Lombardi Surface Mobility Model (S)
The Lombardi Surface Mobility Model (S) subnode is available from the context menu (right-click the Semiconductor Material Model parent node) or from the Physics toolbar, Attributes menu. It changes an input mobility to account for surface effects, particularly surface roughness and scattering due to acoustic phonons. The ‘S’ in brackets indicates that the model includes surface effects only. The mobility model accepts input mobilities of type L, LI, or C as well as user-defined input mobilities.
The set of equations defining the Lombardi Surface mobility model is shown in the Equation section.
Domain Selection
Usually the mobility model domain selection should not be changed from that of the parent Semiconductor Material Model.
Continuation Settings
These settings are the same as for Fletcher Mobility Model (C).
The Semiconductor interface automatically creates a suggested solver sequence for better convergence upon detection of the Lombardi Surface mobility model.
Solving
Lombardi Surface Mobility shows how to use the continuity solver and how to inspect the autogenerated solver sequence when using this mobility model. Application Library path: Semiconductor_Module/Transistors/lombardi_surface_mobility
Input Mobilities
The Electron input mobility μn,in (SI unit: m2/(V⋅s)) parameter is used to define an input mobility. The default is User defined for silicon at equilibrium, 1448 cm2/(V⋅s).
The Hole input mobility μp,in (SI unit: m2/(V⋅s)) defines an input mobility. The default is User defined for silicon at equilibrium 473 cm2/(V⋅s).
Other mobility models of type L (Power Law Mobility Model (L)), LI (Arora Mobility Model (LI), C Fletcher Mobility Model (C), or User-Defined Mobility Model input mobilities can be used as the Electron input mobility and Hole input mobility.
General Parameters
The default for each of the following is taken From material. For User defined enter a different value or expression in the text field.
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Reference temperature Tref (SI unit: K). The default is 1 K.
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Electric field reference Eref (SI unit: V/m). The default is 1 V/cm.
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Doping concentration reference Nref (SI unit: 1/m3). The default is 1 1/cm3.
Electron Parameters
The default for each of the following is taken From material. For User defined enter a different value or expression in the text field.
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Electron delta coefficient δn(SI unit: V/s). The default is 5.82·1014 V/s.
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Electron mobility reference μn,1(SI unit: m2/(V⋅s)). The default is 4.75·107 cm2/(V⋅s).
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Electron mobility reference μn,2(SI unit: m2/(V⋅s)). The default is 1.74·105 cm2/(V⋅s).
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Electron alpha coefficient αn(SI unit: 1). The default is 0.125.
Hole Parameters
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Hole delta coefficient δp (SI unit: V/s). The default is 2.05·1014 V/s.
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Hole mobility reference μp,1(SI unit: m2/(V⋅s)). The default is 9.93·107 cm2/(V⋅s)
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Hole mobility reference μp,2(SI unit: m2/(V⋅s)). The default is 8.84·105 cm2/(V⋅s)
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Hole alpha coefficient αp(SI unit: 1). The default is 0.0317.
Advanced
To display this section, click the Show More Options button () and select Advanced Physics Options. Enter a Current density activation threshold Jtol (SI unit: A/m2). The default is 1·106 A/m2.
Mobility Models and Theory for the Lombardi Surface Mobility Model (S)