Defining the Carrier Mobility
Realistic models for the carrier mobility are important to simulate semiconductor devices with a drift diffusion approach. The mobility is limited by scattering of the carriers within the material. Phenomena that can affect the mobility include:
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Phonons (L): thermally generated acoustic waves traveling through the crystal (scattering by phonons is frequently referred to as lattice scattering, which is somewhat confusing as the lattice itself never scatters the carriers unless perturbed from perfect periodicity).
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Ionized impurities (I): these begin to have an effect at doping levels above approximately 1015 cm−3 at room temperature.
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Carrier-carrier scattering (C)
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Neutral impurity scattering (N): this is important only at low temperatures, typically below 77 K.
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High field velocity saturation (E).
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Surface scattering (S): this includes effects such as interface charges, scattering by surface phonons, and so on. It is important in field effect devices, such as field effect transistors.
The Semiconductor Module includes several predefined mobility models, as well as user-defined models. These models are added as subnodes to the Semiconductor Material Model node.
The letters in the above list (for example, L for phonons) are used to identify which effects a given predefined mobility model incorporates and appears in the name of the feature.
Both user-defined and predefined mobility models can be combined in arbitrary ways. Each mobility model defines an output electron and hole mobility. If appropriate (some filtering occurs in the predefined mobility models to prevent inappropriate combinations), the output mobility can be used as an input to other mobility models. User-defined mobility models accept any of the predefined mobility models as inputs and can be used as inputs for all the predefined mobility models that require an input. The model used within the simulation is selected for electrons and holes by changing the Electron mobility and the Hole mobility settings in the Mobility Model section of the Semiconductor Material Model node, which by default uses a constant mobility obtained from the material properties.
It is important to understand that each type of mobility model subnode only defines mobility variables for electrons and holes that can be used by other models, or by the Semiconductor Material Model parent node. The mobility models for electrons and holes actually used in the simulation are determined by the selections or settings in the Semiconductor Material Model node (the parent node), which do not change when additional mobility model subnodes are added. In order to add a mobility model to a simulation, it is necessary to both add the sequence of mobility model subnodes to the Model Builder, and then to select the required final mobility for the electrons and holes in the Semiconductor Material Model parent node.
In order to implement field dependent mobility models it is usually necessary to add additional dependent variables for the field components used in the model (typically the electric field components parallel to or perpendicular to the current components). This is the approach taken in the Caughey-Thomas Mobility Model (E) and Lombardi Surface Mobility Model (S).
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Mobility Models
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User-Defined Mobility Model
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Power Law Mobility Model (L)
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Arora Mobility Model (LI)
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Fletcher Mobility Model (C)