Nonisothermal Models
The Semiconductor interface is designed to model nonisothermal devices. In order to model heat transfer in the device, an additional Heat Transfer in Solids interface should be added to the model. This physics interface can be used to model the heat transfer within the domain. Appropriate thermal boundary conditions must be added in addition to a heat source term that is supplied by the Semiconductor interface.
To add the heat source term, from the Physics toolbar, Domain menu, select Heat Source. Then click the Heat Source 1 node and select Total heat source (semi) from the list of coupling variables in the General source Q list (note that if several heat sources or Semiconductor interfaces are added then the name of the heat source feature and the semiconductor heat source coupling variable is incremented accordingly). This creates a unidirectionally coupled model (from Semiconductor to Heat Transfer).
To couple the temperature computed by a Heat Transfer interface back into the Semiconductor interface, go to the Model Inputs section of the Semiconductor Material Model 1 node. Under Temperature, T, select Temperature (ht). This creates a bidirectionally coupled, or fully coupled, model, which is best solved using the solution of the unidirectionally coupled model as the initial condition.
Currently COMSOL implements a simplified heat source term incorporating only Joule heating and the heat source due to recombination (see Ref. 28 for a detailed discussion of the appropriate heat source term to be used in semiconductor modeling). The heat source term Q is given by:
where U is the total nonradiative recombination rate computed from summing all the recombination mechanisms except the rates from the Optical Transitions and Indirect Optical Transitions features. U is computed from the mean of the total nonradiative electron and hole recombination rates U = (Un+Up)/2, which are almost always equal except in advanced models.
Additional terms can be added to the heat source manually in the finite element method (the existing terms are available as the variable semi.Q_tot).
The discussion above considers bulk heat sources (for uniform non-graded material). For heterojunctions, the boundary heat source is available as the variable semi.Q_int_tot.
It is not straightforward to add these terms for the finite volume method, as they involve the derivatives of the dependent variables, which must be computed using appropriate expressions.
Some of the boundary conditions for the Semiconductor interface require an equilibrium reference temperature to be defined in order to correctly define the potentials with respect to the equilibrium Fermi energy.
To change this reference temperature, click the Show More Options button () and select Advanced Physics Options. Then adjust the Temperature reference for energy levels (T0) setting in the Temperature Reference section of the Semiconductor interface Settings window. The reference temperature should be within the range of validity of any temperature-dependent material properties used in the model.
When solving a fully coupled nonisothermal semiconductor model, first solve the corresponding unidirectionally coupled model. Then use its solution as the initial condition of the bidirectionally coupled study.
See the model Thermal Analysis of a Bipolar Transistor: Application Library path Semiconductor_Module/Transistors/bipolar_transistor_thermal for an example of a fully coupled nonisothermal system. The example is also available in the Application Gallery at www.comsol.com/model/thermal-analysis-of-a-bipolar-transistor-19701
In the COMSOL Multiphysics Reference Manual:
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Introduction to Solvers and Studies
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Segregated and Segregated Step