Two-dimensional temperature modelling of DH laser diodes using the transmission-line modelling zy - (TLM) method R. Ait-Sadi, PhD A.J. Lowery, PhD B. Tuck zyxwvutsrqpon Indexing terms: Lasers, zyxwvutsrqponmlk Diodes, Modelling ______~ _____~ _____~ ~~ zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Abstract: The two-dimensional temperature dis- tribution in a DH GaAs/GaAlAs laser diode under continuous operation is analysed. The dynamic thermal diffusion equation is solved using the transmission-line modelling (TLM) method. The heating mechanisms included in the model are nonradiative recombination in the active region, partial reabsorption of generated radiation in the active region, absorption of stimu- lated emission in the cladding regions, absorption of spontaneous radiation transferred to the capping and substrate layers, Joule heating of the substrate and scattering loss at the heterojunction interfaces. 1 Introduction In recent years, intense effort has been devoted to the development of semiconductor laser diodes for fibreoptic communication systems. During this development, the double heterostructure (DH) laser has become the pre- ferred light source for optical fibre communications because of its high continuous-wave (CW) optical inten- sity and small operating current [l]. The operating char- acteristics and lifetime of lasers are strongly affected by an increase in temperature: the temperature rise within the laser can cause several undesirable phenomena, such as fluctuation of the intensity and instability during high- temperature operation [2]. These phenomena can ultima- tely lead to degradation and catastrophic failure of the laser [3]. A knowledge of the thermal properties of DH laser diodes is essential for the design of reliable devices for particular applications. In most of the early work [4-91, the heat flow equation was solved analytically using either Fourier series (or transformation) or Laplace trans- formation. The solution provided consisted of solving the heat diffusion equation in an individual layer under the zyxwvut Cl IEE, 1994 Paper 9585A (E13). first received 28th September 1992 and in revised form 15th February 1993 R. Ait-Sadi is with Vector Fields Ltd, 24 Bankside, Kidlington, Oxford OX5 1 JE, United Kingdom A.J. Lowery is with the Photonics Research Laboratory, Department of Electronic Engineering, University of Melbourne, Australia B. Tuck is with the Department of Electrical & Electronic Engineering, University of Nottingham. Nottingham, NG7 ZRD, United Kingdom zyxwvutsrqpon IEE Proc.-Sri. Meas. Technol., Vol. zyxwvutsrqponm 141, No, I, January 1994 assumptions that (i) this layer is homogeneous and iso- tropic, and (ii) the heat sources are centred within the layer of dissipation and uniformly distributed over a stripe width. In only few models [S, lo] was the distribu- tion of the heat sources other than centred line sources. Some of the analytical solutions provided were based on the transformation of the structure from inhomogeneous material to homogeneous materials. The whole structure was then solved at once [8, 91. The problem with these approaches is that they involve the solution of a large number of simultaneous equations to determine the coefficients of the series, using the boundary conditions and the continuity of the heat flow at the interfaces between layers. A numerical method based on successive overrelaxation techniques was proposed [ 111. However, this method appears to be over complex compared to other methods such as the finite difference method and the transmission-line method. This paper covers the development of a thermal model based on the transmission-line modelling (TLM) tech- nique. The TLM method has previously been used for the simulation of diffusion problems, ranging from food processing to semiconductor devices [12]. The method uses shunt-connected lossy transmission lines to model the parameters of systems [13, 141. The objective of this work is to describe a simple numerical thermal model that can determine the temperature distribution in the laser diode with due consideration of all heating pro- cesses. zyxwvu 2 Theory zyxwvut 2.1 TLM method TLM is a well established technique for solving thermal diffusion processes. The application of this method to the diffusion equation has been described by Johns [lS]. Its consistency, accuracy and relationship to other methods has also been established [16]. The important property of this method is that it is discrete in space and time, allow- ing solution on a digital computer. Consider a mesh of transmission lines connected at nodes, modelling a block of material (Fig. 1). As voltages V are only available at discrete positions (the nodes), the model may be regarded as a space-discrete description of a physical process. The pulses travelling between the nodes along the lines in a finite time interval discretise the system. As all lines use the same delay, the pulses arrive at the nodes simultaneously. At each iteration, the pulses incident on the nodes are instantaneously scat- 7