For Detailed Analysis of Semiconductor Devices at the Fundamental Level
MOSFETs, MESFETs, and Schottky Diodes
The Semiconductor Module allows for detailed 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, metal semiconductor field-effect transistors (MESFETs), metal-oxide-semiconductor field-effect transistors (MOSFETs), Schottky diodes, thyristors, and P-N junctions.
Multiphysics effects can often have important influences on semiconductor device performance. Semiconductor processing frequently occurs at high temperatures and, consequently, stresses can be introduced into the materials. Furthermore, high-power devices can generate a significant amount of heat. The Semiconductor Module enables semiconductor device-level modeling on the COMSOL platform, allowing you to easily create customized simulations involving multiple physical effects. Moreover, the software is uniquely transparent, as you are always able to manipulate the model equations, leaving you with complete freedom in the definition of phenomena that are not predefined in the 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. 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.
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 ...
Caughey-Thomas Mobility in a Semiconductor
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 ...
P-N Junction Diode with External Circuit
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 ...
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 be ...
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.
P-N Junction Benchmark Model
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.
Lombardi Surface Mobility in a Semiconductor
Surface acoustic phonons and surface roughness have an important effect on the carrier mobility, especially in the thin inversion layer under the gate in MOSFETs. The Lombardi surface mobility model adds surface scattering resulting from these effects to an existing mobility model using Matthiessen’s rule. This model demonstrates how to use the ...
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. ...
DC Characteristics of a MESFET
In a MESFET, the gate forms a rectifying junction that controls the opening of the channel by varying the depletion width of the junction. In this model we simulate the response of a n-doped GaAs MESFET to different drain and gate voltages. For a n-doped material the electron concentration is expected to be orders of magnitude larger than the ...