The multi-quantum well (MQW) solver is a 1D physics-based solver for calculating optical and electronic properties of multi-quantum well stacks. The solver returns the gain and spontaneous emission coefficients, as well as the electronic band diagram, band structure, and wavefunctions. The results from the MQW solver are often used as inputs for the TWLM element in INTERCONNECT to model edge-emitting semiconductor lasers or electro-absorption modulators.

The MQW solver simulation object in the finite-element integrated design environment (FE IDE) provides a graphic user interface (GUI) for running the MQW simulations. A set of script-based functions (buildmqwmaterial, mqwgain, mqwindex) can also be used to run the MQW solver.

## Inputs

The MQW solver requires the following information about the MQW structure:

- Thickness of each layer in the quantum well stack
- Properties of each material in the stack:
- k · p properties
- band gap
- electron/hole effective mass
- work function

- Effective refractive index of the MQW structure
- Linewidth broadening factor of the gain material

The MQW solver uses the following parameters:

- Carrier density
- Bias electric field
- Temperature

## Outputs

The MQW solver returns the following results:

- Gain and spontaneous emission coefficients
- Complex refractive index of the MQW
- Electronic band diagrams, bandstructures, and wavefunctions
- Exciton energies and wavefunctions (if exciton model is activated)

## MQW Solver Physics

The MQW solver calculates the electronic band structure from the Schroedinger equation based on the 4x4 k⋅p method. The gain and spontaneous emission coefficients are then calculated from the carrier density, electronic band structure and wave functions. Excitons, strain and temperature effects can be included. As a 1D solver, the MQW solver assumes the stack is infinite in the transverse directions. A constant carrier density is assumed along each partition of the stack. For a full description of the MQW solver physics, please see MQW Solver Physics.

## Supported Materials

The method is mainly suitable for III-V materials with a zincblende crystal structure. For a list of supported materials in the default database, please see Material Database in Finite Element IDE.

## Workflow

The MQW solver can be added to the Finite Element IDE with the **MQW** button in the toolbar of the **Design** tab of the Finite Element IDE. The MQW solver GUI can be accessed by right-clicking on the MQW object in the **Objects Tree** and selecting **Edit object** to open the **Edit MQW Gain Solver** window.

The general workflow for using the MQW solver GUI is as follows:

- Create materials for the MQW stack layers
- Set the layers and partitions
- Set the layer strain
- Activate exciton model for electro-absorption modulator simulations (Optional)
- Set the physical parameters, including:
- Temperature
- Carrier density
- Bias electric field
- Effective index
- Linewidth broadening
- Valence band offset

- Set the simulation parameters, including:
- Frequency range and number of points
- Mesh size
- Transverse wave vector range
- Maximum number of eigenvalues (Advanced)

- Set the boundary conditions (Advanced)
- Run the MQW solver
- Extract results

Instead of starting your simulation from scratch, you can also use one of our Application Gallery examples as a starting point for your simulation:

- For laser simulations: Multi-quantum well (MQW) edge emitting laser
- For electro-absorption modulator simulations: GaAs-AlGaAs electro absorption modulator

The MQW solver can also be run using script commands. See buildmqwmaterial, mqwgain, and mqwindex for more information.