On/off-state design of semiconductor doping profiles. (English) Zbl 1160.49021

Burger, Martin; Pinnau, René; Wolfram, Marie-Therese

Commun. Math. Sci. 6, No. 4, 1021-1041 (2008).

From the paper: We consider the multi-objective optimal dopant profiling of semiconductor devices. The two objectives are to gain a higher on-state current while the off-state current is kept small. This design question is treated as a constrained optimization problem, where the constraints are given by the stationary drift-diffusion model for the on-state and the linearized drift-diffusion model for the off-state. Using the doping profile as a state variable and the electrostatic potential as the new design variable, we obtain a simpler optimization problem, whose Karush-Kuhn-Tucker conditions partially decouple. Based on this observation we can construct a very efficient iterative optimization algorithm, which avoids solving the fully coupled drift-diffusion system. Due to the simple structure of the adjoint equations, this algorithm can be easily included into existing semiconductor simulation tools. The efficiency and success of this multi-objective design approach is underlined by various numerical examples.

MSC:

49K20	Optimality conditions for problems involving partial differential equations
35J50	Variational methods for elliptic systems
49N90	Applications of optimal control and differential games
49M05	Numerical methods based on necessary conditions

Keywords:

semiconductor design; drift-diffusion model; Gummel iteration; optimal control; multi-objective; dopant profiling