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 coupled to 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). 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).
Currently COMSOL implements a simplified heat source term incorporating only Joule heating and the heat source due to recombination (see Ref. 26 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 recombination rate computed from summing all the recombination mechanisms. U is computed from the mean of the total 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).
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 nonisothermal semiconductor models, a segregated solver should be used, with the temperature degree of freedom included in a separate segregated group from the carrier densities and the potential.
To add a segregated solver, click the study and from the Study toolbar, click Show Default Solver () (this is not necessary if the Solver Configurations node is already visible in the Model Builder). Expand the Solver Configurations node until you can see either the Stationary Solver 1 or the Time-Dependent Solver 1 node (depending on whether the study is stationary or time-dependent). Right-click the node and select Segregated. Expand the resulting Segregated 1 node and select the Segregated Step node. Then in the General settings section, delete the Temperature (mod1.T) variable from the list. Right-click the Segregated 1 node and add a Segregated Step. In the Settings window for Segregated Step 1, add Temperature (mod1.T) to the list.
The node numbers given above can be altered if multiple studies or study steps are present in the model.
In the COMSOL Multiphysics Reference Manual:
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Introduction to Solvers and Studies
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Segregated and Segregated Step