Adaptive energy discretization of the semiconductor Boltzmann equation

A new deterministic method is presented for solving the semiconductor transport equation of electrons in one‐dimensional silicon device structures. The developed numerical scheme provides a dynamical adaption of the energy discretization to speed up the computation. The adaptive discretization is realized by a time‐ and space‐dependent scaling of the energy variable. Several numerical tests are performed for the bulk case and for a one‐dimensional diode structure. The obtained results prove the efficiency of the proposed method to be significantly increased compared to schemes using fixed energy grids.

Keywords:

• Boltzmann equation
• Adaptive energy discretization
• Semiconductor devices

Acknowledgments

This work was supported by the Fond zur F¨orderung der wissenschaftlichen Forschung, Vienna, under contract number P17438‐N08; by the European community program IHP, contract number HPRN‐CT‐2002‐00282 on behalf of the CNR; and by MURST Cofin 2004 Mathematical Problem of Kinetic Theories.