Semiconductor Module

Semiconductor Module

For Detailed Analysis of Semiconductor Devices at the Fundamental Level


Transistor operation where an applied gate voltage turns the device on and then determines the drain saturation current.

Image made using the COMSOL Multiphysics® software and is provided courtesy of COMSOL.

Semiconductor Module


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.

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).


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Product Features

  • Solve the drift-diffusion equation using the finite volume method with a Scharfetter-Gummel upwinding scheme
  • Relaxation-time approximation used to describe the scattering process
  • Fermi-Dirac and Maxwell-Boltzmann statistics
  • Dedicated features for defining ohmic contacts, Schottky contacts, and gates at boundaries
  • Predefined mobility models for phonon, impurity, and carrier-carrier scatterings, high field velocity saturation, and surface scattering, or you can define your own mobility models
  • Features for Auger, Direct, and Shockley-Read Hall recombination rates, or you can specify your own
  • Specify constant, Gaussian, or your own doping profiles with analytical or interpolation functions
  • Specify discrete and continuous trap levels in the bulk or at insulating gates/surfaces
  • System-level and mixed-device simulations through SPICE circuits
  • Heterojunctions with continuous quasi-Fermi levels or thermionic emission
  • Impact ionization
  • Incomplete ionization
  • Heat transfer effects
  • Direct and indirect optical transitions

Application Areas

  • Bipolar transistors
  • Metal-semiconductor field-effect transistors (MESFETs)
  • Metal-oxide-semiconductor field-effect transistors (MOSFETs)
  • Insulated-gate bipolar transistors (IGBTs)
  • Schottky diodes
  • P-N junctions
  • Solar cells
  • Light-emitting diodes (LEDs)
  • Photodiodes

Models

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 photovoltaic effect is not modeled in detail. Instead, for simplicity, an arbitrary user-defined expression is used for the generation rate. In addition, the Shockley-Read-Hall model is employed to capture the main recombination effect. Under normal operating conditions, photo-generated carriers are swept to each side of the depletion region of the p-n junction. A small forward bias voltage is applied to extract the electrical power, given by the product of the photocurrent and the applied voltage.

» See model.

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 normalized output characteristics of the solar cell with design parameters specified by the user.

The normalized output characteristics are multiplied by the computed average illumination to obtain the output characteristics of the cell at the specified date and location, assuming a simple linear relationship between the output and illumination. The user can then calculate the solar cell’s efficiency and the amount of electricity generation over the course of the day.

The underlying model consists of a 1D silicon PN junction with carrier generation and Shockley-Reed-Hall recombination. The grounded anode is modeled as a thin ohmic contact deposited on an emitter (n-doped region). Similarly, the cathode is modeled as an ideal ohmic contact deposited on the base side (p-doped region) and connected to an external circuit.

» See model.

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.

» See model.

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 breakdown region is entered, where the current increases exponentially for a small increase in the applied voltage. This is due to impact ionization.

This model shows how to use the time dependent solver to model impact ionization in a MOSFET.

» See model.

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 identified from these plots.

» See model.

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 sinusoidal source, a resistor and a ground to form a basic half-wave rectifier circuit. In order to validate the simulation results, the output of the device simulation is compared with the circuit response obtained using a large signal diode model.

» See 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.

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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. The energy levels obtained with the model are then compared between each configuration in order to emphasize the origin of the current transfers, that is, whether it is primarily from holes in the valence band or from electrons in the conduction band. The J-V curves (current density vs. applied voltage) obtained from each simulation are compared with results obtained from the specialized literature.

» See model.

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 an ISFET pH sensor illustrates the procedure to set up the coupling between the semiconductor model and the electrolyte model. It also shows the technique of using a simple global equation to extract operating parameters, without the need to explicitly model the actual feedback circuitry.

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This application computes the emission properties of a AlGaN/InGaN LED. The emission intensity, spectrum, and efficiency are calculated for an applied voltage or as a function of voltage over a selected range. The indium composition in the light-emitting InGaN region can be varied in order to control the emission wavelength. When the emission occurs within the visible spectrum the corresponding color is displayed.

The Semiconductor Module is used to compute the carrier dynamics throughout the device and the corresponding electroluminescence.

» See model.