densities were calculated, the sum of both charge densities (total polarization charge density) is written to: density_polarization_charge.dat (\(\rho_\mathrm{pol}=\rho_\mathrm{pz}+\rho_\mathrm{py}\))
To summarize:
zincblende: density_piezoelectric_charge.dat (\(\rho_\mathrm{pz}\))
wurtzite: density_piezoelectric_charge.dat (\(\rho_\mathrm{pz}\)), density_pyroelectric_charge.dat (\(\rho_\mathrm{py}\)), density_polarization_charge.dat (\(\rho_\mathrm{pol}=\rho_\mathrm{pz}+\rho_\mathrm{py}\))
output_polarization_vector{ }¶
- Calling sequence
strain{ output_polarization_vector{ } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: \(\mathrm{maximum\;1}\)
- Functionality
prints out piezo and pyroelectric polarization vector [C/cm2]. Pyroelectric polarization due to spontaneous polarization apply to wurtzite only. The piezoelectric polarization vector depends on strain and it is zero if no strain is present.
output_polarization_vector{ crystal_system }¶
- Calling sequence
strain{ output_polarization_vector{ crystal_system } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{no}\)
- Functionality
output polarization vector in crystal coordinate system
output_polarization_vector{ simulation_system }¶
- Calling sequence
strain{ output_polarization_vector{ simulation_system } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{yes}\)
- Functionality
output polarization vector in simulation coordinate system
output_polarization_vector{ boxes }¶
- Calling sequence
strain{ output_polarization_vector{ boxes } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{no}\)
- Functionality
—
output_lattice_constants{ }¶
- Calling sequence
strain{ output_lattice_constants{ } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: \(\mathrm{maximum\;1}\)
- Functionality
Output lattice constants to a file …\Structure\lattice_constants.dat
output_lattice_constants{ boxes }¶
- Calling sequence
strain{ output_lattice_constants{ boxes } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{no}\)
- Functionality
—
output_elastic_constants{ }¶
- Calling sequence
strain{ output_elastic_constants{ } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: \(\mathrm{maximum\;1}\)
- Functionality
Output elastic constants.
output_elastic_constants{ boxes }¶
- Calling sequence
strain{ output_elastic_constants{ boxes } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{no}\)
- Functionality
—
output_piezo_constants{ }¶
- Calling sequence
strain{ output_piezo_constants{ } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: \(\mathrm{maximum\;1}\)
- Functionality
Output piezoelectric constants.
output_piezo_constants{ boxes }¶
- Calling sequence
strain{ output_piezo_constants{ boxes } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{no}\)
- Functionality
—
output_second_order_piezo_constants{ }¶
- Calling sequence
strain{ output_second_order_piezo_constants{ } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: \(\mathrm{maximum\;1}\)
- Functionality
Output 2nd order piezoelectric constants.
output_second_order_piezo_constants{ boxes }¶
- Calling sequence
strain{ output_second_order_piezo_constants{ boxes } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{no}\)
- Functionality
—
output_pyro_constants{ }¶
- Calling sequence
strain{ output_pyro_constants{ } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: \(\mathrm{maximum\;1}\)
- Functionality
Output pyroelectric constants, i.e. spontaneous polarization constants.
output_pyro_constants{ boxes }¶
- Calling sequence
strain{ output_pyro_constants{ boxes } }- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: \(\mathrm{choice}\)
choices: \(\mathrm{yes\;/\;no}\)
default: \(\mathrm{no}\)
- Functionality
—