Review of Device Modelling Technique

There are many papers on IGBT models since the invention of IGBT in 1980’s. They can be categorised into three types according to their complexity, accuracy and mathematical method: behavioral models, finite element models and semi-numerical models. In the case of system-level simulation, the desired model should be accurate enough to calculate the power losses for both on-state and switching at different operating conditions. Also, they need to be fast enough for practical applications.

The behavioral models [28,29] simulate the device behavior without considering their in- ternal physics. They are based on the measurements of device characteristics under different operating conditions. These empirical data are fitted with different methods to represent the IGBT behavior. Hence their accuracy depends on the density of measurement points. They are the fastest models since they ignore the device physics. However, the price for the speed is that they cannot give valid results when the device operates outside the fitted range. Furthermore, the internal device behavior such as carrier density and electric field distribution cannot be modeled. Hence this type of model is not suitable for the device design. The most applicable area for the behavioral models is the system-level modelling which requires fast simulation.

Accurate device behaviors can be obtained by solving all the physics based semiconductor equations without assumptions. These equations are highly nonlinear, some of them are

partial differential equations (PDEs). Therefore, finite element method is widely employed to solve these equations. The basic idea of finite element method is to find the approximate solutions for the PDEs using standard techniques such as Euler’s method [30] or Runge- Kutta method [31]. Models using the finite element method [32] require accurate physical equations as well as necessary device data, such as device geometrical information, contact structures, doping densities and carrier lifetime, to solve the equations. The region under study is discretised on to a fixed mesh. The potential and carrier densities are defined at each mesh point. With known boundary condition, the electric field and currents can be derived by solving the PDEs. The results are then used to generate the potential and carrier densities of the neighboring points on the mesh. The accuracy of this type of model depends heavily on the density of the mesh. Normally, the mesh density of the area with steep changes in gradient, such as junctions, are higher than the other areas. This type of model is able to simulate the detailed carrier density and electric field distribution with a well defined mesh and accurate device data. Therefore, they are commonly employed in the device design and optimisation. However due to the time consuming numerical calculations, they are too slow to apply in circuit simulators (one switching event could take hours to run).

The semi-numerical models are partly based on device physics. Some simple models [33,

34] are developed with lumped-charge modelling technique which significantly simplify model equations without losing the basic structural information and internal physical processes in the devices. The basic idea of lumped-charge technique is to separate the space charge region into several specific regions. The carrier densities are assumed to be constant within each region. The electric field and current for each region are calculated based on the carrier density distribution by the physical equations. With these simplifications, the lumped-charge models are faster than the ambipolar diffusion equation (ADE) models, However, with less accuracy.

ADE solution models [35,36] are more complex than the lumped-charge models. For a ADE model, the electric field and carrier storage distribution in the drift region are based on

the PDEs which is derived from device physics with simple boundary conditions while the other part of the device is described by simplified models. Therefore numerical calculations are needed to solve the PDEs. Different approaches for solving the ADE are reported. Strollo uses Laplace transform to transform the ADE from the time domain into the s-domain [37]. Morel et at. solve the ADE by internal approximation [38,39]. Bryant and Palmer [36,40] use Fourier series to solve the ADE and implement the device model in Matlab. Matlab is a widely used programming environment for algorithm development, data analysis and numerical computation. Therefore it is an ideal environment for system-level simulation. The implementation of device model in Matlab allows more compatibility in system simulation and data analysis hence is a desired feature. This model is able to achieve high accuracy with relatively short simulation run time (around 2 seconds for each switching event). The comparison between experiment switching waveforms and simulation results of this model is shown in a previous paper [22]. Furthermore, a simple parameter extraction method is offered for this model to make it practically applicable for different applications [41].

Although the simulation time needed for Bryant’s model is already very short, it still cannot be applied to system-level simulation directly. However, it can be used in a circuit simulator to generate desired device parameters with one switching event under different operating conditions. In this work, device junction temperature is the only desired output from electrothermal simulation. Therefore, power loss LUTs can be generated by running the device model at different operating conditions. During the inverter electrothermal simu- lation, the inverter model generates the power loss by interpolating these LUTs. This could greatly increase the simulation speed while maintaining its accuracy.