The Effective Mass Equation for the Multi-Valley Semiconductors

Abstract

The validity of the multivalley effective mass equation which has been conventionally used by many authors is examined. It is shown that the equation will not describe the intervalley mixing properly. An alternative equation which replaces the conventional equation is derived and discussed. Essential features of the new equation are: the lack of the intervalley mixing via kinetic energy, and the modification of impurity potential by the product of the periodic parts of the Bloch functions at the conduction band minima. Importance of the effect of anisotropy of the effective mass is discussed.