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Modelling guidelines for VCSEL designing

Włodzimierz Nakwaski 

Technical University of Łódź, Institute of Physics, Wólczańska 219, Łódź 93005, Poland


Computer simulations are currently the most efficient and cheap methods in designing and optimisation of device structures. The most exact theoretical approaches are usually also the most time-consuming ones and need powerful computers. In some cases, cheaper simplified modelling simulations are sufficiently accurate. Therefore, an appropriate modelling approach should be chosen taking into account a compromise between our needs and our possibilities.

Modelling of an operation and designing of structures of vertical–cavity surface–emitting diode lasers (VCSELs) requires appropriate mathematical description of physical processes crucial for devices operation, i.e. various optical, electrical, thermal and recombination phenomena taking place within their volumes. Equally important are mutual interactions between above individual processes, usually strongly non-linear and creating a real network of various inter-relations.

Chain is as strong as its weakest link. Analogously, model is as exact as its less exact part. Therefore it is useless to improve exactness of its more accurate parts. All model parts should exhibit similar accuracy.

In VCSEL modelling, it is necessary to choose:

  • between exact but at the same time more involved and more time-consuming vectorial optical approaches and simplified scalar ones,
  • between exact drift-diffusion electrical model and the simplified approach based on the Laplace equation,
  • between rigorous thermal model including electro-thermal phenomena and phonon scattering at layer boundaries and the simplified model based on the thermal conduction equation and a bulk thermal conductivity,
  • between exact microscopic recombination approach including many-body inter-actions and different temperatures of electron, hole and phonon gases and the approach based on the Fermi’s Golden Rule coupled with the carrier and photon phenomenological rate equations,
  • between full optical-electrical-thermal-recombination self-consistency and the partially electrical-thermal self-consistent model coupled with the optical and recombination ones.

Sometimes very accurate theoretical approaches starting from the so called first principles need equally exact values of various model parameters which are very difficult to be determined theoretically and are practically impossible to be measured. Then their rough values are estimated which completely ruins an exactness of the approach. A more recommended method is to use a simpler approach with some parameters taken from experiments which, in a natural way, takes into account all special features of a phenomenon under consideration, even those which have not been included in this simplified approach.

In conclusion, in any individual case, a reasonable compromise should be reached between high modelling fidelity and its practical convenience depending on a main modelling goal, importance of expected results, available equipment and also financial possibilities.


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Related papers

Presentation: Oral at Joint Fith International Conference on Solid State Crystals & Eighth Polish Conference on Crystal Growth, by Włodzimierz Nakwaski
See On-line Journal of Joint Fith International Conference on Solid State Crystals & Eighth Polish Conference on Crystal Growth

Submitted: 2007-01-13 23:26
Revised:   2009-06-07 00:44