On the Minimal Energy State of a Mixture of Charged Classical and Quantum Fluids

✍ Scribed by N. Chaudhuri; A. Unterreiter

• Publisher: John Wiley and Sons
• Year: 2002
• Tongue: English
• Weight: 152 KB
• Volume: 82
• Category: Article
• ISSN: 0044-2267
• DOI: 10.1002/1521-4001(200209)82:9<587::aid-zamm587>3.0.co;2-z

✦ Synopsis

The paper concerns the equilibrium state of ultra small semiconductor devices. Due to the quantum drift diffusion model, electrons and holes behave as a mixture of charged quantum fluids. Typically the involved scaled Planck's constants of holes, x, is significantly smaller than the scaled Planck's constant of electrons. By setting formally x ¼ 0 a well-posed differentialalgebraic system arises. Existence and uniqueness of an equilibrium solution is proved. A rigorous asymptotic analysis shows that this equilibrium solution is the limit (in a rather strong sense) of quantum systems as x ! 0. In particular the ground state energies of the quantum systems converge to the ground state energy of the differential-algebraic system as x ! 0.