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run{}

Specifications for the program execution (program flow)

Note: There are two syntaxes for run{}.

  • New syntax (recommended syntax for versions newer than 2020-05-01)
  • Deprecated syntax (used in versions older than 2020-04-30. Nevertheless, it will still work in later versions.)

 

run{

   structure_only{                       #
If present, calculation is aborted after structure setup, similarly to when the command line flag -s or --structure is set.
     last_region = 5                     #
But differently from the command line flag, if last_region is present, partical structure initialization is performed,
                                         # i.e. the simulation prints out the structure up to the (last) region index 5 (any integer >= 1 can be specified, default is: 1000000).
   }                                     #
This is useful for debugging your structure definition, e.g. if you have a 2D or 3D simulation with many material regions, contact regions, doping regions and generation regions overlapping each other in a complictated way.
                                         #
The files in the output directory Structure/ will then reflect this partial initialization.
                                         #
(Note that in case not all regions are used here, some initialization and output steps related to strain, poisson, current, quantum, cbr, optics, etc. will be omitted in order to avoid inconsistencies.)

   # Strain
   strain{}                              #
solves the strain equation


   # Poisson equation
   poisson{}                             #
solves the Poisson equation


   # Schroedinger equation
   quantum{}                             #
solves the Schrödinger equation
                                         # Exchange-correlation effects (optional) can be included and are calculated from the quantum density. Then the Schrödinger
                                         # equation is solved again but this time including the exchange-correlation potential energy.

   # coupled Current-Poisson equations
   current_poisson{                      #
solves the coupled current and Poisson equations self-consistently
                                         #

      fast_poisson            = yes/no   # (default is: no) If enabled, Newton iterations for Poisson in the middle of the classical current-Poisson iteration will be limited to 1.
                                         # Note that enabling this setting may also influence stability of convergence or change the optimal value for alpha_fermi.
                                         # Typically, fast_poisson = yes increases the number of iterations but significantly reduces the overall execution time.
                                         #
      multi_stage_solve       = yes/no   # (default is: no) Flag in order to solve classical current equation first with
                                         # recombination/generation switched off in order to get a good starting point, and then with
                                         # recombination/generation switched on (if any recombination models are switched on).
                                         # Can be used to improve convergence in some situations but may increase runtime in others.
                                         #
      system_solve            = yes/no   # Alternative new iteration method for classical current-Poisson  (default is: no)
                                         #
This Newton method may provide better convergence for some systems (but may require different values of convergence parameters).
                                         # system_solve = yes results in Fermi levels and potential being simultaneously updated as a system of unknowns during the iteration.
                                         #
Irrespective of its value, system_solve always takes the value of current_repetitions into account.

      iterations              = 30       #
number of iterations for current-Poisson solver (default is: 100)
      fermi_limit             = 2.0      # [eV]
Defines how far the quasi-Fermi levels can move above the highest / below the lowest contact. (0.0 <= fermi_limit <= 10.0; default is: 2.0)
                                         # Except in case of huge bandgaps and extreme photogeneration, the defaults should not require any change.
                                         # At the same time, in the absence of any externally induced photogeneration, these values could be set to zero in order to stabilize the iteration.
      current_repetitions     = 1        # number of current-density iterations (default is: 1). The current equations are repeatedly solved for the quasi-Fermi levels with the densities fixed.
                                         # The current equation for the electrons and for the holes are solved independently with a common and fixed recombination term.
                                         # For each iteration, the densities are adjusted according to the new quasi-Fermi levels of the previous iteration.
                                         # current_repetitions
defines number of these repetitions.
                                         # If generation/recombination is present, using a value > 1 (e.g. 5) may stabilize the iteration and
                                         # sometimes enable faster convergence (larger alpha_fermi may also be possible then).
      limit_repetitions       = no       # yes / no (default is: no). If enabled, the current-density loop is exited early as soon as residual_fermi is reached by the quasi-Fermi levels.

      residual                = 1e5      # (dimension dependent!!!) residual occupation changes (default is: 1e5/cm2 (1D), 1e3/cm (2D), 1e-3 [dimensionless] (3D))

      residual_fermi          = 1e-5     #
residual Fermi level changes (default is: 1e-5 [eV]). This value is also used during quantum_current_poisson.

      alpha_fermi             = 1.0e-5   #
underrelaxation parameter for Fermi level [dimensionless] (0.00001 < alpha_fermi <= 1.0, default is: 1.0)
                                         #
The final quasi-Fermi level for electrons after each iteration is calculated as follows:
                                         # EF,n = ( EF,n of previous iteration ) * ( 1 - alpha_fermi) + ( EF,n of actual iteration ) * alpha_fermi
                                         # This Fermi level is then input to the next iteration.
                                         #
The same holds for the Fermi level EF,p for holes.
                                         # The value of alpha_fermi will change due to alpha_scale during the iterations. The actually used alpha_fermi is now included in
                                         # iteration_current_poisson.dat
and
                                         # iteration_quantum_current_poisson_details.dat
.
      alpha_iterations        = 1000     # number of alpha iterations (default is: 1000)
      alpha_scale             = 0.998    #
alpha scale (default is: 0.998 [dimensionless]) 0.1 <= alpha_scale <= 1.0
                                         #
Both for classical and for quantum iterations, alpha_fermi will be reduced further as
                                         #    alpha_fermi <- max( alpha_fermi * alpha_scale , 1e-5)
                                         #
at each iteration step once the number of iterations exceeds alpha_iterations.
                                         # Use this feature to improve convergence (particularly confergence of Fermi levels) towards the end of the iteration.
                                         # Note that decreasing alpha_fermi too fast (a problem with older versions) will result in the iteration stalling
                                         #
(only the residuals of the densities but none of the Fermi levels decrease).
                                         #
The total current equation may then not be properly conserved.

      output_log              = yes      # Output of convergence of (classical) current-Poisson equation into 'iteration_current_poisson.dat' (default: yes).
   }
                                         #
Note: Both conditions specified by residual and residual_fermi must hold in order to consider a calculation as converged.



   # Schroedinger equation
   quantum_density{                      #
solves the Schrödinger equations (self-consistent density/exchange)
      iterations          = 20           # 
see quantum_poisson{}
      residual            = 1e5          # 
see quantum_poisson{}

      use_subspace        = yes/no       # see quantum_poisson{}
      subspace_iterations      = 1       # 
see quantum_poisson{}
      subspace_residual_factor = 1e12    # 
see quantum_poisson{}

      output_log          = yes/no       # see quantum_poisson{}
   }
 

   # coupled Schroedinger-Poisson equations
                                         #
When quantum_poisson{} is desired, note that additionally either poisson{} or current_poisson{} is required.
   quantum_poisson{                      #
solves the Schrödinger-Poisson equations self-consistently
      iterations          = 20           #
number of iterations, i.e. self-consistency cycles (default is: 30)
      residual            = 1e5          #
(dimension dependent!!!) residual of the integrated total charge carrier density changes (default is: 1e5/cm2 (1D), 1e3/cm (2D), 1e-3 [dimensionless] (3D))
                                         #
(applies to exact Schrödinger equation, not to subspace Schrödinger equation)
                                         #
Note: If you do not include enough eigenstates, the convergence behavior might be affected as the occupation of the eigenstates is not considered in a useful way.

      use_subspace        = yes/no       # solve Schrödinger equation within subspace of eigenvectors of previous iteration
                                         #
as long as achieved residual is larger than desired residual * residual_factor
                                         #
and at least in every second iteration (default is: yes)
      subspace_iterations      = 1       # 1
<= subspace_iterations <= 1000
      subspace_residual_factor = 1e12    #
controls number of subspace iterations (default is: 1e12 [dimensionless]) 2.0 <= subspace_residual_factor
                                         #
                                         #
It holds for use_subspace = yes:
                                         # if (residual in densities > residual * subspace_residual_factor) {
                                         #    use only approximate quantum solutions
                                         # } else {
                                         #    alternate one exact and subspace_iterations approximate quantum solutions
                                         #  }
                                         #  terminate iteration when residual in densities < residual for exact quantum solution
                                         #
                                         #
Use subspace_iterations > 1 to further reduce computational load (i.e. runtime) from exact quantum solutions (the best value is system-dependent).
                                         #
Note that the number of iterations may not change or even increase.
                                         #
In rare cases (e.g. when a huge number of eigenvalues is computed), selecting use_subspace = no may be faster.

      output_log          = yes/no       # Output of convergence of Schrödinger-Poisson equation (residuals for quantum_poisson) into the logfile iteration_quantum.dat (default is: yes)
   }

   # coupled Schroedinger-Current-Poisson equations
                                         #
When quantum_current_poisson{} is desired, note that additionally either poisson{} or current_poisson{} is required.
   quantum_current_poisson{              #
solves the Schrödinger-Current-Poisson equations self-consistently
                                         #
In order to solve the Schrödinger-Current-Poisson equations, current_poisson must be defined in the input file.
      iterations               = 20      #
see quantum_poisson{}
      residual                 = 1e5     #
see quantum_poisson{}

      use_subspace             = yes/no  # see quantum_poisson{}
      subspace_iterations      = 1       #
see quantum_poisson{}
      subspace_residual_factor = 1e12    #
see quantum_poisson{}

      fermi_limit               = 2.0    #
see current_poisson{}
      current_repetitions       = 2      # 
number of current-density iterations (default is: 2). The current equation is repeatedly solved for the quasi-Fermi levels.
                                         # For each iteration, the densities are adjusted according to the new quasi-Fermi levels of the previous iteration.
                                         # current_repetitions defines number of these repetitions.
                                         # If generation/recombination is present, using a value > 1 (e.g. 5) may stabilize the iteration and
                                         # sometimes enable faster convergence (larger alpha_fermi may also be possible then).
      limit_repetitions         = no     # yes / no (default is: no). If enabled, the current-density loop is exited early as soon as residual_fermi is reached by the quasi-Fermi levels.

      residual_fermi      = 1e-5         #
residual Fermi level changes (default is: 1e-5 [eV])

      alpha_fermi         = 1.0e-1       #
The Fermi level is underrelaxed between repetitions using an underrelaxation parameter for the Fermi levels.
                                         #
It should be used once an oscillation of residuals is observed while self-consistently solving
                                         # the Poisson and Schrödinger (and current) equations to improve convergence.
                                         # (default is: 1.0 [dimensionless], possible range: 0.00001 <= alpha_fermi <= 1.0)
                                         #
for further information please read comments on alpha_fermi parameter above
      alpha_iterations    = 1000         #
number of alpha iterations (default is: 1000)
      alpha_scale         = 0.998        #
alpha scale (default is: 0.998 [dimensionless]) 0.1 <= alpha_scale <= 1.0
                                         #
Both for classical and for quantum iterations, alpha_fermi will be reduced further as
                                         #    alpha_fermi <- max( alpha_fermi * alpha_scale , 1e-5)
                                         #
at each iteration step once the number of iterations exceeds alpha_iterations.
                                         # Use this feature to improve convergence (particularly confergence of Fermi levels) towards the end of the iteration.
                                         # Note that decreasing alpha_fermi too fast (a problem with older versions) will result in the iteration stalling
                                         #
(only the residuals of the densities but none of the Fermi levels decrease).
                                         #
The total current equation may then not be properly conserved.

      output_log          = yes/no       # Output of convergence of (quantum) current-Poisson equation (residuals for quantum_current_poisson) into the logfile iteration_quantum_current_poisson.dat (default is: yes)
   }
                                         #
Note: Both conditions specified by residual and residual_fermi are only checked between iterations but not between repetitions.                                                                                             

   # Optics
   optics{}                              #
calculate optical properties, see optics{}
   optical_device{}                      #
calculate optical properties, see optics{}
}

Examples

  • run{            
     structure_only{}             #
    If present, calculation is aborted after structure setup.
    }
  • run{}                         # just sets up the device geometry
  • run{
       strain{}                   # solves the strain equation
    }
  • run{
       strain{}                   #
    solves the strain equation
       quantum{}                  # and then the Schrödinger equation
    }
  • run{
       strain
    {}                   #
    solves the strain equation
       poisson
    {}
       quantum_poisson
    {}          #
    }                             #
    solves the Schrödinger and Poisson equations self-consistently
  • run{
       strain
    {}                   #
    solves the strain equation
       current_poisson
    {}          #
    solves the coupled current and Poisson equations self-consistently
       quantum_current_poisson
    {}  #
    solves the Schrödinger,  Poisson and current equations self-consistently
    }
  • run{
       quantum{}                  #
    solves the Schrödinger equation
       optics{}                   # calculates optical properties
    }

Using the new syntax (quantum_poisson{}, quantum_current_poisson{}), the classical computations (poisson{} or current_poisson{}) can be specified independent from the quantum calculation to be performed, e.g. it is now possible to combine poisson{} with quantum_current_poisson{} to bypass the classical current calculations.

 

Restrictions

  • Poisson: Only maximally one of poisson{} and current_poisson{} can be defined,
    which defines the classical equation to be solved (also as first stage before possibly solving any quantum mechanics).
    If neither is set, only fixed potentials will be used.
  • Quantum: If quantum mechanics is desired, one of quantum{}, quantum_density{}, quantum_poisson{}, and quantum_current_poisson{} must be set.
  • The quantum equations to be solved - only quantum, quantum with self-consistent density/exchange, self-consistent quantum-Poisson, and self-consistent quantum-current-Poisson - are only defined by the choice of quantum{}, quantum_density{}, quantum_poisson{}, and quantum_current_poisson{}, irrespective of the choice of the classical solution method.
    Note that one of poisson{} and current_poisson{} must be set when quantum_poisson{} or quantum_current_poisson{} is desired.
    Use poisson{} in conjunction with quantum_current_poisson{} to skip classical current calculations.
  • Quantum with self-consistent density/exchange is solved by selection of quantum_density{} (users can change parameters in there as needed).

 

Further remarks

  • 2019-01-24: At the end of current_poisson{}, Poisson is now solved once to make the band structure consistent with the Fermi levels. In case of incomplete convergence, the partly converged output is then more in line with physical intuition.
  • Input residuals and tolerances are rescaled to various internal units (often in a dimension-dependent manner, i.e. they are different for 1D, 2D and 3D simulations) before being passed to low-level numerical routines like ARPACK, LAPACK, BLAS, nonlinear solvers, etc. Therefore, diagnostic output from low-level numerical solvers usually contains values which are completely different from those which are output by the high-level physics routines or output into files.
  • There are logfiles that track the converence behavior of the iterations during the simulation.
    The convergence information for the respective self-consistent equations can be plotted. It is best to use a logarithmic scale.
    • iteration_current_poisson.dat                 - current_poisson{}         - Convergence of coupled Current-Poisson with classical densities
    • iteration_quantum_density.dat                 - quantum_density{}         - Convergence of Schrödinger equation with self-consistent density/exchange
    • iteration_quantum_poisson.dat                 - quantum_poisson{}         - Convergence of outer iteration loop for Schrödinger-Poisson
    • iteration_quantum_current_poisson.dat         - quantum_current_poisson{} - Convergence of outer iteration loop, i.e. for Current-Poisson-Schrödinger with quantum densities
    • iteration_quantum_current_poisson_details.dat - quantum_current_poisson{} - Convergence of current equation, i.e. for Current-Poisson with quantum densities

 

Deprecated syntax

run{

   # Strain
   solve_strain{}                        #
solves the strain equation


   # Poisson equation
   solve_poisson{}                       #
solves the Poisson equation


   # Schroedinger equation
   solve_quantum{}                       #
solves the Schrödinger equation
                                         # Exchange-correlation effects (optional) can be included and are calculated from the quantum density. Then the Schrödinger
                                         # equation is solved again but this time including the exchange-correlation potential energy.

   # coupled Current-Poisson equations
   solve_current_poisson{                #
solves the coupled current and Poisson equations self-consistently
                                         #
It is also called once before a Schrödinger-Poisson-Current self-consistent iteration is started but not during the latter.
                                         #

      fast_poisson            = yes/no   # (default is: no) If enabled, Newton iterations for Poisson in the middle of the classical current-Poisson iteration will be limited to 1.
                                         # Note that enabling this setting may also influence stability of convergence or change the optimal value for alpha_fermi.
                                         # Typically, fast_poisson = yes increases the number of iterations but significantly reduces the overall execution time.
                                         #
      multi_stage_solve       = yes/no   # (default is: no) Flag in order to solve classical current equation first with
                                         # recombination/generation switched off in order to get a good starting point, and then with
                                         # recombination/generation switched on (if any recombination models are switched on).
                                         # Can be used to improve convergence in some situations but may increase runtime in others.
                                         #
      use_newmethod           = yes/no   # Alternative new iteration method for classical current-poisson  (default is: no)
                                         #
The Newton method may provide better convergence for some systems (but may require different values of convergence parameters).
                                         # Note that classical current_repetitions currently has no effect when the new method is selected.
      iterations              = 30       #
number of iterations for current-Poisson solver (default is: 100)
      fermi_limit             = 2.0      # [eV]
Defines how far the quasi-Fermi levels can move above the highest / below the lowest contact. (0.0 <= fermi_limit <= 10.0; default is: 2.0)
                                         # Except in case of huge bandgaps and extreme photogeneration, the defaults should not require any change.
                                         # At the same time, in the absence of any externally induced photogeneration, these values could be set to zero in order to stabilize the iteration.
      current_repetitions     = 1        # number of current-density iterations (default is: 1). The current equations are repeatedly solved for the quasi-Fermi levels with the densities fixed.
                                         # The current equation for the electrons and for the holes are solved independently with a common and fixed recombination term.
                                         # For each iteration, the densities are adjusted according to the new quasi-Fermi levels of the previous iteration.
                                         # current_repetitions
defines number of these repetitions.
                                         # If generation/recombination is present, using a value > 1 (e.g. 5) may stabilize the iteration and
                                         # sometimes enable faster convergence (larger alpha_fermi may also be possible then).
      limit_repetitions   = no           # see quantum_current_poisson{}

      residual                = 1e5      # (dimension dependent!!!) residual occupation changes (default is: 1e5/cm2 (1D), 1e3/cm (2D), 1e-3 [dimensionless] (3D))

      residual_fermi          = 1e-5     #
residual Fermi level changes (default is: 1e-5 [eV]). This value is also used during quantum_current_poisson.

      alpha_fermi             = 1.0e-5   #
underrelaxation parameter for Fermi level [dimensionless] (0.00001 < alpha_fermi <= 1.0, default is: 1.0)
                                         #
The final quasi-Fermi level for electrons after each iteration is calculated as follows:
                                         # EF,n = ( EF,n of previous iteration ) * ( 1 - alpha_fermi) + ( EF,n of actual iteration ) * alpha_fermi
                                         # This Fermi level is then input to the next iteration.
                                         #
The same holds for the Fermi level EF,p for holes.
                                         # The value of alpha_fermi will change due to alpha_scale during the iterations. The actually used alpha_fermi is now included in
                                         # iteration_current_poisson.dat
and
                                         # iteration_quantum_current_poisson_details.dat
.
      alpha_iterations        = 1000     # number of alpha iterations (default is: 1000)
      alpha_scale             = 0.998    #
alpha scale (default is: 0.998 [dimensionless]) 0.1 <= alpha_scale <= 1.0
                                         #
Both for classical and for quantum iterations, alpha_fermi will be reduced further as
                                         #    alpha_fermi <- max( alpha_fermi * alpha_scale , 1e-5)
                                         #
at each iteration step once the number of iterations exceeds alpha_iterations.
                                         # Use this feature to improve convergence (particularly confergence of Fermi levels) towards the end of the iteration.
                                         # Note that decreasing alpha_fermi too fast (a problem with older versions) will result in the iteration stalling
                                         #
(only the residuals of the densities but none of the Fermi levels decrease).
                                         #
The total current equation may then not be properly conserved.

      output_log              = yes      # Output of convergence of (classical) current-Poisson equation into 'iteration_current_poisson.dat' (default: yes).
   }
                                         #
Note: Both conditions specified by residual and residual_fermi must hold in order to consider a calculation as converged.




   # coupled Schroedinger-Current-Poisson equations
   outer_iteration{                      #
solves the Schrödinger-Poisson or Schrödinger-Current-Poisson equations self-consistently
                                         #
In order to solve the Schrödinger-Current-Poisson equations, current_poisson must be defined in the input file.
      iterations          = 20           #
see quantum_poisson{}
      residual            = 1e5          #
see quantum_poisson{}

      use_subspace        = yes/no       # see quantum_poisson{}
      subspace_iterations      = 1       #
see quantum_poisson{}
      subspace_residual_factor = 1e12    #
see quantum_poisson{}

      fixed_fermi_levels  = yes/no       # prevent update of Fermi levels. No self-consistent current is computed. (default is: no)
                    
                    #
This freezes all Fermi levels in the outer iteration, i.e. the Fermi levels calculated in the classical current-Poisson are not changed anymore during the outer iteration.
                                         # As results, there is no self-consistency between quantum densities and current equation anymore, but convergence typically is much better.
                                         # The result is essentially a semi-classical approximation which works best if quantum effects do not change the densities too much.
                                         # Note: If fixed_fermi_levels = yes, then current_repetitions, alpha_fermi, and residual_fermi are ignored.

      fermi_limit         = 2.0          #
see current_poisson{}

      current_repetitions = 2            # 
see quantum_current_poisson{}
      limit_repetitions   = no           # see quantum_current_poisson{}

      residual_fermi      = 1e-5         # 
see quantum_current_poisson{}

      alpha_fermi         = 1.0e-1       # 
see quantum_current_poisson{}
      alpha_iterations    = 1000         # 
see quantum_current_poisson{}
      alpha_scale         = 0.998        # 
see quantum_current_poisson{}

      output_log          = yes/no       # Output of convergence of (quantum) current-Poisson equation (residuals for outer_iteration) into the logfile
                                         # iteration_quantum_current_poisson.dat
or
                                         # iteration_quantum_poisson.dat
(default is: yes)
   }
                                         #
Note: both conditions specified by residual and residual_fermi are only checked between iterations but not between repetitions.

Examples

  • run{}                         # just sets up the device geometry
  • run{
       solve_strain{}             #
    solves the strain equation
       solve_quantum{}            #
    and then the Schrödinger equation
    }
  • run{
       solve_poisson
    {}
       solve_quantum
    {}
       outer_iteration
    {}          #
    solves the Schrödinger and Poisson equations self-consistently
    }
  • run{
       solve_current_poisson
    {}    #
    solves the coupled current and Poisson equations self-consistently
       solve_quantum
    {}            #
    solves the Schrödinger equation
       outer_iteration
    {}          #
    solves the Schrödinger,  Poisson and current equations self-consistently
    }

Restrictions

  • Poisson: Only maximally one of solve_poisson{} and solve_current_poisson{} can be defined,
    which defines the classical equation to be solved (also as first stage before possibly solving any quantum mechanics).
    If neither is set, only fixed potentials will be used.
  • Quantum: If quantum mechanics is desired, solve_quantum{} must be set.
  • If, in addition to solve_quantum{} also outer_iteration{} is set,
    - the self-consistent quantum-Poisson equations are self-consistently solved when solve_poisson{} is set or solve_current_poisson{} is set with fixed_fermi_levels = yes, and
    - the self-consistent quantum-current-Poisson equations are self-consistently solved when solve_current_poisson{} is set with fixed_fermi_levels = no.
  • Note that one of solve_poisson{} and solve_current_poisson{} must be set in conjunction with outer_iteration{}.
    And it is not possible to skip classical current calculation if the quantum-current-Poisson equations are to be solved.
  • If outer_iteration{} is not set, solve_quantum{} solves quantum mechanics only, unless both solve_poisson{} and solve_current_poisson{} are not set as well.
    In this case, quantum with self-consistent density/exchange is solved using the default parameters from outer_iteration{} (parameters cannot be changed by users here).