For Detailed Analysis of Semiconductor Devices at the Fundamental Level
Semiconductor and Optoelectronic Device Physics Simulation
The Semiconductor Module provides dedicated tools for the analysis of semiconductor device operation at the fundamental physics level. The module is based on the drift-diffusion equations, using isothermal or nonisothermal transport models. It is useful for simulating a range of practical devices, including bipolar transistors, metal-semiconductor field-effect transistors (MESFETs), metal-oxide-semiconductor field-effect transistors (MOSFETs), insulated-gate bipolar transistors (IGBTs), Schottky diodes, and P-N junctions. A predefined Schrödinger Equation interface allows the modeling of quantum-confined systems such as quantum wells, wires, and dots.
Multiphysics effects often play important roles in semiconductor device performance. The Semiconductor Module enables you to easily create models involving multiple physical effects. For example, thermal effects within a power device can be simulated by adding a heat transfer physics interface (available in the COMSOL Multiphysics® software platform). Optical transitions can also be incorporated to simulate a range of devices such as solar cells, light-emitting diodes (LEDs), and photodiodes (some may require the Wave Optics Module).
- The DC characteristic of a MOS transistor demonstrating transistor operation where an applied gate voltage turns the device on and then determines the drain saturation current.
Make Use of Finite Element or Finite Volume Discretization
You can choose to make use of the finite element or finite volume method when modeling the transport of holes and electrons in the Semiconductor Module. Each method has its set of advantages and disadvantages:
Finite Volume Discretization: Finite volume discretization in the modeling of semiconductor devices inherently conserves current. As a result, it provides the most accurate result for the current density of the charge carriers. The Semiconductor Module uses a Scharfetter-Gummel upwinding scheme for the charge carrier equations. It produces a solution that is constant within each mesh element, so that fluxes can only be constructed on the mesh faces that are adjacent to two mesh elements. Yet, as products in the COMSOL Product Suite are based on the finite element method, this can make it a bit more challenging to set up multiphysics models.
Finite Element Discretization: The finite element method is an energy-conserving method. Consequently, current conservation is not implicit in the technique. To obtain accurate currents, it may be necessary to tighten the default solver tolerances or to refine your mesh. In order to help with numerical stability, a Galerkin least squares stabilization method is included when solving the physics in semiconductor devices. One advantage of modeling semiconductor devices with the finite element method is that you can more easily couple your model to other physics, such as heat transfer or solid mechanics, in a single model.
You Can Model All Types of Semiconductors
The Semiconductor Module is used for modeling semiconductor devices with length scales of 100’s of nm or more, which can still be modeled by a conventional drift-diffusion approach using partial differential equations. Within the product, there is a number of physics interfaces – tools for receiving model inputs to describe a set of physical equations and boundary conditions. These include interfaces for modeling the transport of electrons and holes in semiconductor devices, the electrostatic behavior of such, and an interface for coupling semiconductor simulations to a SPICE circuit simulation.
The Semiconductor interface solves Poisson’s equation in conjunction with the continuity equations for the charge carriers. It solves for both the electron and hole concentrations explicitly. You can choose between solving your model with the finite volume method or the finite element method. The Semiconductor interface includes material models for semiconducting and insulating materials, in addition to boundary conditions for ohmic contacts, Schottky contacts, gates, and a wide range of electrostatics boundary conditions.
Features within the Semiconductor interface describe the mobility property as it is limited by the scattering of carriers within the material. The Semiconductor Module includes several predefined mobility models and the option to create custom, user-defined mobility models. Both these types of models can be combined in arbitrary ways. Each mobility model defines an output electron and hole mobility. The output mobility can be used as an input to other mobility models, while equations can be used to combine mobilities, for example using Matthiessen's rule. The Semiconductor interface also contains features to add Auger, Direct, and Shockley-Read Hall recombination to a semiconducting domain, or you can specify your own recombination rate.
Specifying the doping distribution is critical for the modeling of semiconductor devices. The Semiconductor Module provides a Doping model feature to do this. Constant and user-defined doping profiles can be specified, or an approximate Gaussian doping profile can be used. It is also straightforward to import data from external sources into COMSOL Multiphysics®, which can be treated by built-in interpolation functions.
Along with the Semiconductor interface, the Semiconductor Module comes prepared with enhanced Electrostatics capabilities, available both within the Semiconductor interface and in a standalone Electrostatics interface. System level and mixed device simulations are enabled through a physics interface for electrical circuits with SPICE import capability. When combined with the Wave Optics Module or the RF Module, additional physics interfaces are made available for Optoelectronics simulations. The Semiconductor Module includes an additional material database with properties for several materials. Each model comes with documentation that includes a theoretical background and step-by-step instructions on how to create the model. The models are available in COMSOL as MPH-files that you can open for further investigation. You can use the step-by-step instructions and the actual models as a template for your own modeling and applications.
Si Solar Cell 1D
This tutorial model uses a simple 1D model of a silicon solar cell to illustrate the basic steps to set up and perform a semiconductor simulation with the Semiconductor Module. A user-defined expression is used for the photo-generation rate and the result shows typical I-V and P-V curves of solar cells. The carrier generation mechanism from the ...
Breakdown in a MOSFET
MOSFETs typically operate in three regimes depending on the drain-source voltage for a given gate voltage. Initially the current-voltage relation is linear, this is the Ohmic region. As the drain-source voltage increases the extracted current begins to saturate, this is the saturation region. As the drain-source voltage is further increased the ...
Si Solar Cell with Ray Optics
The Si Solar Cell with Ray Optics app combines the Ray Optics Module and the Semiconductor Module to illustrate the operation of a silicon solar cell for a specific date and location. The Ray Optics Module computes the average illumination for a date and location that are chosen by the app's user. Then, the Semiconductor Module computes the ...
This model shows how to set up a simple Bipolar Transistor model. The output current-voltage characteristics in the common-emitter configuration are computed and the common-emitter current gain is determined.
DC Characteristics of a MOS Transistor (MOSFET)
This model calculates the DC characteristics of a simple MOSFET. The drain current versus gate voltage characteristics are first computed in order to determine the threshold voltage for the device. Then the drain current vs drain voltage characteristics are computed for several gate voltages. The linear and saturation regions for the device can ...
This model extracts spice parameters for a silicon p-n junction diode. The spice parameters are used to create a lumped-element equivalent circuit model of a half-wave rectifier that is compared to a full device level simulation. In this example, a device model is made by connecting a 2D meshed p-n junction diode to a circuit containing a ...
This simple benchmark model computes the potential and carrier concentrations for a one-dimensional p-n junction using both the finite element and finite volume methods. The results are compared with an equivalent device from the book, "Semiconductor Devices: A Simulation Approach," by Kramer and Hitchon.
This one-dimensional model simulates three different heterojunction configurations under forward and reverse bias. The model shows the difference in using the continuous quasi-Fermi levels model as opposed to the thermionic emission model to determine the current transfer occurring between the different materials creating the junction under bias. ...
Simulation of an Ion-sensitive Field-effect Transistor (ISFET)
An ion-sensitive field-effect transistor (ISFET) is constructed by replacing the gate contact of a MOSFET with an electrolyte of interest. The concentration of a specific ionic species in the electrolyte can be determined by measuring the change in the gate voltage due to the interaction between the ions and the gate dielectric. This tutorial of ...
With an increase in the parallel component of the applied field, carriers can gain energies above the ambient thermal energy and be able to transfer energy gained by the field to the lattice by optical phonon emission. The latter effect leads to a saturation of the carriers mobility. The Caughey Thomas mobility model adds high field velocity ...