Nanoelectronic Devices

Appendix IV

Effective Mass Matrix

In order to deal with the acceleration of electrons in a three-dimensional (3D) space, we have to extend the concept of one-dimensional effective mass in Section 1.3.9 to that of 3D effective mass. In a 3D space, both the acceleration and the force are expressed as a vector with three components (a_x, a_y, and a_z for acceleration, and F_x, F_y, and F_z for force). Since each component of the acceleration vector may be a function of all three components of the force vector, we expect that a matrix is required to express the relationship between the acceleration and the force.

Let us consider the acceleration in a 3D space. The acceleration vector is given as

The velocity, , in turn, is related to the energy and the ...