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generation{}

Specifications that define information on generation rate.

 

The generation rate profile is assiged to a certain region.
It can be printed out using the keyword structure{ output_generation{} }.
 

structure{

   ...

   output_generation{            #
output generation rate for each grid point in units of [10^18/(cm3 s)]
      boxes = yes/no             #
(optional)
   }

   region{

   ...

      generation{

         constant{
            rate = 1.0e18               #
generation rate [1/cm3s] (applies to 1D, 2D and 3D)
            add  = yes                  #
(optional) yes or no (default = yes)
         }

         linear{
            rate = [1e18,2e18]          #
start and end value of generation rate [1/cm3s]
            x    = [50.0,100.0]         #
x coordinates of start and end point [nm]
            y    = [50.0,100.0]         #
y coordinates of start and end point [nm] (2D or 3D only)
            z    = [50.0,100.0]         #
z coordinates of start and end point [nm] (3D only)
                                        #
This defines a generation rate profile, which varies linearly along the line from the point (50,50,50) to the point (100,100,100)
                                                                         
   # and stays constant in the perpendicular planes.
            add  = yes                  #
(optional) yes or no (default = yes)
         }


         gaussian1D{                    #
Gaussian distribution function in one direction, constant in perpendicular directions
            rate    = 1.0e18            #
maximum of generation rate [1/cm3s]
            dose    = 1e12              #
dose of implant [cm-2] (integrated density of gaussian function), typical ranges are from 1e11 to 1e16.
                                        #
Either rate or dose has to be specified, but not both simultaneously.
                                        # rate = dose / ( SQRT(2*pi) * sigma_x )
            x       = 50.0              #
x coordinate of Gauss center (ion's projected range Rp, i.e. the depth where most ions stop) [nm]
            sigma_x = 5.0               # root mean square deviation in x direction (statistical fluctuation of Rp) [nm]
            y       = ...               #
(2D or 3D only)
            sigma_y = ...               #
            z       = ...               #
(3D only)
            sigma_z = ...               #
                                        # On
ly one out of x, y, z and the appropriate standard deviation (sigma) has to be specified.
            add  = yes                  #
(optional) yes or no (default = yes)
         }
        
Note: This profile corresponds to LSS theory (Lindhard, Scharff, Schiott theory) for doping - Gaussian distribution of ion implantation.

         gaussian2D{                    #
Gaussian distribution function in two directions, constant in perpendicular direction (2D or 3D only)
            rate    = 1.0e18            #
maximum of generation rate [1/cm3s]
            dose    = 1.0               #
dose of implant [cm-1] (integrated density of 2D gaussian function)
                                        #
Either rate or dose has to be specified, but not both simultaneously.
            x       = 50.0              #
x coordinate of Gauss center [nm]
            sigma_x = 5.0               # root mean square deviation in x direction [nm]
            y       = 50.0              #
y coordinate of Gauss center [nm]
            sigma_y = 5.0               #
root mean square deviation in y direction [nm]
            z       = ...               #
(3D only)
            sigma_z = ...               #
                                        #
Exactly two out of x, y, z and the appropriate standard deviations (sigma) have to be specified.
            add  = yes                  #
(optional) yes or no (default = yes)
         }

         gaussian3D{                    #
Gaussian distribution function in three directions (3D only)
            rate    = 1.0e18            #
maximum of generation rate in [1/cm3s]
            dose    = 1.0               #
dose of implant [dimensionless] (integrated density of 3D gaussian function)
            x       = 50.0              #
x coordinate of Gauss center [nm]
            sigma_x = 5.0               # root mean square deviation in x direction [nm]
            y       = 50.0              #
y coordinate of Gauss center [nm]
            sigma_y = 5.0               #
root mean square deviation in y direction [nm]
            z       = 50.0              #
z coordinate of Gauss center [nm]
            sigma_z = 5.0               #
root mean square deviation in z direction [nm]
                                        # All three
x, y, z and the appropriate standard deviations (sigma) have to be specified.
            add  = yes                  #
(optional) yes or no (default = yes)
         }

         import{                                          # import generation profile from external file.
            import_from = "import_generation_profile"     #
reference to imported data in import{}. The file being imported must have exactly one data component.
         }


      } # generation
   }    # region
}       # structure
 

It is also possible to remove a generation rate from a specific region.

structure{
   region{
      generation{ remove{} }             #
remove generation rate from this region, to keep certain regions free from generation rate.
   }    # region
}       # structure
 

 

Examples (3D)

  • generation{
       gaussian3D{                                 #
    three-dimensional Gaussian profile
          rate = 10.0e18                           #
    generation rate [1/cm3s]
          x = 30        y = 20        z = 20       #
    position of the Gauss center (x,y,z)=(30,20,20)
          sigma_x =  sigma_y = 2   sigma_z = #
    Gauss width along x, y and z directions
       }
       gaussian2D{                                 #
    two-dimensional Gaussian profile (constant profile along z direction)
          rate = 10.0e18                           #
    generation rate [1/cm3s]
          x = 10        y = 20                     #
    position of the Gauss center (x,y)=(10,20)
          sigma_x = 5   sigma_y = 5                #
    Gauss width along x and y directions
       }
    }
     
  • The following figure shows a 3D generation profile (although it says incorrectly "Doping profile 3D" in the figure) that is defined inside a 20 nm x 20 nm x 50 nm cube where the 50 nm are the z direction. The generation rate profile is homogeneous with respect to the (x,y) plane, it only varies along the z direction.



    The generation rate profile is constant between z = 10 nm and z = 25 nm with a rate of 1 x 1018 [1/cm3s]. It has Gaussian shape from z = 25 nm to z = 45 nm (gaussian1D). It is zero between z = 0 nm and z = 10 nm, as well as between z = 45 nm and z = 50 nm.

    If you want to obtain the input file that was used to obtain this 3D generation rate profile plot (constant + Gaussian shape), please contact stefan.birner@nextnano.de.
    -> 3Dgeneration_profile.in

 

doping{} and generation{} is always additive per default (add = yes) (unless import is different),
i.e. each profile adds to the already existing dopants/fixed charges/generation at a given point.
At the same time, using remove{}, all species of the already existing doping or generation concentrations can be removed.
However, there is also the problem that remove{} removes all species of dopants/fixed charges at a given point.
Thus, removing e.g. only donors but not acceptors is difficult.
This problem is solved by the new "add = yes/no" flag, which the user can specify for each profile (and thus for the species of that profile),
whether the profile should add to (which is the default) or replace the already existing concentration of the profile species.

For import{}, this flag has not been implemented yet.