Models for thermal diffusion have been rapidly changing due primarily to the decrease in the available thermal budget for processing as device dimensions shrink. These new models usually add terms to existing equation-based models and may even add equations or change the nature of the system of equations for the model, and, as such, they are impossible to simulate in traditional process simulators such as SUPREM-IV without access to and modification of the source code. This research involves development of a prototyping tool that can efficiently simulate thermal diffusion models given a high-level equation-based description of the model.

Progress:

A new thermal diffusion simulator (ALAMODE) has been developed which allows transient simulation of user-specified diffusion models. The models are specified as systems of coupled partial differential equations drawing terms and expressions from libraries of operators and functions. The systems of equations are described to the simulator using TCL (tool control language) and stored internally using an object-oriented data structure.

The simulator uses a semi-discrete finite element approach to discretize and solve the equations on given 1D-2D-3D mesh. The approach uses finite element for the spatial discretization, providing a system of nonlinear ordinary differential equations. The ODEs are integrated using a variety of timestepping algorithms. Temporal error estimation is used to predict time steps and control the error in the simulation to a user-specified tolerance. Nonlinear solution is handled via standard Newton techniques, and the Jacobian matrix is calculated analytically from the arbitrary expressions represented in the object-oriented data structure using automatic differentiation techniques. Preconditioned iterative algorithms are used for linear solution to compute Newton updates.

ALAMODE has been used successfully to prototype and evaluate models for transient enhanced diffusion (TED) caused by {311} cluster formation and evaporation, dose loss caused by trapping at interfaces, and diffusion in heterojunctions. It has also been used to simulate models involving carbon and carbon clustering in silicon where the models and parameters were originally developed using molecular dynamics simulation and monte carlo techniques.

Recent enhancements involve expansion of the operator and function libraries, restructuring the code for efficiency, and improvements in timestepping algorithms. These enhancements make it possible to quickly develop and simulate an even wider range thermal diffusion models.

Publications and presentations:

SRC Technology Transfer Course on ALAMODE, Stanford University, Aug. 12-13, 1997.

Trips:

SISPAD 97, Boston, MA, Sept. 8-10, 1997.