Abstract
Balance equations based on the moment method for the transport of electrons in silicon semiconductors are presented. The energy band is assumed to be described by the Kane dispersion relation. The closure relations have been obtained by employing the maximum entropy principle.The validity of the constitutive equations for fluxes and production terms of the balance equations has been checked with a comparison to detailed Monte Carlo simulations in the case of bulk silicon.
Highlights
Modeling modern submicron electron devices requires an accurate description of energy transport in order to cope with high-field phenomena such as hot electron propagation, impact ionization and heat generation in the bulk material.for many applications in optoelectronics one needs to describe the transient interaction of electromagnetic radiation with carriers in complex semiconductor materials and since the characteristic times are of order of the electron momentum or energy flux relaxation times, some higher moments of the distribution function are necessarily involved
Boltzmann transport equation by a suitable truncation procedure. This requires making suitable assumptions on: (i) closing the hierarchy by finding appropriate expressions for the N+ order moment in terms of the previous ones; (ii) modeling the production terms on the right hand side of the moment equations which arise from the moments of the collision terms in the Boltzmann transport equation
In this paper we present a recently introduced moment approach in which the closure for the fluxes and for the production terms is based on the maximum entropy principle [13, 14] and check the validity of the constitutive relations by Monte Carlo simulations in bulk silicon
Summary
Modeling modern submicron electron devices requires an accurate description of energy transport in order to cope with high-field phenomena such as hot electron propagation, impact ionization and heat generation in the bulk material. For many applications in optoelectronics one needs to describe the transient interaction of electromagnetic radiation with carriers in complex semiconductor materials and since the characteristic times are of order of the electron momentum or energy flux relaxation times, some higher moments of the distribution function are necessarily involved These phenomena cannot be described satisfactorily within the framework of the driftdiffusion equations (which do not comprise energy as a dynamical variable and are valid only in the quasi-stationary limit).
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