Setting the MQW Solver Layers and Partitions

The MQW solver uses a 1D layer geometry, which can be defined in the Layers tab of the Edit MQW Gain Solver window. To define the layer geometry, the layer thicknesses, materials, and ordering must be specified. Before creating the layer geometry the materials of the layers should be created (see Creating Materials for the MQW Solver).

Defining the layer geometry using the MQW solver GUI involves creating the basic layer structure and (optionally) dividing the layer structure into partitions.

Creating the Basic Layer Structure

The basic layer structure of an MQW stack consists of a series of layers in order defined by their thickness and material. The current layer structure of the MQW stack can be seen in a table in the Layers tab of the Edit MQW Gain Solver window.

To create the layer structure:

1. Add layers to the geometry using the Add layer button.
2. Set the Material and Thickness of each layer by modifying the values in the table. The material can be selected from the materials added to the simulation and the thickness can be any positive value in increments of angstroms.
3. Layers can be selected by clicking on any of the cells in that layers row in the table. Once selected, layers can be moved up or down in the stack geometry using the Move up and Move down buttons, removed with the Remove layer  button, or duplicated using the Duplicate layer button.
4. Extra thickness can be added to the top and bottom layers using the top layer extra thickness and bottom layer extra thickness properties. This is the same as increasing the thickness of the top and bottom layers of the stack in the layer table.

Uncoupled Quantum Wells (QWs) Approximation

Even if there are multiple QWs in the simulation domain quantum mechanical coupling between them may be weak. The electron wave function coherence can be broken over longer distances by the existence of thick barriers or lattice vibrations. If the barriers in the multiple QW structure are thick enough, for example 5 nm or more, it is usually a good approximation to consider QWs between such barriers uncoupled. Also electrons will be scattered by lattice vibrations, or phonons, and the related QW interface fluctuations, such that the electron mean free path does not extend over multiple QWs. Therefore, QWs can usually be considered uncoupled or at most groups of 2-3 QWs may be coupled. For more details about the validity of the uncoupled approximation please refer to the discussion in reference [1].

Uncoupling the QWs helps reduce the simulation time in gain and absorption simulations. The gain simulation without excitons can be performed with many coupled QWs at the expense of increased, but still manageable, simulation time. However, the simulation time in absorption simulations with the exciton model turned on increases quadratically both with the number of QWs and the total number of subbands, so simulations with more than 2 or 3 coupled wells are usually not feasible.

Coupling of QWs is achieved by assigning them to the same partition. Or conversely, uncoupling them is achieved by assigning them to different partitions. Single QW per partition is most commonly used.

Partitioning the Layer Structure

To partition the layer structure:

1. Select enable partitions in the Layers tab of the MQW solver GUI.
2. Specify the number of partitions using the num partitions property.
3. Define the start and end of each partition by setting the values in the partition layer indices table. The partition layer indices should correspond to the quantum barrier layers in the MQW stack between each uncoupled quantum well structure.
4. If the quantum well structures (material and layer thickness) and electric potential are identical, select reuse bandstructure.

When reuse bandstructure is enabled, the bandstructure from the first well will be used for the other wells. This can be useful when the well bandstructures are the same but other quantities, like carrier density, are different across the wells.

Single Quantum Well Approximation

If the MQW stack:

1. has a periodic structure (materials, layer thickness),
2. QWs in the stack are uncoupled, and
3. Electric field, carrier density, and temperature are constant across the stack,

it is possible to simulate just a single quantum well and rescale the results to the full thickness, instead of using partitioning.

Even if parameters like charge density and electric potential vary across the MQW stack, a parameter sweep can be used to obtain results for the different values of these parameters for a single quantum well. The results from the individual simulations can be combined to obtain the results for the entire MQW structure.

The single quantum well approximation is similar to partitioning the structure and selecting the reuse bandstructure option (see Partitioning the Layer Structure), however in that case the results are automatically combined for a specific combination of simulation parameters (carrier density, electric field, temperature). In the single quantum well case, the results are known for the individual quantum wells, so they can be freely recombined for different configurations.

If the single QW method is used, the average charge density at the input to the gain simulation should be scaled accordingly to represent the same local charge density as in the full MQW structure. Similarly, the final single quantum well gain/absorption, spontaneous emission, and complex index results should be scaled onto the full MQW structure. For examples of this, please check one of our laser examples that combine MODE/MQW/INTERCONNECT(TWLM) solvers.

References

1. W. Bardyszewski, "Resonant exciton contributions to quantum-well electroabsorption," Phys. Rev. B, vol. 60, no. 24, p. 16 563.

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