2.6 Employed Simulation Tools

As described above, theoretical models and simulation approaches have been continuously improved and implemented in simulators by various scientific groups. The improvements and developments of some groups already spans decades and continues at the present moment. A list of used simulation tools employed in this work is presented below.

MONJU is a 2D full-band Monte-Carlo device simulator [154]. Such mechanisms as impact ionization, electron-phonon and scattering on ionized impurities are employed in MONJU. The simulator is capable of simulating real devices with real doping profiles. It is employed for the evaluation of the carrier DF, i.e. represents the transport module. MONJU is developed by the group of Prof. Jungemann [154].
MiniMOS-NT is the 2D device and circuit simulator developed at our Institute [163]. The Drift-Diffusion and Hydrodynamics schemes for the Boltzmann transport equation solution are employed in MiniMOS-NT, which are valid for long-channel devices. MiniMOS-NT is much faster than any Monte-Carlo device simulator, thus, MONJU is used only for DF calculations.
SPRING is a spherical harmonics expansion based solver of the Boltzmann transport equation [158,162]. The program is developed by the group of Prof. Jungemann. The available version is applicable for simple 1D structures. It is used for verification of the simulation parameters for evaluation of the carrier DF by MONJU.

The employed simulation procedure to calculate the carrier DF consists of several steps, and is described by the flowchart shown in Figure 2.5.

**Figure 2.5:** The simulation flowchart for the carrier transport block of developed HCD model.

The device topology with a doping profile is obtained from the process simulator and is used as input data for the initial MiniMOS-NT simulation. During this simulation, potential and carrier density distributions are calculated for the chosen stress voltages. The resulting information is then used as input data for MONJU with a NSC/MR approach and for the optimization of the device topology. In some cases, the silicon bulk of the transistor may be as large as 15um. It is obvious that the calculation of the physical quantities using the MC approach is a challenge for such a huge area. Moreover, according to the suggested scheme for HCD modeling, one is interested only in the carrier distribution function at the device interface. Therefore, the simulation efficiency can be increased by reducing the size of the silicon bulk, e.g. the device can be cut at the potential profile saturation point. Furthermore, in the present MC device simulators [154,157], because of computational efficiency, a rectangular grid is used. That is, due to the different types of the simulation grid which are used by MiniMOS-NT and MONJU (triangular and rectangular, respectively), data conversion is necessary. It should be mentioned that the realization of the MC method is possible in the case of triangular grid type but leads to a significant increase of the computational time. An example of the converted n-type LDMOS transistor is demonstrated in Figure 2.6. At the final step of the transport block, the carrier DF is calculated by MONJU. Note, there is no requirement to perform the full procedure every time from the beginning. Several steps, such as the device geometry optimization might be omitted in the case of subsequent simulations.

**Figure 2.6:** The cross section of the high voltage n-type LDMOS transistor (a) before and (b) after the conversion procedure.
(a) (b)

I. Starkov: Comprehensive Physical Modeling of Hot-Carrier Induced Degradation