Analytic Doping Model
Use the Analytic Doping Model to set the doping type and concentration within a Semiconductor Material Model domain. The concentration is defined as a function of the local coordinate system, making this doping method suitable for profiles that are convenient to express in terms of the coordinate axes.
The configuration of doping is critical in semiconductor modeling. You can visualize doping profiles by clicking the preview buttons before solving the model. Two buttons named as Plot Doping Profile for Selected and Plot Net Doping Profile for All are available both in the toolbar and the context menu. The doping profile will be shown in a separate plot window named as Doping Profile Plot. Note that p-type and n-type domains are shown in red and blue color, respectively.
Continuation Settings
In some cases it is desirable to increase the doping from zero or a low value to that required in the simulation during the solution process. This can improve the convergence of the simulation significantly. The continuity settings allow the dopant densities to be weighted by an external parameter, whose value should be between 0 and 1.
By default the Continuation type is set to Use interface continuation parameter. This means that the continuity settings are determined by the Doping and trap density continuation in the Continuation Settings section for The Semiconductor Interface.
To introduce the doping from a specific feature independently of the other features, select User defined and manually enter the Continuation parameter. This should be set to a dimensionless parameter that is swept from zero to 1 using the continuation solver.
Distribution
Choose the type of dopant distribution to apply on the selected domains from the Distribution list: User defined (the default) to enable any expression to be used to define the dopant distribution, or Box to create a block-shaped region of uniform doping away from which the concentration decays to a background level according to a specified profile. The Profile of the distribution away from the uniform region is selected from a list of preset functions.
Impurity
Choose an Impurity type to set the species of the dopants — Acceptor doping (p-type) (the default) or Donor doping (n-type). Once the impurity type is selected, enter a value or expression for the Acceptor concentration NA0 or Donor concentration ND0 (SI unit: 1/m3).
For a User defined Distribution input, you can use any expression in terms of the coordinate system. This expression then defines the dopant concentration through the selected domains (if a constant value is entered this simply assigns a uniform concentration to all selected domains). For a Box distribution, a constant value must be entered and this sets the concentration within the region of uniform doping. The default value for both distributions is a constant value of 1·1016 cm3.
Uniform Region
This section is available when Box is selected under Distribution. It is used to define the location and size of the region of uniform doping.
Set the position of the region using the Base list. Select Corner (the default) or Center.
The Base position r0 (SI unit: m) vector sets the location of the region. When Corner is selected it describes the coordinate of the lower left front corner of the region, and when Center is selected it describes the coordinate of the center of the region. The default value is at the origin of the coordinate system.
The extent of the region is defined with the Width, Depth, and Height inputs. Only the inputs relevant to the dimension of the component to which the feature belongs are displayed, for example, in a 2D component only the Width and Depth are available.
Width W (SI unit: m). This is the extent of the region in the direction parallel to the local x-axes.
Depth D (SI unit: m). This is the extent of the region in the direction parallel to the local y-axes.
Height H (SI unit: m). This is the extent of the region in the direction parallel to the local z-axes.
The default value is 0 for each dimension.
Profile
This section is available when Box is selected under Distribution. Select a Profile away from uniform regionGaussian (the default), Linear, or Error function (erf).
Then select an option from the Specify profile length scale list — Junction depth (available for all profiles), Decay length (available for a Gaussian), Gradient (available for Linear), or Argument factor (available for Error function (erf)).
By default, the Specify different length scales for each direction check box is not selected. It is possible to specify a different profile length scale in each coordinate direction when this check box is selected.
Junction Depth
For Junction depth enter a value for the Junction depth dj (SI unit: m, default value is 1 μm) to specify the location at which the profile concentration drops to equal the Background doping concentration Nb (SI unit: 1/m3). The default background concentration is User defined with a doping concentration of 1·1015 1/cm3. Alternately, the doping distribution from another Analytic Doping Model or Geometric Doping Model can be used as the background concentration.
Each profile has a profile-specific parameter to directly control the length scale of the decay.
Decay Length — for Gaussian profile
For Decay length enter a value for the Decay length lj of the Gaussian decay. (SI unit: m, default value is 1 μm).
Gradient — for Linear profile
For Gradient enter a value for the Gradient Ngrad of the Linear profile (SI unit: 1/m4, default value is 1·1020 1/cm4).
Argument Factor — for Error function (erf) profile
For Argument factor enter a value for the Argument factor m (SI unit: 1/m, default value is 1 (1/μm)) to specify the factor by which the coordinate values are multiplied before being operated on by the erf function.
As when the Junction depth option is used, by default the Specify different length scales for each direction check box is not selected. Select it to specify a different profile length scale in each coordinate direction.