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A hetero-structure laser diode model

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.

Electrical model

Self-consistent solution of Poisson Equation, 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 includes a 1D+z waveguide mode solver. This is used to compute the confinement factor and the resulting mode gain. Both TE and TM polarisations can be considered. Longitudinally, a Fabry Perot cavity is assumed and the photon density is assumed to be uniform along the cavity. The total photon density is determined considering the gain/loss balance in the full cavity.


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

Quaternary alloys

Utilization of quaternary allows is fully supported through the material database.

Gain model

Material gain for quantum well lasers is computed as a function of the wavelength, carrier concentration and temperature, using a parabolic band approximation. Both TE and TM mode gain are computed.


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.

Surface recombination

Recombination at the facets is included via deep trap levels at the mirror.

Bandgap narrowing

Carrier-induced bandgap narrowing is included.

Quantum well

Single and multiple quantum well (MQW) 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.


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.

Thermal overhang

Heat-sink overhang is implemented in the 2D calculation.

Non-injecting mirror

Suppression of current injection at the mirrors is implemented.

Absorbing mirror

Photon absorption, attenuation at the mirrors is implemented

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. The database is ASCII based and you can readily add your own materials as required.

Comparison with Harold XY, Harold EAM and PICWave

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