The running of matrix-type experiments to find out how to build an optimal device is a prohibitively expensive undertaking. Today, efficient and reliable process simulators are required which allow the device to be built and tested by computer before trying it out in the fab.

One of the most important issues in TCAD today is the ability to accurately simulate junction formation processes. The junction depth and steepness determine the electrical properties of the device and because of that one needs to predict the profiles of active substitional concentration of the dopants.

Main challenges for the future of CMOS technology constitute very shallow junctions to minimize short-chanel effects, with low sheet resistance to maximize drive currents.

In order to introduce dopants into silicon, ion implantation is used. This method affords great flexibility in terms of the doping species, the physical location of the dopants, and in manufacturing throughput. Ion implantation involves ionized dopant atoms which are accelerated through an electrostatic field and directed towards the wafer. After being introduced the dopant atoms redistribute through the wafer. Usually this redistribution is intentional; otherwise it could have unpredictable results. The motion of these dopants is mostly caused by diffusion.

After the implantation phase most of the implanted dopant atoms are not in the correct configuration to be electrically active. Increasing the wafer temperature enhances diffusion of the dopants and consequently their electrically activation.

At the beginning of this Chapter I present the physical foundation of the diffusion models. Further, most important models used for the state of the art diffusion simulation are introduced together with the corresponding process conditions. Linearization and discretization schemes for the selected models are motivated and derived. For these models nucleus matrix are constructed which are used in assembling and solving algorithms presented in Chapter 2. Discussed models and solving algorithms are applied for the simulation of demonstrative examples which illustrate the correctness of the developed numerical methods.

- 3.1 The Physics of Diffusion
- 3.2 Interaction of Dopants with Simple Native Point Defects

- 3.3 Equilibrium Diffusion

- 3.4 Nonequilibrium Models
- 3.4.1 Simple Point Defect Model
- 3.4.2 Three-Stream Mulvaney-Richardson Model
- 3.4.3 Five-Stream Dunham Model

- 3.5 Boundary and Interface Conditions
- 3.5.1 Dirichlet Boundary Condition
- 3.5.2 Neumann Boundary Condition
- 3.5.3 Segregation Interface Condition
- 3.5.4 Surface Reactions

- 3.6 The Plus-One Model
- 3.7 Dopant Diffusion in the Presence of Exdendend Crystal Defects
- 3.8 Numerical Handling of the Diffusion Models
- 3.8.1 Discretization of the Simple Diffusion Model
- 3.8.2 Discretization of the Simple Extrinsic Diffusion Model
- 3.8.3 Discretization of the Three-Stream Mulvaney-Richardson Model
- 3.8.4 Analytical Solution of the Segregation Problem for One Dimension
- 3.8.5 Numerical Handling of the Segregation Model

- 3.9 Dosis Conservation
- 3.10 Simulation Results

H. Ceric: Numerical Techniques in Modern TCAD