Some Useful Relations for Analyzing Nanoscale MOSFETs Operating in the   Linear Region
  Several equations used to model and characterize the linear region IV characteristics of nanoscale field-effect transistors are derived. The meaning of carrier mobility at the nanoscale is discussed by defining two related quantities, the apparent mobility and the ballistic mobility. The validity of Matthiessen's Rule for relating the apparent ability to the ballistic and diffusive mobilities is examined. Other questions that arise in the analysis and characterization of nanoscale field-effect transistors are also discussed. These notes are intended to pull together in one place some key equations needed to analyze the linear region performance of nanoscale MOSFETs and to point out some errors in previous publications. 
Mark Lundstrom and Xingshu Sun
cond-mat.mes-hall