5. Modified Energy Transport Model

IN CHAPTER 2 several assumptions and simplifications have been made during derivation of the transport models of different order. Additional information extracted from BOLTZMANN's transport equation by taking higher order moments of the distribution function into account is supposed to improve the agreement between simulations and measurements.

The energy transport model has, compared to the drift-diffusion transport model, the advantage that it provides information about the mean energy (temperature) of the carriers, which can be used to develop better models for, for example the relaxation times, the impact-ionization rates, or the gate tunneling currents. The drawback of including higher order moment equations is that the simulation time increases because of the increased system matrix size. Convergence of the numerical iteration also seems to degrade due to the strong coupling of the equation in the system.

However, the decrease of the gate-length into the deep sub-micron range together with a much slower reduction of the operating voltage leads to high values and large gradients of the electric field in regions of the device which are essential for its physical behavior. Therefore advanced transport models are necessary to capture the non-local effects which occur in scaled devices.

The drift-diffusion transport model is the mostly used one in TCAD. To fit at least the terminal characteristics, which are in most engineering applications in the focus of interest, a saturation velocity of more than twice the bulk value has been used in [61] which definitely does not model the physics inside the device accurately. Furthermore the author mentions that it is unclear whether the value of the saturation velocity is applicable for different MOSFET structures and under different operating conditions. This treatment of the physical parameters merely as fitting parameters may provide short-term fixes to available models but has limited value for predictive simulations.

The increased demands for accurate transport models, combined with the steadily increasing computational power of simulation hardware makes the energy transport model more and more attractive. However, the simulation study of a partially depleted SOI MOSFET presented in Chapter 4 demonstrated the complete breakdown of this transport model. To improve the transport model this chapter will compare the relevant quantities with Monte Carlo simulations, and a modified energy transport model will be derived.

Subsections

• 5.1 Monte Carlo Simulations
  • 5.1.1 Anisotropic Distribution Function
  • 5.1.2 Non-MAXWELLian Closure
  
  
• 5.2 Model Derivation
  • 5.2.1 Anisotropic Distribution Function
  • 5.2.2 Non-MAXWELLian Closure
  
  
• 5.3 Combining the Modifications

M. Gritsch: Numerical Modeling of Silicon-on-Insulator MOSFETs PDF