Transmission Line Matrix: A Tool For Modelingthermo-electric Properties Of Materials And Devices

Transmission-Line-Matrix (TLM) method, originally developed in 1971 as a numerical technique for modeling electromagnetic wave propagation, has since been established as a powerful technique to study diffusion problems, vibration, heat transfer, electromagnetic compatibility, radar, etc. The TLM method is a time and space discrete method that solves field problems using their circuit equivalent. It assembles a lattice of discrete points in space as one-dimensional lines and defines the transmission matrix between lattice points, so that successive calculations can be performed. The physical variable is modeled as a sequence of voltage pulses travelling through this network of transmission lines. The TLM routine operates on the travelling, scattering, and connecting of these pulses in the network. The transmission lines in the model act as delay lines, with the node impulse population being the discrete solution at each time step. TLM is a discrete model which can be solved exactly since approximations are only introduced at the discretisation stage. This is to be contrasted with the traditional approach in which an idealized continuous model is first obtained and then this model is solved approximately. It main advantages are that, it is intuitive and can be simply formulated, explicit, unconditionally stable since it is a passive network which is solved exactly, can be used to model arbitrary and complex structures, inhomogeneous media can be modeled very conveniently, and the impulse response and time domain performance of the system can be obtain straightforwardly. TLM method is used to model self-heating in various two electronic devices and structures: AlGaN/GaN power transistors and insulated gate bipolar transistor (IGBT) modules. Results show that the method is well suited for understanding heat management in microelectronic devices and gives insights for future designs.