MQW solver - Simulation object – Ansys Optics

MQW

[[NOTE:]] For using the MQW solver in FE IDE, it is not necessary to define geometry and simulation region. Only the materials need to be added to the simulation, while all other options related to the MQW solver are defined in the MQW solver object edit window.

Layers tab

The layer table is used to define the thickness, material, strain (optional), and valance band offset (optional) of each layer in the MQW stack. The MQW stack consists of quantum wells and barriers only.

Materials to be included in the layer table must be Semiconductor type and must have k · p properties enabled. Currently supported III-V binary materials already have k · p properties enabled and defined. These values can be further modified by the user to take into account any specific material differences. Ternary and quaternary alloy materials support defining bowing parameters (if known) for each k · p property. Before adding the alloy material to the simulation they need to be converted to semiconductor type. During this conversion, standard interpolation formulas will be used to derive ternary/quaternary semiconductor properties from the alloy base materials. In addition, some of the properties can be set to use custom models for improved accuracy compared to default interpolation.

In addition to k · p properties, the MQW solver uses the band gap, electron effective mass, and work function from Electronic Properties tab in Semiconductor materials.

The strain column in the table is enabled by default, which requires strain input by the user, while the valence band column is disabled by default, which forces the use of a built-in calculator for offsets. This behavior can be changed by the options explained below. Negative values of strain represent compressive strain.

TOP LAYER EXTRA THICKNESS: Extra thickness added to the top layer.
BOTTOM LAYER EXTRA THICKNESS: Extra thickness added to the bottom layer.
GAMMA (eV): Linewidth broadening due to intraband relaxation rate. Represents full width at half maximum of a Lorentzian.
NEFF: Effective index.
OVERRIDE BAND OFFSET: Enable this to directly specify valence band offset in the layer table, instead of using the built-in valence band offsets calculator.
CALCULATE STRAIN: Enable this to use the built-in strain calculator and ignore strain values in the layer table.
- REFERENCE MATERIAL: Select the reference material for calculating strain.
BAND GAP SHRINKAGE CONSTANT (eV m): Includes band gap shrinkage due to carrier density. This option is currently disabled and a scripted workaround can be used. Please refer to one of our laser examples using MQW solver.
ENABLE PARTITIONING: Partitions the MQW structure into independent (uncoupled) partitions.
- REUSE BANDSTRUCTURE: When checked,MQW band structure calculated in the first partition will be reused in all other partitions, reducing simulation time. This is a good approximation whenever partitions have similar band diagram (up to a constant shift).
- NUM PARTITIONS: Define the number of partitions.
- PARTITION LAYER INDICES: Define indices of partition layer. Partition layers must be quantum barriers.

Configuration tab

Frequency / Wavelength / Energy

FREQ TYPE: Select the type of frequency parameter.
FREQ START: Start frequency in THz / micron / eV.
FREQ STOP: Stop frequency in THz / micron / eV.
FREQ NUM POINTS: Number of equidistant frequency points.

Excitons

ENABLE EXCITONS: Turn on exciton model in absorption calculation.
- EXCITON METHOD: Use direct method or variational method for exciton energy calculation.
- ENABLE EXCITON ANGULAR DEPENDENCE: Turn on angular dependence of the exciton wave function in the plane of quantum wells.
- ENABLE CUSTOM EPS DC: Use custom relative static permittivity for the MQW stack, instead of the value derived by the built-in calculator, which is based on the quantum-mechanical average of permittivities of layer materials.
- EPS DC: Value of custom permittivity.

MESH DZ: Grid spacing in the smallest increment of 1Å.

MAX NUM CB SUBBANDS: Maximum number of conduction band subbands used for exciton mixing.

MAX NUM VB SUBBANDS: Maximum number of valance band subbands used for exciton mixing. This does not include spin, so the actual number of subbands is 2x this value.

Transverse Wave Vector

BRILLOUIN ZONE RATIO: Brillouin zone ratio of the transverse wave vector. When the exciton model is turned on the full Brillouin zone is used.
NUM POINTS: Number of equidistant wave vector points over the selected portion of the Brillouin zone. When the exciton model is turned on the points are not equidistant and the full Brillouin zone is used.

kdotp order

Select kdotp order for a desired approximation level regarding the \(k \cdot p\) model.

4x4: basic \(k \cdot p\) model including heavy hole, light hole, and parabolic conduction bands. This option is disabled for wurtzite materials.
6x6: additionally includes the crystal field and spin-orbit split bands.
8x8: additionally includes the coupling between conduction and valence bands.

Higher \(k \cdot p\) orders result in more accurate approximations for the band structure, but require longer simulation time.

Parameters tab

TEMPERATURE (K): Simulation temperature. This parameter is ignored when the exciton model is used and full depletion of the quantum wells is assumed (valence band full, conduction band empty).

Carrier Density

CDEN TYPE: Support two types of carrier density data. This parameter is ignored when the exciton model is used and full depletion of the quantum wells is assumed (valence band full, conduction band empty).
- UNIFORM - Define density profile as a scalar representing average density over the entire MQW stack.
- PARTITIONED - Define spatially dependent density, where each partition has a different density. Used only when partitioning is used.

Electric Field

EFIELD TYPE: Support two types of electric field data.
- UNIFORM - Define uniform electric field in efield.
- TABLE - Define spatially dependent electrostatic potential in the potential table, where electrostatic potential [eV] varies with position x [micron].

Advanced tab

MAX NUM EIGENVALUES: Maximum number of carrier energies to calculate by the eigensolver at each transverse wave vector.

Boundary Conditions

BOUNDARY CONDITIONS: Support two types of boundary conditions.
- HARD WALL - Hard wall at boundaries where wave function drops to zero.
  - CUTOFF (A^(-3/2)) - Threshold wave function slope, one for conduction band (cb) and one for valence band (vb), to reject eigenstates that do not decay enough at the left and right hard-wall boundaries. The QW bound states are those below this threshold.
- PML - Perfectly matched layer at boundaries.
  - CUTOFF - Threshold ratio (PML probability density)/(MQW probability density), one for conduction band (cb) and one for valence band (vb), to reject eigenstates with excess conduction and valence band probability densities located in the PMLs. The QW bound states are those below this threshold.
  - PML LENGTH (microns) - PML thickness for left and right boundaries.
  - PML COEFF TABLE - PML complex coordinate stretching coefficients. Top two elements for left and right PML for the valence band and the bottom two for the conduction band.

Results returned

Syntax	Type	Description
banddiagram	dataset	Conduction and valence band edge including strain, but not including quantum confinement effects.
bandstructure	dataset	(E,kt) band diagram for conduction and valence bands. With the exciton model turned off the attributes are: conduction_band, valence_band_lo, valence_band_up, where the 4x4 k.p basis in the valence band is transformed into two 2x2 bases (lo for lower and up for upper). For more information refer to the MQW solver introduction. With the exciton model turned on the attributes are: conduction_band, valence_band, with the 4x4 k.p basis in the valence band (the basis is not transformed). Parameters are kt and subband.
wavefunction	dataset	Spatial wavefunction for each (E,kt) point. With the exciton model turned off the attributes are: conduction_band_1, valence_band_lo_1, valence_band_lo_2, valence_band_up_1, valence_band_up_2, where the 4x4 k.p basis in the valence band is split into two 2x2 bases (lo for lower and up for upper) and the vectors in each 2x2 basis are designated with 1 and 2. For more information refer to the MQW solver introduction. With the exciton model turned on the attributes are: conduction_band_1, valence_band_1, valence_band_2, valence_band_3, valence_band_4, with the 4x4 k.p basis in the valence band (the basis is not transformed) and the vectors in the 4x4 basis designated with 1, 2, 3, and 4. Parameters are coordinate, kt, and subband.
ome	dataset	Optical matrix element. With excitons turned off: Magnitude squared of the dipole matrix element in the units of \(nm^2\). Attributes are ome_lo_TE, ome_lo_TM, ome_up_TE, ome_up_TM, where TE and TM designate optical modes and up and lo refer to the 2x2 bases, same as for the bandstructure and wavefunction. Parameters are kt (transverse wave vector), CBsubband (conduction band subband index) and VBsubband (valence band subband index). With excitons turned on and variational method chosen: The units of ome are the same as the case with excitons turned off, but the dataset is in the original 4x4 basis. The attributes are ome_TE and ome_TM. The parameters are kt, CBsubband, and VBsubband. With excitons turned on and direct method chosen: Oscillator strength (unitless). Attributes are ome_TE and ome_TM where TE and TM designate optical modes. Parameters are the exciton orbital quantum number (orbital) and angular momentum quantum number (angularMomentum) for the direct method.
emission	dataset	Gain and spontaneous emission coefficients in the units of [1/m]. Attributes are: spontaneous_TE, spontaneous_TM, stimulated_TE, stimulated_TM, where TE and TM stand for electromagnetic modes. Parameters are: frequency/energy/wavelength and ndensity (charge density). Emission coefficients are calculated for the total stack thickness, including barriers. If only quantum well thickness is of interest, excluding barriers, these coefficients should be scaled by multiplying with (total length)/(total qw length). It is important to ensure that emission coefficients apply only to the thickness used for the calculation of the optical mode overlap with the gain region. When using partitioning, there will be overlapping barriers between different partitions, e.g. if partition layer indices are 1, 3, and 5, where 1, 3, and 5 are barriers, those layers will be overlapping. In that case emission coefficients for each partition again apply to the total thickness of that partition, meaning there may be some double-counting with respect to the mode overlap region thickness. To avoid this, emission coefficients in each partition can be scaled to apply to quantum wells only, or to apply to a portion of the partition that does not overlap with adjacent partitions. When the exciton model is turned on the attributes become: absorption_TE, absorption_TM. These represent the absorption coefficients (negative gain) in the units of [1/m]. The spontaneous emission is not calculated due to the assumption of the depleted carrier density in the quantum wells. Parameters are frequency/energy/wavelength and ndensity (charge density).
index	dataset	Complex index \(\bar{n}=\Delta n+i\kappa\). Attributes are: index_TE, index_TM, where TE and TM stand for electromagnetic modes. Parameters are: frequency/energy/wavelength and ndensity (charge density). Same comments regarding index scaling for correct thickness as for emission dataset.
ex	dataset	Exciton energies Ex, if the exciton model is turned on. For the direct method, the exciton energies are a function of exciton orbital quantum number (orbital) and angular momentum quantum number (angularMomentum). For the variational method, the exciton energies are a function of cSubband (conduction band subband index) and vSubband (valence band subband index).
phix	dataset	Exciton wavefunctions PhiX, if the exciton model is turned on. In the direct method, the PhiX is in the momentum (in-plane wavevector) space. The wave function coefficients are parametrized in terms of conduction band subband index (cSubband), valence band subband index (vSubband), transverse wave vector (kt), angular momentum quantum number (angularMomentum), and orbital quantum number (orbital). For the variational method, the exciton wavefunctions are a function of distance (electron-hole coordinate separation), cSubband, and vSubband.

MQW solver - Simulation object