Model Details

HAROLD has a detailed model which accounts for many physical processes, and which will thus enable to you to obtain a comprehensive set of simulation results for your device.

HAROLD is a two-dimensional simulator which solves, self-consistently, the Poisson equation, the current continuity equations, the capture/escape balance equations, the photon rate equation, and the heat flow equation. In addition, it solves the vertical and longitudinal wave equation and Schrödinger’s equation. HAROLD can model both single and multiple quantum well lasers with near-arbitrary structure and composition. In 2D simulations, further longitudinal effects are accounted for: surface recombination at the facets, optical absorption at the facets, and the non-uniformity of the optical field.

Details on the different parts of the model are given below.

Gain Model

Material gain for quantum well and quantum dot lasers is computed as a function of the wavelength, carrier concentration and temperature, using a k.p band mixing model. Both TE and TM mode gain are computed.

Figure: Gain predicted by Harold matching experimental results for MQW structure. Discrepancy intentional to show atmospheric effects discussed more in full publication.

Electrical Model

Self-consistent solution of Poisson Equation, including drift-diffusion, and capture/escape for both holes and electrons.

Thermal Model

Full vertical-longitudinal solution of the heat flow equation, including the substrate, the metal contacts and the heat sinks. Power dissipation is treated locally and includes:

• Joule,
• non-radiative recombination,
• free carrier absorption,
• excess power distribution,
• mirror scattering, and mirror absorption. 

Longitudinal heat flow is considered for the 2D (XZ) calculations.

Optical model

Harold features a multi-transverse optical mode model. It has a built in full-vector 2D+z waveguide mode solver for this purpose. TE and TM polarisations and anything in between are supported as are the effects of nearby metals, the change in mode shape with increasing carrier density and thermal lensing. 

Longitudinally, a Fabry Perot cavity is assumed and the photon density is assumed to be uniform along the cavity. (Harold can be linked to PICWave to relax these assumptions.) The total photon density is determined considering the gain/loss balance in the full cavity.

Capture / Escape

In QW regions, thermal equilibrium between confined and unconfined carriers is not assumed, but described by means of appropriate capture/escape balance equations.

Carrier Recombination

Shockley-Read-Hall, Auger, stimulated and spontaneous recombination processes are included. Advanced features, such as arbitrary specification of deep trap levels, are allowed on a layer-per-layer basis.

Bandgap Narrowing

Carrier-induced bandgap narrowing is included as shown above with redshift of gain peak as current is increases (isothermal simulation of InGaAsP laser).

Quantum Well and Quantum Dot Layers

Single and multiple quantum well (MQW) and quantum dot structures can be modelled; multiple wells need not be identical. The program will determine the energy levels by solving the Schrödinger Equation; for MQW structures it will be solved over the whole MQW region to account for coupling between wells. Wavefunction overlaps are accounted when computing the recombination and gain.

(Figure: 1st and 2nd energy levels to MQW structure including grading)

Facet Modelling 

• Recombination at the facets is included via deep trap levels at the mirror.
• Heat-sink thermal overhang is implemented in the 2D (YZ) model.
• Suppression of current injection at the mirrors is implemented in the 2D (YZ) model.
• Photon absorption, attenuation at the mirrors is implemented in the 2D (YZ) model

Strain

The effect of strain (in QW and barrier layers) on the QW levels is modelled. Anisotropic hole masses resulting from biaxial strain can also be modelled.

Model upgraded to 3D for quantum dots

Tunnelling

The model takes account of quantum tunnelling e.g. at tunnel junctions

Thermionic Emission

The model takes account of thermionic emission effects.

Material Database

A material database is provided, giving parameters for common materials including AlGaAs, InGaAsP, InGaAlAs, gold, copper etc. This provides information for the gain calculations such as band gap, effective masses, refractive index (dispersive models e.g. Adachi), etc. You can also readily add your own materials as required.

Comparison with Harold XY, Harold QCSE and PICWave

Please see here for a comparison of the active component (laser diode, SOA, modulators etc.) modelling capabilities of PICWave, and Harold's optional modules.