Doping Functions

Attention

This tutorial is under construction

Input Files:

  • basics_1D_doping_predefined.in

  • basics_1D_doping_analytic.in (not compatible with demo version)

Introduction

This tutorial is the fifth in our introductory series. In the previous tutorials, we’ve already encountered one pre-defined doping profile - the constant one. In the following, we will see more possibilities to create doping profiles. After completing this tutorial, you will know more about:

  • different doping profiles, namely linear and Gaussian

  • crating custom doping profiles

Keywords: Gaussian1D{}, linear{}, import{}

Main

As an overview, Figure 2.5.2.17 shows all the structures that will be created in this tutorial.

../../../../../_images/Structure1.png

Figure 2.5.2.17 shows doping profiles including linear and Gaussian functions (left) and user defined functions (right).

1. Using pre-defined doping profiles

In this example we demonstrate two pre-defined doping profiles, namely Gaussian and linear profiles. For that we consider the setup in Figure 2.5.2.17 (left). The associated input file is basics_1D_doping_predefined.in.

Specifying regions with dopants

37structure{ # this group is required in every input file
38    output_impurities{ boxes = yes}     # output doping concentration [10^18 cm-3]
39
40    #---------
41    # material
42    #---------
43
44    region{
45        binary{ name = GaAs }           # material: GaAs
46        contact{ name = whatever }      # contact definition
47        everywhere{}                    # region spreads over the complete device
48    }
49
50    region{
51        binary{ name = InAs }           # region: InAs
52        line{ x = [ 20.0, 30.0 ] }      # position: x=20.0 nm to x=30.0 nm
53    }
54
55    #-------
56    # doping
57    #-------
58
59    region{
60        line{ x = [ 30.0, 40.0 ] }      # position: x = 30.0 nm to 40.0 nm
61        doping{                         # add doping to the region
62            gaussian1D{                 # Gaussian doping concentration profile
63                name = "p-type"         # name of impurity
64                conc = 1.0E18           # maximum of doping concentration [cm-3]
65                x = 35                  # x coordinate of Gauss center
66                sigma_x = 1.0           # standard deviation in x direction
67            }
68        }
69    }
70
71    region{
72        line{ x = [ 0.0, 20.0 ] }       # position: x = 0.0 nm to 20.0 nm
73        doping{                         # add doping to the region
74            linear{                     # linear doping concentration profile
75                name = "p-type"         # impurity name
76                conc = [0, 6.0e17]      # start and end value of doping concentration [cm-3]
77                x    = [0.0, 20.0]      # position: x=0.0 nm to x=20.0 nm
78            }
79        }
80    }
81}

We separated the structural set up in two sections: 1) material and 2) doping. In the doping section we use linear{} and gaussian1D{} to specify the doping profiles. For defining the Gaussian profile

\[C_{gaussian}(x)= C_{conc}\frac{1}{\sigma\sqrt{2\pi}} \cdot e^{-\frac{1}{2}(\frac{x- x_0}{\sigma})^2}\]

with the total doping concentration \(C_{conc}\), coordinate of the maximum \(x_0\) and standard deviation \(\sigma\), three parameters has to be specified. For defining the linear profile

\[C_{linear}(x) = \frac{ C_{end} - C_{start} }{ x_{end} - x_{start}} \cdot x + C_{start},\]

we specify start and end value of doping concentration \([y_{start}, y_{end}]\) with the corresponding x coordinates \([x_{start}, x_{end}]\), both as vectors.

Specify impurity species

84impurities{ # required if doping exists
85    acceptor{                   # select the species of dopants
86        name = "p-type"         # select doping regions with name = "p-type"
87        energy = 0.045          # ionization energy of dopants
88        degeneracy = 4          # degeneracy of dopants
89    }
90}

Output

We simulate the device by clicking F8 on the keyboard. In the related output folder you should find a plot of the concentration profile (\(\Rightarrow\) Structure \(\Rightarrow\) density_acceptor.dat) as shown in Figure 2.5.2.18.

../../../../../_images/output_3_3_1doping.png

Figure 2.5.2.18 shows the doping concentration of donors along x.

2. Using custom doping profiles

In this example we introduce custom defined doping profiles. For that we consider the set up in Figure 2.5.2.17 (right). The associated input file is basics_1D_doping_analytic.in

Defining custom functions

20import{ # this group is optional
21    analytic_function{                      # definition of analytic function
22        name = "custom_exp_fun_I"           # name of function
23        function = "1e18 *(1-exp(-x+20))"   # define the function
24    }
25    analytic_function{                      # definition of analytic function
26        name = "custom_exp_fun_II"          # name of fucntion
27        function = "1e18*exp(-x+30)"        # define the function
28    }
29}

In order to create custom doping profiles, we have to define analytical functions in the group import{} first. The analytical expression is given by a string. Later, we can incorporate these functions for adding doping by referring to the corresponding name.

Specifying regions with dopants

 63structure{ # this group is required in every input file
 64    output_impurities{ boxes = yes}                 # output doping concentration [10^18 cm-3]
 65
 66    #---------
 67    # material
 68    #---------
 69
 70    region{
 71        binary{ name = GaAs }                       # material: GaAs
 72        contact{ name = whatever }                  # contact definition
 73        everywhere{}                                # region spreads over the complete device
 74    }
 75
 76    region{
 77        binary{ name = InAs }                       # region: InAs
 78        line{ x = [ 20.0, 30.0 ] }                  # position: x=20.0 nm to x=30.0 nm
 79                                                    # overwrites the previously defined GaAs region
 80    }
 81
 82    #-------
 83    # doping
 84    #-------
 85
 86    region{                                         # region: adds doping
 87        line{ x = [ 20.0, 30.0 ] }                  # position: x=20.0 nm to x=30.0 nm
 88        doping{
 89            import{                                 # reference to import{} group, where custom functions are defined
 90                name = "n-type"                     # name of impurity
 91                import_from = "custom_exp_fun_I"    # import doping profile: custom_exp_fun_I
 92            }
 93        }
 94    }
 95
 96    region{                                         # region: adds doping
 97        line{ x = [ 30.0, 50.0 ] }                  # position: x=30.0 nm to x=50.0 nm
 98        doping{
 99            import{                                 # reference to import{} group, where custom functions are defined
100                name = "n-type"                     # name of impurity
101                import_from = "custom_exp_fun_II"   # import doping profile: custom_exp_fun_II
102            }
103        }
104    }
105}

Inside doping{}, the previously defined functions are used to create custom doping profiles. We import each function (import_from) from the group import{} by referring to the name that we had assigned. The function is then evaluated on the interval specified inside line{} yielding the final doping profile.

Besides the shape of the doping profile we also specify the name, as usually.

Specify impurity species

108impurities{ # required if doping exists
109    acceptor{                   # select the species of dopants
110        name = "p-type"         # select doping regions with name = "p-type"
111        energy = 0.045          # ionization energy of dopants
112        degeneracy = 4          # degeneracy of dopants
113    }
114}

Output

We simulate the device by clicking F8 on the keyboard. In the related output folder you should find a plot of the concentration profile (\(\Rightarrow\) Structure \(\Rightarrow\) density_donor.dat) as shown in Figure 2.5.2.19.

../../../../../_images/output_3_3_2doping.png

Figure 2.5.2.19 The doping concentration of donors along the x direction.

Important things to remember

  • before importing and using our own functions, we first have to define them in the import{} group

Last update: nn/nn/nnnn