This page discusses how to set the non-physical parameters of the MQW solver, including:

- Frequencies
- Mesh spacing
- Transverse wave vector
- Maximum number of eigenvalues

For information on setting the physical parameters (temperature, charge density, etc.) see Setting the Physical Parameters of the MQW Solver.

## Frequencies

The MQW solver results will be calculated at a series of frequency point specified by the user. The range should be large enough to cover the entire spectrum of the effects of interest, and the number of points should be large enough to avoid interpolation errors.

To set the frequencies:

- Select the
**freq type**to**frequency**,**wavelength**, or**energy**in the**Configuration**tab of the**Edit MQW Gain Solver**window. - Set the start value (
**freq start**) and stop value (**freq stop**) for the vector in the units of the chosen**freq type**(THz for**frequency**, microns for**wavelength**, or eV for**energy**). - Set
**freq num points**as the number of frequency points in the frequency vector.

## Mesh Spacing

The MQW stack is discretized in space along the stack, where each point is separated by the mesh spacing. The mesh spacing should be chosen such that the peaks in the wavefunctions are resolved. In general two angstroms is sufficient, but one angstrom can be used for higher accuracy. More peaks in narrow wells require higher mesh density for accurate resolution.

The mesh spacing can be set using the **mesh dz** property of the MQW solver, found in the **Configuration** tab of the **Edit MQW Gain Solver** window. The mesh spacing must be specified in increments of angstroms.

## Transverse Wave Vector

The transverse wave vector is the wave vector in the plane of the quantum wells. It is important to use a sufficiently large part of the Brillouin zone to get accurate carrier density in the quantum wells as a sum over the transverse wave vectors. The larger the transverse wave vector the larger the carrier energy in the quantum well and the smaller the probability of occupation of that energy level. The fraction of the Brillouin zone used in the MQW solver simulation is defined by the **brillouin zone ratio** property.

At higher temperatures, higher transverse wave vectors should be included so a larger **brillouin zone ratio** is required. It is usually enough to include 10% of the Brillouin zone (i.e. \(2\pi/a*0.1\), where \(a\) is the lattice constant) at room temperature and up to 20% at high temperatures. Increasing the number of transverse vector points increases the simulation time.

To set the transverse wave vector:

- Set the
**brillouin zone ratio**in the**Configuration**tab of the**Edit MQW Gain Solver**window as the fraction of the Brillouin zone to be included in the simulation. When the exciton model is used, the entire Brillouin zone is used and this setting is disabled. - Set
**num points**as the number of points in the transverse wave vector. If the exciton model is disabled these points will be equidistant. When the exciton model is enabled the number of points is used, but the spacing between the points is instead defined based on a special quadrature method.

## Maximum Number of Eigenvalues

The number of carrier energies to calculate at each transverse wave vector can be specified with the **max num eigenvalues** property of the MQW solver, found in the **Advanced **tab of the **Edit MQW Gain Solver** window. In general, this value should not have to be changed.

## Order of \( k \cdot p \) Method

The MQW solver solves the Schrodinger equation in conjunction with the \(k \cdot p\) band structure model. Select **kdotp order** (in the **Configuration** tab) for a desired approximation level regarding the \(k \cdot p\) model. On top of the 4x4 model, the 6x6 and 8x8 models include the crystal field and spin-orbit split bands in the resulting band structure. Moreover, the 8x8 model includes the coupling between conduction and valence bands. Therefore, higher orders result in more accurate approximations for the band structure, but require longer simulation time. Note that the 4x4 option is not supported for wurtzite materials.