Failure of extended-moment-equation approaches to describe ballistic transport in submicrometer structures

Lower-order moment-equation models with a general nonlinear closing relation incorporating a priori ballistic and heating effects are studied numerically. Results for an n⁺-n-n⁺ diode show a reasonable agreement of these models with predictions obtained from the numerical solution to the corresponding Boltzmann equation in the nonballistic regime. In the predominantly ballistic regime, all lower-order models fail. A sketch of the parameter range in which these moment-equation models are valid is presented, based on a comparison of the predicted I-V characteristics. The conductance is inadequately described by all models, even in nonballistic cases, due to the high built-in potential, caused by the doping profile present in the device.