1. Introduction and Overview

THE INCREASED speed and capability of computers has had enormous impact on the development of our society. The Internet, advanced software applications like office suits and computer games, speech recognition, advances in telecommunications and the many services that we take for granted are all made feasible only because of the steady performance increase of microchips over time. Judging from what is in development in the research laboratories of many companies and universities, the increased performance of chips will continue to fundamentally change the way we live in the future.

One way to make chips faster is to reduce the size of the transistors. This technique has successfully been used for more than thirty years now [1], following MOORE's law [2] which states that the number of devices per chip doubles roughly every 18 month. Other techniques to increase the speed of chips is to use alternative semiconductor materials and substrates. A substrate that has been under active consideration for the last 30 years is silicon-on-insulator (SOI). In integrated circuits SOI technology improves performance over bulk CMOS technology by 25% to 35% [3], equivalent to two years of bulk CMOS advances. SOI technology also reduces power consumption by a factor of 1.7 to 3. Therefore SOI technology will result in faster computer chips which also require less power--a key requirement for extending the battery life of small, hand-held devices that will be pervasive in the future.

When designing a semiconductor device it is convenient to simulate its characteristics and behavior with software tools before fabricating a prototype in order to reduce the costs and to allow to speed up the whole development.

To simulate the electrical behavior of semiconductor devices with a computer program, it is necessary to have proper physical models of the quantities of interest. A starting point is often BOLTZMANN's transport equation which is a semiclassical transport equation neglecting quantum effects. For devices of microelectronics this simplification is quite valid. Monte Carlo simulators solve BOLTZMANN's transport equation without any further assumptions, but they need a lot of computer resources. Another way to get reasonable results is to use partial differential-equation systems. During the derivation of these systems, various assumptions are made to reduce the complexity of the problem. It is worth noting that although the simulation domain is restricted to a single device or a small circuit, a first principle description of carrier transport is not available under general conditions. Hence appropriate assumptions are taken, which ensure the required accuracy and, at the same time, lend themselves to an efficient numerical solution.

The typical transport model used in the description of the semiconductor device behavior takes only the ohmic and diffusive contributions to carrier transport into account, and is referred to as drift-diffusion transport model. One of its major drawbacks is that the temperatures $ T_n$ and $ T_p$ of the carrier gas are set equal to the lattice temperature, which means that carrier heating is neglected. The energy transport model, on the contrary, is able to retain the information about the carriers' temperature which makes it possible to describe non-local phenomena such as velocity overshoot. The carrier temperature may locally become considerably larger than the lattice temperature. It is thus desirable to take advantage of models able to tackle such effects and predict them with reasonable accuracy. A disadvantage of the energy transport model should be mentioned too. The required computation time is higher compared to that required by the drift-diffusion transport model, and convergence of the numerical solution is harder to achieve.

This work deals with a specific problem of the energy transport model. When simulating partially depleted SOI MOSFETs the standard energy transport model breaks down completely. One obtains anomalous output characteristics which make it impossible to predict the behavior of a real device. By improving the physical assumptions the energy transport model can be modified to overcome these limitations.

This work is organized as follows:

Chapter 2 presents the derivation of the basic semiconductor equations. After putting together a simple transport model in a rather phenomenological way a rigorous derivation of transport models with increasing complexity is performed starting from BOLTZMANN's transport equation by using the moments method.

Chapter 3 treats the discretization of the six-moments transport model obtained in Chapter 2 using a straightforward extension of the SCHARFETTER-GUMMEL discretization scheme. This converts the original differential problem in a usually large nonlinear algebraic system.

The problem related to SOI simulations is presented in Chapter 4. The physical effects are investigated in great detail and an explanation of the effect is given.

In Chapter 5 the energy transport model is modified by taking an anisotropic carrier temperature and a non-MAXWELLian distribution function into account.

Chapter 6 presents empirical models for the anisotropy and the non-MAXWELLian distribution function. Different closure relations are examined and a stable and simple yet effective solution is presented.

Chapter 7 finally summarizes and concludes this text.

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