The Semiconductor Module Physics Interface Guide
Each COMSOL Multiphysics physics interface (for example, the Semiconductor interface or the Schrödinger Equation interface) expresses the relevant physical phenomena in the form of sets of partial or ordinary differential equations, together with appropriate boundary and initial conditions. Each feature added to the physics interface represents a term or condition in the underlying equation set. These features are usually associated with a geometric entity within the model, such as a domain, boundary, edge, or point. 
Figure 5 uses a model similar to the MOSFET application library example to show the Model Builder tree structure, and the Settings window for the selected Semiconductor Material Model 1 feature node. This node adds the semiconductor equations to the simulation within the domains selected. In the Model Inputs section the temperature of the material is specified. It is straightforward to link this temperature to a separate Heat Transfer interface to solve nonisothermal problems — the Semiconductor interface automatically defines an appropriate heat source term that can be readily accessed in a Heat Transfer interface. In the Material Properties section, the Settings window indicates that the relative permittivity and the band gap are inherited from the material properties assigned to the domain. The material properties can be set up as functions of other dependent variables in the model, for example, the temperature. The dopant density is specified by means of multiple additive doping features, which can be used to combine Gaussian and user-defined dopant density profiles to produce the desired profile. Several boundary conditions are also indicated in the model tree. The Ohmic Contact boundary condition is commonly used to model nonrectifying interconnects. The Thin Insulating Gate feature models a gate with a thickness smaller than the typical length scale of the mesh. It is also possible to model gates explicitly, solving Poisson’s equation within the dielectric.
Figure 5: The Model Builder (to the left), and the Settings window for Semiconductor Material Model1 for the selected feature node (to the right). The Equation section in the Settings window shows the model equations.
The Semiconductor interface is the starting point for most simulations. The Semiconductor Module also includes physics interfaces to enable modeling of different physical situations encountered in device design. When a new model is started, these physics interfaces are selected from the Model Wizard.
Figure 6 shows the physics interfaces included with the Semiconductor Module. The two Semiconductor Optoelectronics interfaces are only available with an additional Wave Optics module license.
Figure 6: The Semiconductor Module interfaces as displayed in the Model Wizard for a 3D model. The Semiconductor Optoelectronics interfaces are only available with an additional Wave Optics Module license.
Also see Physics Interface Guide by Space Dimension and Study Type. Below, a brief overview of each of the Semiconductor Module physics interfaces is given.
Electrostatics
The Electrostatics interface (), found under the AC/DC branch in the Model Wizard, solves for the electric potential given the charge distribution in the domain and the voltages applied to boundaries. It is used to model electrostatic devices under static or quasistatic conditions, that is at frequencies sufficiently low that wave propagation effects can be neglected. Many of the features of the Electrostatics interface are included in the Semiconductor interface, where they affect the solution of the electric potential.
Electrical Circuit
The Electrical Circuit interface (), found under the AC/DC branch in the Model Wizard, has the equations to model electrical circuits with or without connections to a distributed fields model. The interface solves for the voltages, currents, and charges associated with the circuit elements. Circuit models can contain passive elements like resistors, capacitors, and inductors as well as active elements such as diodes and transistors. Circuits can be imported from an existing SPICE net list. A typical application of this interface would be to consider the effect of series or parallel lumped components on device behavior.
Transport of Charge Carriers
The Transport of Charge Carriers interface () is used to solve the number density of one or multiple charge carriers. The charge carriers can be charged species such as electrons, ions, and neutral species like molecules and their excited states. Transport and reactions of charge carriers can be handled with this interface. The driving forces for transport can be drift when coupled to an electromagnetic field, convection when coupled to a flow field, and diffusion.
Semiconductor
The Semiconductor interface (), found under the Semiconductor branch in the Model Wizard, solves the drift–diffusion and Poisson’s equations. The physics interface allows both insulating and semiconducting domains to be modeled. The equations account fully for thermal effects, and the interface can be coupled to a heat transfer interface using the temperature model input and the predefined heat source term. This physics interface is appropriate for modeling semiconductor devices.
Semiconductor Optoelectronics, Beam Envelopes
The Semiconductor Optoelectronics, Beam Envelopes () multiphysics interface combines the Semiconductor interface with the Electromagnetic Waves, Beam Envelopes interface. The coupling occurs through the Optical Transitions feature, which adds a stimulated emission generation term (appropriate for direct band-gap materials) on domains in the Semiconductor interface. This term is proportional to the optical intensity in the corresponding Wave Equation, Beam Envelopes feature in the Electromagnetic Waves, Beam Envelopes interface. Additionally spontaneous emission (for direct band-gap materials) can be accounted for. The effect of the light adsorption or emission is accounted for by a corresponding change in the complex permittivity or refractive index in the Wave Equation, Beam Envelopes feature.
This multiphysics interface can be used for modeling devices such as photodiodes, light emitting diodes and laser diodes without quantum wells in direct band gap materials.
Semiconductor Optoelectronics, Frequency Domain
The Semiconductor Optoelectronics, Frequency Domain () multiphysics interface combines the Semiconductor interface with the Electromagnetic Waves, Frequency Domain interface. The coupling occurs through the Optical Transitions feature, which adds a stimulated emission generation term (appropriate for direct band-gap materials) on domains in the Semiconductor interface. This term is proportional to the optical intensity in the corresponding Wave Equation, Electric feature in the Electromagnetic Waves, Frequency Domain interface. Additionally spontaneous emission (for direct band-gap materials) is accounted for. The effect of the light adsorption or emission is accounted for by a corresponding change in the complex permittivity or refractive index in the Wave Equation, Electric feature.
This multiphysics interface can be used for modeling devices such as photodiodes, light emitting diodes and laser diodes without quantum wells in direct band gap materials.
Schrödinger Equation
The Schrödinger Equation interface (), found under the Semiconductor branch in the Model Wizard, solves the Schrödinger equation for a single particle in an external potential. This physics interface is useful for general quantum mechanical problems as well as for quantum confined systems such as quantum wells, wires, and dots (with the envelope function approximation).
Schrödinger–Poisson Equation
The Schrödinger–Poisson Equation multiphysics interface () combines the Schrödinger Equation interface with the Electrostatics interface to model charge carriers in quantum-confined systems. The electric potential from the Electrostatics contributes to the potential energy term in the Schrödinger Equation. A statistically weighted sum of the probability densities from the eigenstates of the Schrödinger Equation contributes to the space charge density in the Electrostatics. A dedicated Schrödinger–Poisson Study Type is available to automatically generate the solver sequence iterations for the self-consistent solution of the bidirectionally coupled system.
This multiphysics interface can be used for modeling quantum confined devices such as quantum wells, wires, and dots.
Physics Interface Guide by Space Dimension and Study Type
The table below lists the physics interfaces available specifically with this module in addition to the COMSOL Multiphysics basic license.
AC/DC
stationary; frequency domain; time dependent; frequency domain; eigenfrequency
stationary; time dependent; stationary source sweep; eigenfrequency; frequency domain; small signal analysis, frequency domain
Electric Discharge
Semiconductor
1 This physics interface is included with the core COMSOL package but has added functionality for this module.
2 Requires both the Wave Optics Module and the Semiconductor Module.