COMSOL 6.2 - Analytic Doping Model

Use the 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

and

are available both in the toolbar and the context menu. The doping profile will be shown in a separate plot window named as

. Note that p-type and n-type domains are shown in red and blue color, respectively.

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.

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By default the is set to . This means that the continuity settings are determined by the in the Continuation Settings section for The Semiconductor Interface.

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To introduce the doping from a specific feature independently of the other features, select and manually enter the . This should be set to a dimensionless parameter that is swept from zero to 1 using the continuation solver.

	For the finite volume method it is recommended that a zero value of the parameter is avoided. Instead, start with a small value (for example, 1e-6) and increase the value of the parameter gradually to 1. The continuation solver usually does not manage the transition from zero to finite doping when the finite volume method is used.

	Solving

Choose the type of dopant distribution to apply on the selected domains from the list: (the default) to enable any expression to be used to define the dopant distribution, or 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.

Choose an to set the species of the dopants — (the default) or . Once the impurity type is selected, enter a value or expression for the NA0 or ND0 (SI unit: 1/m3).

For a 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 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.

This section is available when is selected under . It is used to define the location and size of the region of uniform doping.

Set the position of the region using the list. Select (the default) or .

The r0 (SI unit: m) vector sets the location of the region. When is selected it describes the coordinate of the lower left front corner of the region, and when is selected it describes the coordinate of the center of the region. The default value is at the origin of the coordinate system.

	It is possible to set the height, width, or depth of the region to zero. In 2D, for example, setting the height of the region to zero results in a line of constant doping away from which the profile function decays.

The extent of the region is defined with the , , and 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 and are available.

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W (SI unit: m). This is the extent of the region in the direction parallel to the local x-axes.

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D (SI unit: m). This is the extent of the region in the direction parallel to the local y-axes.

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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.

This section is available when is selected under . Select a — (the default), , or .

Then select an option from the list — (available for all profiles), (available for a Gaussian), (available for ), or (available for ).

By default, the 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.

For enter a value for the dj (SI unit: m, default value is 1 μm) to specify the location at which the profile concentration drops to equal the Nb (SI unit: 1/m3). The default background concentration is 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.

For enter a value for the lj of the Gaussian decay. (SI unit: m, default value is 1 μm).

For enter a value for the Ngrad of the Linear profile (SI unit: 1/m4, default value is −1·1020 1/cm4).

For enter a value for the 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 function.

As when the option is used, by default the check box is not selected. Select it to specify a different profile length scale in each coordinate direction.